Harald Paganetti - Proton Therapy Physics (2011)

PROTON THERAPY
PHYSICS
SerieS editorS: John G WebSter, Slavik tabakov, kWan-hoonG nG
Edited by
Harald Paganetti
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PROTON THERAPY PHYSICS
Physics
K11646
A TAYL OR & F RANCI S BOOK
ISBN: 978-1-4398-3644-6
9 781439 836446
90000
Proton Therapy Physics goes beyond current books on proton therapy to
provide an in-depth overview of the physics aspects of this radiation therapy
modality, eliminating the need to dig through information scattered in the
medical physics literature.
After tracing the history of proton therapy, the book summarizes the atomic and
nuclear physics background necessary for understanding proton interactions
with tissue. It describes the physics of proton accelerators, the parameters
of clinical proton beams, and the mechanisms to generate a conformal dose
distribution in a patient. The text then covers detector systems and measuring
techniques for reference dosimetry, outlines basic quality assurance and
commissioning guidelines, and gives examples of Monte Carlo simulations in
proton therapy.
The book moves on to discussions of treatment planning for single- and
multiple-feld uniform doses, dose calculation concepts and algorithms, and
precision and uncertainties for nonmoving and moving targets. It also examines
computerized treatment plan optimization, methods for in vivo dose or beam
range verifcation, the safety of patients and operating personnel, and the
biological implications of using protons from a physics perspective. The fnal
chapter illustrates the use of risk models for common tissue complications in
treatment optimization.
Along with exploring quality assurance issues and biological considerations,
this practical guide collects the latest clinical studies on the use of protons
in treatment planning and radiation monitoring. Suitable for both newcomers
in medical physics and more seasoned specialists in radiation oncology, the
book helps readers understand the uncertainties and limitations of precisely
shaped dose distribution.
K11646_COVER_final.indd 1 10/31/11 3:21 PM
Proton Therapy
Physics
Series in Medical Physics and Biomedical Engineering
Series Editors: John G Webster, Slavik Tabakov, Kwan-Hoong Ng
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Intelligent and Adaptive Systems in Medicine
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Series in Medical Physics and Biomedical Engineering
A TAYLOR & FRANCI S BOOK
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Edited by
Harald Paganetti
Massachusetts General Hospital and
Harvard Medical School, Boston, USA
Proton Therapy
Physics
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v
Contents
About the Series ................................................................................................... vii
The International Organization for Medical Physics........................................ix
Introduction ............................................................................................................xi
Editor.................................................................................................................... xvii
Contributors ......................................................................................................... xix
1. ProtonTherapy:HistoryandRationale ..................................................... 1
Harald Paganetti
2. PhysicsofProtonInteractionsinMatter ................................................. 19
Bernard Gottschalk
3. ProtonAccelerators ...................................................................................... 61
Marco Schippers
4. CharacteristicsofClinicalProtonBeams .............................................. 103
Hsiao-Ming Lu and Jacob Flanz
5. BeamDeliveryUsingPassiveScattering ............................................... 125
Roelf Slopsema
6. ParticleBeamScanning............................................................................. 157
Jacob Flanz
7. Dosimetry ..................................................................................................... 191
Hugo Palmans
8. QualityAssuranceandCommissioning................................................ 221
Zuofeng Li, Roelf Slopsema, Stella Flampouri, and Daniel K. Yeung
9. MonteCarloSimulations .......................................................................... 265
Harald Paganetti
10. PhysicsofTreatmentPlanningforSingle-FieldUniformDose ....... 305
Martijn Engelsman
11. PhysicsofTreatmentPlanningUsingScannedBeams ...................... 335
Antony Lomax
vi Contents
12. DoseCalculationAlgorithms .................................................................. 381
Benjamin Clasie, Harald Paganetti, and Hanne M. Kooy
13. PrecisionandUncertaintiesinProtonTherapyfor
Nonmoving Targets .................................................................................... 413
Jatinder R. Palta and Daniel K. Yeung
14. PrecisionandUncertaintiesinProtonTherapyfor
Moving Targets ........................................................................................... 435
Martijn Engelsman and Christoph Bert
15. Treatment-PlanningOptimization ......................................................... 461
Alexei V. Trofmov, Jan H. Unkelbach, and David Craft
16. InVivoDoseVerifcation ......................................................................... 489
Katia Parodi
17. BasicAspectsofShielding ....................................................................... 525
Nisy Elizabeth Ipe
18. LateEffectsfromScatteredandSecondaryRadiation ....................... 555
Harald Paganetti
19. ThePhysicsofProtonBiology ................................................................. 593
Harald Paganetti
20. FullyExploitingtheBeneftsofProtons: UsingRiskModelsfor
NormalTissueComplicationsinTreatmentOptimization ............... 627
Peter van Luijk and Marco Schippers
vii
About the Series
The Series in Medical Physics and Biomedical Engineering describes the applica-
tions of physical sciences, engineering, and mathematics in medicine and
clinical research.
The series seeks (but is not restricted to) publications in the following topics:
• Artifcial organs
• Assistive technology
• Bioinformatics
• Bioinstrumentation
• Biomaterials
• Biomechanics
• Biomedical engineering
• Clinical engineering
• Imaging
• Implants
• Medical computing and mathematics
• Medical/surgical devices
• Patient monitoring
• Physiological measurement
• Prosthetics
• Radiation protection, health physics, and dosimetry
• Regulatory issues
• Rehabilitation engineering
• Sports medicine
• Systems physiology
• Telemedicine
• Tissue engineering
• Treatment
The Series in Medical Physics and Biomedical Engineering is an international
series that meets the need for up-to-date texts in this rapidly developing
feld. Books in the series range in level from introductory graduate textbooks
and practical handbooks to more advanced expositions of current research.
The Series in Medical Physics and Biomedical Engineering is the offcial book
series of the International Organization for Medical Physics.
ix
The International Organization
for Medical Physics
The International Organization for Medical Physics (IOMP), founded in
1963, is a scientifc, educational, and professional organization of 76 national
adhering organizations, more than 16,500 individual members, several cor-
porate members, and four international regional organizations.
IOMP is administered by the Council, which includes delegates from each
of the Adhering National Organizations. Regular meetings of the Council
are held electronically as well as every three years at the World Congress
on Medical Physics and Biomedical Engineering. The president and other
offcers form the Executive Committee, and there are also committees cover-
ing the main areas of activity, including education and training, scientifc,
professional relations, and publications.
Objectives
• To contribute to the advancement of medical physics in all its aspects
• To organize international cooperation in medical physics, especially
in developing countries
• To encourage and advise on the formation of national organizations
of medical physics in those countries that lack such organizations
Activities
Offcial journals of the IOMP are Physics in Medicine and Biology, Medical
Physics, and Physiological Measurement. The IOMP publishes a bulletin Medical
Physics World twice a year that is distributed to all members.
A World Congress on Medical Physics and Biomedical Engineering is
held every three years in cooperation with IFMBE through the International
Union for Physics and Engineering Sciences in Medicine. A regionally
based International Conference on Medical Physics is held between World
Congresses. IOMP also sponsors international conferences, workshops, and
courses. IOMP representatives contribute to various international commit-
tees and working groups.
x The International Organization for Medical Physics
The IOMP has several programs to assist medical physicists in developing
countries. The joint IOMP Library Programme supports 69 active libraries in
42 developing countries, and the Used Equipment Programme coordinates
equipment donations. The Travel Assistance Programme provides a limited
number of grants to enable physicists to attend the World Congresses.
The IOMP website is being developed to include a scientifc database of
international standards in medical physics and a virtual education and
resource center.
Information on the activities of the IOMP can be found on its website at
http://www.iomp.org.
xi
Introduction
According to the World Health Organization, cancer is the leading cause of
death worldwide. A large portion of cancer patients (e.g., more than half of
all cancer patients in the United States) receive radiation therapy during the
course of treatment. Radiation therapy is used either as the sole treatment or,
more typically, in combination with other therapies, including surgery and
chemotherapy.
Radiation interacts with tissue via atomic and nuclear interactions. The
energy transferred to and deposited in the tissue in such interactions is
quantifed as “absorbed dose” and expressed in energy (Joules) absorbed per
unit mass (kg), which has the units of Gray (Gy). Depending on the number
and spatial correlation of such interactions, mainly with cellular DNA, they
can result in mutations or complete functional disruption (i.e., cell death).
Assessing radiation damage is a complex problem because the cell typically
does have the limited ability to repair certain types of lesions.
There are many degrees of freedom when administering radiation, for
example, different radiation modalities, doses, and beam directions. The
main focus in research and development of radiation therapy is on eradicat-
ing cancerous tissue while minimizing the irradiation of healthy tissue. The
ideal scenario would be to treat the designated target without damaging any
healthy structures. This is not possible for various reasons such as uncertain-
ties in defning the target volume as well as delivering the therapeutic dose
as planned. Furthermore, applying external beam radiation therapy typically
requires the beam to penetrate healthy tissue in order to reach the target.
Treatment planning in radiation therapy uses mathematical and physical
formalisms to optimize the trade-off between delivering a high and con-
formal dose to the target and limiting the doses to critical structures. The
dose tolerance levels for critical structures, as well as the required doses for
various tumor types, are typically defned on the basis of decades of clinical
experience.
When considering the trade-off between administering the prescribed tar-
get dose and the dose to healthy tissue, the term “therapeutic ratio” is often
used. The therapeutic ratio can be defned as the ratio of the probabilities for
tumor eradication and normal tissue complication. Technological advances
in beam delivery and treatment modality focus mainly on increasing the
therapeutic ratio. Improvements can be achieved, for example, by applying
advanced imaging techniques leading to improved patient setup or tumor
localization.
A gain in the therapeutic ratio can also be expected when using proton
therapy instead of conventional photon or electron therapy. The rationale for
using proton beams instead of photon beams is the feasibility of delivering
xii Introduction
higher doses to the tumor while maintaining the total dose to critical struc-
tures or maintaining the target dose while reducing the total dose to critical
structures.
The most prominent difference between photon and proton beams is the
fnite range of a proton beam. After a short build-up region, photon beams
show an exponentially decreasing energy deposition with increasing
depth in tissue. Except for superfcial lesions, a higher dose to the tumor
compared with the organ at risk can only be achieved by using multiple
beam directions. Furthermore, a homogenous dose distribution can only
be achieved by utilizing various different beam angles, not by delivering
a single feld. In contrast, the energy transferred to tissue by protons is
inversely proportional to the proton velocity as protons lose their energy
mainly in electromagnetic interactions with orbital electrons of atoms. The
more the protons slow down, the higher the energy they transfer to tissue
per track length, causing the maximum dose deposition at a certain depth
in tissue. For a single proton, the peak is very sharp. For a proton beam,
it is broadened into a peak of typically a few millimeters width because
of the statistical distribution of the proton tracks. The peak is called the
Bragg peak (Figure 1). This feature allows pointing a beam toward a criti-
cal structure. The depth and width of the Bragg peak is a function of the
beam energy and the material (tissue) heterogeneity in the beam path.
The peak depth can be infuenced by changing the beam energy and can
thus be positioned within the target for each beam direction. Although
protons from a single beam direction are able to deliver a homogeneous
dose throughout the target (by varying the beam energy), multiple beam
angles are also used in proton therapy to even further optimize the dose
distribution with respect to organs at risk. Note that there is also a slight
difference between photon and proton beams when considering the lateral
penumbra. For large depths (more than ~16 cm), the penumbra for proton
beams is slightly wider than the one for photon beams by typically a few
millimeters. Depending on the site, this can be a slight disadvantage of
proton beams.
Depth in tissue
Bragg peak
Dose
FIGURE 1
Energy deposition as a function of depth for a proton beam leading to the Bragg peak.
xiii Introduction
The physical characteristic of proton beams—their fnite range—can be
used in radiation therapy for increasing the dose to the target or decreas-
ing the dose to organs at risk. Treatment plan comparisons show that
protons offer potential gains for many sites. In some cases, the dose con-
formity that can be reached with intensity-modulated photon therapy
might be comparable to one that can be achieved with proton techniques.
However, because of the difference in physics between photon beams and
proton beams as outlined above, the total energy deposited in the patient
for any treatment will always be higher with photons than with protons.
The use of protons leads to a reduction of the total energy when treating
a given target by a factor of about three compared to standard photon
techniques and by a factor of about two compared to intensity- modulated
photon plans. The irradiation of a smaller volume of normal tissues
compared to conventional modalities allows higher doses to the tumor,
leading to an increased tumor control probability. Furthermore, proton
therapy allows a smaller dose to critical structures while maintaining the
target dose compared to photon techniques. Benefts can thus be expected
particularly for pediatric patients where the irradiation of large volumes
are particularly critical in terms of long-term side effects.
The share of patients treated with proton therapy compared with photon
therapy is currently still low but is expected to increase signifcantly in the
near future, as evidenced by the number of facilities currently planned or
under construction. With the increasing use of protons as radiation therapy
modality comes the need for a better understanding of the characteristics
of protons. Protons are not just heavy photons when it comes to treatment
planning, quality assurance, delivery uncertainties, radiation monitor-
ing, and biological considerations. To fully utilize the advantages of pro-
ton therapy and, just as importantly, to understand the uncertainties and
limitations of precisely shaped dose distribution, proton therapy physics
needs to be understood. Furthermore, the clinical impact and the evidence
for improved outcomes need to be studied. Proton therapy research has
increased signifcantly in the last few years. Figure 2 shows how the number
of proton therapy–related publications in most relevant scientifc journals
has increased over the years.
This book starts with an overview about the history of proton therapy
in Chapter 1. The pioneering work done at a few institutions in the early
days of proton therapy is acknowledged, and the main developments up
to the frst hospital-based facilities are outlined. The chapter concludes
with comments about the original and current clinical rationale for proton
therapy.
The atomic and nuclear physics background necessary for understanding
proton interactions with tissue is summarized in Chapter 2. The chapter cov-
ers the basic physics of protons slowing down in matter independent of their
medical use. The ways in which protons can interact with materials/tissue
is described from both macroscopic (e.g., dose) and microscopic (energy loss
xiv Introduction
kinematics) points of view. Furthermore, Chapter 2 presents equations that
can be used for estimating many characteristics of proton beams.
Chapter 3 describes the physics of proton accelerators, including currently
used techniques (cyclotrons and synchrotrons) and a brief discussion of new
developments. The chapter goes beyond simply summarizing the charac-
teristics of such machines for proton therapy and also describes some of the
main principles of particle accelerator physics.
Chapter 4 outlines the characteristics of clinical proton beams and how the
clinical parameters are connected to the design features and the operational
settings of the beam delivery system. Parameters such as dose rate, beam
intensity, beam energy, beam range, distal falloff, and lateral penumbra are
introduced.
The next two chapters describe in detail how to generate a conformal dose
distribution in the patient. Passive scattered beam delivery systems are dis-
cussed in Chapter 5. Scattering techniques to create a broad beam as well
as range modulation techniques to generate a clinically desired depth–dose
distribution are outlined in detail. Next, Chapter 6 focuses on magnetic beam
scanning systems. Scanning hardware as well as parameters that determine
the scanning beam characteristics (e.g., its time structure and performance)
are discussed. The chapter closes with a discussion of safety and quality
assurance aspects.
Chapter 7 focuses on dosimetry and covers the main detector systems
and measuring techniques for reference dosimetry as well as beam profle
measurements. The underlying dosimetry formalism is reviewed as well
as the basic aspects of microdosimetry. Chapter 8 expands on this topic by
160
Proton therapy research publications
140
120
100
80
N
u
m
b
e
r

o
f

p
u
b
l
i
c
a
t
i
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s
60
40
20
1970 1980 1990
Year
2000 2010
0
FIGURE 2
The number of publications listed in PubMed (a free database of citations on life sciences
and biomedical topics) per year with the phrase equal or similar to “proton radiation ther-
apy” in the title or abstract (). Also shown is an exponential ft of the form Publications =
a × e
b[year-1970]
(solid line).
xv Introduction
outlining the basic quality assurance and commissioning guidelines, includ-
ing acceptance testing. The quality assurance guidelines focus on dosimetry
as well as mechanical and safety issues.
One aspect of increasing importance in the feld of medical physics is the
use of computer simulations to replace or assist experimental methods. After
an introduction to the Monte Carlo particle-tracking method, Chapter  9
demonstrates how Monte Carlo simulations can be used to address various
clinical and research aspects in proton therapy. Examples are treatment head
design studies as well as the simulation of scattered radiation for radiation
protection or dose deposition characteristics for biophysical modeling.
Next, treatment planning is outlined. The treatment planning process is
largely modality independent. Consequently, Chapter 10 covers only proton-
specifc aspects of treatment planning for passive scattering and scanning
delivery for single-feld uniform dose (i.e., homogeneous dose distributions
in the target from each beam direction). Proton-specifc margin consider-
ations and special treatment techniques are discussed.
Chapter 11 describes treatment planning for multiple-feld uniform dose
and intensity-modulated proton therapy using beam scanning. The chal-
lenges and the potential of intensity-modulated treatments are described,
including uncertainties and optimization strategies. A few case studies con-
clude this chapter.
One of the key methods used in treatment planning is the dose calculation
method. Chapter 12 does focus on dose calculation concepts and algorithms.
The formalism for pencil beam algorithms is reviewed from a theoretical
and practical implementation point of view. Further, the Monte Carlo dose
calculation method and hybrid methods are outlined.
One of the advantages of proton therapy is the ability to precisely shape
dose distributions, in particular using the distal falloff due to the fnite beam
range. Uncertainties in the proton beam range limit the use of the fnite range
of proton beams in the patient because more precise dose distributions are
less forgiving in terms of errors and uncertainties. Chapter 13 discusses pre-
cision and uncertainties for nonmoving targets. Special emphasis is on the
dosimetric consequences of heterogeneities. Chapter 14 deals with precision
and uncertainties for moving targets, such as when treating lung cancer with
proton beams. The clinical impact of motion as well as methods of motion
management for minimizing motion effects are outlined.
Computerized treatment planning relies on optimization algorithms to
generate a clinically acceptable plan. Chapter 15 reviews some of the main
aspects of treatment plan optimization including the consideration of some
of the uncertainties discussed in Chapters 13 and 14. Robust and four-
dimensional optimization strategies are described.
Chapter 16 discusses methods for in vivo dose or beam range verifcation.
These include the detection of photons caused by nuclear excitations and of
annihilation photons created after the generation of positron emitters by the
primary proton beam.
xvi Introduction
The safety of patients as well as operating personnel has to be ensured by
proper shielding of a treatment beam. In proton therapy the main concerns
are secondary neutrons. Shielding considerations and measurement meth-
ods are covered in Chapter 17.
The consequences of scattered or secondary radiation that a patient receives
during treatment of the primary cancer could include long-time side effects
such as a second cancer. This aspect is outlined in Chapter 18. Secondary
doses are quantifed, and methods to estimate the risks for radiation-induced
cancers are presented.
Although this book is concerned mainly with proton therapy physics, bio-
logical implications are discussed briefy as they relate directly to physics
aspects. The biological implications of using protons are outlined from a
physics perspective in Chapter 19.
Finally, outcome modeling is summarized in Chapter 20. This fnal chap-
ter illustrates the use of risk models for normal tissue complications in treat-
ment optimization. Proton beams allow precise dose shaping, and thus,
personalized treatment planning might become particularly important for
proton therapy in the future.
The goal of this book is to offer a coherent and instructive overview of
proton therapy physics. It might serve as a practical guide for physicians,
dosimetrists, radiation therapists, and physicists who already have some
experience in radiation oncology. Furthermore, it can serve graduate stu-
dents who are either in a medical physics program or are considering a
career in medical physics. Certainly it is also of interest to physicians in
their last year of medical school or residency who have a desire to under-
stand proton therapy physics. There are some overlaps between different
chapters that could not be avoided because each chapter should be largely
independent. Overall, the book covers most, but certainly not all, aspects of
proton therapy physics.
xvii
Editor
Dr. Harald Paganetti is currently Director of Physics Research at the
Department of Radiation Oncology at Massachusetts General Hospital in
Boston and Associate Professor of Radiation Oncology at Harvard Medical
School.
He received his PhD in experimental nuclear physics in 1992 from the
Rheinische-Friedrich-Wilhelms University in Bonn, Germany, and has been
working in radiation therapy research on experimental as well as theoretical
projects since 1994. He has authored and coauthored more than 100 peer-
reviewed publications, mostly on proton therapy. Dr. Paganetti has been
awarded various research grants from the National Cancer Institute in the
United States. He serves on several editorial boards and is a member of
numerous task groups and committees for associations such as the American
Association of Physicists in Medicine, the International Organization for
Medical Physics, and the National Institutes of Health/National Cancer
Institute.
Dr. Paganetti teaches regularly worldwide on different aspect of proton
therapy physics.
xix
Contributors
ChristophBert
GSI Helmholtzzentrum für
Schwerionenforschung GmbH
Abteilung Biophysik
Darmstadt, Germany
BenjaminClasie
Department of Radiation Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
DavidCraft
Department of Radiation Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
MartijnEngelsman
Department of Radiation Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
StellaFlampouri
University of Florida
Proton Therapy Institute
Jacksonville, Florida
JacobFlanz
Department of Radiation Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
BernardGottschalk
Laboratory for Particle Physics and
Cosmology
Harvard University
Cambridge, Massachusetts
NisyElizabethIpe
Shielding Design, Dosimetry, and
Radiation Protection
San Carlos, California
HanneM.Kooy
Department of Radiation
Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
ZuofengLi
University of Florida
Proton Therapy Institute
Jacksonville, Florida
AntonyLomax
Center for Proton Therapy
Paul Scherrer Institute
Villigen, Switzerland
Hsiao-MingLu
Department of Radiation
Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
xx Contributors
HaraldPaganetti
Department of Radiation Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
HugoPalmans
National Physical Laboratory
Acoustics and Ionising Radiation
Teddington, United Kingdom
JatinderR.Palta
Department of Radiation Oncology
University of Florida
Gainesville, Florida
KatiaParodi
Heidelberg Ion Beam Therapy
Center and Department of
Radiation Oncology
Heidelberg University Clinic
Heidelberg, Germany
MarcoSchippers
Paul Scherrer Institut
Villigen, Switzerland
RoelfSlopsema
University of Florida
Proton Therapy Institute
Jacksonville, Florida
AlexeiV.Trofmov
Department of Radiation
Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
JanH.Unkelbach
Department of Radiation
Oncology
Massachusetts General Hospital
and Harvard Medical School
Proton Therapy Center
Boston, Massachusetts
PetervanLuijk
Department of Radiation
Oncology
University Medical Center
Groningen
University of Groningen
Groningen, The Netherlands
DanielK.Yeung
University of Florida Proton
Therapy Institute
Jacksonville, Florida
Department of Radiation
Oncology
University of Florida
Gainesville, Florida
1
1
Proton Therapy: History and Rationale
HaraldPaganetti
1.1 TheAdventofProtonsinCancerTherapy
The frst medical application of ionizing radiation, using x-rays, occurred in
1895 (1, 2). In the following decades, radiation therapy became one of the main
treatment options in oncology (3). Many improvements have been made with
CONTENTS
1.1 The Advent of Protons in Cancer Therapy................................................. 1
1.2 History of Proton Therapy Facilities ........................................................... 2
1.2.1 Early Days: Lawrence Berkeley Laboratory, Berkeley,
California ............................................................................................ 2
1.2.2 Early Days: Gustav Werner Institute, Uppsala, Sweden .............. 3
1.2.3 Early Days: Harvard Cyclotron Laboratory,
Cambridge, Massachusetts ............................................................... 3
1.2.4 Second Generation: Proton Therapy in Russia .............................. 4
1.2.5 Second Generation: Proton Therapy in Japan ................................ 4
1.2.6 Second Generation: Proton Therapy Worldwide .......................... 5
1.2.7 Hospital-Based Proton Therapy ....................................................... 5
1.2.8 Facilities and Patient Numbers ........................................................ 5
1.3 History of Proton Therapy Devices ............................................................. 7
1.3.1 Proton Accelerators ............................................................................ 7
1.3.2 Mechanically Modulating Proton Beams ....................................... 7
1.3.3 Scattering for Broad Beams .............................................................. 7
1.3.4 Magnetic Beam Scanning ................................................................. 7
1.3.5 Impact of Proton Technology in Other Areas of
Radiation Therapy ............................................................................. 8
1.4 The Clinical Rationale for Using Protons in Cancer Therapy ................. 9
1.4.1 Dose Distributions ............................................................................. 9
1.4.2 Early Clinical Implications ............................................................. 10
1.4.3 Current Clinical Implications ........................................................ 11
1.4.4 Economic Considerations ............................................................... 11
Acknowledgments ................................................................................................ 12
References ............................................................................................................... 12
2 Proton Therapy Physics
respect to how radiation is administered considering biological effects, for
example, the introduction of fractionated radiation therapy in the 1920s and
1930s. Technical advances have been aimed mainly at reducing dose to healthy
tissue while maintaining prescribed doses to the target or increasing the dose
to target structures with either no change or a reduction of dose to normal tis-
sue. Computerized treatment planning, advanced imaging and patient setup,
and the introduction of mega-voltage x-rays are examples of new techniques
that have impacted beam delivery precision during the history of radiation
therapy. Another way of reducing dose to critical structures is to take advan-
tage of dose deposition characteristics offered by different types of particles.
The advantages of proton radiation therapy, compared with “conventional”
photon radiation therapy, were frst outlined by Wilson in 1946 (4). He pre-
sented the idea of utilizing the fnite range and the Bragg peak of proton
beams for treating targets deep within healthy tissue and was thus the frst
to describe the potential of proton beams for medical use. Wilson’s sugges-
tion to use protons (in fact he also extended his thoughts to heavy ions) was
based on the well-known physics of protons as they slowed down during
penetration of tissue.
1.2 HistoryofProtonTherapyFacilities
1.2.1 Early Days: Lawrence Berkeley Laboratory, Berkeley, California
The idea of proton therapy was not immediately picked up at Wilson’s home
institution, Harvard University, but was adopted a couple of years later by
the Lawrence Berkeley Laboratory (LBL) in California. Pioneering the medi-
cal use of protons, Tobias, Anger, and Lawrence (5) in 1952 published their
work on biological studies on mice using protons, deuterons, and helium
beams. Many experiments with mice followed at LBL (6), and the frst patient
was treated in 1954 (7).
The early patients had metastatic breast cancer and received proton irradi-
ation of their pituitary gland for hormone suppression. The bony landmarks
made targeting of the beam feasible. The Bragg peak itself was not utilized.
Instead, using a 340-MeV proton beam, patients were treated with a cross-
fring technique (i.e., using only the plateau region of the depth dose curve).
This approximated a rotational treatment technique to concentrate the dose
in the target. Protons as well as helium beams were applied. Between 1954
and 1957, 30 patients were treated with protons. Initially large single doses
were administered (7), and later fractionated delivery treatment three times
a week was applied (8). The frst patient using the Bragg peak was treated in
1960 for a metastatic lesion in the deltoid muscle, using a helium beam (9).
The LBL program moved to heavier ions entirely in 1975, resulting in several
developments that also benefted proton therapy.
3 Proton Therapy: History and Rationale
1.2.2 Early Days: Gustav Werner Institute, Uppsala, Sweden
In 1955, shortly after the frst proton treatments at LBL, radiation oncologists
in Uppsala, Sweden, became interested in the medical use of protons. Initially,
a series of animal (rabbits and goats) experiments were performed to study
the biological effect of proton radiation (10–12). The frst patient was treated
in 1957 using a 185-MeV cyclotron at the Gustav Werner Institute (12–14).
Subsequently, radiosurgery beams were used to treat intracranial lesions, and
by 1968, 69 patients had been treated (15, 16). Because of limitations in beam
time at the cyclotron, high doses per fraction were administered. Instead of
the cross-fring technique, the use of the Bragg peak was adopted early on by
using large felds and range-modulated beams (14, 17, 18). In fact, the Gustav
Werner Institute was the frst to use range modulation using a ridge flter,
that is, a spread-out Bragg peak (SOBP) with a homogeneous dose plateau at
a certain depth in tissue (14), based on the original idea of Robert Wilson, in
which various mono-energetic proton beams resulting in Bragg peaks were
combined to achieve a homogeneous dose distribution in the target. The pro-
ton therapy program ran from 1957 to 1976 and reopened in 1988 (19).
1.2.3 Early Days: Harvard Cyclotron Laboratory,
Cambridge, Massachusetts
Preclinical work on proton therapy at Harvard University (Harvard
Cyclotron Laboratory [HCL]) started in 1959 (20). The cyclotron at HCL had
suffcient energy (160 MeV) to reach the majority of sites in the human body
up to a depth of about 16 cm. The relative biological effectiveness (RBE) of
proton beams was studied in the 1960s using experiments on chromosome
aberrations in bean roots (21), mortality in mice (22), and skin reactions on
primates (23). Subsequently, the basis for today’s practice of using a clinical
RBE (see Chapter 19) was established (24–27).
The clinical program was based on a collaboration between HCL and the
neurosurgical department of Massachusetts General Hospital (MGH). The
frst patients were treated in 1961 (28). Intracranial targets needed only a
small beam, which could be delivered using a single scattering technique
to broaden the beam. As at LBL, pituitary irradiation was one of the main
targets. Because of the maximum beam energy of 160 MeV, it was decided
to focus on using the Bragg peak instead of applying a crossfre technique.
Until 1975, 732 patients had undergone pituitary irradiation at HCL (29). On
the basis of the growing interest in biomedical research and proton ther-
apy, the facility was expanded by constructing a biomedical annex in 1963.
This was funded by NASA to examine the medical effects of protons. When
the research program funded by the U.S. Offce of Naval Research, which
originally funded the cyclotron, was shut down in 1967, the proton therapy
project was in danger of being terminated. Extensive negotiations between
MGH  and HCL, as well as small grants by the National Cancer Institute
4 Proton Therapy Physics
(NCI) in 1971 and the National Science Foundation (NSF) in 1972 helped,
thus saving the program.
In 1973, the radiation oncology department commenced an extensive proton
therapy program. The frst patient was a four-year-old boy with a posterior
pelvic sarcoma. Subsequently, the potential of the HCL proton beam for treat-
ment of skull-base sarcomas, head-and-neck region carcinomas, and uveal
melanomas was identifed, and several studies on fractionated proton therapy
were performed (30). Furthermore, a series of radiobiological experiments was
done (25). On the basis of the development of a technique to treat choroidal
melanomas at MGH, the Massachusetts Eye and Ear Infrmary, and HCL, mel-
anoma treatments started in 1975 (31) after tests had been done using monkeys
(32, 33). The frst treatments for prostate patients were in the late 1970s (34).
A milestone for the operation at HCL as well as for proton therapy research
in general was a large research grant by the NCI awarded in 1976 to MGH
Radiation Oncology to allow extensive studies on various aspects of proton
therapy. The HCL facility treated a total of 9116 patients until 2002.
1.2.4 Second Generation: Proton Therapy in Russia
Proton therapy began early at three centers in Russia. Research on using pro-
ton beams in radiation oncology had been started in Dubna (Joint Institute for
Nuclear Research [JINR]) and at the Institute of Theoretical and Experimental
Physics (ITEP) in Moscow in 1967. The Dubna facility started treatments in
April 1967, followed by ITEP in 1968 (35–39). A joint project between the
Petersburg Nuclear Physics Institute and the Central Research Institute of
Roentgenology and Radiology (CRIRR) in St. Petersburg launched a proton
therapy program in 1975 in Gatchina, a nuclear physics research facility near
St. Petersburg. The latter treated intracranial diseases using Bragg curve pla-
teau irradiation with a 1-GeV beam (40).
The program at ITEP was the largest of these programs and was based
on a 7.2-GeV proton synchrotron with a medical beam extraction of up to
200 MeV. Patients were treated with broad beams and a ridge flter to create
depth–dose distributions. Starting in 1972, the majority of treatments irradi-
ated the pituitary glands of breast cancer and prostate cancer patients using
the plateau of the Bragg curve (35, 41). By the end of 1981, 575 patients with
various indications had been treated with Bragg peak dose distributions (35).
1.2.5 Second Generation: Proton Therapy in Japan
The history of proton therapy treatments in Japan goes back to 1979 when
the National Institute of Radiological Sciences (NIRS) at Chiba started treat-
ments at a 70-MeV facility (42). Of the 29 patients treated between 1979 and
1984, only 11 received proton therapy alone and 18 received a boost irradia-
tion of protons after either photon beam or fast neutron therapy. The effort
was followed by the use of a 250-MeV beam at the Particle Radiation Medical
5 Proton Therapy: History and Rationale
Science Center in Tsukuba in 1983 using a 250-MeV proton beam obtained
by degrading a 500-MeV beam from a booster synchrotron of the National
Laboratory for High Energy Physics (KEK) (43). Japan has since emerged as
one of the main users of proton and heavy ion therapy.
1.2.6 Second Generation: Proton Therapy Worldwide
The late 1980s and early 1990s saw a number of initiatives starting proton
therapy programs on several continents, for example, at the Paul Scherrer
Institute (PSI) (Switzerland) in 1984, Clatterbridge (U.K.) in 1989, Orsay
(France) in 1991, and iThemba Laboratory for Acclerator Based Sciences
(iThemba LABS) (South Africa) in 1993. In particular the activities at PSI,
starting with a 72-MeV beam for ocular melanoma treatments (44) and after
1996 using a 200-MeV beam, have lead to many technical and treatment
planning improvements in proton therapy.
1.2.7 Hospital-Based Proton Therapy
By the early 1990s, proton therapy was based mainly in research institu-
tions and was used on a modest number of patients, in part because of very
restricted beam time availability at some centers. Then, in 1990, the frst
hospital-based facility was built and started operation at the Loma Linda
University Medical Center (LLUMC) in California (45). The accelerator
system, based on a synchrotron (46), was developed in collaboration with
Fermilab. The gantries were designed by the HCL group (47). By July 1993,
12,914 patients had been treated with protons worldwide—still roughly half
of those at HCL and 25% in Russia (48). Roughly 50% were radiosurgery
patients treated with small felds. However, the facility at Loma Linda would
soon treat the biggest share of proton therapy patients.
It took another few years before the frst commercially available equipment
was installed and in operation at MGH, which transferred the program from
the HCL to its main hospital campus in 2001. At the time when the facility
was purchased, proton therapy was still considered mainly experimental as
part of a research effort. In fact, the construction project was in part funded
by the NCI. The commercial equipment sold to MGH started the interest
of different companies to offer proton therapy solutions and the interest of
major hospitals to buy proton therapy facilities. Many other hospital-based
facilities have been opened since then.
1.2.8 Facilities and Patient Numbers
Table 1.1 lists the facilities and the number of patients treated with protons as of
December 2010. On the basis of the increasing interest in proton therapy and the
number of additional facilities under construction, one can assume that roughly
6000 patients will be treated with protons in 2011 in the United States alone.
6 Proton Therapy Physics
TABLE 1.1
Total Years of Operation and Patients Treated with Protons. Worldwide (as of
12/2010)
Facility
Ocular
Tumors
Only
First
Patient
Last
Patient
Number
of
Patients
Berkeley 184, California 1954 1957 30
Uppsala_1, Sweden 1957 1976 73
Cambridge (Harvard), Massachusetts 1961 2002 9116
Dubna (JINR_1), Russia 1967 1996 124
Chiba (NIRS), Japan • 1979 2002 145
Tsukuba (PMRC_1), Japan 1983 2000 700
Louvain-la-Neuve, Belgium • 1991 1993 21
Bloomington (MPRI_1), Indiana • 1993 1999 34
Moscow (ITEP), Russia 1969 4246
St. Petersburg, Russia 1975 1362
Villigen (PSI_1, 72 MeV), Switzerland • 1984 2010 5458
Uppsala_2, Sweden 1989 1000
Clatterbridge, England • 1989 2021
Loma Linda (LLUMC), California 1990 15000
Nice (CAL), France • 1991 4209
Orsay (CPO), France 1991 5216
iThemba LABS, Somerset West, South Africa 1993 511
UCSF – CNL, California • 1994 1285
Vancouver (TRIUMF), Canada • 1995 152
Villigen (PSI_2, 230 MeV), Switzerland 1996 772
Dubna (JINR_2), Russia 1999 720
Kashiwa (NCC), Japan 1998 772
Berlin (HMI), Germany • 1998 1660
Hyogo (HIBMC), Japan 2001 2382
Tsukuba (PMRC_2), Japan 2001 1849
Boston (MGH-FHBPTC), Massachusetts 2001 4967
Catania (INFN-LNS), Italy • 2002 174
Wakasa Bay (WERC), Japan 2002 2009 62
Shizuoka, Japan 2003 986
Wanjie (WPTC), China 2004 1078
Bloomington (MPRI_2), Indiana 2004 1145
Houston, Texas 2006 2700
Jacksonville, Florida 2006 2679
Ilsan (NCC), South Korea 2007 648
Munich (RPTC), Germany 2009 446
Oklahoma City (ProCurePTC), Oklahoma 2009 21
Heidelberg (HIT), Germany 2010 40
Facilities in operation: 27 Total number of patients treated: 73,804
Source: The Particle Therapy Co-Operative Group (PTCOG) (http://ptcog.web.psi.ch).
7 Proton Therapy: History and Rationale
1.3 HistoryofProtonTherapyDevices
1.3.1 Proton Accelerators
The concept of accelerating particles in a repetitive way with time- dependent
varying potentials led to the invention of the cyclotron by Lawrence in 1929
(49). Cyclotrons accelerate particles while they are circulating in a mag-
netic feld and pass the same accelerating gap several times (see Chapter 3).
Gaining energy, the particles are traveling in spirals and are eventually
extracted. To overcome the energy limitation of a cyclotron, the principle
of phase stability was invented in 1944 (50). One was now able to accelerate
particles of different energy on the same radius, leading to the synchrotron
(see Chapter 3). The synchrotron concept was suggested frst by Oliphant in
1943 (51). Thus, both accelerator types were available when proton therapy
was frst envisaged.
1.3.2 Mechanically Modulating Proton Beams
In his 1946 paper, Wilson introduced the idea of using a rotating wheel of
variable thickness to cover an extended volume with an SOBP (although
he did not defne this term) (4, 52). This technique to produce an SOBP (see
Chapter 5) was adopted by proton facilities such as the HCL (53–55). Others
have used a ridge flter design to shape an SOBP (14, 56, 57).
1.3.3 Scattering for Broad Beams
For treatment sites other than very small targets (e.g., in radiosurgery) pro-
ton beams produced by accelerators result in “pencil” beams that are too
small to cover an extended target. Thus, scattering foils had to be used to
increase their width. To produce a fat dose distribution in lateral direction,
it was ineffcient to use a single-scattering foil because only a small area in
the center of the beam would suffce beam fatness constraints. The double-
scattering system, using two scatterers to achieve a parallel beam producing
a fat dose distribution with high effciency, was developed at the HCL in the
late 1970s (58). The idea was based on similar systems previously designed
for heavy ion and electron beams (59). The double-scattering concept was
later improved using a contoured scatterer system (see Chapter 5) (60).
1.3.4 Magnetic Beam Scanning
The development of beam scanning was a major milestone in proton ther-
apy. The clinical implications of beam scanning were analyzed in the late
1970s and early 1980s (61, 62). The advantage of scanning is not only the need
for fewer beam shaping absorbers in the treatment head (increasing the
8 Proton Therapy Physics
effciency) but also the potential of delivering variable modulation and thus
sparing structures proximal to the SOBP (61).
The concept of using magnets to defect a proton beam (dynamic beam
delivery) is as old as the double-scattering scattering system. The idea to
magnetically defect proton beams for treatment was frst published by
Larsson in 1961 (14). Continuous scanning using an aperture was done in
the 1960s in Uppsala (14). The aim was not to scan the tumor with individual
pencil beams but to replace the scattering system using a sweeping mag-
netic feld. A method using rotating dipoles instead of a scattering system
in order to produce a uniform dose distribution was considered by Koehler,
Schneider, and Sisterton (58). It can be considered as intermediate between
double-scattered broad beam delivery and beam scanning. Similarly, a tech-
nique called wobbling, using magnetic felds to broaden the beam without a
double-scattering system, was developed at Berkeley for heavy ion therapy
because here the material in the beam path when using a double scattering
system produces too much secondary radiation (63).
Full-beam scanning uses small proton beams of variable energy and inten-
sity that are magnetically steered to precisely shape of dose around critical
structures (see Chapter 6). This concept of using beam scanning in three
dimensions for clinical proton beam delivery was developed by Leemann et al.
(64). Many different favors of beam scanning exist. Typical terms are spot,
pixel, voxel, dynamic, and raster scanning. The terminology is not consistent.
The main differences between scanning systems are whether the delivery
is done in a step-and-shoot mode or continuously. Spot scanning, where the
beam spots are delivered one by one with beam off-time in between, covering
the target volume instead of delivering a rectangular scanned feld that has to
be shaped by an aperture, was frst introduced at NIRS using a 70-MeV beam.
Scanning was mainly done to improve the range of the beam by removing a
scattering system. At frst, two-dimensional scanning was applied in combi-
nation with a range-modulating wheel (42). Later, three-dimensional beam
scanning was introduced by using a system with two scanning magnets and
an automatic range degrader to change the spot energy (42, 65–68).
Many studies on different scanning techniques (spot scanning, continuous
scanning) were done in the early 1980s at LBL, and continuous scanning in
three dimensions without collimator was frst done in the early 1990s (69).
Beam scanning can be used in passive scattered proton therapy, but it also
allows creating felds delivering inhomogeneous dose distributions where
only a combination of several felds yields the desired dose distribution in
the target (see Chapter 11). This intensity-modulated proton therapy is cur-
rently on the verge of fnding its way into the clinical routine.
1.3.5 Impact of Proton Technology in Other Areas of Radiation Therapy
Some of the developments in proton therapy have infuenced the way radi-
ation therapy is being conducted also in conventional radiation therapy.
9 Proton Therapy: History and Rationale
External beam radiation therapy requires a geometric description of the inter-
nal patient anatomy. Until the advent of computed tomography (CT) this could
only be obtained from x-ray images, which project the anatomy on a planar
flm. Because conventional radiation therapy uses photons, the imaging x-ray
modality basically just replaces the treating photons. In the case of protons,
which stop in the patient, this method does not suffce for treatment planning.
When proton treatment of cancer patients began at the HCL, positioning of
the target for each treatment feld for each fraction was readily achieved by
the simple use of bi-planar radiographs. The information was used to decide
on potential beam approaches that covered the target in the lateral dimension
for each beam path. Pituitary adenomas and arteriovenous malformation were
the initial targets for proton therapy (16, 70). These lesions could be visualized
on x-rays using contrast material to visualize the vasculature and thus could
be treated without the use of CT imaging. It became clear that in order to uti-
lize the superior dose distribution of proton beams one needed to understand
the impact of density variations for each beam path (30, 71, 72). Thus, the treat-
ment of other sites in the very heterogeneous head and neck region (e.g., para-
nasal sinus or nasopharynx) required additional research on accurate imaging
to visualize the patient’s geometry and densities in the beam path (71).
When CT imaging became available, proton radiation therapy was the
early adaptor, that is, using CT for treatment planning (73–75). The proton
therapy program at HCL, the heavy ion program at LBL, and the pi-meson
program at the University of New Mexico were the frst radiation therapy
programs to install dedicated CT scanners. Some were modifed to allow
imaging in a seated position to mimic the treatment geometry.
Proton therapy paved the way for many other advances in radiation ther-
apy. The proton therapy group at MGH developed the frst computerized
treatment planning program in the early 1980s, which was subsequently
used clinically (76–79). Other developments included the innovative con-
cepts of beam’s eye view and dose-volume histograms, features that have
become standard in radiation therapy today. Sophisticated patient position-
ing was developed frst in proton therapy because the fnite range of proton
beams required a more precise setup than in photon therapy (80).
1.4 TheClinicalRationaleforUsing
ProtonsinCancerTherapy
1.4.1 Dose Distributions
Any new radiation treatment technology has to fnd acceptance amongst
clinicians, for example, by demonstrating improved dose distributions and
suggesting a more favorable treatment outcome (30). A more favorable dose
10 Proton Therapy Physics
distribution is a distribution that is more closely confned to the tumor vol-
ume. This allows reducing the dose to normal structures (decreasing the
normal tissue complication probability) or increasing the dose to the tumor
(increasing the tumor control probability) or both. When proton therapy
became available, it was of interest mainly because it showed dose confor-
mity far superior to any type of conventional photon radiation therapy at
that time (72, 81). Nowadays, it is quite feasible for some tumor shapes to
reach dose conformity to the target with photons that is comparable to the
one achievable with protons, albeit at the expense of using a larger number of
beams. The difference in dose conformity between protons and photons has
certainly decreased since the early days of proton therapy (at least for regu-
lar shaped targets), mainly due to the development of intensity- modulated
photon therapy.
There is a limit to further improving and shaping photon generated dose
distributions because the total energy deposited in the patient and thus to
critical structures cannot be reduced but only distributed differently. Proton
radiation therapy, on the other hand, can achieve signifcant further physical
improvements through the use of scanning-beam technology and intensity-
modulated proton therapy. This will increase the advantage of proton ther-
apy due to advanced dose sculpting potential.
1.4.2 Early Clinical Implications
Target dose distributions can typically be shaped with proton beams by
applying fewer beams than with photons. Proton therapy is of particular
interest for tumors located close to serially organized tissues where a small
local overdose can cause signifcant complications. Protons are ideal for
many targets, specifcally if they are concave-shaped or are close to criti-
cal structures. The advantages of proton therapy could not be utilized right
from the start because of limitations in patient imaging and beam delivery
(e.g., the absence of gantry systems). Proton treatments started with the cross
fring technique and the irradiation of pituitary targets. The proton therapy
program at the HCL began with single fraction treatments of intracranial
lesions (28). In the early 1960s the program of fractionated irradiation was
commenced by the radiation oncologists at HCL and was used for a greatly
expanded number of anatomic sites such as skull base sarcomas, choroidal
melanomas, head and neck carcinomas, and others. Choroidal melanomas
quickly became the most commonly treated tumor at HCL (82). Starting in
1973, all treatments for cancer patients was done by fractionated dose deliv-
ery (30). By the mid-1980s roughly one-third of the treated patients received
intracranial radiosurgery treatments (e.g., arterioveneous maformations)
(83, 84).
Even with a limited number of indications, the distinct advantages of
proton treatments compared to photon treatments were seen early on (85).
One was able to demonstrate clinical effcacy of proton radiation therapy in
11 Proton Therapy: History and Rationale
otherwise poorly manageable diseases such as for chordoma and chondro-
sarcoma of the skull base and the spine (86, 87). These present signifcant
treatment challenges as they are often very close to critical structures (e.g.,
the brain stem, spinal cord, or optic nerves).
1.4.3 Current Clinical Implications
Today proton therapy is a well-established treatment option for many tumor
types and sites. Advantages when using protons in favor of photons have
been shown in terms of tumor control probability and/or normal tissue com-
plications probability. Various dosimetric studies clearly demonstrate supe-
rior normal tissue sparing with protons (88–99). It is well recognized that
protons are extremely valuable to treat tumors close to critical structures
(e.g., for head-and-neck treatments) (100). However, there are circumstances
and treatment sites where the advantage appears to be marginal at best (101).
In the pediatric patient population the impact of the decreased total
absorbed energy in the patient [by a factor of 2–3 (92)] with protons is most
signifcant. The overall quality-of-life and reduction of secondary effects is of
great importance and the reduction in overall normal tissue dose is proven
to be relevant (91). Using protons for cranio-spinal cases can reduce the dose
to the thyroid glands signifcantly. One prime example is the treatment of
medulloblastoma, a malignant tumor that originates in the medulla and
extends into the cerebellum. Treatment with photon radiation therapy invari-
ably causes signifcant dose to the heart, lung, and abdominal tissues as well
as organs at risk in the cranium, something that can largely be avoided using
protons. These facts have boosted proton therapy in particular for pediatric
patients. For example, at MGH about 90% of the pediatric patient population
in radiation oncology is treated with proton therapy. About 60% of those
treated have brain tumors.
Although the dose distributions achievable with protons are superior to
those achievable with photons, it is debatable whether the advantages of pro-
ton therapy are clinically signifcant for all treatment sites. There is an ongo-
ing discussion about the necessity for randomized clinical trials to show a
signifcant advantage in outcome by using protons (102–105). Note that data
on late morbidity are still scarce because of the follow-up of less than 20
years for most patients.
1.4.4 Economic Considerations
Related to the question of clinical trials mentioned above is the cost of health
care, that is, whether the gain in tumor control or reduced tissue complication
is substantial enough to warrant the additional cost of proton therapy. This
is one of the reasons why the treatment of prostate cancer with protons has
been criticized (105, 106), and it has been argued that because of the limited
availability of proton beams, proton therapy might be used predominantly
12 Proton Therapy Physics
for such cases where protons are believed to make the biggest difference (e.g.,
for the pediatric patient population) (107).
Goitein and Jerman (108) estimated that the cost of a proton treatment is
about double the cost of a photon treatment, considering the initial invest-
ment and the operation of a facility. The cost of a proton treatment is expected
to decrease with the advent of more and more facilities. A detailed discus-
sion on the economic aspects of proton therapy is beyond the scope of this
book, and the reader may be referred to publications on this subject (108–111).
Acknowledgments
The author thanks Dr. Herman Suit and Jocelyn Woods for proofreading.
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15 Proton Therapy: History and Rationale
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16 Proton Therapy Physics
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19
2
Physics of Proton Interactions in Matter
BernardGottschalk
CONTENTS
2.1 Introduction .................................................................................................. 20
2.1.1 Depth–Dose Distributions of Various Particles .......................... 20
2.1.2 Proton Interactions .......................................................................... 21
2.1.3 Stopping ............................................................................................ 22
2.1.4 Scattering .......................................................................................... 22
2.1.5 Nuclear Interactions ........................................................................ 23
2.1.6 The Bragg Peak ................................................................................. 24
2.2 Basics .............................................................................................................. 24
2.2.1 Kinematics ........................................................................................ 24
2.2.2 Fluence, Stopping Power, and Dose .............................................. 25
2.2.3 Energy Lost vs. Energy Deposited ................................................ 26
2.2.4 The Fundamental Equation ............................................................ 27
2.2.5 Relation between Dose Rate and Beam Current ......................... 28
2.3 Stopping ........................................................................................................ 29
2.3.1 Range Experiments .......................................................................... 30
2.3.2 Sneak Preview: The Range–Energy Relation ............................... 32
2.3.3 Stopping Power ................................................................................ 32
2.3.4 Mean Projected Range .................................................................... 34
2.3.5 Interpolating Range–Energy Tables .............................................. 35
2.3.6 Range Straggling .............................................................................. 36
2.3.7 Water Equivalence ........................................................................... 37
2.4 Multiple Coulomb Scattering ..................................................................... 37
2.4.1 Experiment ........................................................................................ 38
2.4.2 Highland’s Formula ......................................................................... 38
2.4.3 Molière’s Theory .............................................................................. 39
2.4.4 The Gaussian Approximation ........................................................ 42
2.4.5 Scattering Power .............................................................................. 44
2.4.6 Binary Degraders ............................................................................. 45
2.5 Nuclear Reactions ........................................................................................ 46
2.5.1 Terminology...................................................................................... 46
2.5.2 Overview of Nonelastic Reactions ................................................ 47
2.5.3 Nonelastic Cross Section ................................................................. 48
20 Proton Therapy Physics
2.1 Introduction
This chapter examines the interactions of protons with matter. A full
understanding of these interactions allows us to solve the two main phys-
ics problems that arise in proton radiotherapy: designing beam lines, and
predicting the dose distribution in the patient. This section is a preliminary
non- mathematical survey.
2.1.1 Depth–Dose Distributions of Various Particles
Let’s begin by comparing particles used or formerly used in radiotherapy.
Figure 2.1 shows depth–dose distributions for various particles in a water
tank, water being a convenient proxy for tissue.
The frst two particles (upper left) are neutral. They exhibit a dose buildup
(too short to see for 120 KeV photons) followed by an exponential decay. As
they traverse the water, neutral particles either interact or do not. Thus their
number falls exponentially, but the ones that happen to survive are the same
as when they entered. Dose is actually delivered by atomic electrons set in
motion by the primary particles. It takes a while for the cloud of secondary
electrons to build up in the beam, accounting for the buildup region. This
feature is clinically useful, as it spares the skin.
The remaining particles shown, arranged by increasing mass, are electri-
cally charged. For these, the number of primaries only decreases slightly
with depth (explained later), but the energy of each one decreases continu-
ously, so the entire beam stops at more or less the same depth. Moreover,
charged particles lose more energy per cm as they slow down, so there’s a
2.5.4 Nuclear Buildup: Longitudinal Equilibrium ............................... 49
2.5.5 Test of Nuclear Models .................................................................... 50
2.6 The Bragg Peak ............................................................................................. 52
2.6.1 Beam Energy..................................................................................... 52
2.6.2 Variation of S ≡ −dE/dx with E ....................................................... 52
2.6.3 Range Straggling and Beam Energy Spread ................................ 53
2.6.4 Nuclear Interactions ........................................................................ 54
2.6.5 Beam Size: Transverse Equilibrium .............................................. 54
2.6.6 Source Distance ................................................................................ 55
2.6.7 Dosimeter .......................................................................................... 56
2.6.8 Electronic and Nuclear Buildup; Slit Scattering .......................... 56
2.6.9 Tank Wall and Other Corrections ................................................. 56
2.6.10 Measuring the Bragg Peak .............................................................. 56
2.7 Summary ....................................................................................................... 57
References ............................................................................................................... 57
21 Physics of Proton Interactions in Matter
large dose enhancement just before they stop. This “Bragg peak” is sharper,
the more massive the particle.
The electron peak is very broad because of the small electron mass. The
proton peak is much sharper and falls to zero. Actually, there is some distal
dose from neutrons set in motion by the protons, but it’s about a thousand
times lower than the proton dose, so it doesn’t show up on this plot.
*
The Ne peak is still sharper than the proton peak, but there is some dose
beyond it because some Ne nuclei split into lighter, longer range ions while
traversing the water (“fragmentation”). Pions are of historical interest only.
Their distal dose comes from the stopping pions interacting with the nucleus,
which deposits a local ball of dose.
2.1.2 Proton Interactions
Now let’s narrow our focus to protons. They interact with matter in three
distinct ways. They slow down by myriad collisions with atomic electrons.
They are defected by myriad collisions with atomic nuclei. Finally, they
sometimes have a head-on collision with a nucleus, setting secondary par-
ticles in motion. We’ll call these three processes stopping, scattering, and
nuclear interactions.
Stopping and scattering proceed via the electromagnetic (EM) interac-
tion between the charge of the proton and the charge of atomic electrons or
*
Unwanted neutron dose is a concern in proton therapy because of possible long-term effects
(Chapter 18), but it plays no role in prompt (acute) effects.
0 5 10 15 20 0 5 10 0 5 10 15 20 25
0
0
.5
1.
0
.5
1.
0
.5
1.
0
.5
22 MeV
8 MeV
120 KeV
78 MeV
.05 e
–
.1
160 MeV 400 MeV/A
50 MeV d, Be
6 MeV
14 MeV
1.
0
.5
1.
0
.5
1.
5 10 15 20 0 5 10
Depth in water (cm)
R
e
l
a
t
i
v
e

d
o
s
e
15 20 0 5 10 15 20 25
γ
π
–
μ
–
n e
–
p
+
Ne
FIGURE 2.1
Depth–dose distributions for various particles.
22 Proton Therapy Physics
nucleus, as the case may be. That interaction is simple and well understood.
Therefore, comprehensive and well-tested mathematical theories of stopping
and scattering exist. By contrast, our best overall picture of the nuclear inter-
action is a patchwork of models. Fortunately, nuclear interactions are rela-
tively infrequent, and simple approximations take them into account well
enough for purposes of radiotherapy.
Because we have these tested theories, most physics problems that occur
in proton radiotherapy, whether beam line design or predicting the dose dis-
tribution in the patient, can be solved from frst principles. Complex beam
lines can be designed reliably with computer programs that only take a few
seconds to run. Dose prediction in the patient is far more diffcult and time
consuming, but the diffculties are mathematical. We believe that the under-
lying physics is well understood.
2.1.3 Stopping
The theory of stopping was fully developed by 1933. The important fact
is that protons do stop in solid or liquid matter, and beyond the stopping
point (“end of range”) the dose is negligible. Proton range is approximately
proportional to kinetic energy squared. If the incident proton beam is mono-
energetic, all protons stop at nearly (though not exactly) the same depth. The
slight spread in stopping point, which increases if the incident beam itself
has an energy spread, is called “range straggling.” Most important, the rate
at which the proton loses energy increases as the proton slows down because,
in a given proton–electron collision, more momentum is transferred to the
electron, the longer the proton stays in its vicinity. Thus, the rate of energy
loss or “stopping power” depends on the energy itself and on the stopping
material. When we correct for density, materials high in the periodic table
such as lead (Z = 82) have less stopping power than materials like beryllium
(Z = 4), water, or plastics.
2.1.4 Scattering
The accepted theory of scattering was published in 1947. Except in rare cases,
the defection of a proton by a single atomic nucleus is extremely small.
Therefore the observed angular spread of a proton beam leaving a slab of
matter is mainly due to the random combination of many such defections.
Because of this and the underlying EM interaction, scattering is more prop-
erly known as multiple Coulomb scattering (MCS). If protons scattered in a slab
of matter fall on a screen (Figure 2.2), their spatial distribution is very nearly
Gaussian (the familiar bell curve of statistics). Multiple-scattering theory
predicts, very accurately, the width of that Gaussian given the proton energy
and the slab material and thickness. Proton MCS angles (roughly speaking,
the half-width of the Gaussian) are small: 16° in the very worst case and usu-
ally only a few degrees. Materials high in the periodic table scatter much
23 Physics of Proton Interactions in Matter
more strongly than materials like water, a trend opposite to that of stopping
power (Figure 2.3).
2.1.5 Nuclear Interactions
If a primary proton merely scatters elastically off a nucleus, or leaves it mildly
excited, we are not that interested, because the outgoing proton retains char-
acteristics (energy and angle) similar to its fellows. More interesting are the
occasional “train wrecks” (more properly, nonelastic collisions) where the
proton enters the nucleus and knocks out one or more constituent protons,
neutrons, or light nucleon clusters. These secondaries (which include the
original proton, since we can no longer identify it) tend to have much lower
energies and much larger angles than primary protons. A blob of dose is
deposited just downstream of the reaction site. Some 20% of 160 MeV protons
suffer that kind of reaction before stopping.
L
R
(g/cm
2
)
0
0 10 20 30 40 50 60 70
2
4
6
8
10
12
14
16
18
M
e
V
,

m
R
a
dθ
0
∆E
lead
brass
aluminum
water
lexan
beryllium
FIGURE 2.3
Multiple scattering angle and energy loss for 160-MeV protons traversing 1 g/cm
2
of vari-
ous materials. (Data from M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M.
Seltzer, et al. ICRU Report 49 (1993).)
MP
L
X
0
0
θ
FIGURE 2.2
Multiple Coulomb scattering in a thin slab. MP, measuring plane.
24 Proton Therapy Physics
2.1.6 The Bragg Peak
The three interactions come together to determine the shape of the Bragg
peak. Much of the technique of proton radiotherapy rests on clever manipu-
lations of the Bragg peak, such as spreading it out (Figure 2.4) to cover the
target and spare healthy tissue insofar as possible. Therefore it’s good to
know that we really do understand in detail how the observed shape comes
about.
2.2 Basics
We digress briefy to discuss basic quantities used in describing the pro-
ton radiation feld, before returning to a quantitative discussion of stopping,
scattering, nuclear reactions, and the Bragg peak.
2.2.1 Kinematics
At high energies, the proton behaves like a complex system of “quarks” and
“gluons.” In the much lower radiotherapy energy range 3–300 MeV the proton
is an elementary particle with no internal degrees of freedom, a rest energy
mc
2
= 938.27 MeV and a charge e = +1.602 × 10
–19
C. In the theories of stopping
and scattering described later we occasionally need to compute the proton’s
30
Depth (cm H
2
O)
D
o
s
e
10 20 0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
FIGURE 2.4
Spread-out Bragg peak (SOBP) obtained by adding shifted, appropriately weighted Bragg
peaks. In this example, the range modulator wheel is designed for full modulation, and reduced
modulation is obtained by turning the beam off during unwanted steps (beam gating). The
slight rounding of the proximal corner is a consequence of beam gating (see Chapter 5).
25 Physics of Proton Interactions in Matter
speed v or momentum p, given its kinetic energy E.
*
Radiotherapy protons are
somewhat relativistic (their speed is of order c 300 10 1
6
    × m/s ft/ns), so
the relevant equations (see any textbook on special relativity) are as follows:

β ≡ =
+
v
c
pc
E mc
2

(2.1)

( ) ( ) ( ) . E mc pc mc + = +
2 2 2 2 2

(2.2)
From these, if we frst defne a reduced kinetic energy,

τ ≡
E
mc
2

(2.3)
we can derive several useful equations whose relativistic ( ) τ 1 and non-
relativistic ( ) τ 1 limits are obvious at a glance:

β
2
2
2
1
=
+
+
τ
τ ( )
τ

(2.4)

( ) ( ) pc mc E
2 2
2 = + τ

(2.5)

pv E =
+
+
τ
τ
2
1
.

(2.6)
The last quantity, pv, occurs frequently in MCS theory. For E = 160 MeV we
fnd β = 0.520 (speed just over half the speed of light), pc = 571 MeV, and
pv = 297 MeV.
2.2.2 Fluence, Stopping Power, and Dose
Suppose a beam of protons slows down and eventually stops in a water tank.
At any given depth we may be concerned with the number of protons, their
individual rate of energy loss, or the total rate at which they deposit energy
in the water. Let x (cm) be displacement along the beam direction and y (cm)
be transverse displacement.
The fuence, Φ, is a quantity which depends on position in the water tank.
It is defned as the number of protons, during a given exposure or treatment,
crossing an infnitesimal element of area dA normal to x.
†

Φ ≡
dN
dA
protons
cm
2
.

(2.7)
*
In radiotherapy physics, kinetic energy is often denoted E, unlike particle physics where E
usually stands for total (kinetic + rest) energy.
†
Whether in the beam line or the patient, radiotherapy protons are always directed within
a few degrees of the x axis. Other types of radiation require a more general defnition of
fuence.
26 Proton Therapy Physics
The fuence rate is the time derivative of the fuence
*
:


Φ ≡
d
dt
Φ protons
cm s
2
.

(2.8)
The stopping power is the rate at which a single proton loses kinetic energy:

S
dE
dx
≡ −
MeV
cm
.

(2.9)
The mass stopping power is stopping power “corrected” for density:

S dE
dx ρ ρ
≡ −
1 MeV
g/cm
2

(2.10)
where ρ (g/cm
3
) is the local density of the stopping medium. For instance,
the mass stopping powers of air and water are similar, whereas the stopping
power of air is about a thousand times less than that of water.
†
The physical
absorbed dose, D, at some point in a radiation feld is the energy absorbed per
unit target mass. In SI units,

D≡
J
kg
.

(2.11)
The special unit of dose used in radiation therapy is the Gray: 1 Gy ≡ 1 J/kg.
To give a rough idea of the numbers, a course of proton radiotherapy might
consist of ≈ 70 Gy to ≈ 1000 cm
3
of target volume given in ≈ 35 fractions (2 Gy/
session). However, a single whole- body dose of 4 Gy is lethal (with a probabil-
ity of 50%) even with good medical care. To put this into perspective, assum-
ing the typical thermal power radiated by an adult weighing 80 Kg is 100 W,
a lethal dose of ionizing radiation corresponds to the amount of thermal
energy given off in 3 s! Ionizing radiation is nasty stuff.
An earlier, arguably more convenient unit of physical absorbed dose is the
rad: 1 Gy = 100 rad. Older oncologists frequently hedge, saying “centiGray”
(cGy) instead of rad.
2.2.3 Energy Lost vs. Energy Deposited
It is good to remember that the energy lost by a proton beam exceeds the
energy absorbed locally by the patient or water phantom. A fraction of the
beam’s energy goes into neutral secondaries (γ-rays and neutrons), which
*
Sometimes Φ
⋅
is written φ. In the early literature fuence rate is called “fux.”
†
The often used quantity ρ dx (g/cm
2
) is the areal density or simply the “grams per square
centimeter” of an element of stopping medium of thickness, dx. It is the thickness of a slab
of stopping material times its density. To determine it experimentally, one usually measures,
instead, mass divided by area.
27 Physics of Proton Interactions in Matter
may deposit their energy some distance away (for instance, in the shielding
of the treatment room). Energy is conserved, of course, but only if we take
the region of interest large enough and include the very small fraction that
may go into changing the energy state of target molecules.
2.2.4 The Fundamental Equation
How does physical absorbed dose relate to fuence and stopping power?
Suppose dN protons pass through an infnitesimal cylinder of cross sectional
area dA and thickness dx. In the cylinder

D
dE dx dx dN
dA dx
≡
energy
mass
/
=
− × ×
× ×
( )
ρ

or

D
S
= Φ
ρ

(2.12)
Dose equals fuence times mass stopping power. Proton therapy calculations,
whether beam line design or dose reconstruction in the patient, usually
begin with this formula in one form or another. However, it is not conve-
nient to use SI units throughout. Gray (= J/Kg) is fne, but S/ρ is invariably
in MeV/(g/cm
2
), square meters is far too large an area, and one proton is far
too few. Therefore, let Φ = 1 Gp/cm
2
, where Gp ≡ gigaproton ≡ 10
9
protons,
and let S/ρ = 1 MeV/(g/cm
2
). After appropriate conversions such as 1 MeV =
0.1602 × 10
–12
J we fnd

D
S
= 0 1602 . Gy Φ
ρ

(2.13)
with Φ in Gp/cm
2
and S/ρ in MeV/(g/cm
2
) as usually tabulated.
Another useful form is found by taking the time derivative of Equation 2.13,
expressing fuence rate in terms of proton current density ( ), i A Ne A e
p
/ / = =

Φ
assuming a current density of 1 nA/cm
2
, and converting units. We fnd


D
i
A
S
p
=
ρ
Gy
s

(2.14)
with i
p
/A in nA/cm
2
and S/ρ in MeV/(g/cm
2
). For a current density of
0.0033 nA/cm
2
and S = 5 MeV/(g/cm
2
) (170 MeV protons in water), we fnd

D= = 0 017 1 . Gy/s Gy/min, a typical radiotherapy rate. Typical targets have
areas of several cm
2
and there are various ineffciencies involved (discussed
next), so we have already shown that the proton current entering the treat-
ment head or “nozzle” must be of the order of nA.
In using the last few formulas, we must remember the distinction between
absorbed dose (what we are interested in) and the tabulated stopping power
28 Proton Therapy Physics
which refects energy lost by the beam, somewhat greater as mentioned
earlier. More important, formulas like Eq. 2.14, while extremely useful for
(say) estimating the dose rate that might be had from a proposed machine
and beam line, must never be used to determine the therapy dose delivered
to a patient. That can only be done with the aid of a carefully calibrated
dosimeter!
2.2.5 Relation between Dose Rate and Beam Current
An important task of the accelerator designer is to estimate the proton cur-
rent required for a specifed dose rate. Though we already have a rough
value from the previous section, let’s derive a more precise relation (±10%).
We’ll assume passive beam spreading, but, with a little reinterpretation, the
result applies to magnetic scanning as well. Suppose a target of known cross
sectional area
*
and known extent in depth is treated with a known proton
current at a known incident energy with a passive scattering system which
includes a suitable range modulator (see Chapter 5). What is the dose rate
averaged over one modulator cycle?
Consider Figure 2.5. Eq. 2.14 applies at the entrance to the water tank,
where the dose is uniform over a circle of area A. If we wish to reinterpret
i
p
as the current into the scattering system, we must introduce an effciency
factor ε < 1 because not all the protons that enter the scattering system reach
A. It can be shown [1] that ε ≈ 0.05 for single scattering and ε ≈ 0.45 for double
scattering.
Assuming no range modulation for the time being, the dose of interest
is that at the maximum of the Bragg peak (BP), which is greater than that
at A by f
BP
, the peak-to-entrance ratio of a pristine BP. Therefore, we must
multiply the dose at A by f
BP
. For a typical Bragg peak f
BP
≈ 3.5, surprisingly
independent of energy.
Now, let’s switch on the range modulator, either a rotating “propeller
wheel” or a set of degraders selected by a computer. That reduces the dose
at the maximum of the frst BP (and therefore the dose everywhere in the
SOBP) because now, the deepest peak is only treated a fraction of the time.
*
A is the cross sectional area of a cylinder, coaxial with the beam, circumscribing the target.
Range
modulator
1
1
2
2
A
Second
scatterer Water tank
i
p
FIGURE 2.5
The fgure used in deriving Equation 2.15.
29 Physics of Proton Interactions in Matter
Call that, the fractional dwell time of the frst (deepest) step, f
MOD
. Putting
everything together we fnd, averaged over one modulator cycle,

⟨ ⟩ =







D f f
i
A
S
ε
ρ
BP MOD
p
Gy
s

(2.15)
with i
p
(incident proton current) in nA, A in cm
2
, and S/ρ in MeV/(g/cm
2
).
Strictly speaking S/ρ is the mass stopping power in water at the water tank
entrance, but you can use the incident energy because energy loss in the
beam spreading system is small by design.
It remains to determine f
MOD
as a function of modulation. For zero modula-
tion, f
MOD
= 1. Otherwise, we need to design a set of modulators (1). Figure 2.6
shows f
MOD
as a function of relative modulation for a typical beam spreading
system. The shape of the curve comes mainly from the shape of the Bragg
peak. It is little affected by details of the beam spreading system, so Figure
2.6 can safely be used for rough estimates. Dependence on modulation is
nonlinear. Therefore Eq. 2.15 implies that, whereas dose rate is strictly pro-
portional to inverse area, it is not proportional to thickness (extent in depth)
because the deepest Bragg peak already delivers a considerable dose to the
entire volume whatever the irradiation strategy (passive or scanning).
2.3 Stopping
Protons slow down in matter, mainly through myriad collisions with atomic
electrons. In collisions at a given distance a proton loses more energy, the
f
M
O
D
m
100
/ d
100
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
FIGURE 2.6
Dependence on relative modulation of f
MOD
, the relative dwell time of the deepest step, for a
typical set of range modulators. d
100
is the depth of the distal corner of the SOBP. m
100
is the
distance between the corners.
30 Proton Therapy Physics
longer it interacts with the electron. Therefore the rate of energy loss increases
as the proton slows down, giving rise to the Bragg peak of ionization near
end-of-range, the signature feature of proton radiotherapy. We now explore
all this in detail beginning with the experimental defnition of “range.”
*
2.3.1 Range Experiments
Early workers, on discovering a new form of radiation, invariably began by
seeing how far it would go in various materials. A modern version of that
experiment for protons is shown in Figure 2.7. The beam is monitored, to
allow successive equivalent runs. It then traverses an adjustable thickness
of the material under test. Finally, it stops in a “Faraday cup” (FC), ideally of
such size that any large-angle outgoing particles miss it. After each run we
measure the charge collected by the FC (effectively a proton counter because
the charge of a single proton is well known).
The right hand panel shows, for two different FCs, collected proton charge
per monitor unit vs. thickness of stopping material. A great deal can be
learned from these graphs. Both show a gradual decline followed by a pre-
cipitous drop. The decline comes from nonelastic collisions of protons with
atomic nuclei. Charged secondary particles from such collisions mostly have
short ranges and large angles and therefore do not reach the FC, so we see
only a gradual decline in the primary fuence. Protons that escape this fate—
those that have only electromagnetic (EM) interactions with electrons or
nuclei—all run out of energy at nearly (but not exactly) the same depth and
*
Normally (2) one begins with the theory of stopping power and proceeds to the defnition
of range. We have reversed that order of presentation because range is more immediately
accessible to experiment, because the precise experimental defnition of range is frequently
misunderstood, and because range, determining treatment depth, is very frequently the
quantity of greatest interest.
0
0.0
0.1
0.2
monitor
IC
CH
2
absorbers
Faraday
cup
current
integrator
0.3
n
C
o
u
l

/

3
0

M
U
0.4
0.5
0.6
5 10
g/cm
2
CH
2
15 20
FIGURE 2.7
Experimental defnition of mean projected range. Left: experimental setup. Right: results for
two different Faraday cups. (Based on Harvard Cyclotron Laboratory, unpublished data.)
31 Physics of Proton Interactions in Matter
stop. The mean projected range R
0
(which we will call “range”) is the depth at
which half of them have stopped, as indicated by the arrow. Note that “half”
is measured from the corner of the curve. The range, in other words, is the
amount of material that would stop half the incident protons if nuclear reac-
tions were turned off.
The higher, less linear, curve was taken with an FC much closer to the
degrader stack so some charged secondaries were counted along with the
primary protons. It had a thicker entrance window, so the residual range was
slightly smaller.
Alternatively, proton centers often measure range with a “multilayer
Faraday cup” (MLFC), a stack of metal plates separated by insulating sheets.
Each plate is connected to a current integrator which measures the total
charge stopping in that plate, equivalent to measuring

− = − = −
∫
dN
dx
dN
dxdA
dA
d
dx
Φ

or differential fuence. One observes a sharp peak (center panel of Figure 2.8)
whose maximum (corresponding to the steepest point in the top panel) is
the proton range. At clinical beam currents (nA), an MLFC can measure the
range to ≈ 0.1 mm water equivalent in a few seconds. All data are acquired
simultaneously so no beam monitor is needed.
Depth
D
o
s
e
D
i
ff

fl
u
e
n
c
e
F
l
u
e
n
c
e
FIGURE 2.8
Fluence, differential fuence, and dose as a function of depth for proton beams of a given range
and different energy spreads, illustrating R
0
= d
80
.
32 Proton Therapy Physics
If neither form of FC is available, the range may be measured by scanning
a dosimeter down the x axis of a water tank: a measurement of dose, not
fuence. We observe a Bragg peak, and the question arises: what feature of
the peak corresponds to the mean projected range of the proton beam? The
answer is

R d
0 80
=

(2.16)
where d
80
stands for the depth of water (corrected for tank entrance window,
dosimeter wall thickness, and so forth) at the distal 80% point of the peak.
This purely numerical result (the “80” is not exact, but is close enough), frst
found by A. M. Koehler (private communication, ca. 1982), has been con-
frmed often (3, 4). It follows from the theoretical model of the Bragg peak to
be discussed later.
As Figure 2.8 shows, if we increase the energy spread of the proton beam,
keeping the mean energy the same, the range measured all three ways, in
particular the distal 80% point of the Bragg peak, remains the same.
In summary, the range R
0
of a proton beam is defned as the depth of mate-
rial at which half the protons that undergo only EM interactions have stopped.
It is defned by a fuence measurement. However, a dose measurement may
be used instead, provided the result is properly interpreted (R
0
 = d
80
).
2.3.2 Sneak Preview: The Range–Energy Relation
To give some feeling for the numbers, here is a short range–energy table for
water (2):
Kinetic energy 1 3 10 30 100 300 MeV
Range 0.002 0.014 0.123 0.885 7.718 51.45 cm H
2
O
This justifes our choice of 3–300 MeV as the clinical regime.
Figure 2.9 shows the range–energy relation for some useful materials at
clinical energies. At a given energy, the range expressed in g/cm
2
is greater
(the stopping power is lower) for heavy materials. The basic form is the
same for all materials: nearly linear on a log-log plot. If it were exactly linear,
the relation would be an exact power law R = aE
b
. If the lines were parallel,
b would be the same for all materials, and only a would differ.
As it is, the power varies slightly with E and also with material. We’ll deal
with all that by forgetting about the power law and parameterizing Figure
2.9 separately for each material. Before that, let’s go back to the beginning.
The conventional presentation of stopping theory begins with the Bethe-
Bloch formula for stopping power.
2.3.3 Stopping Power
The theoretical rate of energy loss of a fast charged particle in matter was
derived by Bethe and Bloch around 1933. Good modern accounts with refer-
ences can be found in the range–energy tables of Janni (5) and ICRU Report
33 Physics of Proton Interactions in Matter
49 (2). Specializing to protons, flling in physical constants and ignoring all
corrections (as is permissible in the radiotherapy energy regime 3–300 MeV),
the mass stopping power in an elementary material of atomic number Z and
relative atomic mass A is

S dE
dx
Z
A
W
I
m el
MeV
g/ ρ ρ β
β ≡ − = −






1
0 3072
1
2
2
. ln
ccm
2

(2.17)
where β ≡ v/c of the proton (Eq. 2.4) and

W
m c
m
e
=
−
2
1
2 2
2
β
β

(2.18)
is the largest possible proton energy loss in a single collision with a free elec-
tron. m
e
c
2
≈ 0.511 MeV is the electron rest energy.
I is the mean excitation energy of the target material. It cannot be calculated
to suffcient accuracy from frst principles so it is effectively an adjustable
parameter of the theory. It is found by ftting measured range-energy val-
ues (for materials where those exist) and by interpolation for others. It is
roughly proportional to Z with I/Z ≈ 10 eV, but irregularities due to atomic
shell structure make interpolation diffcult (2). Fortunately S/ρ is logarithmic
brass
Pb
Leman
H
2
O
4
2
3
0.1
2
3
3
2
3
2
3
2
1
10
R
a
n
g
e

(
g
/
c
m
2
)
100
5 6 7 10 2 3 4 5 2 3 4 5 6
Energy (MeV)
100
FIGURE 2.9
Proton range–energy relation around the clinical regime for four useful materials. (Data from
M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et al. ICRU Report
49, 1993.)
34 Proton Therapy Physics
in I so that, at 100 MeV for instance, a relative increase of 1% in I only causes
a ≈ 0.15% decrease in S/ρ (2).
If a material is a mixture of elements, the atoms act separately, and we can
visualize the mixture as a succession of very thin sheets of each constituent
element. That picture leads easily to the Bragg additivity rule:

S
w
S
i
i
i
ρ ρ
=





 ∑

(2.19)
where w
i
is the fraction by weight of the i
th
element. Compounds are more
complicated since their constituent atoms do not act separately. Several strat-
egies are used to deal with that (2). Unfortunately, water is particularly com-
plicated. There is some experimental evidence (6, 7) that Janni (5) is more
accurate than ICRU Report 49 (2) for water.
In short, choosing I is a complicated business requiring considerable famil-
iarity with the experimental literature. It is mainly for this reason that our
own practice is to obtain stopping power and range values by interpolating
generally accepted range–energy tables rather than computing them ab initio.
Tables can differ from each other by 1%–2%, due solely to different choices
of I. A given set of tables may be better for some materials than others. One
percent of range at 180 MeV corresponds to ≈2 mm water. Therefore when the
treatment depth itself depends on it, we must rely on measured ranges in water
and measured water equivalents of other materials, rather than range–energy
tables! However, range–energy tables are invaluable in other calculations
such as beam line design.
Eq. 2.17 refers to the rate of energy loss to atomic electrons only. Protons
also lose energy by elastic scattering on atomic nuclei.
*
This contribution is
less than 0.1% above 1 MeV (5). Janni (5) omits it in the clinical regime, but
ICRU Report 49 (2) includes it. From now on we will refer to the mass stop-
ping power simply as S/ρ.
2.3.4 Mean Projected Range
Once we know S/ρ as a function of β, that is, of E, we can fnd the theoretical
range of a proton by imagining that it enters the material at E
initial
and by sum-
ming the energy loss in very thin slabs until the energy reaches some very low
value E
fnal
(not 0, because Eq. 2.17 diverges there). The choice of E
fnal
is not crit-
ical. Any very small value will do. Formally, in a homogeneous slab of matter

R E
dE
dx
dE
E
E
( )
initial
initial
final
=






−
∫
1
1
ρ
==
∫
dE
S
E
E
/
final
initial
ρ

(2.20)
is the theoretical range in g/cm
2
.
Because of multiple scattering, protons actually travel a wiggly path, so
strictly speaking, the quantity we have computed is the total pathlength
*
That’s different from the nonelastic nuclear reactions which we will discuss later.
35 Physics of Proton Interactions in Matter
rather than the mean projected range, which is smaller by a “detour factor”
resulting from scattering. However, that correction is negligible in the clini-
cal regime (0.9988 for 100 MeV protons in water [2]).
2.3.5 Interpolating Range–Energy Tables
S/ρ varies roughly as 1/β
2
(Eq. 2.17), while β
2
varies roughly as E, so Eq. 2.20
implies that R should vary roughly as E
2
. In fact the exponent is a bit less
than 2. For instance, if we ft a power law to the range in water at 100 and 200
MeV (2), we fnd

R a E E E
b
≈ = g/cm ( in MeV
2
0 00244
1 75
.   )
.

(2.21)
and this is only 0.5% low at 150 MeV. If we chose a different range for the
power-law ft, the constants will come out slightly different.
In working with protons we frequently need R(E) or its inverse E(R) at
arbitrary values for various materials, so it is well to have an accurate and
convenient interpolation routine at hand. The fact that R(E) is nearly a power
law implies that a graph of log R vs. log E is nearly a straight line, as we
have already seen. Figure 2.10, a log-log graph for three materials over an
extended region, shows that the lines eventually curve. From 3-300 MeV they
–0.5
0.1 10 100 1000 2 3 4 1 2 3 4 2 3 2 3 4
0.0
0.5
0.0001
0.001
0.01
0.1
Pb
Be
1
10
100
1000
R
a
n
g
e

(
g
/
c
m
2
)
E
r
r
o
r

(
%
)
Energy (MeV)
FIGURE 2.10
Top: range–energy relation in Be, Cu, and Pb. Bottom: test of cubic spline interpolation. (Data
from M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer, et al. ICRU
Report 49, 1993.)
36 Proton Therapy Physics
are nearly straight, and for Be, Cu, and Pb, nearly parallel: good candidates
for cubic spline interpolation (8) for each material separately. This method, in
effect a different variable power law for each material, is more than adequate
as the lower panel of Figure 2.10 shows.
*
We require only thirteen input val-
ues for each material at 0.1, 0.2, 0.5, 1, …, 500, 1000 MeV. The energy range is
generous because computer programs sometimes stray into forbidden terri-
tory while carrying out their task.
To interpolate a range–energy table by hand, use power law, not linear
interpolation, particularly if the table steps are large. Linear interpolation
gives a systematically high answer as you can see directly from R ≈ aE
2
.
2.3.6 Range Straggling
Since energy loss occurs as a fnite (albeit very large) number of individual
interactions, it has a statistical error. Therefore protons, even if their initial
energy is exactly the same, will not all stop at exactly the same depth. This
is called range straggling, or energy straggling if we focus on fuctuations in
energy loss rather than range. The theory is outlined by Janni (5), who also
evaluates it. Specifcally, he tabulates the standard deviation of straggling
expressed as a percentage of the mean projected range. Figure 2.11, a graph
of his tables, shows range straggling as a function of incident energy for fve
useful materials.
*
This and many other useful procedures are incorporated in a free “proton desk calculator”
LOOKUP by the author (B.G.) (9).
100 50 0 150 200 250 300
Energy (MeV)
0.0
0.5
1.0
1.5
2.0
2.5
lead
brass
water
lexan
beryllium
σ
S
/
R
0

(
%
)
FIGURE 2.11
Range straggling in several materials. (Data from Janni. Proton Range-Energy Tables, 1KeV–10
GeV. Academic Press, 1982).
37 Physics of Proton Interactions in Matter
From the graph, straggling ≈ 1.2% of range for light materials and
only slightly more for heavy materials. A useful consequence is that the
shape of the Bragg peak changes very little when plastic or even some
Pb is substituted for water. That will greatly simplify the design of range
modulators.
2.3.7 Water Equivalence
Water is often used as a proxy for tissue, and it is sometimes necessary to
compute the water equivalent of a degrader. For instance, the second scat-
terer in the standard nozzle used by ion beam applications (IBA) is 0.624 cm
Pb. By how much does that decrease the beam penetration in the patient?
The water equivalent of a given thickness of any material can be computed
exactly if the range–energy relation of the material and that of water are
known (10). Of course the answer is only as accurate as the range–energy
relation. To avoid that problem, the water equivalent can easily be measured,
by placing the degrader upstream of a water tank and measuring the shift
in the Bragg peak, as should always be done if the answer is critical (for
instance, if it determines treatment depth).
If a material is far from water in the periodic table, its water equivalent
depends on incident energy and must be used with caution. Water equiva-
lent is independent of energy only if R(E) of the material on a log-log plot
(Figure 2.9) is parallel to that of water. The water equivalent of 0.6329 cm
Pb is 3.5722 cm at 200 MeV incident but 3.4197 cm at 100 MeV, 1.5 mm less.
By contrast, a plastic degrader has the same water equivalent at any radio-
therapy energy. That said, if the Pb is located at the start of a beam line
and always sees nearly the same proton energy, its water equivalent will be
constant.
2.4 MultipleCoulombScattering
In addition to slowing down in matter, protons scatter, mainly by myriad
collisions with atomic nuclei. The angular defection from a single scatter is
almost always negligible. Therefore the main observed effect is the statisti-
cal outcome (random walk in angle) of countless tiny defections. Hence
“multiple Coulomb scattering” (MCS), “Coulomb” because the underlying
interaction is electrostatic. The MCS angular distribution is very nearly
Gaussian, because it’s the sum of many small random defections (the
Central Limit Theorem). However, it’s not exactly Gaussian: the theorem
does not really apply because large single scatters in the target, though
rare, are not quite rare enough (11). The complete angular distribution has a
Gaussian core with a single scattering tail. For most radiotherapy purposes
38 Proton Therapy Physics
we need only consider the Gaussian part, which contains about 98% of the
protons.
2.4.1 Experiment
Figure 2.2 shows an ideal proton beam entering a target. On emerging the
protons have a nearly Gaussian angular distribution, with an rms spread,
θ
0
. If they then drift through a distance, L, to a measuring plane (MP) with
little or no additional scattering, a nearly Gaussian fuence distribution of
rms spread y
0
= L × θ
0
results. We can use a dosimeter to measure this fuence
distribution because all protons at the MP have very nearly the same energy
or stopping power, so dose is proportional to fuence (Eq. 2.12).
If we want to deduce θ
0
from measurements of y
0
, we need to worry (for
thick targets) about where the protons appear to come from: what is L,
exactly? For thin targets, we need to consider the size of the beam and scat-
tering in air along the drift path. Except for these complications the experi-
ment really is simple, and measured values of θ
0
for a large assortment of
target materials and thicknesses have been reported (12).
2.4.2 Highland’s Formula
The theoretical challenge is (a) to predict the exact form of the MCS angu-
lar distribution and (b) to predict its characteristic width as a function of
proton energy as well as scattering material and thickness. Several more or
less successful theories were published in the 1930s and 1940s. By consensus,
the most elegant, accurate, and comprehensive theory for incident protons is
that of Molière (13, 14), written in German. A paper in English by Bethe (15)
improves on Molière’s somewhat and reconciles it with some of the other
theories. However it omits two aspects of Molière’s theory critically impor-
tant to proton radiotherapy: his generalizations to scattering in arbitrarily
thick targets (large proton energy loss) and compounds and mixtures. The fact
that several American authors were unaware of these generalizations, espe-
cially the frst, led to some errors and confusion in the literature.
We will shortly come to Molière’s theory, at least the bare bones. However,
let us frst present a formula which is nearly as accurate and far easier to
evaluate. In the Gaussian approximation all we need is the dependence of θ
0

on proton energy and scattering material. Highland’s formula for θ
0
(16) is
as follows
*
:

θ
0 10
14 1
1
1
9
+
¸
¸

_
,


¸

1
]
1
.
log
MeV
rad
pv
L
L
L
L
R R

(2.22)
*
The numerical constant, strictly following Highland’s paper, should be 17 5 1 125 2 13 92 .     . . × = / MeV
17 5 1 125 2 13 92 .     . . × = / MeV. However, the 1986 Particle Properties Data Book gave 14.1, which (for whatever
reason) we (12) used in our comparison with experimental data. It has since become the
accepted value.
39 Physics of Proton Interactions in Matter
where pv is the kinematic factor we have already met in Eq. 2.6, L is the
target thickness, and L
R
is the radiation length of the target material, which
can be found in tables. As its form implies, Eq. 2.22 only applies to targets
suffciently thin so that pv does not decrease much from its initial value.
However, it can be generalized (12) to arbitrarily thick targets.
Considering its simplicity, the Highland formula so generalized is com-
prehensive and accurate. Figure 2.12 compares it with experiment for target
materials spanning the periodic table over three decades of normalized tar-
get thickness and two decades of θ
0
. It is worth noting that Highland derived
his formula by ftting a version of Molière theory (12, 16), not by ftting exper-
imental measurements.
2.4.3 Molière’s Theory
Molière’s theory is algebraically complicated.
*
To give you a favor, we will
only treat the simplest case, a target consisting of a single element (atomic
weight A, atomic number Z) which is suffciently thin so that the incident
proton (charge number z, momentum p, speed v) does not lose much energy.
We also assume Z is large enough that scattering by atomic electrons is
negligible. The task is to compute the distribution of proton space angle  θ
given protons of known energy in a target of thickness t g/cm
2
, where
t proton range.
*
The aforementioned free program LOOKUP by the author (B.G.) can be used to compute
MCS theory in all its forms (9).
0.001 0.01 0.1 1
x / R
1
1
10
100
θ
0

(
m
i
l
l
i
r
a
d
)
θ
Highland
Pb
Be
Al
Cu
FIGURE 2.12
Accuracy of Highland’s formula for four elements. x/R
1
is target thickness divided by pro-
ton range at the incident energy. The points are experimental data at 158.6 MeV. (From B.
Gottschalk, A.M. Koehler, R.J. Schneider, J.M. Sisterson M.S. Wagner. Nucl Instr Methods.
1993;B74:467–90. With permission.)
40 Proton Therapy Physics
We frst calculate a characteristic single scattering angle χ
c
given by

χ
c
c t pv
2
3
2
= /( )

(2.23)
where

c N
e
c
c
z Z
A
A 3
2
2
2
2
4 ≡






2
π

( )

(2.24)
where N
A
≈ 6.022 × 10
23
gmolwt
−1
is Avogadro’s number, (e
2
/ħc) ≈ 1/137 is the
fne structure constant, and (ħc) ≈ 197 × 10
−13
MeV cm is the usual conversion
factor. The physical interpretation of χ
c
is that, on average, a proton suffers
exactly one single scatter greater than χ
c
in its traversal of the target.
Next we compute a screening angle χ
a
using

χ χ α
a
2
0
2 2
1 13 3 76 = + ( . . )

(2.25)
where

χ
0
2
2
2
= c pc /( )

(2.26)
and the Born parameter, α, is given by

α β
2
1
2
= c /

(2.27)
where β ≡ v/c of the proton. The constants are

c
e
c
z Z
1
2
2
≡
¸
¸

_
,


¸

1
]
1


(2.28)
and

c
e
c
m c Z
e 2
2
2 1 3
2
1
0 885
≡
¸
¸

_
,


¸

1
]
1
.
( ) .

/

(2.29)
The screening angle is that (very small) angle at which the single scattering
cross section levels off (departs from Rutherford’s 1/θ
4
law) because of the
screening of the nuclear charge by the atomic electrons. One of Molière’s key
insights was that, though MCS depends directly on that angle, it is insensi-
tive to the exact shape of the single scattering cross section near that angle.
Next we compute a quantity,

b
c
a
=






ln
.
χ
χ
2
2
1 167

(2.30)
41 Physics of Proton Interactions in Matter
which is the natural logarithm of the effective number of collisions in the tar-
get. Next, the reduced target thickness, B, is defned as the root of the equation

B B b − = ln

(2.31)
which can be solved by standard numerical methods. B is almost propor-
tional to b in the region of interest.
Finally, Molière’s characteristic multiple scattering angle,

θ χ
M
=
1
2
( )
c
B

(2.32)
is analogous to θ
0
in the Gaussian approximation. Typically it is about 6%
larger.
*
Molière is now positioned to compute the distribution of θ. Defning
a reduced angle,

′ ≡ θ
θ
χ
c
B

(2.33)
he approximates the desired distribution function f(θ) by a power series in
1/B:

f f
f
B
f
B
( ) ( )
( ) ( )
( )
( ) ( )
θ
πθ
θ
θ θ
= ′ +
′
+
′  1
2
1
2
2
0
1 2
2
M 





(2.34)
where

f
n
y dy J y e
y y
n y ( ) /
( )
!
( ) ln ′ = ′





θ θ
1
4 4
0
4
2 2
2

∞
∫
0
n
.

(2.35)
f
(0)
is a Gaussian:

f e
( )
( ) .
0
2
2
′ =
− ′
θ
θ

(2.36)
Molière gives further formulas and tables for f
(1)
and f
(2)
in reference 15.
The foregoing equations, with Bethe’s improved tables for f
(1)
and f
(2)
(15),
permit one to evaluate the scattering probability density f(θ) if the target con-
sists of a single chemical element with Z 1, and the energy loss is small.
Except for rearrangements of physical constants to conform to modern usage,
and the normalization of f(θ), the equations are identical to Molière’s. We reit-
erate that Molière generalized this procedure to arbitrary energy loss, and to
compounds and mixtures (12, 14, 17).
The generalization to low-Z elements, where scattering by atomic elec-
trons (not just the nucleus) is appreciable, is handled two ways in the lit-
erature. Bethe’s approach (15) is simply to substitute Z(Z + 1) for Molière’s
Z
2
wherever it appears. We call this Molière/Bethe. Fano’s approach (12,
*
The 1 2 / is ours; it makes θ
M
more or less equivalent to θ
0
in the Gaussian approximation.
42 Proton Therapy Physics
17, 18) is more complicated: he gives a correction to b. The Molière/Fano
theory fts experimental proton data from 1 MeV to 200 GeV for a wide
variety of materials and thicknesses at the few percent level (12). Since
this is comparable to experimental error, we do not really know how good
Molière’s theory is, but Bethe (15) put it at 1%. There are no adjustable
parameters!
Though the mathematical defnition of B is tortuous, it is easy to show
numerically that B has a simple physical interpretation: it is proportional to
the logarithm of the normalized target thickness. The constant of propor-
tionality depends on the material. Figure 2.13 shows that the angular distri-
bution depends very weakly on B.
2.4.4 The Gaussian Approximation
The frst proton measurements were performed by Bichsel, who bombarded
targets of Al, Ni, Ag, and Au with 0.77- to 4.8-MeV protons from a Van de
Graaff accelerator, using a tilted nuclear track plate detector (19). Figure 2.14
shows the angular distribution plotted in such a way that a Gaussian dis-
tribution yields a straight line. The solid line is the full Molière theory. The
dashed line is f
(0)
(the Gaussian term) alone.
0
0
10
–6
10
–5
10
–4
10
–3
10
–2
10
–1
10
0
10
1
25 50 75 100
( )
2
125
1 2 3 4 5 6
B = 4
B = 12
θ′
(



)
2
2
f
M
θ
′
π
θ
FIGURE 2.13
Molière angular distribution plotted so that a Gaussian would show up as a straight line.
Dashed line: f
(0)
only. Inset: graph near the origin. (From B. Gottschalk, A.M. Koehler, R.J.
Schneider, J.M. Sisterson M.S. Wagner. Nucl Instr Methods. 1993;B74:467–90. With permission.)
43 Physics of Proton Interactions in Matter
Besides showing that Molière theory works well, Figure 2.14 shows that
the distribution for small θ is approximately Gaussian but is not best rep-
resented by just keeping f
(0)
. The higher f ’s also contribute, even at small θ.
This had been noticed earlier by Hanson et al. (20), who suggested using, at
small angles, a Gaussian with a reduced width parameter. In our notation
Hanson’s recommendation reads

θ θ χ
0
1
2
1 2 = ≡ −
H c
B ( . ).

(2.37)
So far, that’s not a time saver because one still has to do the full Molière
computation to evaluate Eq. 2.37. In 1975, however, Highland parameterized
the full Molière/Bethe/Hanson theory, obtaining Eq. 2.22. As already noted,
this simple formula fts experimental data in the Gaussian region nearly as
well as the full theory.
Integration of the Molière angular distribution f(θ) shows that approxi-
mately 98% of the protons fall into the region well described by a Gaussian.
Therefore a single Gaussian distribution suffces for many proton radiother-
apy calculations. If a dose outside the MCS Gaussian core needs to be mod-
eled, the halo of nonelastic nuclear reaction secondaries is usually greater
than the MCS single scattering tail (21).
2 1
1
10
10
2
10
3
10
4
3 4 5 6 7
θ
2
f

(
θ
)
FIGURE 2.14
Figure 5 from Bichsel’s experiment: 2.18-MeV protons scattered from a 3.42-mg/cm
2
Al foil.
(From Hans Bichsel. Phys Rev. 1958;112:182–85. With permission.)
44 Proton Therapy Physics
2.4.5 Scattering Power
Scattering power was introduced by Rossi in 1952 (22), though he did not use
that term. It was resurrected and named by Brahme (23) in connection with
electron radiotherapy, and now appears regularly in discussions of proton
transport. This section is rather technical and may be skipped if you are only
interested in computing multiple scattering in a single homogenous slab, for
which we have already given several methods.
Stepping back a bit, to compute the total energy loss of a proton in a
degrader, we can integrate stopping power over the degrader thickness.
Stopping power, defned by

S x dE dx ( ) ≡ − /

(2.38)
depends on the proton speed, and properties of the degrader material, at x
(Eq. 2.17).
By contrast, in MCS theory, we have outlined the theory without ever men-
tioning the concept of “scattering power.” Nevertheless—if we so desire—
can we (in analogy to stopping theory) defne a scattering power as the rate
of increase of the variance of the MCS angle,
*

T x d dx
y
( ) / ≡ θ
2

(2.39)
such that, integrated over x for a homogeneous slab of arbitrary thickness, it
correctly gives the total MCS angle in the Gaussian approximation, namely
the Molière/Fano/Hanson result? Also, why would we want to do that, since
we already know the answer?
Taking the second question frst, we assert without proof that any proton
transport problem that is, any attempt to handle simultaneously both energy
loss and multiple Coulomb scattering, requires a differential description of
both processes. We must be able to compute, for any infnitesimal step ∆x of
the full degrader, the corresponding infnitesimal changes in energy and
MCS angle. That applies equally to deterministic (e.g., Fermi-Eyges [24]) or
Monte Carlo methods. Furthermore, it is very desirable that any such com-
putation yield results which, at least over some reasonable range, are inde-
pendent of the step size ∆x. That covers our motivation for trying to fnd a
workable T(x), essentially a differential description of Molière’s theory.
As to the frst question, at least six prescriptions for T(x) exist, some con-
siderably more accurate than others (25). We favor (naturally) our own “dif-
ferential Molière” formula:

T x f pv p v
pv x L
S
dM
MeV
( ) ( , )
.
( )
= ×





 dM 1 1
2
15 0 1
(( ) x

(2.40)
*
Current practice favors defning T as the rate of increase of projected angle θ
y
rather than the
space angle θ of Molière’s theory.
45 Physics of Proton Interactions in Matter
where

f pv p v
dM 10
2
0.5244 0.1975 (1 ( / ) ) 0.232 ≡ + − + log
1 1
00 ( /MeV)
0.0098 ( /MeV)
log
log log
10
10 10
pv
pv − ((1 ( / ) )
2
− pv p v
1 1

(2.41)
and

1
2 33219 1
2
2
1 3
L
Nr
Z
A
AZ
e
S
≡ −
−
α
ρ
{ log( ( ) ) }
/

(2.42)
which reproduces Molière/Fano/Hanson theory to ≈ ±2% for normalized
target thicknesses from 0.001 to 0.97 (very thin to nearly stopping) over the
full periodic table (25). L
S
is a scattering length, analogous to radiation length
L
R
, and of the same order of magnitude.
*
pv is the familiar kinematic quantity
(Eq. 2.6) at x, the point of interest, while p
1
v
1
is the same quantity entering the
degrader. Eqs. 2.40–2.42 apply equally well to mixed slabs. We simply regard
L
S
as a (discontinuous) function of x while pv(x) is computed using the appro-
priate range-energy relation in each slab.
An important characteristic of T
dM
(x) is that it is nonlocal via the correction
factor f
dM
. Scattering power depends not only on conditions at x (that is, pv
and L
S
) but on how the protons started out (p
1
v
1
). To take a simple example,
for a 20 MeV proton in Be,
d dx
y
⟨ ⟩ θ
2
/
is smaller if the overlying thickness
of Be is 0.1 cm (protons enter at 23.7 MeV) than if it is 5 cm (protons enter
at 102 MeV). How can that be? How can the proton “know” what has gone
before? The answer is that, unlike stopping, and for that matter, single scat-
tering, multiple Coulomb scattering is not a primitive process! It makes sense
to speak of stopping and single scattering even in an atomic monolayer,
whereas it does not make sense to speak of multiple scattering: there are not
nearly enough collisions. In a sense the factor f
dM
is a measure of the proton’s
progress toward “Gaussianity.” One fnds (25) that any T(x) that has some
nonlocality built into it, some sense of the beam’s history, is more accurate
than any T(x) that does not.
A fnal comment, on step size. We mentioned that any computation, deter-
ministic or Monte Carlo, should converge as a function of ∆x. Over some
range of (suitably small) ∆x’s the answer should not change. Some popu-
lar Monte Carlos do not have this property, and using a scattering power
approach would remedy that. There is no way that the Molière theory or its
proxy, the Highland formula, can be built directly into a Monte Carlo without
introducing step size dependence.
2.4.6 Binary Degraders
Figure 2.3 shows that high-Z materials (e.g., Pb) are better at scattering,
whereas low-Z materials (Be, plastics) are better at stopping. We use Pb if we
*
L
S
/L
R
= 1.42 for Be decreasing monotonically to 1.04 for Pb. For compounds and mixtures L
S

obeys the Bragg additivity rule (Eq. 2.19).
46 Proton Therapy Physics
wish to scatter a beam with minimum energy loss and Be if we wish to slow
down a beam with minimum scattering.
In beam line design we often need to control both scattering and stopping.
Instead of scouring the periodic table for the right combination, we use high-Z/
low-Z sandwiches such as Pb/plastic. Figure 2.5 shows two examples. The
range modulator’s main job is to decrease beam energy in defned steps, but
each step also has to produce the correct MCS angle for the double scattering
system. Conversely, the second scatterer’s main job is to produce the correct
MCS angle as a function of radius, but we also want the same energy loss at
any radius. Mathematical design procedures for such “binary degraders” are
described elsewhere (1, 9).
2.5 NuclearReactions
Although EM interactions of protons dominate, nuclear interactions are by
no means rare. They are far harder to model than stopping and scattering.
Fortunately, their biological effect turns out to be small, while, in the design
of beam spreading systems, they can be taken into account well enough by
using experimentally measured—rather than theoretical or Monte Carlo
generated— Bragg peaks.
2.5.1 Terminology
ICRU63 (27) defnes an elastic nuclear reaction as follows:
• A reaction in which the incident projectile scatters off the target
nucleus, with the total kinetic energy being conserved (the internal
state of the target nucleus and of the projectile are unchanged by the
reaction)
while nonelastic
• … is a general term referring to nuclear interactions that are not
elastic (i.e., kinetic energy is not conserved). For instance, the target
nucleus may undergo breakup, it may be excited into a higher quan-
tum state, or a particle transfer reaction may occur.
and inelastic
• … refers to a specifc type of nonelastic reaction in which the kinetic
energy is not conserved, but the fnal nucleus is the same as the
bombarded nucleus.
47 Physics of Proton Interactions in Matter
Thus,

p p p p + → +
16 16 16 16
O O or O , O ( )

(2.43)
is elastic (
16
O is left in its ground state),

p p p p + → +
16 16 16 16
O O or O , O
* *
( )

(2.44)
is inelastic (* denotes an excited state), and

p p p p p + → + +
16 15 16 15
O N or O , 2 N ( )

(2.45)
(quasi-free proton-proton scattering in oxygen) is nonelastic even if the
15
N nucleus recoils in its ground state, because it took energy—the “binding
energy”—to remove the target proton from the nucleus.
When a proton beam slows down and stops in matter, at any given depth
we call those particles primaries, which have suffered EM interactions (stop-
ping by collisions with atomic electrons and scattering by atomic nuclei).
Particles from inelastic or nonelastic nuclear reactions are called secondaries.
Both fnal state protons in reaction (2.45) are secondaries even though one
(we cannot tell which) was the incident proton. All primaries are protons, of
course, and all neutrons must be secondaries.
Some materials of biological interest, for example, H
2
O, contain free hydro-
gen. When an incident proton scatters off free hydrogen, the secondary pro-
tons emerge with a relative angle of approximately 90° and share the original
kinetic energy. Therefore they look pretty much like secondary protons from
reaction (2.45) and should be included in any tally of nonelastic reactions
even though the reaction is, technically, elastic.
2.5.2 Overview of Nonelastic Reactions
Possible secondaries from nonelastic reactions at therapy energies are
protons, neutrons, γ rays, heavy fragments such as alphas, and the recoil-
ing residual nucleus. Heavy fragments other than alphas are in fact quite
rare. One measure of the relative importance of each is the fraction of initial
energy carried away. For nonelastic interactions of 150-MeV protons with
16
O nuclei, Seltzer (27) fnds the following:
p d t
3
He α Recoils n
0.57 0.016 0.002 0.002 0.029 0.016 0.20
The total energy imparted to charged particles is 0.64. Photons, not listed,
presumably make off with 0.16. These numbers are from a Monte Carlo
model, not direct experiment. Most of the fnal energy is in protons, neu-
trons and photons. Alphas stand out among heavy fragments (the alpha is
particularly stable) but still have only 2.9% of the total energy.
48 Proton Therapy Physics
Though little of the energy goes into heavy fragments, they could in
principle have a signifcant relative biological effect (RBE) because of their
high-ionization density (see Chapter 19). This has been investigated by
Seltzer (27), Paganetti (28, 29), and others, who fnd that RBE enhancement
due to heavy fragments and recoils is, in fact, small. Their high ionization
density is outweighed by the fact that very little energy (that is, dose) goes
into those channels. What RBE enhancement there is comes from the much
more abundant low-energy protons: secondaries and, at the distal end of the
Bragg peak, primaries.
Secondaries typically make large angles with the beam (think billiard
ball collisions) unlike primaries which, even after multiple scattering,
rarely exceed a few degrees. That is important because it means that
secondaries produced in the beam line in scatterers or absorbers will
clear out of the beam for purely geometric reasons before they enter the
patient.
2.5.3 Nonelastic Cross Section
We already know from Figure 2.7 that the nonelastic interaction probability
per g/cm
2
must be fairly independent of energy because the rate of loss of
primary fuence is fairly constant. Janni (5) combines theory with experi-
mental data to evaluate the cross section for various elements. Figure 2.15
shows his result for oxygen, plotted as a function of proton range rather
than energy. Others (27, 30) use slightly different procedures and experi-
mental data, but also fnd that the nonelastic cross section is nearly con-
15 10 5 0 20 25 30 35
R
0
(g/cm
2
)
0
100
200
300
400
500
600
σ
n
o
n
e
l
a
s
t
i
c

(
m
B
)
FIGURE 2.15
Total nonelastic cross section of oxygen versus proton range.
49 Physics of Proton Interactions in Matter
stant at therapy energies, except in the last few cm where it roughly doubles
before falling to zero.
The total interaction probability for a stopping proton is the integral of the
nonelastic cross section over the range. Figure 2.16 shows Janni’s result for
water (5). For example, a 209 MeV proton, with a range of 28 g/cm
2
, has a 24%
probability of a nonelastic reaction before it stops.
2.5.4 Nuclear Buildup: Longitudinal Equilibrium
Figure 2.17, a Bragg peak measured with a vertical proton beam, shows a
small but defnite buildup in the entrance region. That can be explained as
follows. A proton beam emerging from air is accompanied by relatively few
nuclear secondaries because of the low density of air. Nonelastic reactions
increase as soon as the beam hits water, but it takes them a centimeter or two
(the characteristic range of secondary protons) to reach equilibrium. After
that the primary beam has an admixture of secondaries which is nearly
independent of depth. Longitudinal equilibrium has been reached.
Nuclear buildup was frst observed by Carlsson and Carlsson (31) in
1977. The observed dose defect at the entrance was about 2× smaller than
it should be according to the cross section, an observation also true of
Figure 2.17 and still not explained. Incidentally, they also measured elec-
tron buildup, which is larger but has a much shorter characteristic distance
( ) 1 mm . In photon therapy, electron buildup is useful; it leads to skin
sparing. Unfortunately, this is not the case in proton therapy because the
buildup distance is so short.
0
5
10
15
20
25
30
35
15 10 5 0 20 25 30 35
R
0
(g/cm
2
)
P
n
o
n
e
l
a
s
t
i
c

(
%
)
FIGURE 2.16
Probability of a nonelastic interaction versus proton range in water.
50 Proton Therapy Physics
2.5.5 Test of Nuclear Models
Predicting what mix of secondaries, with what energy and angle distribu-
tions, one will get when bombarding a given nucleus with protons of a given
energy is an extremely complicated business, as might be expected. The
nuclear model built into most popular Monte Carlo simulations is a descen-
dant of the Bertini cascade model (32). Basically this model says that at proton
energies signifcantly greater than the proton binding energy, the interaction
begins as a quasi-free scatter off a nuclear proton, neutron, or cluster (alpha
particle) and continues with possible further scatters until the secondaries
emerge, leaving a recoiling residual nucleus behind.
The complexity of the model makes a direct test very desirable. The shape
of the Bragg peak is not a very good test, because the infuence of nuclear
secondaries on the shape is small, as we shall see shortly. A far more precise
test can be made with the aid of a multi-layer Faraday cup (MLFC) like the
one shown in Figure 2.18. It consists of CH
2
(polyethylene) plates, in which
most of the protons and secondaries stop, separated by thin brass charge col-
lection plates.
*
The distribution of charge collected in each channel (Figure
2.19) shows a large peak (here reduced 25× for display purposes) preceded by
a buildup region that comes entirely from nuclear secondaries and refects
the overall projected range of those secondaries. The three nuclear models
tested, including the Bertini model, agree perfectly with each other and
rather well with the experimental data (33).
*
When the “stopping” plates are insulators, as here, it is the induced charge that is measured,
but that equals the stopping charge. Protons stopping in the brass are measured directly.
0
0.0
0.2
0.4
0.6
D
o
s
e

(
r
e
l
a
t
i
v
e
)
0.8
1.0
1.2
4 8 12 16 20
Range (g/cm
2
)
Meas used 20MAR99
24 28 32 36 40
FIGURE 2.17
Nuclear buildup in a Bragg peak. The abscissa should read “depth,” not “range.” (Courtesy of
D. Prieels, Ion Beam Applications s.a..)
51 Physics of Proton Interactions in Matter
FIGURE 2.18
A multilayer Faraday cup with CH
2
plates (aluminum shield not shown).
30
Channel number
Bertini
ISABEL
CEM
Experimental data
p
C
/
G
i
g
a
P
r
o
t
o
n
40 50 60 20 10 0
0
0.5
1
1.5
2
2.5
+
++
+
+
+
+
+
+
+
++
+
+
++
+
+
++
+
+
+
+
+
+
+
+
+
+
+
+++
+
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+++++++ ++++
FIGURE 2.19
Buildup of nuclear secondary fuence, observed with a CH
2
MLFC and compared with various
Monte Carlo nuclear models. (From A. Mascia, J. DeMarco, P. Chow, T. Solberg. Proc. XIVth
Intl. Conf. on the Use of Computers in Radiation Therapy, Seoul, May 10–13, 2004, 478–81. With
permission.)
52 Proton Therapy Physics
2.6 TheBraggPeak
By Bragg peak (BP), we mean the entire depth–dose distribution measured in
a water tank using a suffciently broad, quasi-mono-energetic proton beam.
We need a carefully measured BP in order to design a range modulator to
create a spread-out Bragg peak (SOBP).
Many calculations (Monte Carlo [3], analytical [4], numerical [34], and even
graphical [A. M. Koehler, private communication]). have established that
measured BP’s can be fully explained by combining the physical processes
(stopping, scattering, and nuclear reactions) we have studied so far. In this
section we’ll show qualitatively how each effect comes in. See Figure 2.20, a
sort of summary.
2.6.1 Beam Energy
That determines the depth of the peak. We have already learned that the
mean projected range equals the depth of the distal 80% point (R
0
= d
80
), not
the depth of the maximum.
2.6.2 Variation of S ≡ −dE/dx with E
The fact that the stopping power increases as the protons slow down gives
rise to the upward sweep of the BP.
nuclear reactions take
away fron the peak and
add to this region
this part is a guess
nuclear buildup
or low energy
contamination
10CM.TXT
overall shape from
increase of dE/dx
as proton slows
1/r
2
and transverse
size set peak to
entrance ratio
the
dosimeter
matters
width from
range straggling
and beam
energy spread
depth from
beam energy
FIGURE 2.20
Ingredients of the Bragg peak.
53 Physics of Proton Interactions in Matter
2.6.3 Range Straggling and Beam Energy Spread
The peak’s minimum possible width is related to range straggling, σ
RS
≈
0.012  × range. There may be an additional contribution σ
beam
from beam
energy spread. The width of the peak region and distal falloff depend on the
quadratic sum of the two. More precisely,

d d
20 80
2 1 2
1 3 − = × + . ( )
/
σ σ
RS
2
beam
(2.46)
which is from (A.M. Koehler private communications, 1982).
Modern proton therapy facilities combine BP’s to get a fat dose distribu-
tion in two very different ways. In passive beam spreading, and in some
magnetic scanning systems, degraders just upstream of the patient pull back
the BP, and these displaced BP’s are combined (with appropriate weights) to
produce an SOBP (see Chapter 4). Even though the degraders are not usu-
ally made of water, pulled-back BPs have very nearly the same shape as the
pristine BP because, as we saw earlier, range straggling depends very weakly
on degrader material. The degraders may be controlled by a computer, or the
proper weights and range steps may be built into a classical propeller type
range modulator.
Otherwise, one may change the proton energy at the accelerator. Then,
we must ask how BPs compare at different energies. Because straggling is
nearly a constant fraction of range, the absolute width of the BP decreases
with range (Figure 2.21). Any technique that changes energy at the accelera-
tor must somehow parameterize this change in shape.
0
0
10
20
30
40
50
10 20
g/cm
2
M
e
v

/

(
g
/
c
m
2
)
30
FIGURE 2.21
A set of measured Bragg peaks from 69 to 231 MeV. (Courtesy of D. Prieels, Ion Beam
Applications s.a.)
54 Proton Therapy Physics
2.6.4 Nuclear Interactions
Each nonelastic reaction removes a proton from the EM peak, and the sec-
ondaries (having short ranges and large angles) deposit their energy fur-
ther upstream. Therefore, nuclear interactions lower the peak and raise the
entrance region (Figure 2.22).
2.6.5 Beam Size: Transverse Equilibrium
MCS affects the Bragg peak somewhat indirectly. The BP, like any depth-
dose distribution, obeys D = Φ × (S/ρ) (dose = fuence × mass stopping power).
Suppose we form a “pencil” beam using a small collimator. As the beam
penetrates the water tank, it scatters, so that a given number of protons
occupy more transverse area. In other words, the fuence on the central axis
decreases with depth. That cancels the tendency of the stopping power to
increase with depth. The Bragg peak become less pronounced, the smaller
the collimator, as frst pointed out by Preston and Koehler (35) (Figure 2.23).
To counter that, we need to use a large beam, which we can obtain either
by scattering or magnetic scanning (averaging over an integral number of
scan cycles). Then at any point, say near end-of-range, the dose feld can be
thought of as a bunch of pencil beams laid down next to each other. Protons
originally directed at some small area, dA, but scattered out, are compen-
sated by protons not directed at dA, but scattered in. That compensation
(“transverse equilibrium”) works as long as there are enough nearby pencils
0.0
0
5
10
15
20
25
30
160 MeV
35
40
0.2 0.4 0.6 0.8 1.0
z/r
o
d
D
/
d
z
,

M
e
V

c
m
2
/
g
FIGURE 2.22
Solid line: Bragg peak including nuclear interactions; dashed line: nuclear interactions turned
off. (Data from Martin J. Berger, NIST technical note NISTIR 5226 (1993). Available from the
National Technical Information Service (NTIS), U.S. Department of Commerce, Springfeld,
VA 22161.)
55 Physics of Proton Interactions in Matter
to do the scattering in, that is, as long as the beam surrounding dA is big
enough.
How big is big enough? You need to compute beam spreading in a water
tank, a basic proton transport problem is beyond the scope of this chapter;
see Preston and Koehler (35). There’s a simple experimental test, though. If
you move the scan axis 1 cm to the side and measure the same BP, the beam
is big enough.
A way of getting the right answer with a single pencil beam is to use a
detector which is much larger than the beam even at end of range. Such a
detector sees all the protons at any depth. It integrates radially over the fu-
ence factor, which therefore drops out. To summarize: when measuring the
Bragg peak with a view to large-feld modulator design, either use a small
detector in a broad beam or a large detector in a pencil beam.
2.6.6 Source Distance
To ensure transverse equilibrium, we usually spread the beam transversely,
either by single or double scattering. Either way, the scattering system will
have an effective origin from which the protons appear to spread out as
from the apex of a cone. That cone is smaller at the entrance to the water
tank than deeper into the tank. Put another way, the fuence falls as 1/r
2
,
where r is the distance from the effective origin to the dosimeter. This effect
x-cm WATER
r
c
= 1 mm
r
c
= ∞
2 mm
3 mm
4 mm
2
20
40
D
(
o
,

x
)

D
O
S
E

O
N

A
X
I
S
60
80
100
4 6 8 10 12
FIGURE 2.23
The relative dose on the axis of a uniform circular proton beam of initial range 12 cm of
water and radius r
c
at the collimator. The curve for r
c
= ∞ is experimental; the others are
calculated. (Data from W.M. Preston, A.M. Koehler. The effects of scattering on small pro-
ton beams. Unpublished manuscript (1968), Harvard Cyclotron Laboratory. A facsimile is
available in BGdocs.zip at http://physics.harvard.edu/~gottschalk.)
56 Proton Therapy Physics
lowers the peak-to-entrance dose ratio. It must be corrected, unless the sys-
tem being designed has the same effective r as was used during the BP
measurement.
2.6.7 Dosimeter
Different dosimeters may give different peak/entrance ratios in the same
beam. Sometimes the problem is intrinsic. For instance, some diodes overre-
spond in the peak region (36) relative to a plane-parallel ionization chamber
(IC). Sometimes, the difference is geometric in origin. For instance, a “thim-
ble” IC yields a lower peak/entrance ratio than does a plane-parallel IC (37).
2.6.8 Electronic and Nuclear Buildup; Slit Scattering
Several effects may contaminate the entrance region. You will not normally
see electronic buildup since the buildup distance is very short. Nuclear
buildup may be seen with a vertical beam (beam entering water from air)
but should be ignored, at least with passive beam spreading, because the
range compensator will usually have enough buildup material to mask it.
If there is a collimator near the water tank, slit scattered protons may be
observed as a dose enhancement in the entrance region, so this should be
avoided.
2.6.9 Tank Wall and Other Corrections
For design purposes we usually want a BP which approximates, as well as
possible, what would be seen with the raw beam (no scatterers or degrad-
ers) entering an ideal water tank (no wall) and an ideal dosimeter (no wall).
Because of scatterers, tank wall (usually rather thick in commercial water
phantoms), and dosimeter wall, the frst bit of this ideal BP is not actually
measured. As Figure 2.20 ”this part is a guess” shows, this region can be
approximated well enough by linear extrapolation of the frst bit of the mea-
sured part.
2.6.10 Measuring the Bragg Peak
All the items enumerated should be kept in mind when measuring a BP to
be used in designing a large-feld range modulator. If the dosimeter is small,
make sure the beam is broad. Use the dosimeter you plan to use later for QA.
Set accelerator energy selector slits (if any) at their working setting to get the
same beam energy spread. Record the thickness of all materials upstream
of the dosimeter active volume (scatterers, tank wall, dosimeter wall) so you
can correct the depth in water for them. Be sure you know and record the
effective origin so you can correct the BP for 1/r
2
.
57 Physics of Proton Interactions in Matter
2.7 Summary
We began with a qualitative survey, some basic proton kinematics, and
defnitions of the dosimetric quantities: fuence, stopping power, and dose.
Using these, it was already possible to estimate how much proton current
we need for a given dose rate and treatment volume. We then presented
the basic interactions of protons in some (though by no means complete)
mathematical detail. These processes (stopping, scattering and nonelas-
tic nuclear) interact to determine the shape of the pristine Bragg peak, the
basic proton depth–dose curve from which therapy dose distributions are
constructed.
Stopping and scattering are relatively simple, while nuclear reactions
are relatively rare. The upshot is that many problems arising in proton
radiotherapy physics can be solved from frst principles. That is cer-
tainly true of beam line design. It is also true of dose reconstruction in
the patient, though the mathematical diffculties are formidable. They
mainly relate to the fact that, due to the interplay of inhomogeneities in
the patient (e.g., bones, air, implants) with multiple Coulomb scattering,
protons can arrive at a single point with many different energies (and
therefore, stopping powers). Until now, time-consuming Monte Carlo cal-
culations (see Chapters 9 and 12) are the only fully satisfactory way of
handling this problem.
References
1. B. Gottschalk. Lectures (BGtalks.zip) and a draft textbook (PBS.pdf in BGdocs.
zip) available for free download at http://physics.harvard.edu/~gottschalk or
the Particle Therapy Co-Operative Group (PTCOG) website: http://ptcog.web.
psi.ch/.
2. M.J. Berger, M. Inokuti, H.H. Andersen, H. Bichsel, D. Powers, S.M. Seltzer,
et  al. Stopping Powers and Ranges for Protons and Alpha Particles. ICRU
Report 49 (1993).
3. Martin J. Berger, Penetration of proton beams through water I. Depth-dose
distribution, spectra and LET distribution. NIST technical note NISTIR 5226
(1993). Available from the National Technical Information Service (NTIS), U.S.
Department of Commerce, Springfeld, VA 22161.
4. Thomas Bortfeld. An analytical approximation of the Bragg curve for therapeu-
tic proton beams. Med Phys. 1997;24(12):2024–33.
5. J.F. Janni. Proton Range-Energy Tables, 1KeV–10 GeV. Atomic Data and Nuclear
Data Tables, 27 parts 1 (compounds) and 2 (elements) (Academic Press, 1982).
6. M.F. Moyers, G.B. Coutrakon, A. Ghebremedhin, K. Shahnazi, P. Koss, et al.
Calibration of a proton beam energy monitor. Med Phys. 2007;34(6):1952–66.
58 Proton Therapy Physics
7. Ethan W. Cascio and Surajit Sarkar. A continuously variable water beam
degrader for the radiation test beamline at the Francis H. Burr Proton Therapy
Center. Proc. IEEE Radiation Effects Data Workshop (2007).
8. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Numerical Recipes:
the Art of Scientifc Computing, Cambridge University Press (1986).
9. B. Gottschalk Software (BGware.zip), including Windows executables, special
fles and Fortran source code. Available for free download at http://physics.
harvard.edu/~gottschalk.
10. B. Gottschalk. Comments on “Calculation of water equivalent thickness of
materials of arbitrary density, elemental composition and thickness in proton
beam irradiation.” Phys Med Biol. 2010;55:L29–L30.
11. C. Kittel. Elementary Statistical Physics. Wiley (1967).
12. B. Gottschalk, A.M. Koehler, R.J. Schneider, J.M. Sisterson M.S. Wagner. Multiple
Coulomb scattering of 160 MeV protons. Nucl Instr Methods. 1993;B74:467–90.
We have discovered the following errors: Eq. 2 should read

Ξ( )
( )
χ
π
χ
χ χ
=
+
1
2
2 2 2
c
a
and in Table 1 the heading α should read α
2
, and ×10
9
under
χ
c
2
should read ×10
6
.
13. G. Molière. Theorie der Streuung schneller geladener Teilchen I Einzelstreuung
am abgeschirmten Coulomb-Feld. Z Naturforschg. 1947;2a;133–45.
14. G. Molière. Theorie der Streuung schneller geladenen Teilchen II Mehrfach- und
Vielfachstreuung. Z Naturforschg. 1948;3a;78–97.
15. H.A. Bethe. Molière’s theory of multiple scattering. Phys Rev. 1953;89;1256–66.
Four entries in the second column (the Gaussian) of Table II are slightly incor-
rect (A. Cormack, private communication), but the error (corrected in our pro-
grams) is at worst 1%.
16. V.L. Highland. Some practical remarks on multiple scattering. Nucl Instr
Methods. 1975;129:497–99; Erratum, Nucl Instr Methods. 1971;161:171.
17. W.T. Scott. The theory of small-angle multiple scattering of fast charged par-
ticles. Rev Mod Phys. 1963;35;231–313.
18. U. Fano. Inelastic collisions and the Molière theory of multiple scattering. Phys
Rev. 1954;93:117–20.
19. Hans Bichsel. Multiple scattering of protons. Phys Rev. 1958;112:182–85.
20. A.O. Hanson, L.H. Lanzl, E.M. Lyman, M.B. Scott. Measurement of multiple
scattering of 15.7-MeV electrons. Phys Rev. 1951;84:634–37.
21. E. Pedroni, S. Scheib, T. Böhringer, A. Coray, M. Grossmann, S. Lin, et al.
Experimental characterization and physical modeling of the dose distribution
of scanned proton pencil beams. Phys Med Biol. 2005;50:541–61.
22. Bruno Rossi. High-Energy Particles. Prentice-Hall, New York (1952).
23. A. Brahme. On the optimal choice of scattering foils for electron therapy.
Technical report TRITA-EPP-17, Royal Institute of Technology, Stockholm,
Sweden (1972).
24. H. Svensson, P. Almond, A. Brahme, A. Dutreix, H.K. Leetz. Radiation
Dosimetry: Electron Beams with Energies between 1 and 50 MeV. ICRU Report
35 (1984).
25. B. Gottschalk. On the scattering power of radiotherapy protons. Med Phys.
2010;37(1);352–67.
59 Physics of Proton Interactions in Matter
26. Chadwick et al. Nuclear Data for Neutron and Proton Radiotherapy and for
Radiation Protection. ICRU Report 63 (2000).
27. Stephen M. Seltzer. An assessment of the role of charged secondaries from non-
elastic nuclear interactions by therapy proton beams in water. NIST technical
note NISTIR 5221 (1993). Available from the National Technical Information
Service, NTIS, U.S. Department of Commerce, Springfeld, VA 22161.
28. H. Paganetti, M. Goitein. Radiobiological signifcance of beam line depen-
dent proton energy distributions in a spread-out Bragg peak. Med Phys.
2000;27:1119–26.
29. H. Paganetti, M. Goitein. Biophysical modeling of proton radiation effects based
amorphous track models. Int J Radiat Biol. 2001;77:911–28.
30. Martin J. Berger. Status of proton transport calculations. Unpublished NIST
technical note (June 1992).
31. C.A. Carlsson, G.A. Carlsson. Proton dosimetry with 185 MeV protons:
dose buildup from secondary protons and recoil electrons. Health Phys.
1977;33:481–84.
32. Hugo W. Bertini, Low-energy intranuclear cascade calculation. Phys Rev.
1963;131:1801–21.
33. A. Mascia, J. DeMarco, P. Chow, T. Solberg. Benchmarking the MCNPX nuclear
interaction models for use in the proton therapy energy range. Proc. XIVth Intl.
Conf. on the Use of Computers in Radiation Therapy, Seoul, May 10–13, 2004,
478–81.
34. H. Bichsel, T. Hiraoka. Energy spectra and depth-dose curves for 70 MeV pro-
tons. Int J Quant Chem. 1989;23:565–74.
35. W.M. Preston, A.M. Koehler. The effects of scattering on small proton beams.
Unpublished manuscript (1968), Harvard Cyclotron Laboratory. A facsimile is
available in \BGdocs.zip at http://physics.harvard.edu/~gottschalk.
36. A.M. Koehler. Dosimetry of proton beams using small silicon diodes. Rad Res
Suppl. 1967;7: 53–63. In unpublished errata the author presents a corrected
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37. H. Bichsel. Calculated Bragg curves for ionization chambers of different shapes.
Med Phys. 1995;22(11):1721–26.
61
3
Proton Accelerators
MarcoSchippers
CONTENTS
3.1 Introduction .................................................................................................. 62
3.2 Consequences Imposed by the Dose Application Technique ............... 62
3.2.1 Dose Spreading in Depth ............................................................... 63
3.2.2 Lateral Dose Spreading ................................................................... 63
3.3 Cyclotrons ..................................................................................................... 65
3.3.1 RF System of a Cyclotron ................................................................ 67
3.3.2 Cyclotron Magnet ............................................................................ 70
3.3.3 Technical Issues ................................................................................ 70
3.3.4 The Average Field ............................................................................ 71
3.3.5 Focusing Properties ......................................................................... 73
3.3.6 Proton Source ................................................................................... 77
3.3.7 Practical Issues ................................................................................. 78
3.3.8 Beam Intensity Control ................................................................... 79
3.3.9 Beam Extraction ............................................................................... 79
3.4 Synchrotrons ................................................................................................ 82
3.4.1 Operation .......................................................................................... 83
3.4.2 Ion Source and Injector ................................................................... 84
3.4.3 Acceleration and RF ......................................................................... 86
3.4.4 Extraction .......................................................................................... 87
3.4.5 Recent Developments in Therapy Synchrotrons ......................... 88
3.5 Novel Accelerator Technologies ................................................................. 90
3.5.1 FFAG Accelerators ............................................................................ 90
3.5.2 Linear Accelerators .......................................................................... 91
3.5.3 Linac-Based Systems for Proton Therapy ..................................... 92
3.5.4 Dielectric Wall Accelerator ............................................................. 92
3.5.5 Laser-Driven Accelerators .............................................................. 94
3.6 Concluding Remarks ................................................................................... 97
Acknowledgments ................................................................................................ 98
References ............................................................................................................... 98
62 Proton Therapy Physics
3.1 Introduction
Until the 1990s proton therapy was performed in nuclear physics laborato-
ries that were equipped with a particle accelerator. Typically an (isochro-
nous) cyclotron or a synchrocyclotron was available, and in most cases the
medical program had to compete with the (nuclear) physics program. In this
period most of the pioneering proton therapy research was performed and
most of the dose delivery concepts were developed, for example, in Berkeley,
California (1, 2), Cambridge, Massachusetts (3), PSI (Switzerland) (4–6),
and Uppsala, Sweden (7). When the effcacy and success of proton therapy
became more established, dedicated facilities started to emerge, with the frst
hospital-based facility built in Loma Linda, California (8). Around that time
also commercial companies started to develop accelerators and offered com-
plete treatment facilities, including gantries. Nowadays the cyclotron and the
synchrotron are the two types of accelerators that are offered by companies
and that have proven to be reliable machines in clinical facilities. Many good
textbooks and proceedings of accelerator schools exist on accelerator design
(9, 10), but in this chapter the emphasis will be on relevant issues for proton
therapy to understand the reason for the typical design choices and to become
aware of the important technical and accelerator physics issues that could be
discussed in a selection and acquisition procedure. Also these details will
help to understand striking features one simply encounters when looking at
an accelerator in more detail or that one might read in machine descriptions.
Although proton therapy equipment consists of clearly identifable groups
of components, each having a specifc task, this modularity may mislead-
ingly suggest that these different modules are independent. There is, how-
ever, a very strong interdependence between the design of these components
and the type and quality of the beam delivery system at the patient.
In this chapter the relation between certain accelerator specifcations and
the quality and type of the dose delivery method will be discussed frst, fol-
lowed by a detailed description of the currently used accelerators: the cyclo-
tron and the synchrotron. After a short overview of new developments in
accelerator physics that may be applied in proton therapy in the coming one
or two decades, some words of caution will be given in the conclusions.
3.2 ConsequencesImposedbythe
DoseApplicationTechnique
Several important specifcations of the accelerator and beam delivery system
depend on the chosen technique to apply the proton dose to the tumor. As
these techniques (11) will be described in detail in Chapters 4–6, only aspects
relevant for the accelerator and beam delivery will be discussed here.
63 Proton Accelerators
3.2.1 Dose Spreading in Depth
To distribute the dose in depth, the energy of the protons has to be adjusted
before they enter the patient. In some accelerator types one can accelerate
the protons up to the needed energy and transport these protons to the
patient; examples of such accelerators are synchrotrons, linear accelerators,
and fxed-feld alternating gradient (FFAG) accelerators. It is important that
the change to another beam energy is suffciently fast (to limit the treatment
time and to allow fast switching between treatment rooms) and accurate (to
set the range with suffcient accuracy).
In accelerators such as cyclotrons and synchrocyclotrons this is not pos-
sible, because they work at one specifc proton energy only. To obtain a lower
energy, the protons are slowed down in an adjustable amount of material.
This can be done just after the beam has been extracted from the accelera-
tor, in a degrader, or just before the patient in one of the beam-modifying
devices in the treatment nozzle. In case of the upstream use of a degrader
and in cases where the accelerator can set the energy, all following beam line
magnets must be adjusted according to the chosen energy. This needs some
dedicated requirements for the magnets, the power supplies, and the control
system. If the energy adjustment is performed in the nozzle, a stack with a
variable number of plates (range shifter), a plate with ripples (ridge flter), or
a rotating wheel with an azimuthally changing thickness (range modulation
wheel) is used. Both the upstream location and the nozzle location have their
specifc advantages and disadvantages with respect to transmission, energy
spectrum, and beam emittance (11).
It is important to consider the different uses of an energy varying system.
If it is for adjusting the maximum used range in a certain treatment, or at a
certain gantry angle, it is quite acceptable if the change can be performed
within a few seconds. However, range modulation must be done fast (in the
order of 0.1 s) to limit the treatment time.
Therefore, the following are relevant parameters for the accelerator choice
and the beam transport system design: the needed speed of the energy
change, the accuracy of the obtained energy (range), and the effect on beam
parameters such as intensity, energy spread, and beam broadening.
Currently upstream energy modulation is only performed at PSI (Paul
Scherrer Institut, CH) and at RPTC (Rineker Proton Therapy Center) in
München (D). All other proton therapy facilities use the degrader or accel-
erator energy to set the maximum needed energy in a feld and perform the
modulation in the nozzle.
3.2.2 Lateral Dose Spreading
Beam spreading in the lateral direction is necessary because the typical 1-cm
size of a proton beam is much smaller than typical tumor dimensions. To irra-
diate target volumes of sizes between a few centimeters (e.g., eye treatments)
and up to 30–40 cm (e.g., sarcoma), one needs dedicated beam-spreading
64 Proton Therapy Physics
systems, because spreading the beam by static beam optics alone cannot be
done to this size.
The most commonly used method is passive scattering (Chapter 5), at
which the beam is broadened by multiple scattering of the protons in a (set
of) foil(s) or thin plate(s). Just before the patient the broad beam is collimated
to the shape that matches the tumor shape, as seen from the direction of
the incident beam. Because the beam is going through several millimeters
of material of high atomic number Z, up to 10 MeV will be lost. The larger
the required beam size, the more material will be needed and the more
energy will be lost. When specifying the accelerator energy one should be
aware of this loss. Also one should keep in mind that, if no dedicated beam-
focusing measures are taken, up to 90% of the intensity can be lost at the
collimator(s) in the nozzle, which will generate neutrons (see Chapter 18).
Finally, the beam transport system should provide accurate beam align-
ment with respect to the scattering system. In double-scattering systems a
poor alignment will cause an asymmetry (tilt) in the lateral dose profle at
the tumor. If the necessary beam size is larger than what can reasonably be
accomplished with (double) scattering, beam wobbling can be added to the
system. In a wobbling system, a fast-steering magnet defects the beam and
sweeps it along a certain trajectory, so that an additional area is covered by
the beam. The trajectory can be a circular path, a sawtooth-shaped path, or a
set of parallel lines (raster scanning). This periodic movement of the beam is
repeated many times a second. For the accelerator this implies that an even-
tual periodic time structure in the beam (e.g., beam intensity pulses) should
not interfere with this periodic motion; otherwise severe under- and over-
dosage will occur locally in the dose pattern. In general risks of interference
should be evaluated for any periodic change in the beam characteristics, for
example, due to a range modulator wheel.
The best coverage of the target volume in combination with the lowest
dose in the surrounding normal tissue is obtained with the pencil beam–
scanning technique (see Chapter 6). Here fast-steering magnets (scanning
magnets) are used to aim the beam sequentially at volume elements (voxels)
in the target volume and at each location a specifc dose is deposited. This can
be done on a discrete grid (spot scanning), using a “step-and-shoot” method
(6), or by moving the pencil beam in a continuous way along a certain trajec-
tory within the target volume (raster scanning) (12). For spot scanning the
specifcations on the accelerator are rather relaxed. If the beam is switched
off when one moves to the next spot, the only specifcation of the accelerator
is that the beam intensity should be suffcient. The beam positioning must be
fast and typically must be correct within a millimeter.
Continuous scanning techniques can be grouped into two categories: time
driven and event driven. In the time-driven category, the scanning magnets
have a prescribed speed, and the beam intensity is set as a function of the
position of the pencil beam. In this case the intensity of the beam must be
adjustable within, for example, a fraction of a millisecond (depending on
65 Proton Accelerators
scanning speed) and set to the desired value with an accuracy of a few per-
cent. Unexpected fuctuations or interruptions in the beam intensity or a
pulsed beam are not desired.
In event-driven systems the beam intensity is more or less fxed or just
taken as it comes from the accelerator. The speed of the pencil beam motion
(i.e., the speed by which the scanning magnet changes) is adjusted accord-
ing to the necessary voxel dose and eventually corrected for the actual beam
intensity. With such systems the stability of the beam intensity is less critical,
although too large or too fast fuctuations are diffcult to compensate by the
speed of the scanning magnets. More details of tolerance conditions in scan-
ning systems are discussed in Chapter 6.
An important problem to be dealt with in radiation therapy is the motion of
the tumor and/or critical healthy tissue during the dose administration (see
Chapter 14). This motion can, for example, be caused by breathing. Especially
for time-dependent dose administration techniques, such as pencil beam scan-
ning, this is a problem. Different strategies are being pursued to deal with this
problem. The frst one is beam gating (13–15), at which one suppresses the beam
when the target is not at its correct place. The second one is to perform continu-
ous scanning in a very fast way (16, 17): a target volume of 1 liter is re-scanned
15–20 times during the 2-min dose delivery. One might also apply an on-line
correction of the beam position, the intensity, and the energy to “follow” the
motion (tumor tracking or adaptive scanning) (18). All three methods have
direct implications for accelerator specifcations related to (control of) beam
intensity as a function of time. Typically, pulsed machines are less suitable for
scanning applications, unless the repetition rate is suffciently high (kHz) and
the dose per pulse can be adjusted with suffcient accuracy (a few percent).
3.3 Cyclotrons
Modern isochronous cyclotrons dedicated for proton therapy accelerate pro-
tons to a fxed energy of 230 or 250 MeV (19–22). Compared to the classical
cyclotrons in accelerator laboratories, the new cyclotrons (see Figure 3.1 for
two examples) are rather compact, with a magnet height of approximately
1.5 m and typical diameter between 3.5 m (100 tons) and 5 m (200 tons),
when equipped with superconducting coils or with room temperature coils,
respectively. Usually some extra space is needed above and/or below the
cyclotron for the support devices of the ion source and equipment to open
the machine.
The most important advantages of a cyclotron are the continuous character
of the beam (continuous wave [CW]) and that its intensity can be adjusted
very quickly to virtually any desired value. Although the cyclotron has a
fxed energy, the beam energy at the patient can be adjusted very fast and
66 Proton Therapy Physics
accurately by means of a fast degrader and an appropriate beam line design.
In addition the simplicity of the design concept and the relatively few com-
ponents are often considered as advantages for the reliability and availabil-
ity of the accelerator.
The major components of a typical compact cyclotron are as follows
(Figure 3.2):
• A radio frequency (RF) system, which provides strong electric felds
by which the protons are accelerated
• A strong magnet that confnes the particle trajectories into a spiral-
shaped orbit, so that they can be accelerated repeatedly by the RF voltage
• A proton source in the center of the cyclotron, in which hydrogen
gas is ionized and from which the protons are extracted
• An extraction system that guides the particles that have reached
their maximum energy out of the cyclotron into a beam transport
system
Liquid He
closed circuit
Jacking system
and pumps
Jacking system
pumps
FIGURE 3.1
Top: the 250-MeV superconducting cyclotron of Varian, the frst of which was installed by
ACCEL at the Paul Scherrer Institute, Switzerland. (Adapted from PSI; M. Schillo, M., et al.,
Proc. 16th Int. Conf. Cycl. Appl., 37–39, 2001; Schippers, J.M., et al., Proc. 18th Int. Conf. Cycl.
Appl., 15–17, 2008.) Bottom: the 230-MeV proton cyclotron of IBA (Louvain la Neuve, Belgium),
the frst of which was installed in Boston, MA. (Courtesy of IBA; IBA website: http:// www
.iba-protontherapy.com/.)
67 Proton Accelerators
The RF system consists of usually two or four electrodes (because of their
shape in the frst cyclotrons built, often called “Dee”) that are connected to
a RF generator, driving an oscillating voltage between 30 and 100 kV with a
fxed frequency somewhere in the range of 50–100 MHz. Each Dee consists
of a pair of copper plates on top of each other with a few centimeters in
between. The top and bottom plate are connected to each other near the cen-
ter of the cyclotron and close to the outer radius of the cyclotron. The Dees
are placed between the magnet poles. The magnet iron outside the Dees is
at ground potential. When a proton crosses the gap between the Dee and
the grounded region, it experiences acceleration toward the grounded region
when the Dee voltage is positive. When it approaches the Dee at the negative
voltage phase, the proton is accelerated into the gap between the two plates.
During its trajectory within the electrode or in the ground potential, the pro-
ton is in a region free of electric felds, and at those moments the voltages
on the electrodes change sign. The magnetic feld forces the particle trajec-
tory along a circular orbit, so that it crosses a gap between Dee and ground
several times during one circumference. In the example shown in Figure 3.2
a proton is accelerated eight times during one turn. For example, when the
electrode voltage is 60 kV at the moments of gap crossing, the proton gains
ΔE = 0.48 MeV per turn. Due to the energy gain the radius of the proton orbit
increases, so that it spirals outward. The maximum energy E
max
(typically
230 or 250 MeV) is reached at the outer radius of the cyclotron’s magnetic
feld, after approximately E
max
/ΔE turns (530 in the example).
3.3.1 RF System of a Cyclotron
The RF system is the most challenging subsystem in a cyclotron because
many contradicting requirements need to be dealt with. Important opera-
tional parameters are the RF voltage and the frequency.
Vacuum
chamber Ion source
septum
Area at ground potential
RF “Dee”
Magnet
coil
p
o
l
e
Extractor
-HV
FIGURE 3.2
Schematic view of the major components of a cyclotron: left: the magnet, the RF system (Dees),
and (right) the ion source, and extraction elements. The protons being accelerated are schemati-
cally indicated on their “spikes.”
68 Proton Therapy Physics
A minimum value of the RF voltage is needed to make the frst turn,
which starts at the ion source in the center and must pass apertures and
connections between the top and bottom halves of the Dees; see Figure 3.12
in Section 3.3.6, proton source. A high RF voltage is advantageous because it
yields a large ΔE, which enhances the turn separation. This makes the beam
less sensitive to small local errors in the magnetic feld, and it is a prerequi-
site to obtain high extraction effciency. Further, the period (1/frequency) of
the RF voltage at each Dee must be synchronous to the azimuthal location
of the protons at all radii. The time T, a proton (with electric charge q and
mass m) needs to make one turn with radius r, depends on its velocity v and
the strength of the magnetic feld B. For a circular orbit the Lorentz force Bqv
acts as the centripetal force:

mv
r
Bqv
2
=
.
(3.1)
The proton velocity can be written as v = 2πr/T. With Equation 3.1 this yields
the time required for one turn:

T
m
qB
=
2π
.
(3.2)
Note that this time T does not depend on the radius or the velocity of the
particle. This means that all particles are at the same azimuthal angle in
the cyclotron. As indicated in Figure 3.2, they are all within a cloud resem-
bling a rotating spike of a wheel. Although pulsed at the RF frequency of the
accelerating voltage, the beam intensity extracted from the cyclotron can be
considered a CW for all applications in particle therapy.
The ratio between the RF frequency and the orbit frequency of the protons
must be an integer number, the harmonic number h. In case of one electrode
covering 180° of the pole, one typically uses h = 1, and in case of two or four
electrodes of 45° (as used in Figure 3.2) h = 2 can be used. In Figure 3.3 two
typical RF electrode confgurations are shown.
The magnet pole consists of hills and valleys, and the Dees can be mounted
in the valleys, so that the gap between the upper and lower hill can be mini-
mized. In the IBA and Sumitomo cyclotrons the space in the valley is also
used to mount extraction components. The Dee is mounted on a copper pil-
lar (stem), and the valley wall is covered with a copper sheet (liner). At the
bottom of the valley the stem is connected with the liner. The combination
of Dee, stem, and liner acts as a resonant cavity. This means that a current
can fow back and forth along the stem, with a frequency determined by
the resonance frequency of the cavity. The Dee will get a negative potential
when the electrons fow to the edge of the Dee, and when the electrons fow
to the grounded liner, the Dee will get a positive potential. A quality factor Q
69 Proton Accelerators
of the cavity is defned in terms of the ratio of the energy stored in the cavity
to the energy being dissipated in one RF cycle and can have a value between
3000 and 7000.
The current is driven by a coupler, an antenna that emits the RF power
from the external generator into the cavity. By slightly modifying the volume
of the cavity (e.g., by shifting the connection between stem and liner), the
resonance frequency of the cavity slightly changes. Because the oscillation
frequency is enforced by the RF generator, this detuning of the cavity yields
a change in the power absorbed in the cavity and hence a change in Dee volt-
age. This can be used for fne regulation of the Dee voltages.
The RF currents foat along the inner surface of the cavity and can be of
the order of kiloampere. Also high voltages are obtained across small gaps.
These conditions imply rigorous cooling, good vacuum, and clean surfaces.
A lot of power (60–120 kW) is concentrated in small components, making
the RF system usually one of the most vulnerable subsystems of a cyclotron.
The RF generator operates in the FM frequency range and uses typical
techniques for radio transmitters. Between 100 and 200 kW RF power is
needed in total. The amplifer consists of several stages in series of which the
fnal stage is a high-power vacuum tube (typically a tetrode or triode) (see
Figure 3.4). Recent developments (23) aim for a replacement by many parallel
coupled solid state amplifers. This might potentially offer higher reliability
due to the possibilities of redundant amplifer units.
A cyclotron with a separate amplifer for each Dee can work with smaller
amplifers. In this case the phases of the Dee voltages must be carefully syn-
chronized at the amplifers. It is also possible to connect only one Dee to an
amplifer (which must then provide all power) and to use a coupling to the
other Dees in the central region of the cyclotron. When the Q-value of the
cavities is high enough, it requires only a weak coupling to get all cavities
co-oscillating. In this case the tuning of the cavities must be set such that the
Dees oscillate in the correct phase with respect to each other.
acceleration
gaps
Hill
Dee
R
F

c
u
r
r
e
n
tHill
Magnet
pole
hill
hill
dee
coil
liner
IBA
ACCEL / Varian
liner
liner
Dee
coil
cryosta
t
coupler
Sharp plate
~RF signal
FIGURE 3.3
The IBA/SHI cyclotron (http://www.striba.com) with 2 Dees (left), the Varian cyclotron with 4
Dees (middle), and a sketch of the RF currents in the cavity, creating a voltage across the accel-
eration gap (right). (After Schippers, J.M., Rev. Acc. Sci. Technol. II, 179–200, 2009.)
70 Proton Therapy Physics
3.3.2 Cyclotron Magnet
Specifcations of the magnetic feld are determined by the beam dynamics.
First, the feld must be isochronous: at each radius r it must have the appropri-
ate strength to match the time T a proton needs to make one turn, as given
in Equation 3.2. Second, the shape of the feld lines must provide a focusing
force, to confne the space in which the protons are moving. A small gap
between the upper and lower pole (hills) helps to limit the current in the
main magnet coil but is also advantageous for feld shaping and the reduc-
tion of RF felds outside the Dee.
The real magnetic feld must be correct within a few times 10
−5
. Although
small local deviations can be accepted at some locations, a repetitive encoun-
tering of the beam with such a distortion often leads to systematic trajectory
distortions, yielding instabilities and beam losses. Therefore, careful selec-
tion and shaping of the iron and feld mapping are essential steps in the pro-
duction phase of a cyclotron (24, 25).
Once the cyclotron has been commissioned and the feld optimized, one
usually need not care much anymore about the magnetic feld. Sometimes
small adjustments of the current through the magnet coil are necessary to
compensate for temperature changes of the iron or changes in component
positions after a service. However, when judging cyclotron designs, the
magnet design may have strong implications for the operational quality and
eventual future upgrades of the cyclotron.
3.3.3 Technical Issues
The magnetic feld strength in the commercially available cyclotrons
is between 2 and 3.5 T. Conventional copper magnet coils are used (19,
preamps
&
control
RF power
rectifiers rectifiers transformers
1100A
1 m
C
o
n
t
r
o
l
P
r
e

a
m
p
l
i
f
i
e
r
s
T
r
a
n
s
f
o
r
m
e
r
s
E
n
d

s
t
a
g
e
s
(a) (b)
FIGURE 3.4
(a) Picture of a 150-kW, 72-MHz, RF amplifer. (Adapted from the Paul Scherrer Institute.)
(b) Top view of a design developed by Cryolectra, consisting of six racks flled with 24 solid-
state amplifers of 1.45 kW. (After Getta, M., et al., Proc. PAC09, TU5PFP081, 2009.)
71 Proton Accelerators
20), and for the past few years superconducting coils have been used as
well. Advantages of superconducting coils are the low power consump-
tion (20 kW including cryo-coolers vs. 300–350 kW) and especially the
stronger magnetic feld. This allows the cyclotron to be smaller and less
heavy, but more importantly, because the iron is magnetically saturated,
it makes the magnetic feld much less sensitive to small imperfections in
the iron. Also, when switching on, cycling (a ramping procedure to erase
the “magnetic history,” in which the magnet is frst set at a higher feld
than needed) is not needed. In the superconducting (SC) cyclotron at PSI
(Varian) (21) the coil is cooled by means of liquid helium. As is also visible
in Figure 3.3, the SC coil is suspended in a vacuum cryostat. In addition
to that, the coil is surrounded with a heat shield (at 40 K) and many lay-
ers of super insulation. The outside of the cryostat is at room tempera-
ture. Therefore, opening of the cyclotron does not require warming up
of the coil and temperature effects due to gradual heating of the coil are
not present. Disadvantages of the SC coil are the risk of a quench due to
operational errors (which are normally prevented by the control system)
or when a high-intensity beam is lost or stopped close to the coil and,
although very unlikely, the long downtime in case of a severe technical
problem with the coil or its cryostat.
3.3.4 The Average Field
According to Equation 3.2, the magnetic feld in the cyclotron should be
homogeneous. However, when the energy of the protons becomes larger
than 20–30 MeV, their velocity becomes a considerable fraction of the speed
of light c (v/c = 0.2 at 20 MeV). Because of relativistic effects, this yields an
increase of the proton mass m with respect to its rest mass m
0
:

m r
v r c
m r m ( )
( ) /
( ) =
−
=
1
1
2 2
0 0
γ .
(3.3)
At 20 MeV this is a 2% effect, but at 250 MeV, with v/c = 0.61, this yields
a mass increase of γ = 1.27. In a homogeneous feld this would imply (see
Equation 3.2) that the orbit frequency would drop with energy. With increas-
ing energy (i.e., radius) the protons would lose pace with the acceleration
voltage and would no longer be accelerated.
Until the late 1950s, the method to accelerate protons in a cyclotron to ener-
gies above about 30 MeV was by adapting the RF to the radius of the proton
orbit, a technique that has experienced a revival in recent designs of very
compact high-energy synchrocyclotrons (26). As a consequence of the RF
modulation, the beam intensity extracted from these synchrocyclotrons (the
RF has to modulate its frequency synchronous to the mass increase) is pulsed
at a repetition rate of typically 1 kHz.
72 Proton Therapy Physics
Initially synchrocyclotrons of 160–200 MeV were used for proton therapy
at Harvard, Berkeley, and Uppsala (27). However, the more modern cyclo-
trons use an increase of the magnetic feld with radius to cope with relativis-
tic effects and keep the cyclotron isochronous:

B r r B ( ) ( ) = γ
0
.
(3.4)
Here B
0
is the feld strength that would be needed if relativity were ignored.
As an example, the feld strengths of the 250-MeV cyclotron at PSI (Varian [24])
and the 230-MeV cyclotron of IBA (28) are plotted as a function of radius in
Figure 3.5. With this method, the protons do not loose pace with respect to
the RF signal and the beam remains CW.
Two methods are commonly used to increase the feld with radius. In the
IBA and SHI cyclotrons (11) the gap between the magnet poles is decreas-
ing with radius, as can be seen in Figure 3.3. The method employed in the
SC cyclotron of Varian, takes advantage of the very strong magnetic feld
close to the SC coils. At felds above 2.5 T the iron is saturated and gives
an almost constant (i.e., independent of the current through the coil) contri-
bution of 40-60% to the total magnetic feld. The rest of the feld is coming
directly from the coil (29–31), and this part increases with radius, as shown
in Figure 3.6.
0 10 20 30 40 50 60 70 80
0 20 40 60 80 100 r, cm
90
Radius (cm)
B

(
T
)
Varian
IBA
1.2
1.4
1.6
1.8
2.0
2
2.2
2.4
2.6
2.8
3
3.2
FIGURE 3.5
The average magnetic feld strength as a function of radius. Top: For the IBA cyclotron. (Data
from Karamysheva, G.A., Phys. Part. Nucl. Lett., 6, 84–90, 2009.) Bottom: For the de Varian
SC-cyclotron. (Data from Geisler, A., et al., Proc. 17th Int. Conf. Cyclotr. Appl., 18A3, 2004.)
73 Proton Accelerators
3.3.5 Focusing Properties
A magnetic feld that increases with radius, however, would cause a lack of
vertical beam stability. Contrary to a feld that decreases its strength with
radius, in which particles are pushed back to the median plane by the Lorentz
force after a vertical excursion, particles are pushed toward the poles in a
feld that increases with radius. This is illustrated in Figure 3.7.
The radial variation of a magnetic feld can be expressed by means of a
feld index, n:

n r
r
B r
B r
r
( )
( )
( )
= − ⋅
d
d
.
(3.5)
If B decreases with radius (i.e., dB/dr is negative), n has a positive value, and the
feld has vertically focusing properties. The relativistic correction of Equation
3.4, yields a positive dB/dr, so that the feld index is negative, associated with
defocusing in the vertical plane. In typical proton therapy cyclotrons, the
feld index (Equation 3.5) varies from 0 in the center to approximately −0.5
at extraction. To compensate for this defocusing, additional vertical focusing
40
0
1
2
B

(
T
)
3
50 60
total
coil
iron
Radius (cm)
70 80
FIGURE 3.6
Contributions of the (saturated) iron and the coil to the average magnetic feld.
FIGURE 3.7
Vertically focusing and defocusing in a cyclotron with a magnetic feld that is decreasing with
radius (top) and in a cyclotron with a feld that is increasing with radius (bottom).
74 Proton Therapy Physics
power must be added. This is achieved by a variation of the feld in the azi-
muthal direction, by adding pie-shaped pieces (hills) to the pole, as shown
in Figure 3.8.
Along a turn a proton thus experiences stronger magnetic felds when cross-
ing the pole hills and weaker felds when crossing the valleys (the average
value of the feld along a turn is, of course, equal to the isochronous one). In the
strong feld the orbit is slightly more curved than in the weaker feld. Therefore,
the protons do not cross the boundary between the two regions perpendicu-
larly. When a proton is not traveling in the median plane, it will experience
an azimuthal component of the magnetic feld, which is no longer parallel to
the beam. This component creates a vertical component of the Lorentz force,
proportional to the difference in feld strength, the distance of the proton to
the midplane and tan(φ)/r, with φ being the angle between the trajectory and
the normal to the feld step. Depending on the traveling direction, this force
is directed either toward the median plane or toward the pole. This repetitive
focusing and defocusing always results in a net focusing force. The focusing
strength of these feld steps is often expressed by means of the futter, F(r):

F r
B r B r
B r
( )
( ) ( )
( )
=
−
2
2
2

(3.6)
where the brackets <> denote the average over one turn. Typical values of
futter can be in the order of 0.05. With increasing saturation of the iron, the
0
Hill
Valley
Hill
Pole extension
Magnet
pole
Valley
B(R)
B
z
(

)
2fB
0
π
(radian)

2π
f
f
f
f
d d
d d
r
FIGURE 3.8
Pie-shaped hills and valleys on a pole give an azimuthally (θ) varying magnetic feld strength.
At the hills, the orbit has a smaller radius of curvature due to the stronger feld. Because the
boundary between hill and valley is not crossed perpendicularly, alternating vertical focusing
and defocusing occurs at these boundaries.
75 Proton Accelerators
nominator in Equation 3.6 becomes constant and above a certain radius the
futter decreases with radius. In addition the vertical Lorentz force decreases
with increasing r. Therefore, the focusing effect of the futter must be
enhanced with increasing radius in the cyclotron. This is done by increasing
the angle between the proton trajectory and the feld step with radius; the
hill must be twisted to a spiral with spiral angle ψ(r), as shown in Figure 3.9
and as was also visible in Figure 3.3.
The restoring forces ensure vertical stability. The proton tracks perform a
vertical oscillation around the equilibrium orbit in the median plane with
frequency or tune Q
z
(instead of Q the symbol ν is also frequently used for
these betatron oscillations). The strength of the focusing is given by Q
z
2
: a
strong focusing yields a high betatron frequency. The total focusing power
in the vertical plane can then be written as the sum of the above contribu-
tions. For such an azimuthally varying feld (AVF) cyclotron consisting of N
sectors (hills), one gets the following:

Q r n r
N
N
F r r
z
2
2
2
2
1
1 2 ( ) ( ) ( )( tan ( )) ≈ +
−
+ ψ
. (3.7)
Typical values of Q
z
are about 0.2, which suffces for the (weak) vertical
focusing.
At the extraction of the cyclotron Q
z
can increase to very large values (>1)
due to the grazing crossing of the fringe feld at the outer edge of the cyclotron
pole. Therefore, it is important to guide the protons as fast as possible through
this region to prevent a too dramatic increase of the vertical beam size.
In a cyclotron, focusing in the horizontal plane is rather straightforward and
is automatically achieved because the isochronicity requirement of Equation
3.4 determines a fxed relation between the horizontal (= radial) betatron fre-
quency Q
r
and the relativistic mass increase γ(r) defned in Equation 3.3:

Q r n r r
r
( ) ( ) ( )
2 2
1 ≈ − = γ
.
(3.8)
Valley
Hill
R

FIGURE 3.9
By twisting the hill into a spiral shape, the angle y increases with radius, so that the vertical
focusing is maintained at a large radius.
76 Proton Therapy Physics
In addition there is a contribution of a few percent from the spiral shaped
hills and valleys. The quantity Q
r
is always greater than unity; radial focus-
ing is strong. Note that the second equality in Equation 3.8 is valid until the
feld starts to fatten off just before extraction because there the isochronicity
criterion is not maintained anymore (this depends on the extraction method,
as will be discussed later in this section). The horizontal betatron frequency
plays an important role in the central region and at the extraction. In these
regions dB/dr = 0, so n = 0 and Q
r
≈ 1. As illustrated in Figure 3.10 such an
oscillation yields in fact a radial shift of the orbit. In the central region the
initial centering is quite sensitive to small-feld distortions. These can cause
an accumulation of orbit shifts and lead to large precessions (changes in the
position of the orbit center) of the beam orbits. In a working machine beam-
centering corrections may be necessary after a service involving exchange
of components. Slight shifts of electrode positions or of the ion source may
result in such centering errors. However, corrections can be made easily with
small trim coils attached on the pole or by changing the insertion depth of
iron trim rods in pockets in the central pole region.
Just before the extraction radius, the Q
r
= 1 resonance is crossed again, and
this is used to extract the beam, as will be discussed later.
Although in some designs a betatron resonance is used to advantage, in
general one must be very careful. Excitation of a resonance will cause an
increase of the oscillation amplitude and may have beam loss as a conse-
quence. Also coupling resonances, in which there is an exchange of amplitude
between radial and vertical oscillations, are possible. In general resonances
occur at radii in the cyclotron, where
mQ
r
(r) + nQ
z
(r) = p, in which m, n, and p are integer numbers. (3.9)
+
–
S
h
i
f
t

o
f

o
r
b
i
t

c
e
n
t
e
r
FIGURE 3.10
At the Q
r
= 1 betatron resonance the center of the orbit is shifted by a small magnetic bump.
77 Proton Accelerators
In the design phase of the machine one tries to adjust the spiral and fut-
ter to avoid such resonances. If a resonance cannot be avoided, one tries to
tune the feld (and RF voltage) such that it is crossed in a minimum number
of turns, so that small errors in the magnetic feld do not have the chance to
excite such resonances.
After commissioning of the cyclotron, the tunes are fxed and one only
needs to be aware of resonances in case of small changes in orbit positions
due to machine changes, or upgrades.
3.3.6 Proton Source
Currently all commercially available cyclotrons are equipped with a proton
source in the center of the cyclotron. External sources are only of interest if
other particles also need to be accelerated. The internal sources operate by
exploiting the Penning effect (32, 33): the ionization of gas by energetic elec-
trons in an electrical discharge.
The ion source consists of two cathodes at a negative voltage of a few
kilovolts located at each end of a vertical hollow cylinder at ground poten-
tial (chimney), into which also the H
2
gas is fushed (about 1 cm
3
/min) (see
Figure 3.11). Free electrons are created by heating a flament or, in the case
of a “cold-cathode source,” by spontaneous emission from the cathode in the
strong electric feld between cathode and ground. In this feld the electrons
Internal “cold cathode” proton source
Chimney filled with plasma
pole
pole
-80 KV
Dee 1
Dee 3
arc
cathode, -HV
Vertical
deflection plates
Cathode, -HV
Cooling water
FIGURE 3.11
Schematic view of the ion source of the “cold-cathode” type (= no flament used) and the frst
few turns.
78 Proton Therapy Physics
are accelerated, and they will ionize the gas. They are confned along the
magnetic feld lines and bounce up and down between the cathodes, thus
increasing the ionization of the gas.
The ions (H
+
, H
2
+
, H
–
, etc.) and electrons form a plasma that flls the chim-
ney volume. Because a plasma is an electric conductor, external electric felds
hardly penetrate the plasma. However, protons and other ions that diffuse
to a little hole in the chimney wall will experience the electric feld from the
nearest Dee (the puller). When the Dee is at negative potential, protons that
escape from the plasma will accelerate toward the Dee. If they arrive at the
right phase, they will cross the gap to the puller and will be further acceler-
ated, as shown in Figure 3.12. Because of the narrow acceptance windows in
time and in the further acceleration path, only a fraction of the protons leav-
ing the source is actually being accelerated.
3.3.7 Practical Issues
Important specifcations of the ion source are: the total proton current
extracted from the source within a not too large emittance, the stability of
the intensity, and the time between services (goes on cost of operational
Dee 4
Dee 3
slit
Dee 2
H
2+
H
-
P
r
o
t
o
n
s

t
h
a
t
s
t
a
r
t
e
d
t
o
o

l
a
t
e
chimney
Dee 1
p
u
l
l
e
r
P
r
o
t
o
n
s
I
n
f
i
r
s
t

t
u
r
n
FIGURE 3.12
Orbits in the central region of different ion species coming out of the source. To prevent accel-
eration of unwanted particles, a slit is selecting the protons that travel at the correct RF phase.
The radii of the orbits are determined by the amplitude of the RF voltage, which should be high
enough to get around the obstacles in the central region.
79 Proton Accelerators
time of the cyclotron). At an ion source service, one typically exchanges
flaments (if used), cathodes (worn out by sputtering), and the chimney
(extraction hole increases by sputtering). Modest operational conditions
and a careful material choice (heat properties, electron emission, sputter-
ing resistance) are of importance to obtain a source lifetime of 1–2 weeks or
even up to a month.
3.3.8 Beam Intensity Control
The beam intensity is regulated by adjusting the arc current between the
cathodes and ground, the gas fow and the current through the flament (if
present). Usually the proton current reacts rather slowly (milliseconds to sec-
onds) to changes in these parameters. In these kinds of sources it has been
observed that an intensity increase also leads to an increase of the emittance
(beam divergence) of the beam coming out of the source (34). By selecting
the fraction of the beam around the maximum of the emittance, a very stable
beam intensity (a few percent at kilohertz band width) can be obtained rou-
tinely (35). This is essential for fast line scanning.
In the IBA cyclotron the beam intensity is regulated at the source by a
feedback loop from the measured beam intensity. At PSI the ion source is
operated at a fxed setting. A pair of adjustable radial apertures (phase slits)
close to the cyclotron’s center sets the maximum intensity. Between 0 and
this maximum, the intensity is regulated with an accuracy of 5% within
50 μs by a vertically defecting electric feld and a vertical collimator, cutting
the beam in the frst few turns, as shown in Figure 3.13. This fast intensity
regulation at the vertical collimator by the vertical defector (see Figure 3.14)
is used for intensity control during line scanning.
3.3.9 Beam Extraction
The extraction effciency is an important specifcation of a cyclotron. A low
effciency means severe beam losses, which will cause radioactive compo-
nents in the cyclotron (36) and enhanced wear and dirt deposition on insula-
tors. This reduces the availability of the cyclotron and increases the radiation
dose to the maintenance staff. Considering that an extraction effciency of
25% implies nine times (!) more lost protons per extracted proton, compared
with a cyclotron with 75% extraction effciency, one should strive for extrac-
tion effciencies of at least 60–70%.
The major problems to overcome with the extraction of the beam from
a compact cyclotron are to separate the protons to be extracted from those
that still have to make one or more turns and to prevent destruction of the
extracted beam in the grazing passage of the rapidly decreasing fringe feld.
The design of the extraction is therefore aimed at an increase of the orbit
separation at the appropriate location and to cross the fringe feld as quickly
as possible, followed by a reduction of the vertical focusing to compensate
80 Proton Therapy Physics
for a vertical over-focusing and by a horizontal focusing to keep a moderate
beam width.
The extraction is performed by several extraction elements, of which the
frst one is a septum (see Figure 3.2). This thin vertical blade is aligned par-
allel to the beam and separates the extracted beam from the ones that still
have to make one or more turns. The septum should be able to withstand
power dissipation due to beam particles that hit the septum. A bar-shaped
cathode is positioned parallel to the septum at a larger radial position. The
electric feld between this cathode (at several tens of kilovolts) and the sep-
tum defects the beam more outward into a channel between the coils and
through the yoke. In this extraction channel additional steering and the (de)
focusing is performed by permanent magnets and/or feld-shaping iron
blocks.
Close to extraction radius the orbit separation is decreasing because of
two effects. First, the radius of each orbit increases linearly with the momen-
tum p and thus approximately with √E. A constant ΔE thus leads to smaller
Beam passes at
vertical collimator
(Defl. = 1 kV)
Foil burns on the
lower collimator jaw
Radius in cyclotron (a.u.)
4
effects of
vertical
deflector
2
0
0 1000
puller
Defl. = 1 kV
Apertures of vertical collimator
Azimuthal angle in cyclotron (degr)
2000
V
e
r
t
i
c
a
l

p
o
s
i
t
i
o
n

(
m
m
)
–2
–4
100 120 140
FIGURE 3.13
In the PSI cyclotron a fast regulation of the beam current is performed by means of vertical
defection of the beam (top). The aperture (middle) is crossed six times. Bottom: Beam passages
at the lower aperture limiter by means of foil burns. Due to the vertical betatron oscillations,
the beam is mostly cut at the frst three crossings.
81 Proton Accelerators
distances between sequential orbits. In addition ΔE decreases because of loss
of isochronism in the decreasing magnetic feld (see Figure 3.5 and the inset
in Figure 3.15).
The orbit separation can be increased by exciting the Q
r
= 1 resonance
to shift the center of the orbits. This already creates a larger separation
between two turns, as shown in Figure 3.10. However, a stronger effect can
E
x
t
r
a
c
t
e
d

b
e
a
m

i
n
t
e
n
s
i
t
y
Voltage on vert.defl. (kV)
0 1 2
FIGURE 3.14
The extracted beam intensity as a function of the voltage on the vertically defecting plates,
mounted in Dee 3 of the PSI cyclotron.
255
252.5
250
247.5
245
242.5
240
79.5
extracted
beam
ese orbits do
not exist (extracted)
3.0
2.0
1.0
0
0.7
kick at Q
r
=1
septum location
Radius
0.75 0.8 0.85
Radius (m)
B (T)
Q
r
γ
0

=

u
80 80.5 81 81.5 82 82.5
Radius (cm)
Septum
Consecutive turns
E
n
e
r
g
y

(
M
e
V
)
W
i
t
h

fi
e
l
d

b
u
m
p
N
o

fi
e
l
d

b
u
m
p
FIGURE 3.15
To obtain a large-turn separation, one uses the precession of the orbits, after exciting the
Q
r
 = 1 resonance at the radius where the feld index n = 0. The precession is caused by a phase
advance of the betatron oscillation due to Q
r
< 1 beyond the resonance. To illustrate the preces-
sion, orbits also are drawn, which do not exist when the beam is extracted. Along the radial
direction the precession shifts consecutive turns to smaller radii, followed by a jump to a large
radius. This is the optimal location for a septum to split off the extracted beam.
82 Proton Therapy Physics
be achieved when a precession of the orbits is used, which becomes effective
a few turns later. Because of the decreasing magnetic feld beyond the maxi-
mum, Q
r
starts to decrease. For Q
r
< 1 the phase of the betatron resonance
starts to shift to a larger azimuth, and an orbit precession is starting, as illus-
trated in Figure 3.15. When looking along one radial line, one then observes
that the orbit with next higher energy is at smaller radius than the previous
one. However, when continuing the precession with a few turns, this will be
followed by a sudden increase of the distance between two sequential orbits,
as demonstrated in Figure 3.15. This is an optimal location for a septum that
splits the extracted beam off.
The resonance is excited by kicking the beam with a magnetic bump, cre-
ated with little coils or with iron trim rods. The orbit separation is further
increased by a high-energy gain per turn and by a using a small horizontal
beam emittance already at the beginning of the acceleration. A high-energy
gain per turn is accomplished by high Dee voltages and many Dees and by
limiting the phase slip due to loss of isochronicity after crossing the feld
maximum. A small horizontal emittance can be achieved by cutting the
beam suffciently with slits and collimators in the central region (low energy:
low power loss and low or no activation). Application of this resonant extrac-
tion method in the PSI cyclotron (Varian) has resulted in a routinely obtained
extraction effciency of 80%.
In the IBA and SHI cyclotrons another approach, self-extraction, is pur-
sued (10). In these cyclotrons the acceleration continues to a maximum pos-
sible radius, and the feld is kept isochronous by using a elliptical pole gap
(visible in Figure 3.3). This gap is very narrow at the pole edge, so that the
feld drops to zero in a very short radial distance (see Figure 3.5). With this
technique one strives to guide the beam out of the main feld and through
the fringe feld very quickly. A groove in one hill is made near the extraction
radius, to get the extraction at a well-specifed azimuthal angle. The beam is
defected further by means of a septum and extraction cathode. To limit the
beam size, also in these cyclotrons several (de)focusing elements are follow-
ing a septum.
3.4 Synchrotrons
The first hospital-based proton therapy facility at Loma Linda Medical
Center (California) was equipped with a synchrotron built by Fermilab
(37) (Figure 3.16) and started operation in 1992 (8). Equipment based
on the design used at Loma Linda has become commercially available
from Optivus Proton Therapy (San Bernadino, CA) (38). The proton syn-
chrotron designed by Hitachi (13) (see Figure 3.16) is in use at centers in
Tsukuba and Fukui in Japan and also at MD-Anderson Cancer Center
83 Proton Accelerators
in Houston, Texas, and one by Mitsubishi in Shizuoka, Fukushima, and
Kagoshima, Japan (39). All machines provide protons between 70 and
250 MeV.
For proton therapy synchrotrons and cyclotrons are quite competitive,
but for heavy-ion therapy synchrotrons are currently the only machines in
operation. Recognized advantages of a synchrotron are that the protons are
accelerated until the desired energy, that almost no radioactivity is created
due to beam losses (40), and that low-energy protons have the same intensity
as high-energy protons (no transmission loss in a degrader [41]).
The space required for a proton synchrotron is larger than for a cyclotron:
the synchrotron itself has a diameter of 6–8 m, and the injection system con-
sisting of an ion source, one or two linear accelerators in series (radio fre-
quency quadrupole [RFQ] and drift tube linac [DTL]), and a beam transport
system has a length of 6–10 m. At the Loma Linda facility, a relatively small
footprint has been achieved by mounting the injector on top of the synchro-
tron. A synchrotron (+ injection) consists of many small components that can
be built in series and that gives relatively easy access to the machine parts.
3.4.1 Operation
The acceleration process in a synchrotron is in cycles (spills), each consisting
of the following:
• Filling of the ring with a bunch of 2 × 10
10
protons of 2 MeV (Loma
Linda) or 10
11
protons of 7 MeV (Hitachi, Mitsubishi)
• Acceleration until the desired energy between 70 and 250 MeV
QD
BM
BM
SX
QF
ST
R1.4 m QD
Septum Magnet
for extraction
BM
BM
SM
ST
SX
BM1
BMPi
BMPi
BM
ST
QF
QF
RF
acceleration
stage
7m
QD
QD
ST
Deflector for
extraction
Beam from
injector
QF
RFC
QD
Extraction
RF Kicker
E
x
t
r
a
c
t
e
d

b
e
a
m
i
n
j
e
c
t
i
o
n
RF cavity
FIGURE 3.16
Left: the synchrotron used at Loma Linda with the 2-MeV injector mounted on top of the syn-
chrotron ring. (Adapted from Coutrakon, G., PTCOG 47, 2008, and PTCOG 49, 2010.) Right: The
synchrotron of Hitachi (injector not shown). (Adapted from Hiramoto, K., et al., Nucl. Instr.
Methods B, 261, 786–790, 2007, and http://www.tassauusa.org.)
84 Proton Therapy Physics
• Slow extraction of the protons into the beam line
• Ramping down to the initial situation, eventually with deceleration
and dumping unused protons at low energy
This sequence (shown in Figure 3.17) takes too long to be useful for energy
modulation. The energy selected to be extracted is chosen for each gantry
angle used in a treatment and is equal to the maximum energy used at that
angle. Modulation is then done in the nozzle by means of a modulator wheel
or ridge flters.
A synchrotron itself consists mainly of a lattice with bending mag-
nets and focusing elements. Quadrupole magnets are used to focus the
beam, and sextupole magnets are used to increase the acceptance of beam
energy spread. In some synchrotrons, the bending magnets are shaped
such that the focusing properties are added to the bending feld. By apply-
ing strong focusing schemes (feld index n >> 1) small beam diameters
can be achieved. The periodicity of the lattice imposes also a periodic
shape of the beam envelope. However, in the design care must be taken
that the period of the betatron oscillation of individual protons does not
coincide with a characteristic dimension of the machine, such as the cir-
cumference. The huge number (~10
9
) of revolutions a proton makes in the
ring yields an extreme sensitivity to small errors in magnet alignment,
magnetic felds, or power supply ripples, which easily induces a periodic
distortion. In the design phase the focusing lattice (quadrupole strengths)
is designed such that the working points (the tunes) are far away from a
betatron resonance condition (Equation 3.9); otherwise this will unavoid-
ably lead to beam loss.
3.4.2 Ion Source and Injector
For the proton ion sources there is a wide choice of commercially avail-
able types, typically based on ionization by microwaves and a special
confguration of coils or a permanent magnet to confne the electrons
Time
B
e
a
m

e
n
e
r
g
y
Injection
Acceleration
Deceleration
Slow extraction
< 0.5 sec 0.5 – 5 sec.
FIGURE 3.17
A typical spill from a synchrotron. The machine is flled with protons of 2 or 7 MeV; the pro-
tons are accelerated to the desired energy and slowly extracted. The unused remaining protons
are decelerated and dumped.
85 Proton Accelerators
(33, 42). The source is usually set at a positive potential, to preaccelerate
the protons toward an RFQ, acting as frst linear accelerator. An RFQ
consists of four rods, parallel to the beam direction. Each rod is shaped
with a wave-like structure along its length, as shown in Figure 3.18. The
rods are mounted in a resonant cavity such that the pairs of opposing
rods have a 180° phase shift of the RF voltage with respect to the orthogo-
nal pair. The component of the electric feld along the beam direction
provides the acceleration, and the radial components provide focusing.
Acceleration up to 2–3 MeV is achieved, and subsequently the protons can
be accelerated to 7 MeV in a DTL (see Figure 3.18). Also the operation of
a DTL is based on electromagnetic oscillations in tuned structures. The
structures support a traveling wave of alternating voltages on cylindri-
cal electrodes between which the protons are accelerated. The electrode
lengths increase along the tube, in accordance with the velocity of the
accelerated particles.
Injection in the ring must be done at the correct phase with respect to
the RF of the ring. One can inject all particles at once (single turn injection)
or gradually add particles to the circulating beam. Because the injection
system should not touch the already circulating beam, the new protons are
added next to the protons that are already in the ring. The emittance of
the circulating beam therefore increases, until the acceptance of the ring is
flled.
To reduce treatment time it is important to fll the ring with as many pro-
tons as possible. This gives possibilities to lengthen the extraction phase
and to reduce dead time between spills (43). The maximum intensity in
the machine is limited by space charge or coulomb repulsion forces. The
higher the injection energy, the lower these defocusing space charge forces
and thus the higher the amount of protons that can be stored in the ring.
For single-turn injection, intensity may also be limited by the maximum
beam current from the injector to fll the ring in one turn. The maximum
intensity can be increased by allowing more circulating bunches at the
same moment in the ring and by modifying the time structure of the RF
Electrodes
Acceleration gaps
~V
RF
FIGURE 3.18
Typical RFQ and DTL linac confgurations, for a preaccelerator to inject the beam into the
synchrotron.
86 Proton Therapy Physics
voltage across the acceleration gap, to spread the bunch in the longitudinal
direction (12).
3.4.3 Acceleration and RF
The acceleration phase usually lasts approximately 0.5 s and thus takes
place over many turns (~10
6
). The energy of the circulating particle bunch is
increased in an RF cavity located in the ring. The increasing proton momen-
tum p needs a synchronous increase of the magnet strengths in the ring,
because the protons must remain in an orbit with a constant average radius.
Following Equation 3.1 this yields

p
Bq
r const = = .
(3.10)
The increase of the magnetic feld drives the frequency of the RF voltage: the
frequency must remain synchronous to the increasing revolution frequency
(~1–8 MHz) and increases (nonlinearly) in time:

f p
r
p
m p
( )
( )
=
1
2
0
π γ
.
(3.11)
Therefore the RF cavities are nonresonant (quality factor Q < 1) wide-band
structures and of moderate power (12). A widely used type of cavity is
the induction cell, such as the one developed by Hitachi (44), as shown in
Figure 3.19.
An induction cavity consists of ferrite rings (magnetic cores) that sur-
round the beam pipe. Around each core a coil has been wound, to induce a
accelerating gap magnetic core
RF current (FINEMET)
inner
conductor
outer
conductor
multifeed
coupling
RF power source
( solid-state amp.)
FIGURE 3.19
The RF acceleration device used in a synchrotron consists of an induction cavity, flled with
magnetic cores. The cores drive an RF current (dashed line) which causes an RF voltage across
the acceleration gap in the center of the cavity. (Adapted from Saito, K., et al., Nucl. Instr.
Methods A., 402, 1–13, 1998.)
87 Proton Accelerators
magnetic feld in the ring. The electric current through the coil is driven with
the RF frequency and induces an RF magnetic feld in the ferrite ring. On its
turn, this varying feld induces an electric current in the beam pipe, which
acts as the inner conductor. An outer conductor surrounding the cores is
closing the loop for this driven current. However, in the center of the device
the inner conductor is interrupted. Across the gap an RF voltage of a few
hundred volts is built up by the RF current, so that protons that cross the gap
at the correct RF phase will be accelerated. This moderate RF voltage is suf-
fcient, because the protons pass the gap many times during the acceleration
phase. The applied frequency and voltage need to be controlled as a func-
tion of the magnetic feld in the ring magnets, as given in Equation 3.11. The
system is much simpler than the high-power, narrow bandwidth systems
used for cyclotrons. The RF power can be generated with reliable solid-state
amplifers.
3.4.4 Extraction
Instead of fast extraction in a single turn, a slow extraction scheme is nec-
essary for accurate dose application at which the beam is spread over the
tumor with scanning techniques or with additional range modulation. The
time during which protons are extracted varies between 0.5 and 5 s, depend-
ing on the amount needed at the extracted energy. The extracted beam inten-
sity can be regulated and is constant on average, but at several kilohertz, a
ripple or noise of up to 50% is present. This ripple depends on the extraction
method and is caused by the extreme sensitivity of the beam orbit to small
misalignments and to ripples in power supplies.
Several methods to extract the beam are currently applied (see Figure 3.20).
Resonant extraction–based schemes, in which the machine tune is slowly
shifted toward a resonance (e.g., Q
r
= 1/2 or 1/3), in effect narrow the stable
phase space of the beam, because resonance bands are approached by the
set tune. Particles with a large oscillation amplitude will then slide into the
unstable region of the phase space, so that their oscillation amplitude will
grow until they pass the extraction septum at the external side. The shift of
the beam tune is performed by changing the felds of specifc quadrupoles
and/or sextupoles in the ring (37). However, while getting the phase space of
the circulating beam more and more empty, the quadrupoles need to shift the
tune closer and closer to the resonance to catch the protons with the smallest
amplitudes as well. A disadvantageous consequence of this method is that
the position and/or size and/or energy of the extracted beam are varying at
the entrance of the beam line during the extraction period.
Alternatively one can give quasi-random sideward kicks to the beam with
a dedicated RF kicker. The RF knock-out method increases the circulating
beam emittance, and particles that are kicked out of the stability region are
guided to the extraction septum. With this method the extracted beam posi-
tion, size, and momentum remain constant during the spill (12). This method
88 Proton Therapy Physics
also easily allows a fast on-off switching of the extracted beam intensity,
which is conveniently used for gating on the respiration motion of the patient
(45, 46).
In both methods the extracted intensity is controlled by a feedback of a
beam intensity monitor on the acting extraction elements.
The horizontal emittance and momentum spread of a beam from a syn-
chrotron is typically up to a factor 10 smaller than the emittance of a cyclo-
tron beam. However, the emittance shows large asymmetries, which must
be taken into account for preserving an angular independence of the beam
characteristics when using rotating gantry systems.
3.4.5 Recent Developments in Therapy Synchrotrons
Scale reduction is of interest for synchrotron systems. Balakin et al. (47) are
building a small ring of 5 m in diameter for proton acceleration up to 330 MeV.
The protons are injected by a 1-MeV linear accelerator. Similar studies of a
Beam pipe Stability limit
Near resonance:
decreased stability region
Unstable orbits
extracted
Unstable orbits
extracted
RF kicker increases
emittance
Resonant extraction
RF Knock-out
Normal tune; no extraction
beam
FIGURE 3.20
The betatron oscillation amplitude of the unperturbed beam tune (top) remains below the sta-
bility limit. In a resonant extraction method (middle) the tune is continuously shifted toward
a resonance, which brings the stability limits tighter. The particles exceeding their amplitude
outside the stability region will be extracted. In the resonant extraction scheme (bottom) the
beam is kicked randomly, and the amplitude is increasing. Particles leaving the original stabil-
ity region will be extracted.
89 Proton Accelerators
“table top” proton/carbon ion synchrotron are reported by Endo et al. (KEK,
Tsukuba, Japan) (48). The relatively low cost of such accelerators is expected
to be the major advantage of these small machines.
Efforts toward a more rapid cycle of the synchrotron have been reported
in the last few years. In a proposal for a rapid-cycling synchrotron (49), the
beam is kicked out in a single turn extraction after single-turn beam injection
and acceleration to the desired energy. This sequence is repeated at ~30 Hz.
Single-turn extraction implies, however, that the amount of protons per
pulse can be adjusted very accurately. A slow extraction combined with
fast cycling has been demonstrated in the Hitachi synchrotron (43); see
Figure 3.21a.
A considerable decrease in the unused time between the spills can also be
obtained when the ring is not completely ramped down, flled, and ramped
up to the next energy. When there are suffcient protons in the ring, one
could ramp down to the next energy, extract the necessary amount of pro-
tons, and repeat this until all protons have been used (50). First attempts
(Figure 3.21b) to explore this method at the HIMAC synchrotron have been
reported recently (50). Of course, use of this method implies suffciently
high initial beam intensities in the ring as well as very good control of the
extracted beam intensity.
Extraction
beam
energy
B
e
a
m

e
n
e
r
g
y
Time
a)
b)
Energy changes of
extracted beam
during a spill
Time[sec]
0 4 8 12 16 20
beam
intensity
Injection
FIGURE 3.21
(a) Spill structure of a rapid cycling synchrotron. (Adapted from K. Hiramoto, Synchrotrons,
educational session PTCOG 49, 2010.) After single turn beam injection and acceleration to the
desired energy, the beam is used after a slow extraction; (b) energy variation during a spill.
The  beam energy is decreased in small steps during the slow extraction process. (Adapted
from Iwata, Y., et al., Proc. IPAC10, MOPEA008, 79–81, 2010.)
90 Proton Therapy Physics
3.5 NovelAcceleratorTechnologies
All other acceleration principles that are being investigated by differ-
ent groups are aiming at scale reduction, with an affordable single treat-
ment room facility as goal. This would decrease the fnancial gap due to
the scale difference between current photon therapy and the typical state of
the art multiroom proton therapy centers. Although the costs per treatment
room are not expected to be lower than for a facility with multiple rooms,
the initial investment costs will of course be lower. Such facilities may be
of advantage for certain regions, for example, a city with a population of a
few million people, located relatively far away from other population cen-
ters. For extended regions with more homogeneously spread populations as
in Europe, the large centers with multiple treatment rooms are expected to
operate more economically.
3.5.1 FFAG Accelerators
For several years, it has been investigated whether a fxed-feld alternating
gradient (FFAG) accelerator would be a suitable accelerator for proton ther-
apy (51–57). In this concept, the AVF cyclotron described above is split up
in separate sector magnets, with alternating signs of the magnetic felds, as
schematically shown in Figure 3.22. The RF frequency is varying, similar to
that in a synchrocyclotron. The beam optics in scaling FFAGs is designed
such that the betatron frequencies of the orbits at all energies are equal, so
that all orbits are scaled replicas of each other.
In nonscaling FFAGs the tunes are allowed to vary, and even the peri-
odicity of the magnet structure is decoupled from the beam motion. In
fact this scheme resembles a (curved) linear accelerator with very strong
alternating focusing and defocusing elements. Because of the very strong
focusing properties, the nonscaling FFAGs are smaller than the scaling
FFAGs. However, the magnet design and large gradients of opposing signs
make the design process very complicated. Also, the cavity and RF gen-
erator are complicated: high electric felds are needed, but also a varying
frequency.
a) b)
focusing defocusing
h
i
g
h

e
n
e
r
g
y
l
o
w

e
n
e
r
g
y
h
i
g
h

e
n
e
r
g
y
l
o
w

e
n
e
r
g
y
defoc defoc foc foc
FIGURE 3.22
Schematic confguration and orbit structure of (a) a scaling FFAG and (b) a nonscaling FFAG.
91 Proton Accelerators
The major advantage of FFAGs is the very large acceptance in beam energy
and emittance, which is useful in particle physics applications that need
reacceleration of reaction products.
A possible advantage of an FFAG in proton therapy may be its capacity
to have much faster repetition rates than synchrotrons and synchrocyclo-
trons and thus achieve high-beam intensities. Also the optics and magnetic
feld setting may change from pulse to pulse, allowing fast energy changes
between each pulse (53). On the other hand the scaling FFAGs are not small
(radius 7–8 m) or light (150–200 tons). The nonscaling FFAGs are very com-
plex to design, to build, and to operate and need very complex RF amplifers.
Both types of FFAGs need a ~10-MeV injection system, which can be a cyclo-
tron or another FFAG (52).
For proton therapy the most promising spin-off from FFAG technology
is the use of the very strong gradients, alternating along a beam line. This
FFAG-type of beam optics is proposed for a new type of gantry design (58).
The large-momentum acceptance may prevent the need of changing mag-
netic feld when changing beam energy. This could speed up the energy
modulation considerably.
3.5.2 Linear Accelerators
Linear accelerators are the most widely used accelerators in radiation therapy.
Electrons are accelerated to typically 6-25 MeV and create Bremsstrahlung
photons in a target or are used directly. However, compared to electrons, it
is much more diffcult to accelerate protons or heavy ions with linear accel-
erators. This is because electrons quickly reach relativistic velocities and can
be assumed to have a constant speed, close to the speed of light. This allows
long repetitive structures of equal dimensions, all working at the same phase
shift with respect to each other. Protons of 250 MeV have only reached 61%
of the speed of light, so here one must take the increase of speed into account
within the whole accelerator structure. For this reason the low-energy part
of a linear accelerator consists of stages with different types of accelerators,
for example, such as those used in a synchrotron injector described above.
For proton therapy an important issue of linear accelerators is the time
structure of the beam. Many developments have occured to improve the
time structure toward high frequency (3 GHz) and a repetition rate as high
as possible (100–200 Hz) to allow for spot scanning. The RF power is gener-
ated by a series of klystrons, each driving a section of the linac.
A linear accelerator made of sequentially operating acceleration stages
offers the natural advantage to allow rapid (determined by repetition rate)
and continuous energy variation of the accelerated beam. This can be accom-
plished by switching off the output RF power of a number of klystrons and
by adjusting the power of the last active klystron. If a high enough repetition
rate and suffcient accuracy of the dose per pulse can be achieved, a linac
may then be suitable for rapid spot scanning.
92 Proton Therapy Physics
3.5.3 Linac-Based Systems for Proton Therapy
To overcome the problems at low energies, the cyclinac concept has been
developed (59). Here a cyclotron of 60 MeV (more recently 30 MeV) is used
as an injector for a linear accelerator with side-coupled cavities (SCLs). The
small 3-GHz structures allow the use of very strong electric felds. This
reduces the number of acceleration cavities and thus the length of the accel-
erator. A prototype of the linac LIBO (Linac Booster) with a design value of
the accelerating feld of 15.7 MV/m has been made and tested successfully
(60): a gradient of up to 27 MV/m was reached. In the fnal design this linac
will consist of several tanks, each with a number of copper cavities made
of basic units. These “half-cell plates” are built with very-high-accuracy
machining. The RF in each tank is driven by a klystron. A possible layout
of a clinical facility is shown in Figure 3.23. Recently a new cavity design
to cover the energy range 15-66 MeV has been presented (61), which would
allow a relatively cheap commercial cyclotron as injector.
Higher gradients of the accelerating electric feld and thus shorter struc-
tures are a natural line of development; however, there are limits to what
can be achieved. The frst limitation is given by the peak power that can be
injected into a linac tank, and the second limitation is the maximum electric
feld on the surface of the cavity wall. In case of low velocities CCLs, this is
four to fve times larger than the average accelerating feld. From many data
on breakdown phenomena collected during the last 20 years, the limit of
the acceleration feld in 3-GHz CCLs seems to be just above 30 MV/m (62).
Higher frequencies (e.g., 5.7 GHz) will also allow stronger acceleration felds,
but at the cost of a reduced transversal acceptance.
3.5.4 Dielectric Wall Accelerator
In induction cavities the achievable electric RF feld across a vacuum gap
seems to be limited to 10-20 MV/m. However, the longitudinal space taken
Isotope production
targets
Cyclotron (30 MeV)
L
in
e
a
r
a
c
c
e
le
r
a
t
o
r
T
r
e
a
t
m
e
n
t

r
o
o
m
s
FIGURE 3.23
Layout of the cyclotron driven linac concept. A 30-MeV cyclotron is used for isotope produc-
tion or injects protons into a linear accelerator of the LIBO type. (Adapted from Amaldi, U.,
et al., Nucl. Instr. Methods Phys. Res. A, 579, 924–936, 2007.)
93 Proton Accelerators
by the ferrite cores adds to the length of the accelerator and reduces the
effectively obtainable average acceleration feld to only a few megavolts
per meter. In systems that have been developed to replace the ferrite core,
an insulating ring is mounted around an acceleration gap. The ring is sur-
rounded by a dielectric, which is sandwiched between two conducting
sheets. One sheet has been put on a high voltage, and the other sheet is
grounded. A sudden shorting of the high voltage to ground creates a trav-
eling voltage wave in the dielectric, which leads to a strong longitudinal
electric feld at the inside of the insulating ring (63). This coreless induction
accelerator is limited by the breakdown feld strengths in the dielectric and
along the insulator surface.
Along the surface of the insulator a spark typically develops by electrons
that repeatedly bombard the surface, thus creating an electron avalanche. To
obtain a very strong accelerating feld, one can prevent the development of a
spark by shortening the time that the feld is present. For conventional insula-
tors shortening the high-voltage pulse from 1000 to 1 ns yields an increase of
the surface breakdown feld from 5 to 20 MV/m. During the last decade new
castable dielectrics have been developed as well as a new insulator confgu-
ration. This is made of a stack of foating conductors sandwiched between
sheets of insulators. With this high-gradient insulator (HGI) an increase of a
factor 5 in the surface breakdown feld strength has been demonstrated (64).
A dielectric wall accelerator (DWA) can be constructed by stacking rings of
HGI material, and at frequent intervals along the stack a conducting sheet
is inserted and connected to a high-voltage switching circuit (Blumleins).
These switches are normally open. When these laser-driven switches are
closed, an electric feld is produced at the inside of the HGI ring. By succes-
sive closing of the switches along the stack, the region of strong electric feld
is shifted along the stack, and protons traveling in phase with this wave will
be accelerated.
An average accelerating feld of more than 100 MV/m can be possible
for 3-ns pulses, as has been demonstrated on small HGI samples (65). This
would allow an accelerator design of about 2-m length for 200-MeV pro-
tons, as shown in Figure 3.24. This concept has been further developed
in the design of a single-room treatment facility, to be put on the market
scanning
system
HGI rings
~5000 electrodes, each with 2 HV switches (25 kV)
2 ns pulses
at 10 Hz
with 100 mA protons
FIGURE 3.24
The DWA consists of a stack of special insulators, between which a traveling electric feld of 100
MV/m is traveling. Protons are accelerated and aimed at a voxel in the target. (Adapted from
Caporaso et al., Nucl. Instr. Methods B, 261, 777, 2007; Caporaso et al., Proc. PAC 2009 TH3GAI02;
TomoTherapy. Website: http://www.tomotherapy.com/news/view/20070614_tomo_proton/.)
94 Proton Therapy Physics
by the company TomoTherapy (66). The system is pulsed with a repeti-
tion frequency of several tens of hertz. Energy variation per pulse can be
achieved by setting only the appropriate amount of switches. An interest-
ing feature may be the possibility to impose a variation of the accelerating
feld of a few percent. This may offer a potential for energy spread and
transverse spreading of the beam, which can be of interest for eye treat-
ments (≤70 MeV).
The key components for a DWA are operating at the limit of current tech-
nology: high-gradient vacuum insulators, high bulk breakdown strength
dielectrics for pulse-forming circuits, and switches that operate at high volt-
age. To cope with distortions inherent to the use of Blumleins, other acceler-
ating architectures that surround the HGI (induction concentrator) are also
being studied (65).
In this challenging project there are still some obstacles to overcome, and
the system is not expected to be simple or very small in size due to insula-
tion, cooling requirements (67), and the distance needed behind a scanning
system. At this moment the achieved repetition rate of several tens of Hertz
is too slow for scanning. A very important aspect for proton therapy with
respect to the ion source is the safe and accurate control of the very high
amount of protons per pulse, which is still part of the developments of the
proton source (68).
3.5.5 Laser-Driven Accelerators
The approach of using a laser to generate energetic proton beams for proton
therapy can be of interest, because the laser and light transmission compo-
nents can be installed in normal rooms, without the need of heavy concrete
shielding. Further, one might save a lot of weight when the easily transport-
able light beam is coupled on a rotatable gantry, because magnets are not
needed anymore. Also scanning the light beam would in principle provide
opportunities for pencil beam scanning. A concept of these ideas is illus-
trated in Figure 3.25 (69).
The acceleration of particles by means of strong laser pulses is developing
in a young and vastly changing feld (70). At the moment most experience
has been obtained with the target normal sheet acceleration (TNSA) method
(71). As shown in Figure 3.26, a high-intensity laser irradiates the front side
of a solid target, which may be saturated with hydrogen when protons are
to be accelerated. At the front surface, a plasma is created due to the energy
absorption in the foil. The electrons in this plasma are heated to high ener-
gies and penetrate through the target and emerge from the rear surface. This
induces strong electrostatic felds, which pull ions and the protons out of the
target at its rear surface.
The highest proton energies observed in this method are about 20 MeV
(72). This has been achieved with a laser power intensity of 6 × 10
19
W/cm
2

and a pulse length of 320 fs. Currently, much work is being done to model
95 Proton Accelerators
the interaction of the laser with the target and to make predictions for other
target geometries and materials (see the curve in Figure 3.27) (72). The
observed agreement between experimental data and scaling laws derived
from fuid models and numerical simulations have yielded an accurate
description of the acceleration of proton beams for a large range of laser and
target parameters (73). Extrapolation of this model to calculate the optimum
target and laser beam parameters for delivering a 200-MeV beam from dif-
ferent thicknesses of targets indicate that the needed laser power is as high
as 10
22
W/cm
2
.
Apart from the quest to obtain higher proton energies, the obtained energy
spectrum is also of concern. The observed energy spectra (Figure 3.28) show
a broad continuum (74) that is not suitable for proton therapy. Although
some flter and energy compression techniques are proposed (69), one must
be aware of neutron production when simple fltering techniques are used
just before the patient.
c
d
f
e
a
x
y
Laser target
emitting protons
and energy filter
protons
Couch
L
i
g
h
t

g
u
i
d
e
c
o
m
i
n
g

f
r
o
m

l
a
s
e
r
b
Mirror
FIGURE 3.25
The concept of a treatment facility using protons that are generated by a laser. (Adapted from
Ma, C.M., et al., Laser Phys. 16, 639–646, 2006.)
+
++
+
+
+
+
+
+
+
+
in foil, doped with hydrogen
Laser light
Laser light
pushes
electrons out
Electric field from electrons
accelerates protons out of foil
–
–
–
–
–
–
–
––
– –
–
– –
–
–
–
+
+
+
+
+
+
FIGURE 3.26
An intensive laser accelerates electrons from a proton-enriched area (polymer) at the far side
of a titanium foil. This creates a strong electric feld that accelerates protons out of the surface.
(Adapted from Schwoerer, H., et al., Nat. [Lond.] 439, 445–448, 2006.)
96 Proton Therapy Physics
Even though the feld is developing very fast (75), it is expected that
it will  still take many years to develop a laser-driven medical facility for
proton/ion therapy (76).
First of all one currently relies on a huge extrapolation from the values on
which the current models are based to power densities above 10
22
W/cm
2
.
No experimental results have yet been obtained for this regime. The physi-
cal systems are highly complex and suffer from instabilities and uncer-
tainties. To date it is by no means certain that placing such a higher-power
pulse on the target will lead to the desired energy of protons at the required
intensity (77).
Second, the obtained proton beam intensities are still far too low, for exam-
ple, 10
9
protons per pulse in a broad energy spectrum (72) or 10
8
protons per
pulse with a peak energy still well below 10 MeV (78). Even neglecting losses
due to energy selection and collimation of the proton beam, this would
require an increase of the repetition rate to 10–100 Hz, which is currently at
the limit of the advertised new generation lasers.
0
10
4
10
5
10
6
10
7
10
8
10
9
2 4 6
Proton energy (MeV)
N
r

o
f

p
r
o
t
o
n
s

p
e
r

p
u
l
s
e
8 10
FIGURE 3.28
Measured proton energy spectrum, obtained with a peak laser power of 6 × 10
19
W/cm
2
, focused
at a thin aluminum foil. (Adapted from Malka, V., et al., Med. Phys. 31, 1587–1592, 2004.)
25
20
15
10
M
a
x
i
m
u
m

p
r
o
t
o
n

e
n
e
r
g
y

(
M
e
V
)
5
0
0
0 4 8
Laser energy (J)
Model derived
from scaling laws,
fitted to the data
12
2×10
19
4×10
19
6×10
19
Laser intensity (W cm
–2
)
FIGURE 3.27
The measured and modeled proton intensities as a function of laser power. (Adapted from
Fuchs, J., et al., Nat. Phys. 2, 48–54, 2006.)
97 Proton Accelerators
An alternative method uses radiation pressure acceleration (RPA), some-
times referred to as the laser piston regime (79). Here the light pressure of
a laser pulse incident on a foil, with thickness less than 100 nm, accelerates
the whole foil as a plasma slab. Simulations predict that the RPA method can
provide higher proton energies and less energy spread than TNSA. However,
the RPA method faces even more technological challenges.
3.6 ConcludingRemarks
The AVF isochronous cyclotron and the synchrotron will remain the work-
horses in proton therapy for the coming decade. These machines are still
being improved, and a huge amount of experience and expertise has been
built up to operate these machines safely and reliably. The systems have been
discussed at conferences and in expert review panels and have undergone
certifcation processes at various authorities. This process has taken about
two decades, hereby even not taking into account the valuable work done by
the pioneers in the laboratories in the decades before.
New developments such as those discussed in this chapter are to be encour-
aged and are essential to make proton therapy as accessible for patients as
photon therapy. However, a few words of caution should be addressed here.
Providing a source of protons of therapeutically interesting energy is not suf-
fcient for operating a patient treatment facility. The beam characteristics at
the patient (energy, energy spread, beam size and emittance, intensity, time
structure, reproducibility, low-neutron background) are of major importance
and the safety requirements to prevent a wrong dose or dose at a wrong loca-
tion in the patient should not be underestimated.
Safety actions typically lead to switching the beam off. However, the avail-
ability of the beam is as important in a running treatment program. This is
not only for the convenience of the patient and to obtain good accuracy, but
also to prevent errors due to neglecting or bypassing frequently occurring
system warnings.
Therefore, before a claim is made that a new technology will soon outdate
the currently used systems, it frst needs to be proven that the new technol-
ogy can at least provide the same quality of the treatment as used today.
Next one should realize that the claimed advantage very often goes at the
cost of compromising other parameters. Here the consequences of “cheap”
protons providing inadequate treatments should not be underestimated:
apart from the consequences for the patients themselves, suboptimal treat-
ment results will have a catastrophic impact on proton therapy in general
when the treatment outcomes are not signifcantly better than those of pho-
ton treatments. This will endanger the operation of centers in which good,
high-quality treatments are being given.
98 Proton Therapy Physics
Also the reliability of the new technology should be evaluated critically.
Does this new technique allow patient treatments at least 14 hours a day,
5–6 days a week, without major interruptions? Furthermore, in relation to
implementation into clinical practice, an honest and fair estimate should be
given of the time it will take to have the new technology available, mature,
and safely and routinely useable in a clinical environment. To make a claim,
as some vendors do, that a frst system release to customers is planned for
2–3 years after announcing the successful frst proof of principle, is simply
misleading and usually much more optimistic than realistic estimates of the
developers themselves.
Acknowledgments
I thank my colleagues from the Division of Large Scale Research Facilities
and the Center of Proton Therapy at the Paul Scherrer Institut for sharing
their valuable and long years’ experience with me. Knowing how an accel-
erator works in principle is one thing, but the organization and detailed
knowledge needed to develop, use, and maintain a reliable and safe treat-
ment facility is another thing. Especially I thank Christian Baumgarten,
Markus Schneider, and Rudolf Dölling for reading and commenting on the
manuscript. Also I acknowledge the numerous discussions and interesting
details I have learned from my colleagues at proton therapy centers and the
international community of accelerator physicists during conferences, site
visits, and personal discussions.
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103
4
Characteristics of Clinical Proton Beams
Hsiao-MingLuandJacobFlanz
The characteristics of a proton beam are largely determined by the intrinsic
physical properties of the protons, the accelerators generating the beam, and
the devices used to control the beam. Different beam nozzle designs can affect
the beam properties substantially. Before one can design nozzle-beam-shaping
systems, such as those discussed in the next couple of chapters, we will explore
here the basic beam properties from a clinical point of view and how the clini-
cal requirement could be related to the design features and the operational set-
tings of the delivery system. Although the majority of proton therapy treatments
today are given by scattered beams, the use of scanning beams has now evolved
outside of research facilities, so our discussions will consider both such systems.
4.1 ProtonDoseDelivery
Despite the distinguished properties as a physical particle, protons are used
in therapy in more or less the same manner as photons used in conventional
radiotherapy. Indeed, its relative biological effectiveness (RBE) does depend
CONTENTS
4.1 Proton Dose Delivery ................................................................................ 103
4.2 Beam Specifcations ................................................................................... 105
4.2.1 Scattering Systems ......................................................................... 106
4.2.2 Pencil Beam Scanning ................................................................... 108
4.3 Beam Energy and Treatment Depths ...................................................... 109
4.4 Field Size ..................................................................................................... 110
4.5 Dose Rate..................................................................................................... 111
4.6 Lateral Penumbra ....................................................................................... 113
4.7 Distal Penumbra......................................................................................... 117
4.8 Dose Uniformity ........................................................................................ 118
4.9 Characteristics of Proton Therapy Treatment ........................................ 119
Summary .............................................................................................................. 122
References ............................................................................................................. 122
104 Proton Therapy Physics
on the linear energy transfer (LET) and can become substantially large at
the falling edge of the Bragg peak. However, as discussed in Chapter 19, the
overall effect can be accounted for by a constant RBE value of 1.1 in most
situations. As a result, one can essentially prescribe proton treatment with
the same amount of cobalt equivalent dose for the same level of expected
local control as in a conventional therapy treatment. Proton doses are pre-
scribed in Gy(RBE) (1). The application of a constant RBE is often viewed as
an advantage of protons over heavier particles with much more complicated
radiological effects, given the rich and invaluable clinical experiences about
local control and normal tissue toxicity obtained from conventional radio-
therapy over many years and from many patients. For this reason, we will
consider only the physical dose in the following discussions.
In current practice of radiotherapy, treatment is usually prescribed to a vol-
ume of tissue in the patient, that is, the target volume. A number of volumes
with different defnitions are often used to guide the treatment planning and
delivery processes. These include gross target volume (GTV), clinical target
volume (CTV), and planning target volume (PTV). For a more detailed expla-
nation of these volumes and their implications in the treatment process, see
Chapter 10.
The objective of the treatment is that every tissue element in the target
volume should receive the same amount of dose, in order to achieve the
same level of cell response based on relatively simple biological models. The
patient may receive multiple courses of treatments and each course may have
a different target volume prescribed to a different dose, but for each fraction
the goal is to deliver a homogeneous dose distribution to the target volume
of the treatment course.
During proton treatment, at any one point in time the accelerator and the
beam transport system can only transport to the patient a mono-energetic
beam with a small cross section. The depth–dose distribution of such a
pencil-like beam is the Bragg peak with a sharp peak in depth (introduced
in Chapter 2). It has a Gaussian-shaped cross section and is highly variable.
To obtain a homogenous depth–dose distribution over the target volume for
the rationale discussed above, one must build a superposition of many Bragg
peaks with the proper intensities and locations. As an example, Figure 4.1
shows the depth–dose distribution (solid line) in a homogeneous medium
of such a superposition for the case in which a homogeneous distribution is
achieved in a single feld. It contains a number of Bragg peaks (dotted lines)
in the same beam direction, but with different incident proton energies and
thus different Bragg peak locations spread out in depth, therefore, the term
spread-out Bragg peaks (SOBPs).
The dose distribution in Figure 4.1 shows several features. First, it delivers
a uniform dose distribution in depth across the target volume (darker grey
area). Second, it preserves the sharp distal fall of the Bragg peak: therefore the
ability of the proton beam to spare normal tissue behind the target volume
(light grey area). On the proximal side of the target volume, the dose changes
105 Characteristics of Clinical Proton Beams
gradually (i.e., a soft knee). Third, the total entrance dose has increased from
about 30% due to the deepest Bragg peak to nearly 80% due to the additional
shallower peaks. These features are the main clinically relevant properties of
the proton beam in the longitudinal direction.
Two main categories of methods are used to produce superpositions of
Bragg peaks for clinical use. They either use materials in the beam path to
modify the beam energy, or to modify the energy coming from the accelera-
tor, as described in detail in Chapters 5 and 6. In the following sections, we
briefy describe the principles of these methods and the specifcation of the
beams they produce.
4.2 BeamSpecifications
A number of parameters are needed to describe the physical properties of
the proton beam. Historically, they are often defned in relation to the man-
ner in which the beam is produced and characterized by measurements.
The beam model for treatment planning also needs to be specifed by a
set of parameters. It is critical from the clinical point of view that these
two sets of parameters be unifed to avoid any potential confusion or mis-
representation. That is, the same set of parameters is used to describe the
beam model in the treatment-planning system, to specify the desired beam
production in the beam control system, and to specify the quality assurance
measurements. For this reason, we will discuss here only those specifca-
tions currently adopted clinically. Readers interested in the historical evolu-
tion of the beam specifcations for various purposes should see references
provided herein.
0
0
10
20
30
40
50
60
70
80
90
100
110
120
130
2 4 6 8 10 12 14
Water equivalent path length (cm)
D
o
s
e

(
%
)
Target volume
Normal
tissue
FIGURE 4.1
A schematic view of SOBP construction, showing the SOBP depth–dose distribution (solid
line) and the component Bragg peaks (dashed lines).
106 Proton Therapy Physics
4.2.1 Scattering Systems
In systems that use beam scattering to spread the beam, the small beam com-
ing to the nozzle is scattered to a large area and the scatterers are specially
designed so that the beam has a uniform penetration and uniform inten-
sity across the scattered area specifed for clinical use. At the same time,
the energy of the beam is modulated to spread out the location of the Bragg
peaks over the target volume in depth. The system is usually confgured to
produce a homogeneous dose distribution with the same penetration across
the beam, as shown in Figure 4.1. For patient treatment, the beam is colli-
mated by an aperture to match the target volume and a range compensator
(usually a Lucite block with varying thicknesses) to “pull back” the most
distant Bragg peaks to conform to the distal surface of the target volume (see
Chapter 5).
Figure 4.2 shows the parameters used to describe the SOBP dose distribu-
tion. The distribution is normalized to 100% at the dose plateau. The param-
eters are defned in terms of positions in depth at the given dose levels: d20,
d80, and d90 at the distal end, with p90 and p98 on the proximal side.
The distal margin of the SOBP is given by the distance between d20 and
d80, corresponding to the 20% and 80% dose levels. This quantity has been
termed distal dose falloff (DDF) (1). The dose at the surface entrance is also a
useful parameter for characterizing the dosimetric property.
The most clinically relevant parameters are the beam range and modula-
tion width of the SOBP. The beam range is defned as the depth of penetra-
tion at 90%, that is, d90. Historically, the modulation width was defned as
the width of the dose plateau at the 90% level, that is, the distance in depth
from p90 to d90. In our institution, however, we recently changed our def-
nition of modulation width to Mod98, as indicated in Figure 4.2, for the
following advantages (2):
1. For SOBP distributions with large modulation width, the proximal
“knee” becomes much softer. As a result, the p90 value becomes
overly sensitive. A small difference in dose normalization, or mea-
surement, for the same SOBP, could result in a large difference in
p90. The p98 point, on the other hand, is at the steepest part of the
knee and is therefore well-defned.
2. For cases where the target volume extends close to the patient body
surface, the dose plateau of the SOBP must extend close to surface as
well to provide full dose coverage. In that case, the p90 point would
go outside of the body surface and becomes totally undefned,
whereas the p98 is still valid. Mod98 clearly refects better the extent
of the high dose region required to cover the target volume.
Figure 4.3 shows the lateral dose distribution at the middle of the SOBP
dose plateau produced by a scattering system with the beam range of 13 cm
107 Characteristics of Clinical Proton Beams
and a modulation width of 5 cm (m98). The feld size is defned at the 50%
level, as for a photon feld. For the lateral penumbra, both 20%–80% and
50%–95% values are used for the specifcation. Although the former is used
traditionally to refect the general quality of the penumbra, the latter is par-
ticularly needed for determining the margins of aperture for a given treat-
ment beam (see Chapter 10).
The absolute dose delivered by the SOBP feld is controlled by the monitor
unit ion chamber located downstream from the scatterers and range modu-
lators. The SOBP beam has a well-defned output factor, expressed as the
dose measured at the dose plateau of the SOBP in centi-Gray per monitor
unit reading (cGy/MU), as for the photon beam. The difference here is that
the output factor depends on both the beam range and modulator width.
For a given SOBP treatment feld with a specifc combination of range and
0
0
20
50
80
90
100
2 4 6 8 10 12 14
Water equivalent path length (cm)
Distal margin
Dose at entrance
p90
p98
d90
d80
d20
Range
Mod98
D
o
s
e

(
%
)
FIGURE 4.2
Specifcation of SOBP depth–dose distribution produced by scattering.
0
–3 –2 –1 0
Lateral position (cm)
20-80%
50-95%
Field size
1 2 3
20
50
80
95
100
D
o
s
e

(
%
)
FIGURE 4.3
Specifcation of lateral dose distribution produced by scattering.
108 Proton Therapy Physics
modulation width, the output factor must be frst determined either by mea-
surement or by modeling (3, 4). The required monitor unit for the treatment
delivery can then be computed for the prescribed dose. The calibration of
the monitor unit chamber follows the procedure described in IAEA Report
398 (5). Note that the dose calibration is usually based on the physics dose,
whereas the prescription is given in Cobalt Gray equivalent (CGE). The
proper conversion of 1.1 must be included in the monitor unit computation
(Chapter 19).
4.2.2 Pencil Beam Scanning
In pencil beam scanning, the pencil beam transported to the beam nozzle
by the beam transport system is directly sent into the patient without inter-
acting with any scattering or energy-modulation devices (Chapter 5). An
orthogonal pair of magnetic dipoles is used to steer the thin beam to reach
the full lateral extent of the target volume. The dose distribution is delivered
by placing the Bragg peak in the patient one location at a time and then
one layer at a time by varying the beam energy. Three main categories of
dose delivery have been used: uniform scanning, single-feld uniform dose
(SFUD), and multifeld uniform dose (MFUD).
Uniform scanning uses a fxed scanning pattern with constant beam
intensity for each layer. The relative intensities of the layers are fxed to pro-
duce a fat dose plateau longitudinally for a homogeneous medium. It also
uses an aperture for beam collimation and a range compensator for distal
conformity, just as for beams produced by scattering. However, the size of
the spread-out beam is only slightly larger than the aperture size and can
result in lower secondary radiation when compared to a non-optimized scat-
tered beam feld. The dose distributions produced by uniform scanning are
largely the same as those by scattering, except that the maximum feld size
is no longer limited by the scattering system. Because of this, the beam is
treated in the same manner as scattering in treatment planning, as well as in
delivery. That is, the beam is specifed by the range and modulation width
for the overall dose distribution as those given in Figure 4.2, rather than the
energy and intensity of each individual Bragg peak (6).
For SFUD, both the scanning pattern and the beam intensity are custom-
ized for a treatment feld, but the resultant dose distribution by each feld is
still uniform over the target volume. This is not required in MFUD, often
termed as intensity-modulated proton therapy (IMPT), where the homoge-
neous dose distribution over the target volume is constructed only by the
combination of two or more treatment felds (Chapter 10).
For both SFUD and MFUD, the treatment planning system considers
each pencil beam Bragg peak explicitly, rather than their combinations of
any type as for uniform scanning or scattering. The concept of modulation
width becomes irrelevant. The specifcation of a treatment beam is basically
a list of Bragg peaks, each with the energy of the proton, the lateral location
109 Characteristics of Clinical Proton Beams
of the peak projected unto the isocenter plane, and the number of protons,
often given in the unit of Giga-protons (10
9
). In this case, the quality of the
beam is determined largely by the quality of the individual pencil beam. The
dose distribution of the pencil beam is essentially a Bragg peak longitudi-
nally and a Gaussian transversely. The width of the peak refects the energy
spread of the protons, and the sigma of the Gaussian gives the spot size of
the beam. Note the spot size is defned as the width of the Gaussian in air at
the isocenter (Chapter 6).
4.3 BeamEnergyandTreatmentDepths
In treatment by scattering, each beam is usually made to deliver a homoge-
neous dose distribution covering the entire target volume, except for the case
of patching or matching (Chapter 10). That is, for a given beam direction, the
deepest Bragg peak must reach the deepest point of the target volume with
suffcient margins considering the various effects due to the distal penum-
bra and uncertainties in treatment planning and patient setup. In treatment
by pencil beam scanning where the intensity and the energy of each pencil
beam can be controlled individually, the homogenous dose coverage can be
achieved by multiple beams from multiple directions. In that case, not all the
beams have to reach the distal edges of the target volume.
Ideally, the treatment beam should take the shortest paths to reach the
tumor to minimize the volume of normal tissue on the beam path. However,
the entrance dose of the proton beam is often substantial and it is necessary
to spread it out over the normal tissue around the target volume by using
multiple beam directions including those with long beam paths. Beam direc-
tion may also be restricted by the geometric position of the target volume in
relation to the nearby critical organs. Prostate treatment is such an example
where the rectum is situated right next to the prostate on the posterior side.
Naturally, the best approach is from the anterior so that the sharp distal fall-
off of the proton beam can be used to cover the target volume while sparing
the rectum behind. This would require, however, a precise control of the
beam range in patient with millimeter accuracy, which is not currently pos-
sible. As a result, one can only use lateral felds with a substantially long
beam path going through more than half of the patient’s body (7).
At our facility, the beam is supplied by cyclotron at 230 MeV, with the
beam range in water at about 34 cm. In scattering mode, the maximum treat-
ment depth achievable is 29.3 cm (2). Although it is large enough for most
patients, occasionally some deep-seated tumors (e.g., prostate or pancreas) in
an exceptionally large patient could beneft from a longer range. The mini-
mum range achievable in our scattering system is 4.6 cm. The need for a
lower value could occur, for example, for pediatric patients, or for superfcial
110 Proton Therapy Physics
target volumes such as postmastectomy chest wall. In these cases, one could
shorten the range by increasing the minimum thickness of the compensator,
although it could increase the distance between the patient and the aper-
ture thereby degrading the lateral penumbra of the beam. In the pencil beam
scanning mode at our facility, the maximum beam range is 32 cm whereas
the minimum is 7 cm. Again the range shifter must be used for superfcial
target volumes.
As mentioned earlier, range uncertainty in patient has been a challeng-
ing issue for proton therapy. Some techniques have shown promising results
(Chapter 15) but have not been used widely in the clinic. As a result, most
of treatments do not use the distal fall off for narrow margin sparing. The
exception is the patching technique, where the distal end of the patch feld
meets the lateral penumbra of the through beam (Chapter 10). In that situa-
tion, a large range uncertainty can substantially distort the designed treat-
ment dose distribution. Even in a homogenous medium, a millimeter change
of the beam range could create hot or cold spots of 5%–10%. For this reason,
the patching technique is used for shallower target volumes, mostly in head
and neck area, requiring only short beam paths and thus relatively small
range uncertainty in patient. Moreover, alternate patch points are used and
rotated daily to even out the potential hot and cold spots. In any case, it is
critical that the delivery system can maintain an accurate beam range.
4.4 FieldSize
The majority of cases treated by protons have relatively small target vol-
umes, with a few exceptions including medulloblastoma and large sarco-
mas. As proton treatment facilities become more accessible, proton treatment
will expand to more indications including late-stage diseases often with
nodal involvement and thus much larger target volumes, or multiple tar-
gets. Although one can, in principle, design the system to provide always the
largest feld size possible, practical considerations must be included, such
as nozzle size, gantry size, and dose rate. In scattering systems, large feld
size requires large and heavy apertures and compensators that are diffcult
to handle (Chapter 5). For pencil beam scanning, larger feld size requires
stronger or longer scanning magnets.
The IBA (Ion Beam Application) scattering system used at our institution
has a feld size up to 25 cm in diameter, although the effective feld width up
to 2% dose heterogeneity is about 22 cm. The system has three sizes of snouts:
12, 18, and 25 cm in diameter. The smaller snout allows for lighter aper-
tures and compensators, and most importantly closer patient contact leav-
ing smaller air gaps and thus better lateral beam penumbra preservation. At
our facility, the 12-cm snout is used for close to 70% of treatment felds, with
111 Characteristics of Clinical Proton Beams
18- and 25-cm snouts at about 15% each. Note that we currently limit prostate
treatment to less than 10 per day. The usage of the small feld size could be
substantially larger at centers with signifcantly more prostate patients.
At our facility, the feld size for pencil beam scanning is a rectangle of 30 ×
40 cm at the isocenter. The substantially larger feld size is particularly useful
for the treatment of medulloblastoma, one of the treatments that benefts the
most from proton therapy. The target volume in this case is the entire CNS
including the whole brain and the spinal cavity extending inferiorly nearly
to the coccyx and could be as long as 80+ cm, particularly with young adult
patients. With scattering, the treatment is often broken into four parts using
fve felds, two laterals for brain, and three abutting spinal felds each cover-
ing a portion of the spinal cavity. Feathering must be used to even out the hot
and cold spots at the junction. With repeated setup verifcations between dif-
ferent felds due to the isocenter move, the entire treatment could take 30–40
minutes. Any increase of feld size allowing for a smaller number of felds
will be substantially appreciated by both patient and staff.
4.5 DoseRate
An external beam radiotherapy system must be able to produce a high
enough dose rate so that the treatment can be delivered in a reasonably short
amount of time. This is not only in consideration of the effciency in facility
utilization. It is directly related to treatment quality. In most of the treat-
ment procedures today, the patient is frst set up by image guidance (e.g.,
two-dimensional radiography, cone-beam computed tomography, and por-
tal imaging), and the treatment is then delivered using one or a few treat-
ment felds, under the assumption that the patient does not change his/her
body confguration from the time of the last imaging to the completion of
the dose delivery. Although this assumption is more valid for certain types
of treatment with appropriate patient immobilization devices than for oth-
ers, it is clear that the longer the treatment takes, the more likely the patient
will change the body confguration and affect the quality of the treatment.
Typically, proton treatment setup used to take more time than photon treat-
ment given the required accuracy for the treatment, as mentioned above;
however with the advancement of image guidance in photon treatments,
similar setup times can occur.
It was found in a recent study that during prostate treatment, the target
volume can stay within a 5-mm margin only for 5 min. If an endorectal bal-
loon is used, the margin is reduced to 3 mm but still only for 5 min (S. Both,
private communication). In this case, the lack of suffciently high dose rate
would require increasing the planning margins of the target volume and
delivering more doses to normal tissues nearby. Patient fatigue is another
112 Proton Therapy Physics
consideration for reducing the treatment time, particularly for elderly or
pediatric patients. However, this does not mean that one should use the
highest dose rate possible. Instead, it should be low enough to give the opera-
tor a reasonable amount of time to stop the treatment in response to sudden
patient movement or any unanticipated equipment problems.
The majority of the therapy patients today are treated with a regular frac-
tionation schedule with a daily dose of 1.8–2.0 Gy. The most commonly
used dose rate for conformal photon treatment is 2–4 Gy/min. For intensity-
modulated radiation therapy (IMRT) treatment, an even higher dose rate
(e.g., 6 Gy/min) is often used because each segment of the multileaf collima-
tor (MLC) pattern can irradiate only a small portion of the target volume.
Note that even with such a high dose rate, the treatment may still take a
long time because of the large number of segments in each feld and the
large number of feld directions used. This is the main reason for the recent
trend toward arc delivery together with intensity modulation, for example,
RapidArc, volumetric-modulated arc therapy (VMAT), and tomotherapy.
Proton treatment, on the other hand, does not usually require a large num-
ber of treatment felds for each treatment fraction because of its superior-
ity in minimizing dose to normal tissues around the target volume. A large
number of felds may be needed to satisfy the total dose constraints on the
critical organs over the whole treatment course, but only a subset of these
felds are suffcient to deliver the daily prescription with acceptable dose tol-
erance for the surrounding normal tissues. Most of treatment uses two felds
a day, alternating between different feld combinations.
For regular fractionated treatment (i.e., 1.8–2.0 Gy per fraction), this means
0.9–1.0 Gy per feld. Dose rates consistent with delivering a feld in up to a
few minutes are consistent with the targeting issues identifed above and
still much less than the overall setup time. A dose rate of 1.0–4.0 Gy/min will
be reasonable, but the intensity required of the accelerator to achieve this
dose rate is highly dependent on the target feld size. Naturally, for hypofrac-
tionated treatment a much higher dose rate will be desirable. The extreme
case is stereotactic radiosurgery treatment where each feld could deliver up
to 8 Gy. Another type of treatment where a higher dose rate may be appreci-
ated is respiratory gating where the beam is turned on only for a portion of
the respiration cycle, usually 30% centered on the end of respiration phase
(8). Ideally, the dose rate should be three times more than normal if the usual
amount time is to be used for the treatment. However, the dose rate should
not be too high, given that the treatment is to be delivered over a suffcient
number of respiratory cycles to average out the uncertainties due to breath-
ing irregularities.
The dose rate ultimately depends on the beam current transported to the
nozzle entrance where it is to be scattered in scattering mode or to be guided
into the patient directly in scanning mode. This largely depends on the capa-
bility of the accelerator and the energy selection system. For some cyclotrons,
the beam current can be continuous and generally has a high operating
113 Characteristics of Clinical Proton Beams
current (e.g., 300 nA at the cyclotron exit). However, the fxed energy of the
beam must be reduced by the energy selection system to the appropriate
value before being sent to the patient and this could reduce the beam current
signifcantly. As a result, the smaller is the beam range required, the lower
the dose rate. For synchrotron-based accelerators, dose rate does not depend
on the beam energy as much, given the absence of the energy selection sys-
tem. However, the beam is not delivered continuously but in “spills,” and the
overall peak beam current reaching the nozzle must be adjusted accordingly
to allow adequate average beam intensity.
In scattering mode, the dose rate also depends on the scattering design,
particularly the intended feld size. Obviously, the larger the feld size, the
lower the dose rate for a given beam current intensity at the nozzle entrance.
In fact, in some situations the scattering system was designed to give a small
feld size for particular types of treatment, for example, for prostate treat-
ment only where the maximum feld size is 12 cm in diameter.
For our system in scattering mode, the dose rate for 4.6-cm beam range is
1.5 Gy/min at the maximum beam current (i.e., 300 nA at the cyclotron exit).
At a beam range of 16 cm, the dose rate can be as high as 10 Gy/min.
For pencil beam scanning, the dose can be delivered spot-by-spot (in
step-n-shoot mode) or line-by-line (in continuous scanning) and then layer-
by-layer. The overall dose rate is usually specifed by the time to deliver a
uniform dose to a 10-cm cube, or 1 liter of tissue equivalent material. Note
that this depends not only on the beam current intensity for each scan layer,
but also the time between the layers for beam energy change and the corre-
sponding adjustments of the beam transport system. For the same incident
beam current, the effective dose rate will also depend signifcantly on the
target size to be treated.
4.6 LateralPenumbra
A sharp lateral penumbra is essential for sparing critical organs adjacent to
the target volume. This happens to be one of the most attractive features of
the proton beam. The lateral penumbra achievable in the patient depends
on the design of the beam delivery system and also the nature of interac-
tion between protons and tissues in the patient. The beam nozzle is gener-
ally designed to keep the penumbra as sharp as possible, although in some
situations a less sharp penumbra may be benefcial, for example, for beam
patching (Chapter 10). Another example is for treatments where large patient
setup uncertainties must be tolerated.
For scattering, the lateral beam penumbra is affected by the source size
and source position, the position of the aperture, the range compensator, the
air gap between the compensator and patient’s body surface, and naturally,
114 Proton Therapy Physics
the depth of tissue that the beam must penetrate before reaching the target
volume (Chapter 5). The scatterers and the modulator determine the source
size and are positioned far upstream, as far as possible from the aperture,
resulting a much longer source-to-axis distance (SAD), >200 cm, than that
for photon beams (100 cm). The aperture should be as close to the patient as
possible to reduce the effect of source size. This also reduces the air gap that
degrades the penumbra substantially (Chapter 5).
In the patient, a proton beam interacts with tissues very differently from
megavoltage photon beams (Chapter 2). For the latter, the main mechanism
is attenuation due to Compton scattering where the scattered photons essen-
tially escape from the beam. As a result, the lateral penumbra is mainly
determined by the beam source size and source position, and increases
only moderately as the beam goes through the patient. For protons, on the
other hand, the main interacting mechanism is multiple Coulomb scattering
(MCS). A proton changes its direction very little after each interaction, but
stays in the beam. The change accumulates rapidly and increases the beam
penumbra much faster than in the case of a photon beam.
Figure 4.4 plots the lateral penumbra for a 6-MV photon beam and that
for a scattered proton beam (range, 14 cm; modulation width, 10 cm), at
both 4- and 10-cm depths. Clearly, the proton penumbras are much sharper
than the photon counterparts. However, it increases drastically as depth
increases from 4 to 10 cm, whereas the photon penumbra increase is moder-
ate. Figure 4.5 shows the increase of beam penumbra of protons over deeper
depths, again together with those for higher energy photon beams.
Overall, at shallower depths, the proton penumbra (both 20%–80% and
50%–95%) is smaller than that of photon beams, but it increases rapidly with
depth and becomes larger than the 15-MV photon beam for depths greater
0
Lateral position (cm)
–1 –0.8 –0.6 –0.4 –0.2 0.2 0.4 0.6 0.8 1
Photon (4 cm)
Photon (10 cm)
Proton (4 cm)
Proton (10 cm)
0
10
20
30
40
50
60
70
80
90
100
110
D
o
s
e

(
%
)
FIGURE 4.4
Lateral beam profles in the penumbra region for scattered beam with range of 14 cm and
modulation width of 10 cm (m98) at both 4- and 10-cm depths in water. The profles of a 6-MV
photon beam at the two depths are also shown for comparison.
115 Characteristics of Clinical Proton Beams
than 17 cm for 20%–80% and 22 cm for 50%–95%. It is interesting to note that
this is the typical treatment depth in current prostate treatment where only
bilateral felds are used. It is exactly the reason why proton plans do not dem-
onstrate any substantial dosimetric beneft over IMRT in terms of dose to ante-
rior part of the rectal wall situated right next to the prostate target volume (7).
Safai, Bortfeld, and Engelsman (9) investigated the properties of the lat-
eral beam penumbra for a scattering system. Figure 4.6 shows the measured
and modeled penumbra (20%–80%) as a function of depth in water for two
broad pristine Bragg peaks with ranges 22.1 cm (T
0
= 183 MeV) and 7.85 cm
(T
0
= 102 MeV), where T
0
denotes the initial beam energy. Two sets of data
were obtained for each beam range, with and without a 4-cm-thick plate of
poly(methyl methacrylate) (PMMA) to simulate the contribution of the range
compensator. The air gap was 10 cm without the PMMA and 6 cm with it.
For all confgurations, the penumbra increases with depth, as was the case
shown in Figure 4.5. The lower energy beam starts with a slightly larger
value at the surface, but increases much more rapidly than the higher energy
beam. The PMMA plate broadens the penumbra for both beam energies,
more at a depth than near the surface because of reduced beam energy. At
the end of the beam range, the penumbras are comparable with or without
the PMMA plate. Note that although the data given here are from pristine
15 cm
8
0
–
2
0

%

D
i
s
t
a
n
c
e

(
c
m
)
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Proton (R28/M10) 18 MV 15 MV
20 cm 25 cm
15 cm
5
0
–
9
5

%

D
i
s
t
a
n
c
e

(
c
m
)
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Proton (R28/M10) 18 MV 15 MV
20 cm
Depth (cm)
25 cm
FIGURE 4.5
Measured lateral beam penumbra (20%–80% upper and 50%–95% lower) as functions of depth
in water for 15- and 18-MV photon beam and for a scattering beam with range of 28 cm and
modulation width of 10 cm.
116 Proton Therapy Physics
Bragg peaks without range modulation, it was shown that the lateral penum-
bra of SOBP felds is almost independent of the beam modulation width and,
therefore, follows the same trend described here (10, 11).
In pencil beam scanning, the main source of the penumbra broadening
before the patient is the scattering by the air column extending from the end
of the nozzle to the patient’s body surface. Safai, Bortfeld, and Engelsman
modeled this effect for a single Gaussian beam (σ = 3 mm) and compared the
results with a broad Gaussian beam but with an aperture and compensator (9).
It was found that if the vacuum window is at the same upstream location as
in a scattering system, the penumbra for the uncollimated pencil beam is sig-
nifcantly larger than that for the collimated beam at the surface. Of course no
scanning system would have an air column that long. In depth of water, how-
ever, the uncollimated penumbra increased much slower than the collimated
and became less than the latter at larger depths that were greater than 18 cm.
This is partly due to the very different effective source positions (i.e., diver-
gence) of the beam. Overall, the collimated penumbra is superior at shallow
depths, but is inferior at greater depths. The authors concluded that for most of
the clinical sites (e.g., head and neck) the penumbra of a pencil beam is inferior
to that of a collimated divergent beam, unless the vacuum window is moved
downstream substantially or the beam spot size is reduced to 5 mm or less (9).
The investigation reported in Safai’s work focused on the penumbra of a single
pencil beam. Clinically, what is more relevant in terms of organ sparing is the
Depth in water (d
w
) [cm]
P
e
n
u
m
b
r
a

(
8
0
%
–
2
0
%
)

[
c
m
]
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.2
0.4
0.6
0.8
1
1.2
T
0
= 183 MeV
T
0
= 102 MeV
measurement w/o PMMA
measurement w/4.0 cm PMMA
prediction
1.4
1.6
2 4 6 8 10 12 14 16 18 20 22 24 26
0 2 4 6 8 10 12 14 16 18 20 22 24 26
FIGURE 4.6
Measured (symbols) and modeled (lines) lateral beam penumbra (20%-80%) as functions of
depth in water for two scattered beams with beam ranges of 21.1 cm (left) and 7.85 cm (right),
with and without 4.0-cm plate of PMMA. (From Safai S, et al., Phys Med Biol., 53, 1729, 2008.
With permission).
117 Characteristics of Clinical Proton Beams
lateral penumbra of the composite dose distribution as the superposition by all
individual pencil beams used for a treatment feld. As discussed in Chapter 6,
such a superposition with a uniform dose plateau can be built by using evenly
spaced pencil beams with a constant intensity, but the resultant composite lateral
penumbra will be broader than that for the individual pencil beam. However,
composite doses with an equally acceptable dose plateau can also be obtained
by using nonuniform spacing together with modulated intensities optimized to
produce a much sharper penumbra, nearly the same as for a single pencil beam.
For either case, though, the smaller the spot size for the individual pencil beam,
the narrower the lateral penumbra of the total dose distribution.
Is it always better to have a smaller spot size for proton beam scanning?
Trofmov and Bortfeld studied the issue in their efforts to develop a set of
clinically relevant specifcations for pencil beam scanning (12). They pointed
out that, for deep tumors, a fner pencil beam would not necessarily lead to
any signifcant improvement in dose conformity, simply because the main
contribution to the spot size at the tumor comes from MCS along the beam
path in patient. For shallower target volumes, they performed treatment
planning using a range of spot sizes for a head and neck case where this
perhaps matters the most. It was found that reducing the spot size from 8
to 5 mm led to a marked improvement in dose conformality for the target
volume, whereas the difference was not as dramatic from 5 to 3 mm. They
concluded that for most clinical cases, pencil beams of widths σ = 5 mm will
be suffcient for delivery of the target-conformal planned dose with a high
precision. Reducing the beam spot size below 5 mm does not lead to substan-
tial improvement in the target coverage or sparing of healthy tissue.
4.7 DistalPenumbra
The distal penumbra of the SOBP dose distribution is determined primarily
by the deepest few Bragg peaks. The penumbra (50%–95%) is the smallest
with only the deepest peak, but increases up to a millimeter as more peaks
are added to build up the dose plateau as shown in Figure 4.1. In relatively
homogeneous medium without a high gradient in tissue density, the distal
beam penumbra is always much sharper than the lateral one. It increases
moderately with energy due to range straggling in the patient and also by
scattering and range modulation components in the nozzle if scattering is
used. The former is unavoidable, but the latter can be eliminated by using
pencil beam scanning, or minimized by reducing the water equivalent
thickness of those components. For the scattering system at Massachusetts
General Hospital (MGH), the distal penumbra increases monotonically from
3.5 to 5.0 mm (20%–80%) over the beam range of 4.8 to 25 cm. However, for
a beam range of 25 to 28 cm, the penumbra is only 4.7 mm, actually smaller
due to the use of a very thin second scatter.
118 Proton Therapy Physics
When high-gradient tissue inhomogeneity is present, range mixing can
occur. The distal penumbra can be degraded substantially and could be much
larger than the lateral penumbra. The extreme case is when the beam passes
along the interface between a high-density and a lower density medium,
where the distal dose falloff can be seriously distorted. The situation is inves-
tigated in Schaffner, Pedroni, and Lomax (13). Needless to say, the compen-
sator causes additional range straggling that will also increase the distal
penumbra. A thick compensator and in particular those with sharp variations
in thickness should be avoided if possible.
It should be pointed out that although the distal beam penumbra is much
sharper than the lateral, it is not always used clinically for tight margin spar-
ing because of uncertainties in predicting the beam range in the patient
(Chapter 13). The recent development using posttreatment PET (positron
emission tomography) imaging based on treatment-induced isotope activi-
ties has shown very promising results for in vivo range verifcation, as
described in Chapter 16. Although it works well mainly for coregistered
bony structures in the head and neck, for soft tissue target volumes in other
parts of the body the accuracy drops substantially for various reasons. In
any case, the method is still at the research stage and is not widely available.
In current practice, the range uncertainty issue is managed by adding an
additional amount to the beam range in treatment planning, usually 3.5%, to
head off the potential “undershooting” (Chapter 10). Although this guaran-
tees the coverage of the distal aspect of the target volume, it also risks over-
dosing the normal tissue behind the target volume. A good example is the
treatment of prostate cancer mentioned above. Anterior or anterior oblique
felds have never been used, despite the fact that such felds can utilize the
sharp distal penumbra (~4 mm for 50%–95%) to separate the prostate and the
rectum behind. Instead, only lateral felds are used, relying solely on the much
broader lateral beam penumbra (>10 mm for 50%–95%) to spare the rectum.
The reason is because when a water-flled endorectal balloon is used to immo-
bilize the prostate, as widely practiced, the anterior rectal wall is only about
5 mm thick and is situated right next to the posterior side of the prostate in
many areas. If an anterior feld is used for treatment, the typical beam range is
about 15 cm and its 3.5% will be 5 mm, just the thickness of the anterior rectal
wall. Therefore, the usual method of adding extra range will risk delivering
the full dose to the anterior rectal wall, which is clearly unacceptable given
rectal bleeding as the leading treatment toxicity for prostate treatment.
4.8 DoseUniformity
A proton beam has the unique ability that a single beam can be used to
deliver a homogeneous dose across the entire target volume, as opposed
to a photon beam where multiple felds must be used to achieve a similar
119 Characteristics of Clinical Proton Beams
coverage through superposition. In scattering, this is achieved by carefully
designing the scattering components including scatterers and range modula-
tors (or ridge flters in some systems) so that the dose in the SOBP is uniform
in the dose plateau both in depth and laterally across the feld size required.
Naturally, this specifcation is for a homogeneous phantom, whereas in
patient it could be larger due to the effect of tissue inhomogeneity.
The details of the scattering systems will be discussed in Chapter 5. We
only comment here that given the sensitive dependence of the scattering
property on the beam energy, it is a formidable task to design a scattering
system that accommodates all clinically relevant beam ranges with suff-
cient quality and at the same time provides convenience and effciency that
are critical in day-to-day clinical practice. With a method developed only
recently, it was possible to optimize a critical component of the system so
that for all the beam ranges, the dose uniformity in depth is within 2% (2).
Note that the double-scattering system is very sensitive to beam steering
and a slight change in the beam spot position on the scatters can seriously
affect the feld fatness and symmetry. This requires an effective monitor-
ing system and also frequent quality assurance verifcations by indepen-
dent means.
For pencil beam scanning, the total dose distribution is constructed by
individually delivered Bragg peaks and its uniformity will directly depend
on the accuracy of the delivery (i.e., the beam energy and the spot location).
Inaccuracies in the beam energy will create uneven distances between adja-
cent layers in depth and thus cause ripples in depth that could exceed the
2% requirement, particularly at the shallower part where the Bragg peak is
distinctively narrow. Across the feld, when the spot is not accurately posi-
tioned as planned, the superposed Gaussian distribution will contain spikes
and valleys, both of which could exceed the uniformity requirement. The
accuracy requirement in delivery for keeping an acceptable level of dose uni-
formity and how it is achieved with the current technological capability will
be discussed in Chapter 6.
4.9 CharacteristicsofProtonTherapyTreatment
The distinguished physical characteristics of the proton beam discussed
above also result in some special characteristics of the proton therapy treat-
ment itself in comparison to treatment by photon and/or electron beams.
Proton beams have been used to treat nearly all major types of cancer at all
treatment sites (e.g., central nervous system, head and neck, lung, esophagus,
liver/pancreas, prostate, rectum, and sarcomas), and the list is ever increas-
ing. Recently, a proton beam was used for postmastectomy irradiation for
the frst time. Although these conditions are also treated by photon/electron
120 Proton Therapy Physics
beams, which is the only choice for the majority of patients today, treatment
using protons can be quite different, given the unique physical properties of
the beam.
Undoubtedly, the sharp distal dose falloff gives the proton the most impor-
tant advantage in sparing normal tissues near the target volume. The clinical
implication of this is best illustrated by the spine felds used in the treatment
of medulloblastoma, a condition occurring most often in pediatric and/or
young adult patients. The protons from a posterior beam stop right behind
the spinal target volume, leaving no dose to the rest of the body, whereas a
photon treatment would give up to 50% of the prescription dose to the ante-
rior portion of the body (14). Another unique feature made possible by the
sharp distal falloff is the patching technique widely used in scattering and
uniform scanning (Chapter 10).
We must note that although the sharp distal dose falloff can offer great
potentials for normal tissue sparing, it also makes the dose distribution
extremely sensitive to uncertainties in treatment planning and patient setup
(Chapter 13). The range of the proton beam in the patient depends largely on
the water equivalent path length (WEPL) along the beam. If the WEPL value
changes by 1 cm, the location of the distal falloff will change by 1 cm, causing
either an undershoot, missing the distal portion of the target volume by one
full centimeter, or an overshoot, delivering full dose to a centimeter of normal
tissue behind the target volume. In contrast, the same magnitude of change in
WEPL in a photon treatment will only change the dose at most by 3%–4%, for
example, for a 10-MV beam. A patient setup error in an IMRT treatment may
cause a shift of the so-called “dose cloud,” missing some peripheral regions
of the target volume. In a proton treatment, the same error may also distort
the dose cloud substantially, due to the mismatch between the beam energy
distribution and the tissue heterogeneities along the beam path.
The presence of a dose plateau in Figure 4.1 means that a single proton feld
can deliver the uniform dose to the target volume, which is not possible with
photon or electron beams. This allows for the use of only one or two felds for
each treatment fraction to deliver the prescription dose, although the whole
treatment course may use a large number of treatment felds to spread the
dose to normal tissues. Many patients are treated in this manner, that is,
with only one or two felds per fraction, but with different felds or feld
combinations on different days. This is very different compared to a photon
treatment where each fraction uses the same number of felds throughout
the treatment course.
When the total prescription dose for a fraction is delivered by only one or
two felds, the uncertainties involved in each feld become much more impor-
tant. This plus the sensitive nature of the proton dose distribution mentioned
above determines that proton treatment requires highly accurate patient
setup. Note that because the treatment beam stops in the patient completely,
a photon-like portal imaging is not possible and one must rely entirely on
x-ray imaging. Usually, the patient is frst setup with an orthogonal pair of
121 Characteristics of Clinical Proton Beams
images to produce the correct anatomical confguration, and then for each
treatment feld, the patient is imaged again along the beam direction, often
with the aperture when available, to ensure target volume coverage and nor-
mal structure avoidance. As a result, the time for patient setup is generally
longer than with a photon treatment.
Can treatment be delivered with only fxed beam line, rather than a gan-
try system? This seems to be a question relevant only in particle therapy. A
gantry system is large and expensive. Moreover, the beam transport system
on the gantry adds another layer of complexity to the whole system. The
answer to this question really depends on the specifc treatment site and
treatment techniques involved. Treatments of ocular melanoma have always
used fxed beam lines. At Francis H. Burr Proton Therapy Center (FHBPTC)
at MGH, a fxed horizontal beam is also used to perform stereotaxic radio-
surgery and stereotaxic radiotherapy treatment by placing the patient in an
immobilization system called STAR (Stereotactic Alignment Radiosurgery)
system with six degrees of freedom. Current prostate treatment uses only
lateral beams as mentioned earlier and therefore can be treated by only fxed
horizontal beam lines as indeed practiced at some centers. For other treat-
ment approaches using anterior and anterior oblique beams currently under
development, the gantry will be required. For some treatment sites such as
nasopharynx and skull base chordoma, however, it is clearly diffcult with-
out a gantry. Figure 4.7 shows the number of felds at each gantry angle for
all the patients treated in a 12-month period for one gantry treatment room
at FHBPTC. Of all the felds, 23% used only lateral beams, 41% used just the
four normal angles (0°, 90°, 180°, and 270°), and 59% used other gantry angles.
Interestingly, the treatment planners only varied the gantry angle at 5° incre-
ments. One can interpret this graph to indicate that it may be possible to treat
patients with a combination of fxed-feld beams and a gantry, instead of
building multiple-gantry systems. There may be some logistical issues, but
the data are interesting.
0
N
u
m
b
e
r

o
f

fi
e
l
d
s
0
200
400
600
800
1000
1200
1400
1600
90 180
Gantry angle (degree)
270
FIGURE 4.7
Distribution of the number of treatment felds over gantry angles for all patients treated in a
gantry room over a 12-month period.
122 Proton Therapy Physics
Summary
A survey of the properties of proton beams and how they are used in clini-
cal treatment has been presented. Although proton therapy has existed for
decades, the more widespread use is only from a few to several years old,
and current clinical practice is now being augmented by investigations of
the effects of modifying the beam properties. It is interesting to point out
that one of the characteristics of proton beams is that their properties can,
in fact, be modifed. Thus it becomes even more important to understand
what works best clinically and to evaluate the design of any proposed beam-
spreading system, considering how it will be used clinically. One issue may
be the construction of multipurpose systems as opposed to single-use sys-
tems. In much the same way that a gantry is more expensive than a fxed
beam line, the use of a beam for multiple treatment sites may also be more
expensive. However with the increase in the use of scanning beams, this
may not be an issue any longer. The properties of the beam must be matched
to the characteristics of the clinical target and the beam delivery modality,
and understanding how the beam characteristics can be used and modifed
is an essential part of optimal treatment delivery.
References
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125
5
Beam Delivery Using Passive Scattering
RoelfSlopsema
Passive scattering is a delivery technique in which scattering and range-
shifting materials spread the proton beam. After the protons are accelerated,
either by a cyclotron or synchrotron, they are transported into the treatment
room through the beam line (see Chapter 3). The proton beam that reaches
the treatment room is mono-energetic and has a lateral spread of only a few
millimeters. Without modifcation this beam would give a dose distribution
that is clinically not very useful. Along the beam axis the dose is initially
fairly constant, but peaks sharply toward the end of travel of the protons
(Bragg peak). In the lateral direction the profle would be a Gaussian with a
spread on the order of a centimeter. Clinical use of the proton beam requires
both spreading the beam to a useful uniform area in the lateral direction
as well as creating a uniform dose distribution in the depth direction. The
CONTENTS
5.1 Scattering Techniques ............................................................................... 126
5.1.1 Flat Scatterer ................................................................................... 126
5.1.2 Contoured Scatterer ....................................................................... 127
5.1.3 Dual-Ring Scatterer ....................................................................... 130
5.1.4 Occluding Rings ............................................................................. 130
5.2 Range Modulation Techniques ................................................................ 130
5.2.1 Range Modulation Principles ....................................................... 131
5.2.2 Energy Stacking ............................................................................. 133
5.2.3 RM Wheels ...................................................................................... 134
5.2.4 Ridge Filters .................................................................................... 140
5.3 Conforming Techniques ........................................................................... 142
5.3.1 Aperture .......................................................................................... 142
5.3.2 Multileaf Collimator ...................................................................... 143
5.3.3 Range Compensator ...................................................................... 144
5.4 Scattering Systems ..................................................................................... 146
5.4.1 Large-Field Double-Scattering Systems ...................................... 147
5.4.2 Single-Scattering System for Eye Treatments ............................ 151
5.5 Conclusion .................................................................................................. 152
References ............................................................................................................. 153
126 Proton Therapy Physics
main function of the treatment head, or nozzle, is shaping the proton beam
into a clinically useful three-dimensional (3D) dose distribution. In general
two methods of lateral beam spreading are applied: passive scattering, in
which high-Z materials scatter the proton beam to the desired dimension,
and magnetic beam scanning, in which magnetic felds sweep the proton
beam over a desired area. Scattering systems are described in this chapter;
scanning systems are the topic of Chapter 6. In the depth direction a uniform
dose region is created by adding Bragg peaks that are shifted in depth and
given an appropriate weight to obtain a fat dose region called the spread-
out Bragg peak (SOBP). This method of adding pristine peaks is called range
modulation. The number of peaks that is added proximally can be varied,
varying the extent of the uniform region in depth. Combining scattering and
range modulation gives a uniform dose distribution shaped like a cylinder.
Field-specifc apertures and range compensators conform the dose to the tar-
get. The aperture blocks the beam outside the target and conforms the beam
laterally. The range compensator is a variable range shifter that conforms the
beam to the distal end of the target. In this chapter we will frst describe the
basic techniques of scattering and range modulation. Next the design and
application of apertures and range compensators is discussed. In the fnal
section several complete scattering systems are discussed, combining scat-
tering technique, range modulation method, and conforming devices.
5.1 ScatteringTechniques
5.1.1 Flat Scatterer
The simplest scattering system is a single, fat scatterer that spreads a small
proton beam into a Gaussian-like profle (Figure 5.1A). A collimator (aper-
ture) blocks the beam outside the central high dose region. To keep the dose
variation over the profle within clinically acceptable limits, most of the
beam will need to be blocked. For a Gaussian beam profle with spread, σ,
the effciency, η, defned as the proportion of protons inside a useful radius,
R, is given by the following (1):

η
σ
= −
−
1
1
2
2
e
R ( / )
(5.1)
It follows that the fraction of protons outside the useful radius is equal to
the relative dose at the useful radius (when normalizing to the central axis).
Allowing for a dose variation of ±2.5% over the profle and setting the useful
radius at the 95% dose level, results in an effciency of only 100% − 95% = 5%.
Because of this low effciency, requiring relatively large beam currents and
127 Beam Delivery Using Passive Scattering
generating high production of secondary neutrons, spreading using a fat
scatterer (single scattering) is limited to small felds with a diameter typi-
cally not exceeding ~7 cm. Besides its simplicity, the advantage of a single
fat scatterer over more complex scattering techniques is the potential for a
very sharp lateral penumbra. Most of the scattering occurs in a single loca-
tion limiting the angular diffusion of the beam. Especially if the scatterer is
placed far upstream of the fnal collimator, a very sharp lateral penumbra
can be achieved. The feld size limitation and sharp dose falloff make single
scattering ideal for eye treatments (2–8) and intracranial radiosurgery (9).
Typically the scatters are made of high-Z materials, such as lead or tanta-
lum, providing the largest amount of scattering for the lowest energy (range)
loss. A scattering system that allows variation of the thickness of the scat-
tering material can be used to maintain scattering power for varying proton
energy. An example of such a system has a binary set of scatterers (with
each scattering foil double the thickness of the previous) that can be inde-
pendently moved in or out of the beam path.
5.1.2 Contoured Scatterer
A better effciency can be achieved by scattering more of the central pro-
tons to the outside and creating a fat profle (Figure 5.1B). The shape of a
contoured scatterer, thick in the center and thin on the outside, has been
optimized to do this (10, 11). Typically a fat scatterer (frst scatterer) spreads
the beam onto the contoured scatterer (second scatterer) that fattens out the
A. Single Scattering with flat scatterer
D. Double Scattering with occluding ring
B. Double Scattering with contoured scatterer
C. Double Scattering with dual ring
FIGURE 5.1
Schematic representation of the single-scattering technique using a fat scatterer (A) and dou-
ble-scattering techniques using a contoured scatterer (B), dual ring (C), and occluding ring (D).
Dashed lines, lateral profle without aperture; solid lines, with aperture.
128 Proton Therapy Physics
profle at some distance. This type of system is called a double-scattering
system. Mathematically the lateral dose distribution Φ(r) created by a dou-
ble-scattering system can be described as follows:

Φ( ) exp
'
r
z
r
z
FS FS FS FS
=
( )
−
( )





∫
1
2
2
0
2 2
2
π θ θ
π




⋅
( ) ( )
∫
1
2
0
z r
CS CS
R
θ

'
× −
−
( ) ( )








⋅ exp
( ')
'
  '


r r
z r
r d
CS CS
2
2
θ

r d ' , φ (5.2)
where z
FS
and z
CS
are the distance from the frst and second scatterer to
the plane of interest; θ
FS
is the characteristic scattering angle of the frst fat
scatterer (which is constant), θ
CS
is the characteristic scattering angle of the
contoured scatterer that depends on radial position r′. R is the radius of the
contoured scatterer assuming all protons outside R are blocked. The radial
coordinates r′ and R of the contoured scatterer are projected from the frst
scatterer onto the plane of interest. The frst exponential in the equation
gives the fuence of the beam hitting the contoured scatterer at position r′.
Without the contoured scatterer the dose distribution would be equal to this
term. The second exponential describes the operation of the contoured scat-
terer. It describes the proportion of protons hitting the second scatterer at
position r′ and ending up in position r. This depends on the distance between
r′ and r and the angular spread added by contoured scatterer, which is a
function of the characteristic scattering angle (i.e., thickness) at location r′.
By integrating over all positions, r′, the dose in point r is found. (Note that
we have made some simplifcations here such as Gaussian scattering, rota-
tional symmetry, thin scatterers, and a small parallel entrance beam. More
realistic properties will complicate the formulation, but can typically still be
described analytically.) Given a desired fat dose distribution Φ(r), it is not
possible to analytically solve Equation 5.2 and fnd the required shape of
the contoured scatterer θ
CS
(r′). Instead the shape of the contoured scatterer is
determined using numerical methods. The scattering shape is described by
a parameterized function such as a cubic spline through a limited number of
points whose thickness is optimized (11) or a modifed cosine with four inde-
pendent variables (10). The variables of the contoured scatterer are optimized
in combination with the scattering power of the frst scatterer to obtain a
dose distribution of desired size and acceptable uniformity. Effciency can
be made an additional objective in the optimization. Effciencies of up to 45%
can be obtained, signifcantly larger than in single scattering.
Protons hitting the center of the contoured scatterer lose more energy
than those going through the thinner parts at the periphery. To avoid a
concave distortion of the distal isodose plane, with the range increasing
away from the beam axis, energy compensation is applied to the contoured
129 Beam Delivery Using Passive Scattering
scatterer. A high-Z scattering material (lead, brass) is combined with
a low-Z compensation material (plastic). The thickness of the two mate-
rials is designed to provide constant energy loss, while maintaining the
appropriate scattering power variation. The thickness of the high-Z mate-
rial decreases with distance from the axis, whereas the thickness of the
compensating low-Z material increases. Figure 5.2 shows a schematic of
an energy-compensated scatterer. Note that energy compensation will
increase the total water equivalent thickness of the scatterer because the
compensation material increases the scattering power on the outside of the
scatterer, which needs to be compensated for by adding additional scatter-
ing material in the center. The energy of the protons entering the nozzle
needs to be increased to achieve the same range in the patient as with an
uncompensated scatterer.
The dose distribution is sensitive to misalignments of the beam with
respect to the second scatterer. A displacement of the beam increases the
fuence on one side of the second scatterer and reduces it on the other side,
causing a tilt in the dose profle at isocenter. To keep the symmetry within
clinical tolerance, the alignment of the beam typically needs to be better
than ~1 mm. The large distance between the fnal steering magnet of the
beam line and the second scatterer makes this diffcult to achieve without
a feedback mechanism. By monitoring the profle symmetry downstream
of the second scatterer (e.g., using strip ionization chambers), the fnal steer-
ing magnets can be controlled maintaining a fat profle (12). In addition to
misalignment, the profle is sensitive to variations in beam size at the second
scatterer level. If the profle is too large, the dose profle will have “horns”; if
the profle is too small the dose profle will be “domed.” If the second scat-
terer is placed far enough downstream, meaning that its physical size is large
enough, the width of the beam onto it will be dominated by the scattering
of the frst scatterer and variations in beam spot size at the nozzle entrance
will not play a role.
3 cm
16 cm
0.6 cm
Lexan
lead
FIGURE 5.2
Schematic cross section of an energy-compensated contoured scatterer in the IBA universal
nozzle.
130 Proton Therapy Physics
5.1.3 Dual-Ring Scatterer
An alternative to the contoured scatterer is the dual-ring scatterer (13). It
consists of a central disk made of a high-Z material (lead, tungsten) and a
surrounding ring of a lower-Z material (aluminum, Lucite). The physical
thickness of the outer ring is chosen such that the energy loss is equal (or
close) to the energy loss in the central disk. A frst, the fat scatterer spreads
the beam onto the dual-ring scatterer. The central disk produces a Gaussian-
like profle, and the ring produces an annulus-shaped profle, which com-
bine to produce a uniform profle at the isocenter (Figure 5.1C). In the design
the projected scattering radius of the frst scatterer and of the two dual-ring
materials, together with the diameter of the central disk, are optimized to
generate a fat dose profle of the desired size (14). Because of the binary
nature of the dual-ring, the dose distribution is not perfectly fat. A small
cold spot is allowed at the level of the interface between the two materials.
Like the contoured scatterer, the dual-ring system is sensitive to both beam
alignment and phase-space changes.
5.1.4 Occluding Rings
Most double-scattering systems today use a contoured or dual-ring scatterer,
but occluding rings combined with a fat second scatterer can also fatten
the profle (15). Instead of scattering the central protons outward they are
blocked (Figure 5.1D). The “hole” created in the fuence distribution is flled
in by scattering through a fat, second scatterer. Larger-feld sizes can be
obtained by not just blocking the center but by adding one or more occlud-
ing rings. Optimization of the ring diameters and the frst scatterer power
results in a fat dose distribution. Because the protons are not redistributed
but blocked, the effciency of an occluding ring system drops signifcantly as
the number of rings and maximum feld size are increased. It is signifcantly
lower than for the contoured scatterers. The energy loss is smaller though,
because a relatively thin second scatterer foil is needed to spread out  the
beam. The geometry of the occluding rings makes them just as sensitive
to beam misalignment as the contoured scatterers.
5.2 RangeModulationTechniques
When looking at the depth–dose curve of a mono-energetic proton beam, it
is obvious that the Bragg peak is too sharp to cover a target of any reason-
able size. By combining proton beams of decreasing energy, range modula-
tion transforms the pristine Bragg peak into a uniform depth–dose region
called the SOBP. Addition of Bragg peaks shifted in depth and weighted
131 Beam Delivery Using Passive Scattering
appropriately yields a uniform dose. Depending on the size of the target to
be covered, the extent of the uniform region can be adjusted by changing the
number of added peaks (Figure 5.3). Several range modulation techniques are
applied in proton therapy: energy stacking, range modulator (RM) wheels,
and ridge flters. After exploring some of the general principles of range mod-
ulation and SOBP construction, we discuss each of these techniques in detail.
5.2.1 Range Modulation Principles
Using a power-law approximation of proton stopping power, it is possible to
analytically describe the Bragg peaks and calculate the optimal weights for
an SOBP (16). In reality the shape of the Bragg peak is complex and depends
on the energy spread and scattering properties of the delivery system.
Measured Bragg curves are used and the weights are determined numeri-
cally using simple optimization algorithm (17–19). Mathematically the prob-
lem can be described as follows:

SOBP(R, d) PP(R , d),
i
= ⋅
=
∑
w
i
i
N
1
(5.3)
5
50
7%7%7%8%8%9%10%
11%
12%
13%
15%
17%
20%
25%
36%
85%
16 peaks: full mod, 95% skin dose
12 peaks: 7.6 cm mod, 79% skin dose
8 peaks: 4.8 cm mod, 65% skin dose
4 peaks: 2.1 cm mod, 47% skin dose
sigma = 3%
sigma = 2%
sigma = 4%
Maximal uniformity
Smallest fall-off
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
100
90
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
100
50
100
10
A B
C D
5 10
5
Depth [g/cm
2
] Depth [g/cm
2
]
10 8 10
103%
FIGURE 5.3
Creation of the SOBP with a range of 10 g/cm
2
. (A) Subplot of the weights of the pristine peaks
when creating a full modulation SOBP. (B) Subplot of the SOBP of various modulation width
are shown. (C) Subplot of the effect of a change in pristine peak energy spread on the SOBP.
(D) Subplot of the alternative methods of optimization at the distal end of the SOBP are shown.
132 Proton Therapy Physics
where PP(R
i
, d) is the pristine peak depth–dose curve with range R
i
, w
i
is
the relative contribution of peak i to the SOBP given by the ratio between
the maximum dose in the peak and the SOBP plateau dose, N is the number
of peaks summed, and SOBP(R, d) is the resulting spread-out depth–dose
curve with range R. The weights w
i
are optimized, minimizing the differ-
ence between SOBP(R, d) and an ideal, presumably uniform, dose distribu-
tion. Figure 5.3A shows the optimization of an SOBP with a range of 10 g/cm
2

and full dose up to skin. The range shift between the pristine peaks is fxed
at 6 mm, and 16 pristine peaks are required to obtain a full skin dose. The
peak weights drop exponentially from 85% of the plateau dose for the distal
layer, to 36% for the second layer, down to 7% for the most proximal layers.
The increasing contribution of dose from the more distal layers reduces the
dose required for more proximal layers to reach the plateau. The extent of
the uniform dose region can be varied by changing the number of pristine
peaks delivered. Figure 5.3B shows the SOBP when the distal 12, 8, or 4 lay-
ers are delivered, resulting in a 90%–90% modulation width of 7.6, 4.8, and
2.1 g/cm
2
.
All peaks add dose to the skin. The distal peaks have a small skin dose
due to the rising shape of the Bragg curve but have a large weight. Proximal
peaks have larger skin-to-peak dose ratio, but their contribution to the SOBP
is less. These competing effects result in a relationship between modulation
width and skin dose that is not far from linear. The skin dose also depends
on the SOBP range decreasing with increasing range.
Although the range of the individual pristine peaks can be made a variable
in the SOBP optimization process, good results are obtained by keeping the
range shift (pullback) between the peaks constant and setting it equal to the
80% width of the individual peaks (11). A larger pullback between the peaks
results in a ripple in the dose distribution, but a smaller pullback does not
improve uniformity. In Figure 5.3C the SOBP is shown when the width of
the peaks is set to 5 or 7 mm, but the pullback is kept at 6 mm. The sharper
peaks generate a strong ripple in the SOBP, whereas the wider peaks do not
change the uniformity of the plateau, they just deteriorate the sharpness of
the corners. It is interesting to consider that we have not reoptimized the
weights here. The sharper peaks generate a ripple but not a tilt in the pla-
teau, suggesting that the weights are still optimal. This effect has also been
observed experimentally when changing the energy spread of the proton
beam entering the nozzle (20).
A choice needs to be made at the distal end of the SOBP when optimizing
the weights. One can either make the dose as fat as possible or make the
distal falloff as sharp as possible (Figure 5.3D). If the extent of the desired
uniform dose region is limited to a point halfway between the distal two
peaks, the dose distribution can be made completely fat, but the distal dose
falloff exhibits a fairly large shoulder and distal falloff. The falloff can be
made sharper by increasing the weight of the distal peak while decreasing
the weight of the second peak. The resulting dose distribution acquires a hot
133 Beam Delivery Using Passive Scattering
spot at the distal end of the uniform region and a cold spot more proximally.
For the SOBP in Figure 5.3D the 95%–20% distal falloff is decreased from 6.8
to 5.5 mm when limiting the hot spot to 103%. An additional consideration
here is the biological effect. Several studies have shown that the radiologi-
cal bioeffectiveness (RBE) increases in the shoulder and distal falloff of the
SOBP (see Chapter 19). Optimizing for the sharpest falloff might result in
even larger hot spots in biological effect. Whichever approach is taken, it
should be mimicked in the treatment-planning algorithm (21).
5.2.2 Energy Stacking
Changing the energy of the protons entering the nozzle is conceptually the
easiest method of range modulation because it requires no dedicated nozzle
elements. Between layers the energy is changed at the accelerator level, either
by changing the extracted synchrotron energy or the energy-selection system
setting at the exit of the cyclotron (Chapter 3). By accurately controlling the
number of protons delivered for a given energy, for example, by terminat-
ing the beam once a preset number of monitor units in the reference ioniza-
tion chamber is reached, the appropriate SOBP weighting is realized. A major
advantage of this form of range modulation is that the protons do not need to
interact with a range shifter inside the nozzle. Range-shifting material scatters
the protons increasing the lateral penumbra, straggles the protons increasing
the energy spread and distal falloff, and generates neutrons  (22). However,
energy stacking with range shifting upstream is not applied in current clini-
cal scattering systems. The frst reason for this is the technological challenge
of quickly switching energy between layers. Not only the accelerator energy
needs to change, but also the beam transport magnets need to be adjusted
to account for the change in proton energy of protons transported into the
room. Current (cyclotron-based) systems have diffculty switching the energy
in less than about 5 s. For a feld with a modulation width of 10 g/cm
2
deliv-
ered in 16 layers, the switching overhead would be more than a minute. (In
pencil beam scanning [Chapter 6], range shifting in the nozzle is not a viable
alternative because of beam spot size requirements. So, it looks like there is no
escaping this challenge.) The second issue with energy stacking is the poten-
tial of interplay effects with organ motion (Chapter 14). Dose uniformity is
only achieved if every point in the SOBP gets exactly the contribution from
each of the pristine peaks as determined during optimization. Intrafraction
motion can cause the depth of a voxel to vary over time. (Note that the depth
can change when the voxel itself moves with respect to upstream nonhomo-
geneous target tissue, including range compensator, or when upstream tissue
moves with respect to the stationary voxel.) If the depth of a voxel changes
between two energy layers contributing to that voxel, the dose contribution of
each of the pristine peaks will no longer match the optimized layer weight-
ing. Hot and cold spots in the depth–dose curve will be the result of motion-
induced depth changes during energy stacking.
134 Proton Therapy Physics
The problem of changing accelerator energy and beam-transport set-
tings can be avoided by applying range shifting inside the nozzle, although
the issue of interplay effects remains. The accelerator energy is set to the
appropriate energy for the distal pristine peak. After delivering the dose for
the distal layer, an absorber with a water equivalent thickness equal to the
desired pullback is inserted in the beam path, and the next layer is delivered.
The absorber thickness is increased sequentially while stepping through the
energy layers. Low-Z materials, such as plastic or water, are the preferred
range-shifter materials because they provide the least amount of scattering
per unit of range shift. Several types of variable range shifters have been
implemented, including a variable water column that uses a moveable piston
to accurately adjust the amount of water in a cylinder, a binary set of plastic
plates that can be moved independently into the beam path, and a double-
wedge variable absorber (23). Like the upstream method, energy stacking in
the nozzle also is not used much in clinical scattering systems.
5.2.3 RM Wheels
In his original article on proton therapy, Wilson proposed an RM wheel as a
method to spread the dose: “This can easily be accomplished by interposing
a rotating wheel of variable thickness, corresponding to the tumor thickness,
between the source and the patient” (24). Koehler, Schneider, and Sisterson
were the frst to report implementation of an RM wheel (25). The RM wheel
has been and continues to be the method of range modulation in most clini-
cal proton-scattering systems.
An RM wheel has steps of varying thickness, each step corresponding to a
pristine peak in the SOBP. When the wheel rotates in the beam, the steps are
sequentially irradiated. The thickness of a step determines the range shift of
that pristine peak; the angular width of the step determines the number of
protons hitting the step, and thus the weight of the pristine peak. By progres-
sively increasing the step thickness while making the angular width smaller,
a fat SOBP can be constructed. Like the range shifters used in energy stack-
ing, modulator wheels are preferentially made of low-Z materials to limit
scattering. Plastics (Plexiglas, Lexan) are often used, but for wheels that need
to provide large range shifts and that are mounted in nozzles where space is
limited, carbon (26) and aluminum (27) have been applied.
Figure 5.4 shows a range modulator used at the Harvard Cyclotron
Laboratory. Symmetrically cut fan-shaped sheets of Plexiglas are stacked
together, repeating the modulation pattern four times per wheel revolu-
tion. Because the wheel is mounted close to the patient where the beam is
already spread out, the dimension of the wheel is relatively large (~85-cm
diameter). The size of the RM wheel can be made smaller by moving it fur-
ther upstream. A smaller RM wheel allows higher rotational speeds and for
easier, even automatic, exchange of wheels. Figure 5.5 shows an example of
such an “upstream propeller” from the Ion Beam Application (IBA) universal
135 Beam Delivery Using Passive Scattering
nozzle (26). It is located 2.8 m from isocenter where the size of the beam is
in the order of 8-mm FWHM (full-width at half-maximum). Here the range
modulator pattern can be made small enough that three separate 3-cm range
modulator tracks are combined on one 34-cm-diameter wheel. On this wheel
the range modulation pattern is not repeated. The high rotational speed
(10 Hz) requires that the wheel is accurately balanced, and counterweights
FIGURE 5.4
Range modulator wheel used at the Harvard Cyclotron Laboratory. (Courtesy of B. Gottschalk.)
FIGURE 5.5
Range modulator wheel combining three range modulation tracks as installed in the IBA uni-
versal nozzle. (Note that the outer track is used in range shifting for uniform scanning.)
136 Proton Therapy Physics
are mounted on the outside of the wheel to compensate the uneven weight
distribution in the tracks. (Note that the angular width of the steps in the
outer track is constant. This track is used as a variable range shifter with
the wheel in stationary position when energy stacking in uniform scanning
mode.)
The drawback of an upstream propeller is a larger dependence on energy.
The steps of an RM wheel are optimized to give a fat dose distribution for
a specifc energy. When the incident energy (i.e., the range of the SOBP) is
changed, the weights are no longer optimal, and the SOBP no longer fat.
The main reason for the change in SOBP is the change in scattering power of
the RM wheel steps with energy. (Change in energy spread and source-to-
skin distance [SSD] also play a role but are less important.) Combined with
the large drift distance to the isocenter, small changes in range modulator
scattering power can cause large changes in fuence at the isocenter. When
the energy of the proton beam increases, the scattering in the RM steps will
decrease. For the thinnest step the scattering in the RM wheel will not con-
tribute much to the total spread at the isocenter, which is dominated by scat-
tering in other nozzle elements (such as the second scatterer) and the target.
With increasing step thickness, range modulator scattering will contribute
progressively more to the spread at the isocenter. A change in scattering
power will affect the spread of the proximal layers more than the distal lay-
ers. Consequently, the increase in fuence on the beam axis associated with
the decreased spread will be larger for the thicker than for the thinner steps.
The increased relative weight of the proximal layers tilts the SOBP, which
acquires a negative slope. The spread of the beam at the isocenter is not only
proportional to the scattering angle of the range modulator steps, but to the
drift space between range modulator and isocenter. For large downstream
propellers, the energy dependence is less because of the shorter drift space
between the RM wheel and the patient.
The way to avoid this problem is using a scatter-compensated RM wheel.
By combining a low-Z (plastic, carbon, aluminum) and a high-Z material
(lead, tungsten) each step is given the appropriate range shift but with con-
stant scattering power. Starting with only high-Z material for the thinnest
step, the thickness of high-Z is progressively reduced, whereas the thick-
ness of low-Z material is increased for thicker steps. As with the energy-
compensated contoured scatterer the scatter-compensated RM wheel has
larger water equivalent thickness than an uncompensated wheel.
Even with scatter compensation an upstream RM wheel is useable within
a limited range span. The ability of cyclotrons to accurately and quickly vary
the beam current (by manipulating the ion source current) allows for a further
extension of the range over which an RM wheel can be used. By changing
the beam current as function of RM wheel position, the number of protons
hitting a step can be adjusted, and the intrinsic weight of the step, defned by
its angular width, can be adjusted (28). Figure 5.6 shows how an SOBP with a
negative slope (~1.3%/cm) is made fat by a beam current modulation profle
137 Beam Delivery Using Passive Scattering
that decreases the beam current by a factor of 2 when moving from the thin
to the thick RM steps. Beam current modulation involves a complex feedback
control system that needs to be closely monitored during irradiation. Drifts in
ion source output, feedback ionization chamber response, and RM wheel tim-
ings can cause large dose deviations (29).
We have seen that the range span an RM wheel can cover varies from a sin-
gle range for an upstream wheel that is not scatter-compensated and covers
a large modulation, up to a signifcant range span for a scatter-compensated
wheel with beam current modulation. How many different modulation
widths can an RM wheel deliver? The thickest step determines the maxi-
mum shift in range between the most distal and proximal Bragg peaks and
defnes the maximum modulation width of a wheel. If the whole track is irra-
diated, the maximum modulation width is always delivered, and a library of
0
30
40
50
60
70
80
20 40 60 80
Time (ms)
C
u
r
r
e
n
t

i
n
t
e
n
s
i
t
y

(
%
)
100
(a)
(b)
0
86
88
90
92
94
D
o
s
e

(
%
)
96
98
100
102
104
106
108
110
No beam current
modulation
Optimized BCM
measured
Optimized BCM
calculated
2 4 6 8
Depth (cm)
10 12 14 16
FIGURE 5.6
By varying the beam current (top) synchronized with the RM wheel position a tilted SOBP
can be made fat (bottom). (Reproduced from Lu and Kooy, Med. Phys., 33, 1281, 2006. With
permission.)
138 Proton Therapy Physics
wheels is required to cover different target sizes. Alternatively the beam can
be turned on and off (gated) synchronized with wheel position. Every wheel
revolution the beam is turned on at the frst step and off at the step corre-
sponding to the most proximal layer needed to cover the target. By varying
the number of steps irradiated the modulation width can be varied, up to the
maximum modulation width for which a wheel is designed when all steps
are irradiated. Modulation width control using beam gating is applied in
both cyclotron and synchrotron systems. In cyclotron systems beam gating
is performed by cutting the ion source current (26) and in synchrotron sys-
tems by turning off the extraction RF power (30). Instead of switching on and
off the beam, a block can be used to cover the part of the modulator wheel
that should not be irradiated. Figure 5.7 shows an example of two modulator
blocks from an ocular scattering system. The same blocks can be used on
different RM wheels and each wheel-block combination corresponds to a
specifc range and modulation width. The limited overall range and modula-
tion span required for eye treatments result in a manageable wheel and block
library.
For every revolution of the RM wheel the SOBP is delivered. If the rotational
speed is high enough, the delivery can be considered quasi-instantaneous,
and the issues related to interplay effects with organ motion disappear.
Typical rotational speeds of 6–10 Hz are larger than organ motion frequen-
cies. Repetition of the range modulation pattern as seen before (Figure 5.4)
increases the frequency of SOBP delivery even more. Synchrotron systems
have an additional speed requirement because the beam spill structure is
generally not synchronized with the wheel rotation. The start and end of
each spill occur at random wheel positions (within the gating window).
Enough complete SOBPs need to be delivered per beam spill to avoid unac-
ceptable perturbations by partial SOBPs delivered at the start and end of
each spill (23). The dose variation, ε, for a wheel with n repetitions spinning
FIGURE 5.7
Two modulator wheel blocks (left) determining the modulation width for an RM wheel (right)
in the IBA eyeline.
139 Beam Delivery Using Passive Scattering
at f Hz in a beam with a spill time of τ s, is equal to 1/(nfτ) (23). Limiting the
dose variation to 1% for a rotational speed of 10 Hz and a spill time of 2.5 s
requires four repetitions.
Making the range modulation pattern smaller, by moving the wheel
upstream and repeating the pattern, will start to affect the delivered dose dis-
tribution once the size of the steps becomes smaller than the beam spot (31).
When the beam is gated, the beam spot not only covers the gating step but
spills onto neighboring steps. The steps thicker than the gating step receive
some protons, and thinner steps receive less than their full weight, resulting
in a softening of the shoulder at the proximal end of the uniform region.
Figure 5.8 shows the effect of “partial shining” for a RM wheel designed for
a range of 15 g/cm
2
and full modulation width (30 steps). The track radius
is 12.5 cm, and the beam spot is Gaussian with a sigma of 0.7 cm. The beam
is gated on step 20, which has an arc length of 1.1 cm when there is no rep-
etition. Repeating the pattern one, four, or six times reduces the extent of
the 100% dose region by 0.2, 1.8, or 2.8 cm compared to an infnitesimally
small beam. Note that proximal to the 90% dose level the dose hardly varies
and that the integral dose decreases. This can be explained by the fact that
although the protons not delivered on the thinner steps are all delivered on
the thicker steps, these steps contribute less dose because they are pulled
back and deposit more dose in the RM wheel.
no spread
1 repetition
4 repetitions
6 repetitions
5
0.8
0.9
1
10
Depth [g/cm
2
]
R
e
l
a
t
i
v
e

d
o
s
e

[
-
]
FIGURE 5.8
The effect of the beam spilling onto multiple steps of the RM wheel when it is gated off.
Proximal region of the SOBP is shown for an infnitesimal small beam and for a beam with a
7-mm sigma and one, four, or six repetitions of the modulation pattern on a 25-cm-diameter
wheel.
140 Proton Therapy Physics
5.2.4 Ridge Filters
Ridge flters have been applied in proton therapy for at least as long as modu-
lator wheels (32, 33), and although less wide spread than RM wheels, they
are used in several clinical scattering systems today (34–36). The principle of
the ridge flter is the same as the modulator wheel: the thickness of the ridge
flter steps determines the pullback of the peaks, and the width of the steps
sets the weight of the peaks. Figure 5.9 shows a ridge flter designed for a
modulation width of 6 cm. Protons hitting the tip of the ridge will form the
most proximal peak in the SOBP; protons passing outside the ridge will form
the distal peak. The thickness and width of steps in-between is optimized
to provide a fat SOBP. The energy lost depends on the location where the
protons hit the flter. To avoid a dependence of the SOBP shape on lateral
position, the ridge is made small enough that the incident proton angular
diffusion and scattering in the ridge flter smooth out any positional depen-
dence. In the optimization of the ridge shape the scattering can be taken
into account (37, 38). The width of the ridges is typically 5 mm in systems
that have the ridge flter downstream of the second scatterer. By arranging
many bar-shape ridges in parallel, a large beam area can be covered. Spiral
ridge flters rely on the same principles as bar ridge flters, but the ridges are
arranged in a circular pattern (39).
Manufacturing constraints need to be taken into account when design-
ing ridge flters. The total height needs to be limited to avoid ridges that are
too sharp to be accurately machined. This limits the maximum modulation
width that can be achieved. Traditionally ridge flters are made of high-Z
materials, like brass, that can be machined accurately. The large stopping
power of brass limits the height and gradient of the ridges, but its scattering
power has a negative effect on the lateral penumbra. With improvement of
machining technology, lower-Z materials like aluminum (37) and even plas-
tics have been used.
A B
0
0.25 0.25 0
Ridge base (cm)
0.5
H
e
i
g
h
t

o
f

r
i
d
g
e

(
c
m
)
1.0
1.5
2.0
2.5
FIGURE 5.9
(A) Bar ridge flter designed to modulate the beam to a 6-cm SOBP. (B) The cross section of a
ridge. (Reproduced from Akagi et al., Phys. Med. Biol., 48, N301, 2003. With permission.)
141 Beam Delivery Using Passive Scattering
As we have seen, energy stacking delivers the pristine peaks sequen-
tially in time. Spinning modulator wheels deliver them sequentially as
well, but are repeated every cycle of the wheel, delivering the SOBP quasi-
instantaneously. The ridge flter delivers all pristine peaks at the same time,
making SOBP delivery truly instantaneous. This makes ridge flters suitable
for range modulation in systems in which the beam itself has a time struc-
ture, like synchrotron-based scattering systems with a pulsed beam of low
duty cycle or uniform scanning systems in which the beam is scanned over
a ridge flter (40, 41).
The main drawback of ridge flters is the fact that they can only be used
for a single modulation width. A possible solution is tilting the bar ridge
flter (41 and references within). Rotating the ridge flter θ degrees in the
plane of the beam axis and the long axis of the ridges increases the thick-
ness of all ridge steps by 1/cos(θ). Unlike the gated modulator wheel that
increases modulation by adding more pristine peaks, the tilted ridge flter
keeps the same number of peaks but increases the pullback between the
peaks. The number of steps in the ridge needs to be large enough to avoid
a ripple in the SOBP at maximum tilt. Feasibility has been shown experi-
mentally for a ridge flter increasing modulation width from 10 to 14.5 cm
when tilting 45° (41).
The miniature ridge flter is designed to be used in combination with
energy stacking (42). It spreads the mono-energetic Bragg peak into a
wider peak; energy stacking combines multiple range-shifted wide peaks
into an SOBP. In this hybrid delivery technique the number of energy lay-
ers is reduced compared to pure energy stacking. The delivery effciency
is increased, whereas interplay effects with respect to organ motion are
reduced. The modulation width can be varied although with a worse resolu-
tion than can be obtained with pure energy stacking or gated RM wheels. On
the downside, the broadening of the peaks deteriorates the distal falloff of the
SOBP. In another method of combining the ridge flter and energy stacking,
the miniature ridge flter is used to combine the distal pristine peaks into a
small-modulation SOBP width, and energy stacking is used to vary the mod-
ulation by adding mono-energetic pristine peaks proximally (N. Schreuder
and G. Mathot, private communication, December 2010). Application of these
forms of range modulation has only been reported in uniform scanning sys-
tems, but could in principle be applied in scattering systems as well. A min-
iature ridge flter can also extend the energy range over which a ridge flter
can be applied (43). If the beam energy is decreased below the energy for
which a ridge flter is designed, the width of the peaks will become sharper
(specifcally for synchrotron systems that have a small energy spread at low
energies), the pullback between peaks is no longer optimal, and a ripple
appears in the SOBP. To counter the sharpening of the peaks, a miniature
ripple flter increases the energy spread of the protons and widens the peaks.
A library of a few ridge flters and mini-ridge flters can cover the complete
clinical range span.
142 Proton Therapy Physics
5.3 ConformingTechniques
The second scatterer spreads the beam to a uniform lateral distribution; the
RM wheel spreads the dose to a uniform depth–dose distribution. Clearly
something is needed to conform the dose to the target. As in conventional
external radiotherapy, a block, called an aperture in proton therapy, shapes
the dose laterally. Alternatively, a multileaf collimator (MLC) can be used.
Unlike conventional radiotherapy, the sharp distal falloff of the proton beam
allows conforming the beam to the distal end of the target. A range compen-
sator is designed to perform this function.
5.3.1 Aperture
The shape of the aperture is defned by the shape of the target projected
along the beam axis with added margins accounting for penumbra width
and setup uncertainty. Because of the large geometric source size of a proton-
scattering system, it is important to bring the aperture close to the patient.
Large air gaps infate the lateral penumbra undesirably. The aperture and
range compensator are mounted together on a snout. The snout travels along
the beam axis and brings the aperture close to patient skin. Based on the
snout position, the virtual source-to-axis distance (SAD) of the scattering
system, and the projection of the target onto the isocenter plane, a simple
back projection gives the physical shape of the aperture.
The primary physical consideration in selecting aperture material is stop-
ping power. High-Z materials are the obvious choice as they stop the protons
in the shortest physical distance. From a practical point of view we want a
material that can be manufactured easily and cheaply. The two materials that
are commonly used are brass and cerrobend. Brass apertures are cut with a
milling machine; cerroband apertures are poured into a mold. It should be
pointed out that such an aperture will completely stop the beam. Because of
the fnite range of the protons the chance is zero that a primary proton will
traverse the complete aperture. Unlike x-ray therapy, leakage of primary pro-
tons through the aperture does not exist. This does not mean that all protons
hitting the aperture will be absorbed. Protons hitting the upstream face close
to the aperture opening can escape through the inner surface of the opening;
protons hitting the inner surface can scatter out of the aperture through the
inner surface or escape through the downstream face. These slit-scattered
protons perturb the dose distribution specifcally at shallow depth and near
the feld boundary (44, 45).
The aperture and snout are the largest contributors of neutrons to the
patient (46) (see Chapter 18). Not only do they completely absorb high-
energy protons in material with a large cross section for neutron produc-
tion, they do it close to the patient. Several approaches to reduce neutrons
have been investigated. Changing the aperture material would not reduce
143 Beam Delivery Using Passive Scattering
the neutron dose dramatically. Stopping 235-MeV protons in nickel instead
of brass reduces the neutron dose by about 15% (47). A bigger reduction can
be obtained by using a precollimator, limiting the number of protons hitting
the aperture (47–49). A related radiation safety issue is the activation of the
apertures (50,  51). Activation levels are low enough to avoid special proce-
dures in the daily handling of the apertures by staff. For disposal of the aper-
tures, activation levels need to be below the background. Irradiation of brass
yields several isotopes with relevant activation and half-lives (
58
Co − T
1/2
=
71 d,
57
Co − T
1/2
= 271 d). In typical clinical practice apertures are stored for
about two weeks when activation has reached background levels.
5.3.2 Multileaf Collimator
In conventional radiotherapy the MLC has become the standard feld-
shaping device. Perhaps surprisingly MLCs are currently not applied much
in proton therapy. The vast majority of proton treatments today use custom-
made apertures. A possible explanation might be that scattering systems
with their apertures and range compensators are expected to be replaced
by pencil beam scanning systems that do not need feld-shaping hardware
(Chapter 6). Implementation of an MLC could be seen as an unnecessary
intermediate step. Related is the fact that even if an MLC replaces the aper-
ture block, the feld-specifc range compensators still need to be manufac-
tured and installed in-between treatment felds. Still, the MLC is receiving
more attention of late, and several centers have successfully implemented an
MLC in their proton-scattering system (9; McDonough J., private communi-
cation, December 2010).
The main issues when considering an MLC for proton therapy are not
different from conventional radiotherapy: penumbra and conformity, leak-
age, neutron production, and activation. An additional concern is clearance:
given the large source size of many proton-scattering systems, it is important
to bring the fnal collimator as close as possible to the patient, which might
be diffcult with bulky MLCs.
In collaboration with Varian, the University of Pennsylvania has developed
a proton MLC to be used with their IBA universal nozzle (McDonough J., pri-
vate communication, December 2010). It consists of two banks of 50 tungsten
leaves. Leaf width is 4.4 mm; leaf height 6 cm. The parallel and abutting sides
have steps of 0.45 and 0.30 mm, respectively, to limit leakage. For a 30-cm
snout position the maximum projected opening is 25 × 18 cm
2
. Preliminary
results show that the scalloping effect of the leaves on the dose distribution
is clinically acceptable. Multiple scattering of the protons in the target smear
out the leaf effects with depth. Although tungsten has a higher neutron yield
than brass, maximum neutron dose levels for a 230-MeV proton beam are
about 20% lower for the MLC compared to a 6.5-cm brass aperture. This is
presumably because of the self-shielding effect of the additional tungsten
on top of the 3.5 cm required to stop a 230-MeV proton beam (about 6-cm
144 Proton Therapy Physics
brass is required). This self-shielding also limits the measured activation
on the downstream face to levels far below regulatory limits. In addition to
the MLC a “range compensator loader” has been installed that can hold up
to two compensators and eliminates the need to go into the room between
felds.
Massachusetts General Hospital has implemented a mini-MLC in its
radiosurgery beam line (9). Although this MLC was designed for stereotactic
treatments on a linear accelerator, it behaves well in the proton beam. For a
typical feld, agreement between an MLC-shaped and a custom aperture–
shaped feld is within 1.5 mm or 2%. The leakage dose is below the measure-
ment threshold (0.3%). The neutron dose for the MLC is 1.5–1.8 times higher
than for the brass aperture.
Alternative applications of the MLC in proton therapy have been consid-
ered. Tayama et al. have described the MLC as a precollimator to a custom-
made aperture (48). By reducing the proton fux onto the fnal aperture, the
neutron dose to the patient is signifcantly reduced. Bues et al. has proposed
the MLC as a method to sharpen the penumbra in low-energy, spot-scanning
treatments (52). Full-blown, intensity-modulated proton therapy (IMPT)
using MLCs, equivalent to intensity-modulated radiotherapy with photons,
might conceptually seem appealing. However, the large ineffciency of such
an approach, resulting in high neutron doses and activation, makes it hard
to see it as a reasonable alternative to IMPT using scanned proton pencil
beams (Chapter 6). On the other hand, the fexibility of the MLC can be used
to improve dose conformity compared to a single-aperture feld. In systems
that apply energy stacking to create the SOBP, the MLC opening can be opti-
mized per energy layer (53). Because each point of the target needs to get the
dose contributions of all upstream layers to achieve full dose, the collimator
opening for a layer can never be larger than the opening of the previous lay-
ers. The collimator can only be progressively closed while stepping from the
distal to the proximal layers. Improved proximal conformity will only be
achieved in convex targets.
5.3.3 Range Compensator
The range compensator conforms the dose to the distal end of the target.
Figure 5.10 shows a schematic representation of the application of range com-
pensation. The water-equivalent depth of the distal end of the target var-
ies with lateral position. It is a function of the shape of both external body
contour and target, as well as of the composition of the tissue in-between.
The range compensator is designed to remove the depth variation by adding
more absorbing material in areas where the depth is small and less where it is
large. For example, the energy loss in the high-density structure in Figure 5.10
is compensated for by removing more material from the compensator. It
is obvious that each treatment feld has a unique compensator. Designing
the range compensator is an important part of the treatment-planning
145 Beam Delivery Using Passive Scattering
process. Most algorithms use a ray-tracing algorithm to determine the water-
equivalent depth of selected points on the distal surface of the target (54–56).
The deepest point will determine the required proton range. For each of
the other points, the difference in depth with the deepest point determines
required pullback. The matrix of pullbacks is divided by the compensator’s
relative stopping power to obtain physical thickness. To accurately model the
effect of the real compensator, the milling pattern as described below can be
applied to the compensator model before the fnal dose calculation.
Correct compensation is only achieved if the range compensator is exactly
aligned to the geometry and heterogeneities for which it compensates.
Misalignment causes the dose to fall short, resulting in underdosage of the
target, and/or to overshoot, resulting in dose to normal tissue distal to the
target. Smearing is a geometrical operation applied to the range compensa-
tor to account for uncertainties (Chapter 10).
Ideally the range compensator provides pullback with as little scattering
as possible. Scattering decreases the compensator’s conforming ability and
generates undesirable cold and hot spots inside the target. Low-Z, high-
density materials give the least scattering per energy loss. Lucite and wax are
the two materials most commonly used. Proponents of wax favor it because
it is easier (faster) to mill, has lower cost, and can be recycled. Lucite users
value its transparency, which allows for visual screening for air pockets and
validation of the iso-height lines by placing it on a paper printout during
quality assurance. A standard milling machine mills the desired profle into
a blank compensator. Resolution needs to be weighed against speed when
selecting drill bit size and spacing. The smallest drill provides the best lateral
resolution in conforming the dose, but it takes the longest to drill. Because
of scattering there is a lower limit below which reduction of the drill bit
A
C
range
compensator
skin
target
high-density
heterogeneity
B
FIGURE 5.10
Schematic representation of the application of a range compensator that compensates for the
shape of the body entrance, the distal target shape, and inhomogeneities.
146 Proton Therapy Physics
size does not signifcantly improve conformity anymore. A typical drilling
pattern will use a 5-mm-diameter drill bit and a spacing of 5 mm. For such
a pattern, machining times (for Lucite) range from 10 min for a small brain
lesion, 45 min for a prostate, and up to 4 h for a 2-L sarcoma feld.
The tapering (angle) of the drill bit affects the magnitude of the dose per-
turbation created by large range compensator gradients (57). A gradient
in the range compensator will scatter more protons from the thick part to
the thin part than vice versa, creating a cold spot beyond the thicker part
and a hot spot beyond the thinner part. If the gradient is exactly parallel to
the beam axis the magnitude of the dose perturbation is maximal. When
irradiating a 4-cm-deep, 0.5-cm-diameter hole in acrylic with 160-MeV pro-
tons, ±20% dose perturbations are observed 1 cm downstream. By apply-
ing a tapered drill bit, the gradient becomes less steep, reducing the dose
perturbation to ±15%/±5% for a 1.5º/3º tapering, respectively. A 3º tapering
is common because it reduces the scattering to an acceptable level without
compromising the lateral resolution too much in most clinical situations.
An interesting approach to limit the compensator scattering perturba-
tions is the bi-material range compensator (58). By combining the low-Z
compensating material with a high-Z scattering material a compensator
can be designed with the desired range compensation pattern but also with
constant scattering power. (This is similar to the approach taken with the
scatter-compensated RM wheel described above.) The drawback of such
an approach, besides added complexity in design, fabrication, and quality
assurance, is that it increases the overall compensator thickness. As result a
bi-material compensator requires larger proton range and has worse lateral
penumbra because of increased scattering.
5.4 ScatteringSystems
In the previous sections we discussed the individual elements of passive
scattering systems. In this section we will focus on integrated scattering sys-
tems. The number of different scattering systems is almost as big as the num-
ber of proton therapy centers. This makes a general description of scattering
systems complicated. The approach taken here is to discuss a few represen-
tative scattering systems in more or less detail. We will describe the scat-
tering systems and refer to Gottschalk (11) for a detailed discussion of the
design methods and tools. First we will discuss several “general purpose”
scattering systems. These large-feld double-scattering systems can be seen
as the proton equivalent to the standard x-ray linear accelerators. They have
been designed to treat a large variety of target sizes and depths and are gan-
try mounted. Next we will discuss a single-scattering system that has been
designed to treat a specifc target, the eye. This system is mounted at the
147 Beam Delivery Using Passive Scattering
end of a fxed beam line. It should be emphasized that the choice of scatter-
ing systems discussed is purely based on their familiarity to the author and
availability in the literature, not on presumed superiority over other systems.
5.4.1 Large-Field Double-Scattering Systems
Table 5.1 gives an overview of three commercially available, turnkey proton
therapy systems that use double scattering on a gantry (26, 30, 59). Two of the
systems have a synchrotron, and the third a cyclotron. The three systems
are similar in design, all applying RM wheels to create the SOBP and a con-
toured second scatterer to fatten the lateral profle. The Optivus system has
the RM wheel downstream of the second scatterer, and both the Hitachi and
IBA systems have an upstream range modulator.
Figure 5.11 shows the layout of the IBA universal nozzle in detail. It is called
universal because it permits irradiations not only in double-scattering mode,
but also in single-scattering, uniform-scanning, and pencil beam–scanning
modes. The Hitachi nozzle, which has only the double-scattering delivery
mode, is shown in Figure 5.12.
The IBA nozzle uses two contoured scatterers to spread the beam to a uni-
form feld diameter of 24 cm for ranges from 4.6 to 23.9 g/cm
2
in water. The
amount of scattering material (frst and second scatterer) needed to scatter
the beam to this feld size reduces the maximum cyclotron range (~34 g/cm
2
)
signifcantly. To treat deeper seated targets a third, thinner second scatterer
is added that allows treatments up to 28.4 g/cm
2
depth, but with a limited
feld diameter of up to 14 cm. All three contoured scatterers are energy com-
pensated, combining Lexan and lead. They are mounted together on a large
wheel that is located 178 cm from the isocenter. Before the start of irradiation
TABLE 5.1
Commercially Available Turnkey Proton Therapy Systems with Double Scattering
Manufacturer Installations Accelerator
Range
Modulation
Lateral
Spreading
Optivus Loma Linda University
Medical Center (1991)
Synchrotron
(250MeV)
RM Wheel
Downstream
Contoured
scatterer
Ion Beam
Applications
Massachusetts General
Hospital (2001)
Wanjie Hospital, Wanjie, China
(2004)
University of Florida (2006)
National Cancer Center, Ilsan,
South Korea (2006)
University of Pennsylvania
(2009)
Institute Curie, Paris, France
(2010)
Cyclotron
(235MeV)
RM Wheel
Upstream
Contoured
scatterer
Hitachi M.D. Anderson Cancer Center
(2006)
Synchrotron
(250MeV)
RM Wheel
Upstream
Contoured
scatterer
148 Proton Therapy Physics
the appropriate scatterer is rotated into the beam path. The variable collima-
tors are set to block the beam outside the aperture opening. Unlike the IBA
nozzle that always spreads the beam to the maximum feld diameter, the
Hitachi nozzle has contoured scatterers optimized for different feld sizes.
By scattering the beam less for smaller targets the effciency of the system is
improved, increasing maximum dose rate and range and reducing produc-
tion of secondary neutrons in the nozzle. In addition, the lateral penumbra
is improved for small felds. The system provides three feld sizes: 25 × 25,
Range modulator wheels
Magnet 2
Jaws (X and Y)
(and range verifier)
Snout retraction area
Water phantom
Snout IC2 and IC3
Second scatterers
First
scatterers
Magnet 1
IC1
FIGURE 5.11
Schematic layout of the IBA universal nozzle. (Reproduced from Paganetti et al., Med. Phys.,
31, 2107, 2004. With permission.)
Beam
Profile Monitor
X-Ray Tube
Range
Shifters
Laser Marker
Block
Collimator
Square
Collimator
Multi Layer
Faraday Cup
Snout
Isocenter
Range
Modulation
Wheel
Second
Scatterers
Main Dose
Monitor
Sub Dose
Monitor
Reference Dose Monitor
FIGURE 5.12
Schematic layout of the Hitachi large-feld scattering nozzle. (Reproduced from Smith et al.,
Med. Phys., 36, 4068, 2009. With permission.)
149 Beam Delivery Using Passive Scattering
18 × 18, and 10 × 10 cm
2
. For each feld size, three second scatterers cover the
whole range span, resulting in a total of nine second scatterers. The maxi-
mum range for each of the feld sizes is 25.0, 28.5, and 32.4 g/cm
2
, respec-
tively. It is interesting to see that the maximum range for the 10 × 10-cm
2
feld
size is 4.0 g/cm
2
larger than the maximum range for the equivalent feld size
(
2 10 14 ⋅ =
-cm diameter) in the IBA nozzle. This is equal to the difference
in maximum accelerator range. (The synchrotron energy of 250 MeV corre-
sponds to a range in water of 38 g/cm
2
and the cyclotron energy of 235 MeV
to a range of 34 g/cm
2
.) The thickness of the scattering material required is
similar because of the similar position of the scattering elements inside both
nozzles.
The Hitachi system extracts eight energies from the synchrotron. An RM
wheel has been designed for each of the 24 energy and feld-size combina-
tions. The steps of the RM wheel are scatter compensated resulting in a con-
stant scattering power over the steps. As range-shifting material plastic or
aluminum is used and for scattering compensation tungsten. The wheel not
only acts as a modulator, but also as the frst scatterer in the double- scattering
system. Additional tungsten is added to provide, combined with the sec-
ond scatterer, the desired uniform feld size at the isocenter. The fne range
adjustment in the Hitachi nozzle is done with a variable range shifter located
downstream of the second scatterer. In the IBA nozzle the range adjustment
is done by changing the energy of the protons entering the nozzle (using
the energy-selection system at the exit of the cyclotron). As a result the RM
wheels are not used at a single energy, but for a range of energies. As the
beam energy increases the scattering power of both the RM wheel and sec-
ond scatterer decreases, resulting in a nonfat lateral profle at the isocenter.
This can be compensated for by adding additional scattering material to the
frst scatterer. In the IBA nozzle adjustment of scattering is done by the fxed
scatterer, a binary set of lead foils that can be inserted independently into
the beam path and that is located upstream of the RM wheel. The RM wheel
and frst scatterer combine to form a frst scatterer with variable scattering
power. The RM steps are scatter compensated, limiting the effect of change
in scattering power on the pristine peak weights and increasing the range of
energies over which a fat depth–dose curve is generated. Still, an RM wheel
track can only be used for a range span of 0.4 g/cm
2
for the lowest ranges and
up to 2.0 g/cm
2
for the highest ranges. By applying beam current modula-
tion, adjusting the beam current as a function of modulator wheel position,
the number of modulator wheels can be limited. A total of fve modulator
wheel tracks covers the complete energy range. Unlike the Hitachi system
where the RM wheels are loaded manually, the IBA nozzle has an auto-
mated system. Three range modulator tracks are combined on a single wheel
(Figure 5.5), and three wheels are mounted on a large wheel whose position
determines which track is in the beam path. (The four remaining tracks are
used in single scattering and uniform scanning.) Because the cyclotron gen-
erates a continuous beam, the speed requirements are not very stringent for
150 Proton Therapy Physics
the IBA RM wheels. They spin at 600 rpm, and the modulation pattern is not
repeated. The Hitachi RM wheels spin at 400 rpm, and the modulation pat-
tern is repeated six times per revolution, washing out the effects of the beam
pulse structure on the SOBP shape. In both systems the beam’s turning on
and off is synchronized with the wheel rotation, allowing for variation of the
modulation width. The repetition of the pattern on the Hitachi wheel causes
more beam spilling over the steps and a softer shoulder on the proximal side
of the SOBP compared to the single pattern of the IBA track.
Both nozzles have ionization chambers at the entrance and exit of the noz-
zle to monitor the beam properties and terminate the beam once the pre-
scribed dose has been reached. A snout that can move along the beam axis
holds the aperture and range compensator and collimates the beam outside
the aperture. Both systems have a library of three snouts. Depending on the
feld size, the appropriate snout is installed before treatment.
The dosimetric properties of the delivery system depend mostly on the
design of the scattering system. Figure 5.13 shows the virtual SAD of the IBA
nozzle, determined by back-projecting the 50% feld width in air as mea-
sured in several planes along the beam axis. For all ranges the source posi-
tion falls between the range modulator (270 cm) and the second scatterer
(178 cm) as expected. For options that use the same second scatterer, the SAD
increases continuously with range. Given all that has been said before, it is
not that diffcult to explain the observed behavior. The scattering power of
the second scatterer decreases as the range increases. To compensate, the
scattering power of the frst scatterer is increased either by adding additional
scattering material to the RM wheel (between options) or by increasing the
fxed scatterer thickness (within an option). (An option is a combination of
10
220
240
V
i
r
t
u
a
l

S
A
D

[
c
m
]
260
SS1
SS2
SS3
20
Range [g/cm
2
]
30
FIGURE 5.13
Virtual SAD as function of range in patient for the double-scattering options of the IBA uni-
versal nozzle.
151 Beam Delivery Using Passive Scattering
an RM wheel track and second scatterer.) The increased scattering power of
the frst scatterer pulls the source toward it, increasing the SAD. The small-
feld second scatterer is thinner than the two large-feld second scatterers,
resulting in a source position closer to the frst scatterer and a larger SAD.
Figure  5.14 shows the source size as function of range. The source size is
determined by measuring the lateral penumbra in air at several distances
from a square aperture. The measured 80%–20% penumbra is back-projected
to a nominal source position of 230 cm. The source size of the large-feld
options (options 1–7) is signifcantly smaller than the small-feld option
(option 8). The additional scattering to spread the beam to a larger diameter
increases the angular confusion of the beam. Within the large-feld options
the source size decreases continuously with range.
5.4.2 Single-Scattering System for Eye Treatments
Ocular tumors have been successfully treated with protons for decades. Most
eye lines spread the beam with single scattering (2, 4, 5, 7, 8) or an occlud-
ing beam stopper (3, 6), although contoured second scatterers (30) have been
applied as well. Figure 5.15 shows the IBA eye line whose design is based
on the eye line at the Centre de Protonthérapie Orsay in France. The beam is
brought into the room at a fxed energy of 105 MeV. After passing through a
beam monitor, the protons hit the RM wheel spinning at 1200 rpm. The RM
wheels are not scatter-compensated and can be used within a very small
range span (0.2–0.4 g/cm
2
). Eleven wheels are required to cover ranges from
0.3 to 3.4 g/cm
2
. The wheels are designed for full modulation, and blocks are
used to vary the modulation width (Figure 5.7). The blocks are made of brass
2
10 20 30
4
S
o
u
r
c
e

s
i
z
e

[
c
m
]
Range [g/cm
2
]
option 1 - step 1
option 2 - step 1
option 3 - step 1
option 4 - step 1
option 5 - step 1
option 6 - step 1
option 7 - step 1
option 8 - step 1
option 5 - steps 1, 6, 13
option 8 - steps 1, 3, 5
FIGURE 5.14
Effective source size as function of range in patient for the double-scattering options in the IBA
universal nozzle.
152 Proton Therapy Physics
and are 1.2 cm thick. Both the RM wheel and block are loaded manually.
Next the beam passes through a variable range shifter and scatterer system.
For a given range and feld size the appropriate Lucite range shifter plates
and lead scattering foils are selected. A brass collimator blocks the majority
of protons. The neutron shield downstream of the collimator is intended to
absorb most of the neutrons generated in this collimation. The virtual source
position of this system is located between the RM wheel and the variable
range shifter system where most of the scattering takes place. The resulting
SAD is about 150 cm. Because the distance between the RM wheel and vari-
able range shifter is small, the angular diffusion of the beam and thus the
effective source size are small. Given the large SAD and small source size,
the penumbra of this system is very sharp. The 80%–20% penumbra in air at
7 cm from the fnal aperture is 1.2 mm.
5.5 Conclusion
Proton-scattering systems have some major drawbacks compared to scan-
ning systems. The protons interact with the scattering and range modulation
material in the nozzle. They lose energy, decreasing the maximum pen-
etration depth of the beam, and gain angular diffusion, increasing lateral
penumbra. Nuclear interactions will cause activation and create unwanted
secondary particles such as neutrons. Apertures and range compensa-
tors need to be made for every treatment feld requiring an expensive and
labor-intensive fabrication and quality assurance process. In a state-of-the-
art proton scanning system no feld-specifc hardware is required, and no
Vacuum
window
105 MeV
protons
Ionization
chambers
Collimator &
neutron shield
Aperture
Variable
range
shifter
Range
modulator
wheel
Fixed
range
shifter
180 cm
FIGURE 5.15
Schematic representation of the IBA eye line that applies single scattering to spread the beam.
153 Beam Delivery Using Passive Scattering
interaction of the proton beam with nozzle material occurs. Depending on
the size and shape of the target, a scanning system also allows for better dose
conformity, reducing the integral nontarget dose. Still, the vast majority of
proton therapy treatments worldwide has been and continues to be delivered
with scattering systems (60). The main reason for this is the robustness of typi-
cal scattering systems. As long as the correct nozzle elements are placed in
the beam path (either stationary or rotating), the delivered dose will be cor-
rect. No sophisticated beam control and feedback systems are required as in
a pencil beam–scanning system. Also the dose delivery itself is more robust
in that it is less sensitive to organ motion. In a scattering delivery the whole
target will be irradiated (quasi) instantaneously; in a scanning delivery, dif-
ferent parts of the target will be irradiated sequentially. With the develop-
ment and implementation of more scanning-based proton therapy systems in
the coming years, it will become clear if scanning will become the prevalent
mode of delivery or if scattering will remain the dominant technology.
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157
6
Particle Beam Scanning
JacobFlanz
CONTENTS
6.1 Introduction ................................................................................................ 158
6.1.1 General Description of Scanning ................................................ 159
6.1.2 Limits of Scanning Implementations .......................................... 160
6.1.3 Safety ............................................................................................... 162
6.2 Parameters That Affect the Beam and Dose Delivery .......................... 162
6.2.1 Static Beam Parameters ................................................................. 162
6.2.1.1 Depth–Dose Distribution ............................................... 162
6.2.1.2 Transverse Dose Distribution and Modulation .......... 163
6.2.2 Motion Beam Parameters.............................................................. 167
6.2.2.1 Motion Effects .................................................................. 167
6.3 Time Sequence of Beam Scanning Tasks ................................................ 169
6.3.1 Scanning Techniques .................................................................... 170
6.3.2 Contributions to Time ................................................................... 172
6.4 Scanning Hardware .................................................................................. 174
6.4.1 Adjust the Beam Properties .......................................................... 175
6.4.1.1 Energy ............................................................................... 175
6.4.1.2 Size .................................................................................... 175
6.4.1.3 Position on the Target ..................................................... 176
6.4.1.4 Scan Patterns .................................................................... 177
6.4.2 Dose Rate......................................................................................... 177
6.5 Scanning Instrumentation and Calibration ........................................... 177
6.5.1 Calibration ...................................................................................... 178
6.5.2 Calibration of the Beam Position at the Isocenter ..................... 178
6.5.3 Calibration of the Beam Size at the Isocenter ............................ 179
6.5.4 Calibration of the Dose Delivery at the Isocenter ..................... 179
6.5.5 On-line Verifcation of Beam Position ......................................... 180
6.5.6 Beam Steering Corrections ........................................................... 180
6.6 Scanning Gantries ..................................................................................... 181
6.7 Beam Property Quality Assurance (QA) ................................................ 183
6.8 Safety ........................................................................................................... 184
6.8.1 Safety Strategy ................................................................................ 185
6.8.2 Beyond Safety ................................................................................. 185
6.9 Summary ..................................................................................................... 187
158 Proton Therapy Physics
6.1 Introduction
The dimensions of a clinical target are typically different from the dimensions
of an unmodifed particle beam. The beam extracted and transported from
a typical accelerator will have dimensions on the order of millimeters and
will have a narrow energy spectrum that results in a narrow spread of ranges
in a target. Therefore that beam has to be spread out in three dimensions to
match the target volume. In this chapter the method of spreading called beam
scanning will be described. Beam scanning is quite a general technique, and
although it has acquired many acronyms such as PBS (particle beam scanning
or pencil beam scanning), IMPT (intensity-modulated proton therapy), and
SS (spot scanning), coming from specifc implementations of the technology
and limitations of accelerator beam properties. These acronyms only serve to
minimize the power and generality of this beam spreading approach.
Particle beam scanning (hereafter abbreviated as PBS) can be defned as
the act of moving a charged particle beam of particular properties and per-
haps changing one or more of the properties of that beam for the purpose
of spreading the dose deposited by a beam throughout the target volume.
Some examples (nonexhaustive) of these properties include position, size,
range, and intensity, which are all adjusted in such a way as to deposit the
appropriate dose at the correct location and time. Physical equipment in the
system is used to control these properties. For example, the beam position on
target can be controlled using magnetic felds or other mechanical motion
techniques. Other properties are modifed using other equipment. When a
beam penetrates the target, it delivers dose to the intercepting volume along
the beam trajectory. The goal of this beam delivery is to deliver dose accord-
ing to a prescription. This prescription provides a map of the dose that is
necessary to deliver at each region in the target. The beam parameters can
and should be able to change on a location-by-location basis; for example,
two locations can have different ranges or beam size.
In the transverse dimension, there are a variety of ways of moving the
beam across the target. Some of these methods include the following:
• Scanning by mechanical motions
• Physically moving the target with respect to a fxed beam position
• Mechanically moving a bending magnet to change the position
of the transported beam
• Using an adjustable collimator to effectively adjust the location/
region of the beam
Acknowledgments .............................................................................................. 188
References ............................................................................................................. 188
159 Particle Beam Scanning
• Scanning by magnetic feld variation to bend the beam trajectory
• Scanning an unmodifed beam (sometimes called a pencil beam)
• Scanning a slightly scattered beam, so that the beam scanned on
the target is a larger size. This is called “wobbling.”
• Combinations of the above
• Two-dimensional (2D) “ribbon” scanning of a beam wide in the
dimension perpendicular to the direction of motion, with the
beam extent adjusted by a variable collimator
• Scanning the beam magnetically in one dimension and moving
the target mechanically in the other dimension
• Other combinations are possible
In fact, the frst implementation of a scanning beam was demonstrated in
Japan using a novel system including a range modulator wheel to modu-
late the beam range while scanning the beam transversely with magnetic
dipoles (1). As implied by the above, the beam size used in scanning can be
varied. An unmodifed (nonscattered or tightly focused) beam is sometimes
called a pencil beam, although sometimes this term is used for a beam that
has a dimension on the order of a few millimeters. It is possible to obtain a
raw, unmodifed (unscattered and uncollimated) beam that is on the order
of several millimeters or even a centimeter, in which case, one can consider
using the term “crayon beam,” owing to the larger size. In any case, it is
more important to defne the terms and understand the regime being con-
sidered than to rely on ill-defned acronyms. The longest implementations of
the scanning modality have been ongoing at the Paul Scherrer Institute (PSI)
(2) and at the Gesellschaft fur Schwerionenforschung (GSI) (3). The most
recent implementations were in commercial and academic hospital collabo-
rations at the University of Texas MD Anderson Cancer Treatment Center
and Massachusetts General Hospital (MGH) in the earlier and latter part of
2009, respectively.
6.1.1 General Description of Scanning
Beam scanning is the process of spreading the beam over the target volume
by moving the beam throughout the target. Pictorially, Figure 6.1 describes
the scanning process. It is important to understand that true beam scanning
could involve the variation of many parameters of the beam while it is being
scanned. A beam at position A, can be characterized by a variety of parame-
ters including the vector transverse coordinate X
A
(x
A ,
y
A
), its energy E
A
, which
determines its depth (the third dimension), the beam current I
A
, the beam size
(a vector since it may be different in x and y) σ
A
, and others. The beam deposits
a dose D
A
in the voxel around A. After that dose is deposited, having stayed at
A for a time t
A
, the beam is moved to location B. The time it takes to move from
160 Proton Therapy Physics
location A to location B is t
AB
. The beam current during that movement is I
AB
,
which could be a function of position. The velocity that the beam moves from
position A to B is v
AB
= (X
B
− X
A
)/t
AB
, and the average beam current change rate
between A and B is dI/dt = (I
B
− I
A
)/t
AB
. In this way we have defned all the
variables that are necessary in the delivery of beam scanning.
6.1.2 Limits of Scanning Implementations
The above description appears intrinsically discrete or digital. Usually there
are two interpretations of this description related to one extreme or the
other. This has unfortunately caused confusion in the specifcation of the
system and in the terminology. In one extreme when t
A
= 0, the beam does
not stop at a particular location, and its motion is characterized by v
AB
. Also,
in such a case, the concept of I
A
is undefned, but rather the quantity I
AB
is rel-
evant. This extreme has been called continuous or raster or line scanning. It
is the equivalent beam motion as that used in the old CRT (cathode ray tube)
televisions. In the other extreme, when t
A
>0, it has been called spot scan-
ning or sometimes also raster scanning. However the distinction between
these extremes in the case when t
A
is suffciently small and/or x
B
− x
A
<< σ
A
is not relevant. Whether or not the t
A
= 0 limit is reached is an implementa-
tion decision or is based on physically realizable quantities. Thus the level
of discreteness of motion, measurement limitations, and control will all lead
to the method that will be used to control the beam and contribute to the
implementation.
In the case when the beam fully stops at a given point A, it may be neces-
sary to measure D
A
at that location, if the integrated current is not reliable;
however, even when the beam does not “stop” at a given point, it is neces-
sary to measure some form of the quantity D
A
at places on a three-dimen-
sional (3D) grid in the target volume in order to compare with the desired
dose distribution. A simplifed way of looking at this is to identify two dif-
ferent extremes of implementation that we will call dose- and time-driven
scanning as depicted in Figure 6.2 (left and right, respectively). These more
(x
A
, y
A
, E
A
, σ
A
, I
A
, D
A
, t
A
)
I
AB
, D
AB
, t
AB
, v
AB
(x
B
, y
B
, E
B
, σ
B
, I
B
, D
B
, t
B
)
A
B
FIGURE 6.1
Parameters useful in describing the scanning process. Beam A with the indicated parameters
is modifed to beam B, with modifed parameters.
161 Particle Beam Scanning
adequately describe the type of implementation and the properties required
of the accelerator. In dose-driven scanning, the beam motion is controlled by
whether the desired dose has been achieved at each location. The require-
ments on beam current control are light. In time-driven scanning, the beam
motion is determined by the time the beam spends in any given region and
is very dependent upon the beam current and/or beam velocity. Note that
so-called spot scanning can be implemented in either a dose- or time-driven
mode. Even the case in which the beam is not stopped (moving continuously,
sometimes called line or raster scanning) can be approximated by a series
of small moves and can be implemented both in the time- and dose-driven
modes. Also note that the implementation chosen normally depends on the
ability of the accelerator to deliver well-controlled beams and whether the
beam is continuous or pulsed.
The control of these quantities, whether open loop or closed loop, is a
subject of importance. In an ideal world, all quantities would be perfect. In
another idealistic world all parameters would be controlled in a closed-loop
mode and verifed. In the physical world, when measurements are made in
fnite times, open-loop delivery and correction or feed-forward processes are
needed. In the case when t
A
≠ 0, such as in Figure 6.2 (left), the dose is deliv-
ered in quantized doses and that there might be a correction for the next
quantum of dose. This allows the beam delivery to be independent of the
quantity (below the desired dose) and the quality of the beam current. The
beam is stopped (or moved) when the desired dose is reached independent
of its time dependence. However, if t
A
= 0, then the position of the beam at
any given time is not known (due to the Heisenberg uncertainty principle),
and the fact that it takes time to make the dose measurement may necessitate
an analysis and dose distribution correction after the fact. In any case, one
will have to identify the time scale for measurement and control for each
parameter and/or device and defne the control strategy to obtain the appro-
priate dose distribution.
Time
Time
Current
Dose
Position
Current
Dose
Position
Dose driven “spot” scanning
Time driven (can also be achieved by dose driven methods)
Raster or line or continuous scanning
FIGURE 6.2
Graphs of beam current, position, and dose delivered in the dose- (left) and time-driven (right)
techniques, during a one-line scan.
162 Proton Therapy Physics
6.1.3 Safety
The highest importance must be given to a safe and accurate delivery of
dose to the patient. The scanning system must ensure that the correct dose
fdelity is achieved, which includes giving the right dose to the right place
and not giving the wrong dose to any place. The methods used to ensure
this will place severe constraints on the implementation of the scanning
system. This will impact the control strategy mentioned earlier given the
time constants built into the system. Also, a safety plan should contain the
defnitions of the required types of redundancy and sensors to be used and
therefore help defne the interfaces with which the scanning system will
interact.
6.2 ParametersThatAffecttheBeamandDoseDelivery
The goal of radiotherapy implementation is to deliver the prescribed dose
to the target with the prescribed dose distribution. In general, the dose
fdelity (conformality to the prescription) is given by properly controlling
and checking the beam properties at any given time or integrated over
any given time interval. Each of the devices affecting or measuring the
beam properties can be controlled and/or measured in a fnite time period
or continuously, depending on the measuring device (e.g., power supply
current vs. beam position). The scanning system will control equipment
parameters, read back instrumentation parameters, and make decisions
about the settings of the equipment parameters based on the instrumenta-
tion parameters.
It is useful to separate the discussion of beam parameters into the static
and motion regimes. The former refers to the unperturbed property of the
beam when it is not in motion, and the latter includes effects arising from
the motion.
6.2.1 Static Beam Parameters
6.2.1.1 Depth–Dose Distribution
The depth–dose distribution will be determined by the superposition of the
Bragg peaks used in the delivery of the dose volume. Unlike a spread-out
Bragg peak (SOBP) as used in the scattering technique (see Chapter 5), the
delivery of a scanned beam can be general. An example of a nonuniform
depth (single feld) dose distribution required for a prostate carcinoma is
shown in the top curve of Figure 6.3. However, without any scatterers, the
width and distal falloff of a Bragg peak for shallower depth is smaller, and
creating a smooth dose distribution by superposition of these depth doses
163 Particle Beam Scanning
is diffcult, as shown in the bottom curve for a base of skull ependymoma
of Figure 6.3 (J. Hubeau, Private communication). A range shifter or ridge
flter is generally used for this situation; thus, even the scanning beam may
be modifed. It should be added that although scanning is sometimes con-
sidered beam delivery without modifying devices, use of a range compensa-
tor can provide advantages in some situations. This would allow one beam
range to be used to irradiate an irregular shape distally and thus reduce the
number of energy levels required for the dose delivery.
6.2.1.2 Transverse Dose Distribution and Modulation
The transverse dose distribution is given by a superposition of the trans-
verse raw beam profles. Much depends on the shape of that raw beam. A
beam is a collection of particles. The distribution of particles in a beam is
typically statistical, and owing to the physics of the source of ions and the
accelerator, the 2D (position and angle) phase space, in each plane, results in
a distribution as shown in Figure 6.4, top left. An integrated projection along
either the position (horizontal) or angular (vertical) axis results in a Gaussian
distribution as shown in the darker curve in the histogram projections. The
lighter curve is the distribution with limited statistics. The properly spaced
Gaussian has a special shape with magic properties. A superposition of
Gaussians results in a fat distribution. There is also considerable tolerance
to the relative positions of these beams before their spacing affects the over-
all distribution. On the other hand, an asymmetric beam, or one that has a
transverse falloff with a different shape than a Gaussian, will lead to much
tighter beam-positioning tolerances.
0
0
10
20
30
40
50
60
50 100 150 200 250 300
Depth dose in water (mm)
D
o
s
e

(
G
y
)
FIGURE 6.3
Two nonuniform, but realistic longitudinal dose distributions. The one at shallower range
(bottom curve) suffers from the narrower Bragg peak and is less smooth when the Bragg peak
spacing is too far apart compared to the deeper top curve.
164 Proton Therapy Physics
The sharpness of the Gaussian beam falloff will determine the sharpest
dose falloff possible with a clinical beam. Figure 6.5 shows some of the fea-
tures of a Gaussian beam, which is characterized by the following:

y e
x
=
−






1
2
2
σ
. (6.1)
0
0
0.2
I
n
t
e
n
s
i
t
y

o
f

b
e
a
m

(
r
e
l
a
t
i
v
e
)
0.4
0.6
0.8
1
1 2
Distance from center of Gaussian
(relative dimension)
3
Organ at risk
Half width half max
T
a
r
g
e
t

r
e
g
i
o
n
4 5 6
FIGURE 6.5
A graph of the intensity versus distance of a Gaussian beam. An example of regions of target
(left dashed box) and organ at risk (right dashed box) are shown to relate that spacing to the
Gaussian parameters.
#particles
Transverse position
0
0
–1
–1
–2
–2
–3
–3
–4
–4
–3
3
4
y
–4
–5
–5
1 2 3 4 5
–3 –4 3 4 5
1
2
3
4
T
r
a
n
s
v
e
r
s
e

a
n
g
l
e
#
p
a
r
t
i
c
l
e
s
FIGURE 6.4
Statistical coordinates of particles in a beam defned by position and angle. The side and bot-
tom graphs are histogram projections of the two dimensions (bottom, position; side, angle),
showing the Gaussian distribution.
165 Particle Beam Scanning
The beam sigma (σ) is the single parameter characterizing the Gaussian
shape. The full-width at half-maximum (FWHM) is given by 2.35σ. In partic-
ular, if the Gaussian is unmodifed (no collimator to produce sharper edges)
and one wants to separate the target (Figure 6.5, left dashed box) from a
critical structure in such a way that the critical structure does not receive
more than, say, 50% of the target dose (Figure 6.5, right dashed box), the dis-
tance between the target and this critical structure has to be at least 0.85σ.
This sets the scale of the beam size needed for different treatment sites. For
example, if the target and organ at risk are separated by 5 mm, then the beam
sigma should be smaller than approximately 6 mm. Alternatively, one might
modify the beam or apply an aperture to sharpen an edge. Apertures are
generally thought of as an inconvenience and expense when confused with
the type used in scattering systems which are built to collimate a large beam
and installed near the patient. However, one can conceive of a beam optics
solution that allows a sharper edge to be created upstream of the target, and
the beam on target is imaged from this aperture so that the beam that is
scanned has a sharper edge at the target, the solution frst proposed by Flanz
at PTCOG in 2002 and subsequently implemented by Pedroni et al. (4). Of
course, if the beam traverses too much material on the way to the target, the
multiple scattering in this material will broaden the beam again. The clinical
utility of smaller beams has yet to be determined. Some initial treatment-
planning studies have been conducted in order to evaluate the dose volume
histograms and dose to critical structures as a function of the size of the
beam (5). Examples of these comparisons are shown in Figure 6.6. Note the
100
50
R
e
l
a
t
i
v
e

v
o
l
u
m
e

(
%
)
0
60 70
A) CTV
B) Left parotid
D) Nasopharynx
Dose (Gy)
80 90 0
IMRT
IMPT σ = 8 mm
IMPT σ = 5 mm
IMPT σ = 3 mm
IMRT
IMPT σ = 8 mm
IMPT σ = 5 mm
IMPT σ = 3 mm
20
Dose (Gy-RBE)
40 60
100
50
R
e
l
a
t
i
v
e

v
o
l
u
m
e

(
%
)
0
100
50
R
e
l
a
t
i
v
e

v
o
l
u
m
e

(
%
)
0
100
50
R
e
l
a
t
i
v
e

v
o
l
u
m
e

(
%
)
0
0 20
C) Brainstem
Dose (Gy-RBE)
40 60 0 20
Dose (Gy-RBE)
40 60 80
FIGURE 6.6
Dose volume histograms for one treatment site planned with different size Gaussian beams
and intensity-modulated photons. (A) CTV; (B) left parotid; (C) brainstem; (D) nasopharynx.
The clinical impact of these differences is not yet known, but the relative quantitative impor-
tance of these parameters can be seen (Courtesy of Alex Trofmov).
166 Proton Therapy Physics
relative values of the dose-volume histograms for various beam sizes and
for comparison purposes also for a highly conformal photon plan. Because
some of these types of plans are a bit subjective, in that different planners
may achieve different results, one has to be careful comparing them; how-
ever, there the curves show an interesting indication of the relative impor-
tance of the beam sigma in this particular case.
If one is scanning the unmodifed Gaussian beam, the scanning method
affects the falloff at the edge of the feld, as shown in Figure 6.7A. The addition
of spaced Gaussians results in a larger-than-optimal edge falloff distance.
However, in much the same way that one sharpens the edge of an SOBP by
emphasizing the Bragg peak at the distal edge, it is possible to achieve simi-
lar results by modifying the distribution of the number of protons across the
feld as shown in Figure 6.7B (2, 6). Thus, to achieve a fat distribution with
optimal edges, it is necessary to modulate the dose delivered across the tar-
get even for a single-feld delivery.
Finally, it is important to realize that the transverse dose delivered at any
given depth will depend on the overall depth dose. Consider, for example, a
dose distribution that is desired to be uniform after the delivery of a single
feld, which is called a single-feld uniform dose (SFUD) (see Chapter 10).
Figure 6.8 (left) shows an actual example of a treated feld under such condi-
tions (7). Figure 6.8 (right, bottom) shows the 2D transverse dose distribution
along the transverse section A at this depth. Looking, now at a shallower
depth B, one has to account for the proximal tail of the depth–dose distribu-
tion that was delivered to A and thus a lower dose is delivered in the center
of B. The resulting transverse dose distribution in the transverse section B
is shown in Figure 6.8 (right, top), and one can see a typical “island-of-dose”
pattern for these felds. Thus, the dose across the shallower depth is also
a highly modulated distribution, in order to obtain an optimized uniform
feld throughout the volume.
0.0
0 50 100 150
Position (arbitrary units)
Uniform intensity profile Nonuniform intensity profile
A) B)
200 0 50 100 150
Position (arbitrary units)
200
0.2
0.4
0.6
0.8
1.0
1.2
R
e
l
a
t
i
v
e

d
o
s
e
0.0
0.2
0.4
0.6
0.8
1.0
1.2
R
e
l
a
t
i
v
e

d
o
s
e
FIGURE 6.7
(A) A superposition of equal space and equal amplitude Gaussian beams. (B) A nonuniformly
spaced and modulated dose distribution also resulting in an acceptable uniform overall dose
with a sharper penumbra.
167 Particle Beam Scanning
These last two examples highlight the fact that the dose distribution for
most felds delivered will naturally be characterized by a dose modulation
pattern. In common usage today, the term IMPT is used in contrast to SFUD
to indicate a single-feld delivery that is not uniform vs. a single-feld deliv-
ery that is uniform. In the former, subsequent felds are delivered to fnish
the desired dose pattern, and, for example, results in a dose-uniform overall
volume. However, in the IMPT mode, especially in the dose-driven case, the
intensity is not normally modulated. Furthermore, in the case of the SFUD
delivery, the dose is modulated, just as it is in what has been called IMPT.
Therefore, the beam delivery methods are NOT different and are just particle
beam scanning (PBS). Understanding these distinctions and care to not use
an incorrect term such as IMPT, is vital in properly specifying a scanning
beam system.
6.2.2 Motion Beam Parameters
6.2.2.1 Motion Effects
It is useful to note that the dose delivered to the target can be affected by
motion. This includes the motion of the beam and the motion of the target
(8, 9), The latter will be covered in Chapter 14, and the former will be men-
tioned here. In the case of dose-driven spot scanning, the dose delivered is
what one would expect from a static beam. Indeed, in the extreme example,
20 40
80
60
40
20
–
1
0
.
0
–
8
.
0
–
6
.
0
–
4
.
0
–
2
.
0
0
.
0
2
.
0
4
.
0
6
.
0
8
.
0
1
0
.
0
[cm]X
[cm]Y 100% = 35.5875 cGy
A
B
60
11.0
10
50
96
98
100
102
105
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
–1.0
–2.0
–3.0
–4.0
–5.0
–6.0
–7.0
–8.0
–9.0
–10.0
–11.0
FIGURE 6.8
(Seecolorinsert.) Left: an actual treatment plan for a SFUD delivery. Right: cross sections of
the dose distribution required to achieve the overall uniform dose, at the two depths indicated
by the magenta arrows labeled as A (deeper depth, bottom) and B (more proximal depth, top).
168 Proton Therapy Physics
the beam is only turned on when it is at the correct location. If, however, the
beam is not turned off before moving to the next spot, the dose delivered
during the motion must be accounted for and the fnal dose will depend on
the stability and predictability of the current delivered.
In the other extreme example, wherein the beam is continuously moving,
there are a variety of effects to consider. One may desire to change the dose
from one location to another, and this change can be as extreme as turning
off the beam. If one does not stop the motion of the beam (which is pos-
sible, but also takes time), one has to account for the distance that the beam
travels while the intensity is changing. This is illustrated in Figure 6.9 (top),
where there are several Gaussians, each one displaced a given distance (as
time evolves and the beam moves) and each one with a smaller amplitude
as the beam is being turned off. Integrating these Gaussians results in the
overall dose distribution, or the effective penumbra. For example, a moder-
ate scanning dipole with an effective 30-Hz frequency that sweeps over 30
cm results in an effective sweep speed of 18 m/s. If one wants to effect the
desired intensity change before the beam moves 1 mm, this requires that
0
0
1 2 3 4
0 1 2 3
Transverse distance (relative)
Ramped beam
Snapshot of Gaussian beams at
different positions as the beam moves.
Scaled Gaussian
R
e
l
a
t
i
v
e

a
m
p
l
i
t
u
d
e
R
e
l
a
t
i
v
e

a
m
p
l
i
t
u
d
e
4
FIGURE 6.9
Top: reducing amplitude of a Gaussian beam at specifc locations (multiexposure snapshots)
along its path as the beam intensity is being reduced. Bottom: difference between the effec-
tive penumbra (top curve) and the unmodifed pure Gaussian (bottom curve) penumbra for
this case.
169 Particle Beam Scanning
change to be done within 55 μs. Figure 6.9 (bottom) shows an example of
the effective increase in beam size owing to the motion shown in the upper
curve. At 20 m/s, with a 3-mm sigma, beam off in 500 μs produces a penum-
bra growth, from the undisturbed Gaussian of the lower curve to the ramped
beam above, of 70% (3–5-mm sigma). Similarly the effect is only 10% for a
beam with a 1-cm sigma, because the absolute distance traveled does not
change and the relative distance is smaller.
6.3 TimeSequenceofBeamScanningTasks
The events that take place during a scanning sequence will determine the
time required to deliver the treatment plan, and depending on motion
effects, will determine the actually delivered dose distribution. One can
consider that the treatment plan is a 3D map (it will probably grow into
four- dimensional maps as adaptive therapy evolves). How this map is to be
delivered can have nothing to do with the treatment plan, other than deliver-
ing the correct dose to the correct voxel within tolerance, but it is related to
the scanning implementation. For example, in some situations it is advanta-
geous to vary the beam energy frst and the position second or to mix the two.
Figure 6.10 illustrates these different sequences. In the top panel, the ellip-
soidal volume is scanned frst in the transverse direction, as indicated by the
transverse planes shown, and then the beam energy is modifed to move the
beam in the third dimension. Scanning may be used to conform to a distal
layer without a range compensator by adjusting the feld size as a function
of the distal depth. Alternatively, the depth direction can be combined with
Beam
Beam
Depth
T
r
a
n
s
v
e
r
s
e


FIGURE 6.10
Two styles of scanning with different time sequence. Top: sketch showing the beam paint-
ing the transverse cross section frst (left, right, up and down) and then changing the range.
Bottom: sketch shows changing the range and one coordinate (left and right) before changing
the third coordinate (up or down).
170 Proton Therapy Physics
one transverse direction frst, followed by a motion to the other transverse
direction. Scanning can also be used to deliver dose to each of these layers,
but less than the total required dose, so that the layers may be repainted
([10] or see Chapter 14) repeatedly to compensate for organ motion or just to
deliver a time-dependent feld position with a variation of range. Focusing
on the transverse positions, the pattern delivered can be optimized and will
be based on the implementation specifcs. All of the variations can be inde-
pendent of the treatment plan. Therefore there will be the equivalent of an
intensity-modulated x-ray therapy sequencer (a series of multileaf collimator
settings), or more accurately, for scanning, a trajectory manipulator that con-
verts the treatment plan into something closer to what should be delivered.
Of course, it should be possible for the treatment-planning software to read
this manipulated map to be sure that the treatment plan is unaffected (espe-
cially if interpolation is required).
Although some accelerators have certain beam delivery limitations with
respect to the time-optimized order of the steps described above, new accel-
erators being developed may not and will be able to vary quickly the beam
energy, spot size and position, and current.
6.3.1 Scanning Techniques
Various types of scanning have been identifed. For example, there is the
dose-driven spot scanning technique used at PSI (2), a variation on that one
used at GSI (11) in which the beam is not turned off between spots and there
is, time-driven continuous scanning, which is still, to this day, a research and
development area. There is the general feeling that the main advantage of a
continuous raster technique would be that of speed, not necessarily speed in
delivering all the dose in a feld, but speed in covering a dose layer with a
fraction of the dose and the possibility to repeat it several times.
One type of continuous scanning method can be characterized by a con-
stant beam defection speed on the target. The beam intensity is modulated
to adjust the dose per voxel. The constant beam defection rate translates into
very benign requirements for the defection magnet power supply (essen-
tially a constant voltage).
In time-driven spot scanning, the beam intensity is attempted to be held
constant. The dose per voxel is controlled by the time the beam spends on
each spot. Between spots, the beam is defected as fast as possible by apply-
ing the maximum power supply voltage to the defection magnet. This
method requires a high-compliance power supply and more sophisticated
control circuitry.
Assuming the motion is similar (same average speed) in both situa-
tions, it is clear that the shortest time to deliver the dose is by a method
that can deliver the beam with a maximum dose rate. In fact, the velocity
of the scan can be used to control the dose deposited during continuous
scanning, instead of modulating the beam intensity and possibly allowing
171 Particle Beam Scanning
the maximum dose rate to continue, or using a spot-by-spot approach can
always allow the maximum dose rate. There are different limitations to each
of these approaches.
Figure 6.11 contains two graphs in which the top curve is dose rate and
the bottom curve is scan speed. The left panel represents a constant velocity
scan, and the right panel shows a constant dose rate scan, whereby the dose
in a voxel is modulated by the scan speed. Both deliver the same modulated
dose to the target. It is instructive to compare these two cases.
In the case of constant speed, one can examine several scenarios. Let us
assume, in arbitrary units, that we have a dose rate less than 1. If the veloc-
ity (in arbitrary units) is 1, then the time to deliver this scan is, say, t1. If
we increase the speed by a factor of 2, but do not increase the dose rate, for
each scan—because the time it took to cover the area was reduced by one-
half—the dose delivered is also one-half. Therefore one would have to rescan
twice, and the overall time is not affected. If we double the dose rate, then we
must increase the scan speed by a factor of 2, or the dose delivered during
time t1 would be twice the required dose. In this way we can reduce the time
by one-half. Again, increasing the scan speed without increasing the dose
rate does not gain any time.
In the case of constant dose rate one can examine similar scenarios. Using a
scan speed of 1 is not good, because, as seen in the graphs of Figure 6.11, it
was desired to reduce the dose in the center of the scan; therefore, the speed
has to be increased in the center of the scan. If for example, the ratio of maxi-
mum to minimum dose during the scan is a factor of 2, we can consider a
solution with the speed starting at 1 and rising to 2 in the middle of the scan.
This will take approximately 1.5 times the original time. However increasing
the dose rate will further reduce the time.
Conclusion: Although it may seem trivial, the dose rate limitation is the
main issue. Given a dose rate, faster speed only buys you repainting, not
time. However if you have higher dose rate, you need scan speed to use it.
Dose rate (x)
Speed (x)
x direction
A
m
p
l
i
t
u
d
e
Dose rate (x)
Speed (x)
x direction
A
m
p
l
i
t
u
d
e
FIGURE 6.11
Graphs of the amplitudes of either dose rate or speed as a function of position during a trans-
verse scan. This shows an example of two extremes of scanning dose delivery. Left: a constant
speed scan with an irregular desired dose distribution; right: a constant dose scan, with the
same desired irregular dose distribution.
172 Proton Therapy Physics
This brings up one of the safety issues. In the process of radiotherapy one
can “not” prevent an overdose; one can only react in suffcient time to stop
the overdose from becoming relevant. Therefore, depending on the system
parameters, including dose readout time and beam control time, one is lim-
ited in dose rate by these instrumentation time constants.
6.3.2 Contributions to Time
It is helpful to consider, within safety limits, how to best deliver an effcient
scanned beam. One can identify the contributions to the scanning time per layer:
• Beam control
• Time to change beam intensity or to turn it on and off. An exam-
ple of this is shown in the current-modulated scope trace shown
in Figure 6.12A.
• Time to irradiate a location (dose rate)
• As discussed earlier with respect to the dose rate—the faster
the better, but for safety reasons the maximum dose rate will be
inversely proportional to the time to measure and stop the beam.
• Time to move from spot to spot
• Note that in time-driven scanning mode, the maximum dose rate
depends on maximum scan speed; the instrumentation time con-
stants and the maximum scanning speed depends on the time it
takes for a beam current change and the desired effective penumbra.
• Scanning magnets
• Time to change the magnetic feld is a balance between speed
and accuracy. Some practical limitations such as the voltage
available also come into play. An example of a moving beam is
shown in Figure 6.12B. Also important is the time to detect that
the magnets are settled.
• Instrumentation
• As in all the above contributions, instrumentation plays a crucial
role. For example, the time to read the dose is determined by a
number of factors including the ion drift time in the ionization
chambers (ICs) and the speed of the electronics readout. The graph
in Figure 6.12C shows multiple rise times as the resistors of an IC
electronic unit were modifed to achieve faster response times.
It is useful to separate the timing information into that required to deposit
the dose, the time needed by the scanning magnets to move the beam
between adjacent locations, and the time taken by other equipment such as
the dosimetry system. Once this is done, there are a variety of parameters
that can be explored. Among these are the relative time of the extreme of
173 Particle Beam Scanning
spot scanning compared with continuous scanning, as a function of dose
rate (or beam current) as shown in Figure 6.13. For the very specifc condi-
tions explored here and for one energy layer, the top curve in Figure 6.13A
includes fve repaintings of spot scanning with 2 cm sigma (5 Spot 2); the
middle curve is spot scanning for one repainting (1 Spot 0.5), and the bot-
tom curve is raster scanning (Raster 0.5), which, because of the high speed
used, requires multiple repaintings anyway. Owing to the extra steps in a
spot scanning method in which the beam is turned on and off (not all dose-
driven methods require this!), there is indeed some increase in irradiation
time. However, for some realistic parameters, for a given layer the difference
may only be a fraction of a second; when considering the overall time of the
irradiation (including the time to change the energy, which is normally a few
seconds, but can be as low as fractions of a second), the difference can be less
than half a minute, assuming repainting with both methods, as shown in
Figure 6.13B. This plot is typical for the case in which the time to change the
energy is relatively signifcant (e.g., seconds).
50
0
0.4
N
o
r
m
a
l
i
z
e
d

s
i
g
n
a
l
0.2
0.6
0.8
Sum of the IC2 strip
Mean of I
ctydo
over 2 msec
1
100 150
Time in m sec
200 250 300
A) B)
–12.0
–12.0 –8.0 –4.0 0.0 4.0 8.0 12.0
–10.0
–8.0
–6.0
–4.0
–2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
T
r
a
n
s
v
e
r
s
e

y

p
o
s
i
t
i
o
n
Transverse x position
0
0.4
N
o
r
m
a
l
i
z
e
d

r
e
s
p
o
n
s
e

o
f
I
C
2

+

I
C
E
E
U

(
a
.
u
.
)
0.2
0.6
0.8
1
20 30 40
Acquisition time (msec)
50 60
C)
FIGURE 6.12
(A) A graph of beam intensity (signal) versus time showing an example of beam current modu-
lation. (B) A scintillator screen image of a beam position change requiring a fnite time (and
distance). (C) The time response of an IC for different electronic confgurations.
174 Proton Therapy Physics
6.4 ScanningHardware
The unmodifed accelerator beam must be spread out throughout the target
volume, and the appropriate dose must be delivered. The hardware required
to do this can be divided into two main categories: (1) equipment to adjust
the beam properties and (2) instrumentation to measure the beam properties.
The equipment used for these manipulations at the MGH system devel-
oped jointly by Ion Beam Applications (IBA) and MGH is summarized in
0
0
A)
B)
5 10
Current (nA)
15 20
0 5 10
Current (nA)
15 20
0.5
1
1.5
T
i
m
e

(
m
i
n
)
2
2.5
3
1 Spot 2
1 Spot 0.5
5 Spot 2
5 Spot 0.5
Raster 2
Raster 0.5
0
500
1000
1500
T
i
m
e

(
m
s
e
c
)
2000
2500
5 Spot Raster 1 Spot
FIGURE 6.13
(A) The time to irradiate one layer as a function of beam current. (Safety issues are not included,
or there would be a hard cutoff with an upper limit of beam current.) (B) Curves includes the
time for energy change for a full volumetric delivery with different currents and different
beam sizes (e.g., 5 Spot 0.5 = 5 repaintings of spot scanning with a beam size sigma of 0.5 cm).
The raster beam is scanned as many times as needed to deliver the appropriate dose, as fast
as allowed.
175 Particle Beam Scanning
Figure 6.14. The equipment in these fgures, from left to right, includes a
quadrupole doublet to control the beam size, a pair of scanning dipoles to
defect the beam to the desired position, and ICs to measure the dose, posi-
tion, and beam profles. Other commercial scanning systems are depicted in
Figure 6.15.
6.4.1 Adjust the Beam Properties
The equipment that is used to deliver the dose introduces physical con-
straints and therefore limits the types of patterns that can be applied and
the timing that is possible. The scanning patterns that will be allowed are
determined by the ability to adjust the relevant beam properties.
6.4.1.1 Energy
In the case of scanning the beam range is normally given by the accelerated
beam energy or the beam energy resulting from a degrader system and per-
haps is slightly further modifed by a minimum of material in the beam path.
Any material in the beam path will scatter the beam (see Chapter 2) and
increase the beam emittance which is related to the beam size.
6.4.1.2 Size
The beam size is determined by the intrinsic emittance of the beam as modi-
fed by the beam-focusing elements in the beam line. Sometimes a set of fnal
quadrupoles can be used to fne-tune the beam size in the nozzle.
Dipole vacuum
chamber
Quadrupole
vacuum chamber
p
Quadrupole magnets
Dipole magnets
Ion chambers
Brass snout Isocenter
Proton
beam
FIGURE 6.14
The equipment used to defect and measure the beam for the MGH/IBA system is diagrammed
at the top and the beam defections resulting from the magnetic felds at the botttom.
176 Proton Therapy Physics
6.4.1.3 Position on the Target
It takes two parameters to defne a trajectory. One must control the position
and angle of the beam. Assuming one already knows the position and angle
of the beam entering the scanning dipoles (Figure 6.14, left side), the excita-
tion of the magnetic feld in the scanning dipoles will determine the fnal
beam path angle and thus the location of the beam in the target as shown at
the bottom of Figure 6.14.
The overall system of power supply and dipole will determine the speed
of the scan. The relation, V = L di/dt, indicates that the faster the scan (di/dt)
the higher the voltage (V) requirements, which also depend on the magnet
design such as the inductance (L).
Ionization
chamber
Scanning
quadrupoles
Scanning
dipoles
X-ray
equipment
Beam modifying
equipment
(when needed)
Beam
Profile
monitor
Scanning
magnets
Helium
chamber
Spot position
monitor
Dose monitor 1, 2
Iso
center
A) B)
C)
FIGURE 6.15
(A) The scanning nozzle of Hitachi as implemented at MD Anderson. (Courtesy of Hitachi.) (B)
The IBA scanning nozzle. (Courtesy of IBA.) (C) The dedicated PBS nozzle vertical. (Courtesy
of IBA.)
177 Particle Beam Scanning
6.4.1.4 Scan Patterns
We can call “feld area” the area in which we expect the beam to be deliv-
ered according to a particular pattern of scan lines with a certain distance
between scan lines. If one chooses a pattern with constant frequencies along
the x and y axes ( fx and fy, respectively) a Lissijoux pattern results with a
spacing between the painted lines. To reach the required line spacing (δ),
which depends on the beam size and desired overlap, the frequency ratios
could be adjusted. If you change the frequency ratio, a = fy/fx, while keep-
ing nearly the same sizes for the scanning area, one can theoretically adapt
the pattern to reach any required line spacing with a repeating pattern.
However, the limitations on frequencies and speeds along both axes due to
the hardware inherent to any power supply will limit the lowest reachable
spacing between scan lines. One way to solve this is to work around those
hardware limitations and modify the relative phasing of the frequencies.
This will reduce the distance between the scanning lines because the scan
will not repeat for a to-be-defned number of cycles.
In the ideal case, the beam trajectory is arbitrary and one is not dependent
on a set of fxed frequencies; however, there will always be a dependence on
the hardware constraints of the system.
6.4.2 Dose Rate
The highest dose rate available is almost completely determined by the
extracted current from the accelerator, assuming that there are no losses in
the beam path or in the case of a degraded energy beam that the beam inten-
sity will be reduced by the scattering resulting from a degrader system (see
Chapter 3) and the collimation system that contains a fxed amount of beam
losses. The highest dose rate allowable will be determined by the parameters
of the instrumentation and beam control.
6.5 ScanningInstrumentationandCalibration
We can divide the situation for which we must measure the beam proper-
ties into on-line (during Treatment) measurements and off-line (during non-
treatment times) measurements. The latter includes calibration and quality
assurance (QA). It is important to decide how to verify that the beam is
entering the target with the correct parameters. Introducing a monitor that
intercepts the beam will affect the beam profle in a potentially adverse way.
Weighing the optimized beam parameters with the impact of measurements
on safety is a complicated process. For example, there can be an IC to deter-
mine the beam position entering the scanning dipoles or not. One can argue
that downstream ICs that measure the position of the beam before the patient
178 Proton Therapy Physics
is suffcient; however, this can depend on the distance of these chambers to
the patient. If they are close, then the beam angle will not play a signifcant
role, but if they are far, the angle could be cause for consideration. The overall
system design is important in determining the optimum confguration of
instrumentation.
6.5.1 Calibration
A signifcant amount of measurements is necessary to both characterize
the system performance and to calibrate the system settings so that the
desired performances can be achieved. Some of the tools that can be used
are depicted in Figure 6.16. Depending on the system, some of these devices
might be embedded in the system, and some might require external imple-
mentation, for example, at the isocenter.
6.5.2 Calibration of the Beam Position at the Isocenter
It is necessary to ensure that the scanning dipoles can position the beam
on the target at the desired location. Given the safety impact of this quan-
tity, multiple levels of redundancy should be used to monitor the status of
the scanning dipole, including redundant current measurements, voltage
measurements, and magnetic feld measurements as well as the status of the
power supply. This, together with input trajectory information fully charac-
terizes the defection of the beam. Providing a functional redundancy with
IC strips can be used to further augment the redundancy in beam position;
however, this is usually installed upstream of the isocenter. Thus a device
Devices embeded in the system
IC23
10 mm
Hall probe
MLFC
DCCT
Matrix
FC
MC
BPC
MLIC
BIS
Devices used at the isocenter
FIGURE 6.16
Some instrumentation used includes the following: MLFC (multilayer Faraday cup), DCCT
(DC current transformer), FC (Faraday cup), MC (monitor chamber), BIS (beam imag-
ing scintillator), BPC (Bragg peak chamber), and IC23 (ionization chambers in the MGH
system).
179 Particle Beam Scanning
mounted at the isocenter is useful for calibration. In Figure 6.17, the MatriXX
(12) was used at the isocenter to measure the defection as a function of set
point voltage and to calibrate the magnet settings as well as the upstream IC.
These calibrations result in position accuracy of ±0.7 mm, under the condi-
tions of this measurement.
6.5.3 Calibration of the Beam Size at the Isocenter
The beam size performance was discussed previously in the section on beam
performance. Measurements can been made using the BIS and the MatriXX.
Figure 6.17 shows some MatriXX results.
6.5.4 Calibration of the Dose Delivery at the Isocenter
There is a series of steps that are necessary to perform all the calibrations
required to enable accurate dose delivery, including
• Calibration from charge to the monitor unit (MU)
• Characterization of the beam turn-off time
• IC effects
With respect to the beam turn-off time, a plot of the difference between the
expected dose and actual dose as a function of dose rate will help deter-
mine this time. The slope of this curve is related to the beam turn-off time.
Measurements of this sort may result in a parameter that requires the beam
to be shut off in advance of reaching the desired dose at a spot.
The signal from the IC itself can depend on the beam current due to
recombination effects. The maximum beam current will be limited by the
IC response.
–15 –10 –5 0 5 10 15
–15
–10
–5
0
5
10
15
FIGURE 6.17
Beam spots at the Isocenter using a MatriXX (11) IC system. The lower axis is the horizontal
position, and the abscissa is the vertical beam position.
180 Proton Therapy Physics
6.5.5 On-line Verification of Beam Position
The tolerances applied to the beam properties during a treatment are dic-
tated by the clinical tolerance. However, a beam position cannot be mea-
sured with suffcient accuracy, by an IC, until suffcient charge is collected.
Therefore the beam position (and size) measurement may have to be delayed.
Other measurements may be quicker.
A good scanning system will record the on-line measurement data and
compare it with the expected values within the specifed tolerances. An
example of this is shown in Figure 6.18. These are plots of the scanning mag-
net current values as a function of spot positions. Included on these plots are
the measured spots, the expected values, and the high and low thresholds.
Similar plots can be made of the scanning magnet feld and power supply
parameters. It is a fact that much calibration must been done in order to opti-
mize the speed when it is important and to focus on the accuracy when it is
important. Adjustment of the tolerances is a very important and time con-
suming part of the calibration process.
6.5.6 Beam Steering Corrections
Although signifcant time can be spent on calibrating the position and in try-
ing to understand all the effects that contribute to mispositioning, not all the
effects may be understood; so it is necessary to consider how to best deliver
an irradiation if not all parameters are, a priori, perfect. Given the desire to
reduce the time for an irradiation and to continue an irradiation once started,
assuming all the parameters are within tolerances, it is possible to apply
some robust techniques in correcting the beam position if deviations occur.
Four methods have been developed:
1. Deck reckoning via the algorithmic tables or formulas
2. Beam tuning on the frst layer (if an energy layer approach is used)
0 2000
–3
S
M
P
S

X

[
V
]
–2
–1
0
1
2
3
4000 6000
Element ID [-]
X plot
Expected slews
Expected spots
LOW threshold
HIGH threshold
Measured
Measured spots
8000 10000 0 2000
–3
S
M
P
S

X

[
V
]
–2
–1
0
1
2
3
4000 6000
Element ID [-]
Y plot
8000 10000
FIGURE 6.18
An example of an on-line data analysis system monitoring each of the axes of the scanning
dipole power supply (left and right) as a function of an element of the treatment plan. Also
contained is the actual measured x and y power supply current behavior. (Courtesy of Pyramid
Technical Systems and IBA)
181 Particle Beam Scanning
3. Adaptive beam tuning, which applies the position offset corrected
in the frst energy layer to all subsequent layers
4. Adaptive scanning magnet correction, which corrects the beam
position within a scan
Together, these approaches signifcantly enhance the precision of the abso-
lute beam position and provide a degree of robustness so that the irradiation
is less sensitive to potential beam positioning fuctuations.
Figure 6.19 shows an example of the beam position correction processes.
The vertical axis is the beam position in millimeters, and the horizontal axis
is the layer number for a 3D irradiation. The top curve is the measured posi-
tion of the beam without corrections, for a contrived case. (Note in particular
the discontinuity between layers 2 and 3.) The middle (just below the top)
curve shows the result from adaptive beam tuning, which was implemented
during the frst layer. Thus all subsequent layers are corrected by the same
amount; however, there was a discontinuity between the second and third
layers. Finally, the bottom curve shows the result of the adaptive scanning
magnet correction. In this example the threshold is set at 1.6 mm. Note that
in layers 3, 7, etc., the measured beam position exceeds the threshold and
the scanning magnet is used for correction. This correction is applied to the
entire map. The mispositioning is measured and reacted to before a dose of
any clinical signifcance is delivered with the beam out of tolerance.
6.6 ScanningGantries
The delivery of any beam will be characterized by the relative orientation
of the beam and the patient target. Although, in general, either the patient
–2
0
5 10
Depth layer number
(SM = Scanning magnet)
After turning (middle curve)
After turning and SM steering (lower curve)
No turning, no SM steering
15 20 25 30
2
D
e
v
i
a
t
i
o
n

f
r
o
m

d
e
s
i
r
e
d
p
o
s
i
t
i
o
n

(
m
m
)
4
6
8
10
12
14
0
FIGURE 6.19
Data (offset vs. time) obtained from a simulated beam position correction process. The top
curve shows the raw data (purposely misaligned position both during the frst and third depth
layers). The middle curve is corrected from the frst position (but purposely modifed subse-
quently). The bottom curve is corrected each time the beam exceeds the maximum offset.
182 Proton Therapy Physics
or the beam orientation can be manipulated, for the most part, nonplanar
beams are delivered by rotating gantries that manipulate the beam from the
horizontal orientation to an orientation perpendicular to a patient in a prone
or supine, horizontal, position. Although the subject of gantry design and
implementation is large, the beam delivery modality can have a signifcant
impact on their design. For the most part, a gantry that contains a scattering
beam delivery system will have that scattering system immediately after the
last bending dipole of the gantry. The scattered beam becomes very large and
uniform, and further transport by magnets will require very large magnet
apertures and may negatively affect the particle distribution. However, in
the case of PBS, with an unmodifed beam, the potential geometries expand
since there is no scattering system. The frst gantry to take advantage of this
possibility is shown in Figure 6.20A (13). This gantry is also compact in the
vertical dimension by setting the patient position away from the gantry rota-
tion axis. Inserting the scanning dipoles before the last gantry dipole allows
one to minimize the space between the last gantry dipole and the target, at a
cost of a large aperture in the gantry dipole to accept the diverging scanned
beam. It is possible to obtain a variety of optical solutions that will control
the angle of the scanned beam at the target. For example, the beam angle
can be anything from parallel to the actual angle the beam was bent by the
scanning dipole and magnifed beyond that. Additional geometries include
A)
B)
C)
S
S
S
S
S
T
T
I
I
I
T
S
GD
GD
GD
FIGURE 6.20
Depictions of three types of gantry geometries capable of providing scanning beams.
(A)  Geometry of the frst scanning proton gantry with both scanning dipoles upstream of
the last gantry bending dipole. (Courtesy of E. Pedroni.) (B) Geometry of the Hitachi scan-
ning gantry with scanning dipoles downstream of the last gantry dipole. A drawing of the
physical gantries are in the left of each box, and the line drawing to the right shows the scan-
ning dipole(s) (lighter colored blocks with S inscribed), gantry dipole (darker wedge with
GD), the instrumentation (I), and an ellipse representing the target (T). (Courtesy of Hitachi.)
(C) Geometry of the scanning dipoles split upstream and downstream of the gantry dipole.
183 Particle Beam Scanning
positioning the scanning dipoles before or after the last gantry dipoles as
well as the inclusion of focusing elements, which will affect both the beam
size and effective scanning beam angle (or effective source-to-axis distance
[SAD]). Some of these geometries are shown in the sketches of Figure 6.20B,
as implemented by Hitachi, for example, and the one in Figure 6.20C in which
the scanning dipoles are split before and after the gantry dipole with the
appropriate beam optics in between. In cases where the dipoles are together,
they can be replaced by a single combined dipole (14), if there is suffcient dis-
tance to achieve the desired feld size. Many more combinations are possible.
6.7 BeamPropertyQualityAssurance(QA)
One can have a friendly, long, discussion about all the aspects of the beam
that have to be correct in order to achieve the desired dose within a 3D feld
that contains nonuniform feld distributions. However, one way to cut that
discussion short is to fnd a way to measure some of the important beam
properties explicitly and to do so in a very short time.
One such method is a test pattern that can measure many important proper-
ties of the beam in a very short time. It takes a few seconds to deliver that pattern,
and the dose delivered is displayed on a MatriXX or BIS monitor. This pattern
has the capability, with analysis, to give the beam position, size, and dose.
An example of this with an automated analysis tool is shown in Figure 6.21A
and B. The grayscale in Figure 6.21A shows the pattern assuming perfect
0 –15
–15 –10 –5 5 10 15 0
–10
–5
y

(
c
m
)
0
5
10
15
200
400
600
800
1000
1200
1400
1600
1800
2000
A) B)
x (cm)
sigmaY
sigmaX
position (x, y)
dose
FIGURE 6.21
(Seecolorinsert.)(A) A theoretically designed scan test pattern. (B) A result of a measurement
with a larger beam size and some of the parameters that can be obtained through analysis
using this pattern.
184 Proton Therapy Physics
beam resolution. Figure 6.21B, in living color, shows the results when this
pattern is delivered with the MGH scanning beam. In this case, an unfo-
cused beam with a sigma of about 1 cm was used. Also indicated are some
of the regions in the pattern that can be used to analyze beam position, dose,
and beam size. It is envisioned to repeat this test pattern daily, after the scan-
ning system hardware is confgured and to use this data as QA testing.
Finally, it is necessary to determine the correspondence of the beam posi-
tion and the imaging fducials. One way to do this is to generate an exposure
with the x-ray tube and produce an image of the x-ray crosshairs on the same
screen as that which is measuring the QA pattern. This completes the cor-
relation between the beam and the patient setup data.
6.8 Safety
Particle beam scanning is a modality to deliver a particle beam while achiev-
ing a high degree of irradiation conformality to the desired target. As a form
of radiation, it is desired to minimize the radiation delivered outside the tar-
get. Underdosing the target can also have undesirable results. The dose out-
side the target may be acceptable as defned by the medical prescription.
The equipment must be capable of ensuring that target dose is delivered and
unwanted dose is not delivered by detecting both the target and unwanted
dose and stopping the irradiation in suffcient time to prevent too high a
quantity of undesirable dose. Thus the accuracy in some cases will in part be
determined by the specifcations of the instrumentation used to detect beam
properties. One must ensure that
1. The appropriate dose is delivered
2. The dose distribution is correctly delivered
3. The dose is delivered to the correct location
One way to help ensure that a system can operate in a safe manner is to
evaluate the failure modes and develop a strategy that leads to a safe and
consistent mitigation of all conceived failures. For the PBS, a comprehensive
failure mode and effects analysis (FMEA) and hazard analysis should be
done. Elements of the process include the following:
• Possible hazards/effect on the beam
• Risk mitigation method
• Hardware detection
• Software safety
• Functional redundancy (measurement of delivery beam properties)
185 Particle Beam Scanning
• Clinical protocol
• What has to be done for QA?
• What should a therapist/physicist do?
6.8.1 Safety Strategy
To develop an appropriate strategy, a philosophy of risk mitigation is needed.
The following questions should be posed:
• What needs to be set to determine a property (e.g., magnets and scat-
tering for beam size)?
• Are there other factors (that we do not control) that can determine a
property (e.g., accelerator-extracted beam trajectory)?
• What can be monitored to determine that the setting of the device is
correct? Are there redundant ways to monitor it (e.g., limit switches
or current transformers)?
• Is there a direct way to measure that beam property (e.g., ICs or
range verifers)?
• What can be done with software, and what can be done with
hardware?
• What additional QA can or should be done?
6.8.2 Beyond Safety
An old adage says that “the safest system is one that does not work.” We can-
not always expect everything to be perfect, and therefore we look for some
ways to be insensitive to errors or to correct errors in a fast and accurate way
that allows treatment to continue. For example, the system should accept a
“pause, stop, and resume” command.
If the beam has been paused or stopped before the irradiation has com-
pleted and it is desired to complete that irradiation, this process must
account for all the dose that has been previously delivered. Unlike scat-
tering, where the entire volume is irradiated almost simultaneously, in
the  case of scanning there is a time dependence to the beam delivery. In
the case of recovering a treatment after it has been stopped or paused, the
measurement of the dose already delivered is crucial. Figure 6.22 shows
the case irradiation of a particular layer. The numbered sections are vox-
els, and by the time of the pause, the gray flled-in boxes have been irra-
diated, whereas box 11 is only partially irradiated. The rightmost panel
represents the desired irradiation of the remaining voxels upon resuming
the irradiation.
Treatment-planning simulations have been carried out to understand
the effect on different types of fields. For example, in a plan (Figure
6.23) with a 34-Gy highly modulated field, a scenario could be created in
186 Proton Therapy Physics
which there are localized changes of ~6 Gy = ~16%. This does not show
up in the dose-volume histogram, but does contribute to the desired
accuracy of the already delivered dose. Note that in this case, if thou-
sands of spots are used, 0.1% can result in missing 10 spots. If those 10
spots are in a highly nonuniform distribution, the results are a bit unpre-
dictable or at least nonintuitive. At MGH it has been determined that
0.7-MU accuracy or limitation on the noise that contributes to the dose
100
5 10 15 20
Dose [Gy]
CTV Spinal cord
25 30 35
Dose [Gy]
40 30 20 10
Nominal
1MU repainted
1MU skipped
80
60
40
20
%

V
o
l
u
m
e


Dose (Gv)
0
30 32 34 36 38 40 42
100
80
60
40
20
%

V
o
l
u
m
e


Dose (Gv)
0
20 22 24 26 28 30 32
FIGURE 6.23
(Seecolorinsert.)Treatment-planning example of an interrupted scanning beam delivery to
determine the accuracy required of knowing the actually delivered monitor units, in order to
accurately resume the treatment. The left treatment plan shows a local under dose, CTV, clini-
cal target volume. Right: spinal cord.
1 2 3 4 5
6
11
7 8 9 10
12 13 14
Starting map Irradiation interrupted Irradiation resumed
FIGURE 6.22
Illustration of an interrupted scanning map and the recovery and continuation.
187 Particle Beam Scanning
measurement is required. This gives an acceptable dose distribution for
the cases examined.
6.9 Summary
PBS represents a technical improvement in obtaining the most confor-
mal dose distributions possible with particles. Additionally it allows for
dose delivery without patient-specific hardware. This allows for the most
efficient beam delivery modality. One can envision multiple-field irra-
diations being delivered without entering the treatment room between
fields.
The depth–dose distribution together with the conformality of this
approach leads to a minimization of beam felds necessary for an excellent
dose distribution.
The overall system is in fact simpler in the number of elements required
than a scattering system; however, the implementation of the system with
respect to timing and tolerances is more challenging.
Given the fact that for a scanned beam it is not normally necessary to pre-
pare, in advance, elements that will control the beam delivery, it is ideally
suited for adaptive radiotherapy. Adaptation is not only relevant for intrafrac-
tion effects, but can also be important for interfraction effects. Indeed the
largest obstacle to widespread use of scanning in all body sites is the factor
of organ motion. In general the scanning technique contains fexibility to
compensate for all types of organ motion effects: if the treatment planning
can be adapted to account for these effects and if the accelerator system is
nimble enough to compensate.
As is the case in all particle beam–spreading methods, the tolerances asso-
ciated with the delivery of the particle beam are more stringent than those
associated with photon beam delivery; however, the gains in dose confor-
mality, effciency, and compensatory power are all signifcant with the use of
the beam scanning modality.
Accelerator, beam line, and scanning systems have previously been
built for scattering beam delivery; however, newer systems can be opti-
mized for scanning and provide more fexibility for adaptive and fast
beam delivery.
On the whole, the cost of delivering a beam using scanning can be lower
than other alternatives and the treatment more effcient, thus positively con-
tributing to the cost effectiveness of particle therapy.
The beam scanning modality is now integrated into hospital-based clinical
treatment facilities and is not just in the laboratory environment anymore.
This represents a new phase in the evolution of accessible particle beam ther-
apy and research.
188 Proton Therapy Physics
Acknowledgments
The author recognizes the tireless efforts invested by Dr. Claise, who has
devoted considerable time and energy in the commissioning of the MGH
scanning system. This has been augmented with the help of Dr. Bentefour of
IBA. In addition, the works of Drs. Dowdell, Kooy, and Trofmov have been
instrumental to the MGH portion of the work reported in this chapter. The
author also acknowledges Ion Beam Applications s.a. (IBA) and the National
Cancer Institute for their support of some of the work reported herein. The
author thanks the editor, Dr. Paganetti, for the invitation to prepare this
chapter and for providing help in editing. Finally, thanks are owed to the
author’s wife, Nancy and children, Adam and Scott, for their patience dur-
ing the nights and weekends (yes this took more than one night) spent in the
preparation of this chapter.
References
1. Kanai T, Kawachi K, Kumamoto Y, Ogawa H, Yamada T, Matsuzawa H, et al.
Spot scanning system for proton radiotherapy. Med Phys. 1980;7:365–9.
2. Pedroni E, Bacher R, Blattmann H, Bohringer T, Coray A, Lomax A, et al. The
200-MeV proton therapy project at the Paul Scherrer Institute: conceptual design
and practical realization. Med Phys. 1995;22:37–53.
3. Haberer T, Becher W, Schardt D, Kraft G. Magnetic scanning system for heavy
ion therapy. Nucl Instrum Methods Phys Res A. 1993;330:296–305.
4. Pedroni E, Bearpark R, Bohringer T, Coray A, Duppich J, Forss S, et al. The
PSI Gantry 2: a second generation proton scanning gantry. Z Med Phys.
2004;14(1):25–34.
5. Trofmov A, Bortfeld T. Optimization of beam parameters and treatment plan-
ning for intensity modulated proton therapy. Technol Cancer Res Treat. 2003
Oct;2(5);437–44.
6. Staples JW, Ludewigt BA. 1993 Proceedings Particle Accelerator Conference:
1759–61.
7. Kooy HM, Clasie BM, Lu HM, Madden TM, Bentefour H, Depauw N, et al.
A case study in proton pencil-beam scanning delivery, Int J Radiat Oncol Biol
Phys. 2010 Feb 1;76(2):624–30.
8. Saito N, Bert C, Chaudhri N, Gemmel A, Schardt D, Durante M, et al. Speed
and accuracy of a beam tracking system for treatment of moving targets with
scanned ion beams. Phys Med Biol. 2009 Aug 21;54(16):4849–62.
9. Haberer et al. N.I.M. 1993;A;330:296–305.
10. Seco J, Robertson D, Trofmov A, Paganetti H. Breathing interplay effects during
proton beam scanning: simulation and statistical analysis. Phys Med Biol. 2009
Jul 21;54(14):N283–94.
11. Eickhoff H, Haberer T, Kraft G, Krause U, Richter M, Steiner R, et al. The GSI
Cancer Therapy Project. Strahlenther Onkol. 1999 Jun;175 Suppl2:21–24.
189 Particle Beam Scanning
12. Herzen J, Todorovic M, Cremers F, Platz V, Alvers D, Bartels A, et al. Dosimetric
evaluation of a 2D pixel ionization chamber for implementation in clinical rou-
tine. Phys Med Biol. 2007 Feb 21;52(4):1197–208.
13. Peroni E, Enge H. Beam optics design of compact gantry for proton therapy,
Med Biol Eng Comput. 1995 May;33(3):271–77.
14. Anferov V. Combined x-y scanning magnet for conformal proton radiation ther-
apy. Med Phys. 2005;32(3):815–18.
191
7
Dosimetry
HugoPalmans
The accuracy needed in dosimetry should be considered in view of the
requirement for the dose delivered to the target volume for which, in gen-
eral, required relative standard uncertainty levels between 3% and 5% have
been quoted (1). Reference dosimetry, which is only one step in a chain of
procedures leading to dose delivery, should thus be done with uncertainties
well below that, typically better than 1%. For relative dosimetry, the uncer-
tainty requirements are usually a bit more relaxed. The frst section of this
chapter discusses the detectors used for proton beam dosimetry and their
particular characteristics in protons compared with photons, the second one
discusses their application to reference and relative dosimetry, and the chap-
ter ends with a section on microdosimetry.
7.1 Detectors
An up-to-date review of clinical high-energy photon and electron dosimetry
can be found in Reference 2. The main issues that complicate proton beam
CONTENTS
7.1 Detectors ..................................................................................................... 191
7.1.1 Calorimeters ................................................................................... 192
7.1.2 Fluence-Based Measurements ...................................................... 197
7.1.3 Ionization Chambers ..................................................................... 198
7.1.4 Detectors for Profle Measurements ............................................ 202
7.2 Reference Dosimetry ................................................................................. 207
7.2.1 History of Reference Dosimetry for Protons ............................. 207
7.2.2 Recommendations of IAEA TRS-398 and ICRU Report 78 ...... 209
7.3 Microdosimetry.......................................................................................... 211
7.3.1 Microdosimetric Quantities ......................................................... 212
7.3.2 Experimental Microdosimetry .................................................... 212
References ............................................................................................................. 215
192 Proton Therapy Physics
dosimetry compared with photon and electron dosimetry are the poorer
knowledge of stopping powers and other electronic interaction quantities,
the increased ionization density characterized by a larger linear energy
transfer (LET), and the occurrence of nonelastic nuclear interactions. These
are all of concern related to detector response, and the latter two effects con-
tribute to the energy-dependent dose response that all detectors exhibit in
proton beams.
The frst three detectors that will be discussed are the main instruments
used for absolute dosimetry: calorimeters, Faraday cups, and ionization
chambers. Those three subsections are then followed by a subsection on
detectors for relative dose distributions.
7.1.1 Calorimeters
Calorimeters provide the most direct method to measure the quantity of
interest in reference dosimetry for radiotherapy, which is the absorbed
dose-to-water. Relevant quantities such as biological response and isoef-
fective dose are also defned with reference to the absorbed dose-to-water.
The most direct way of measuring this quantity is by use of water calo-
rimeters, but calorimeters using different absorbed media such as graphite
or the tissue-equivalent plastic A-150 have been used for the same pur-
pose as well. The latter require in addition to the measurement of dose to
the calorimeter medium, a conversion procedure to derive the absorbed
dose-to-water.
In calorimetry, the temperature increase in the medium, ∆T
med
, as a result
of the energy deposited by ionizing radiation, is measured with high preci-
sion. Absorbed dose to the medium, D
med
, is then obtained by multiplying
with the specifc heat capacity of the medium, c
med
, and the necessary correc-
tion factors:

D c T
h
k
i med med med
= ⋅ ⋅
−
⋅ Π
1
1
(7.1)
where h is the physicochemical heat defect that represents the (fractional)
energy that has been deposited by ionizing radiation but is taken away from
the medium by any changes of its physical or chemical state and Πk
i
is the
product of correction factors for heat transported away or toward the meas-
urement point, feld nonuniformity and changed scatter and attenuation
due to the presence of nonmedium-equivalent materials. The specifc heat
capacity is normally obtained from measuring the temperature rise in the
medium due to electrical energy dissipation, either in a separate experiment
or within the calorimeter setup.
The operation of calorimeters in photon and electron beams has been
described extensively (1, 4) and for proton beams operating and understand-
ing calorimeter response is very similar. The main additional issues that
193 Dosimetry
need to be considered are the chemical heat defect, thermal heat conduction,
and dose conversions between different media.
The heat defect is defned as follows:

h
E E
E
=
−
a h
a

(7.2)
where E
a
is the energy from ionizing radiation absorbed locally and E
h
is
the energy appearing as heat, and thus as a temperature rise when no latent
heat absorption is involved. If no change of the physicochemical state of the
medium takes place then the heat defect is zero. If the net heat balance of
processes after the absorption of energy is endothermic the heat defect is
positive, whereas it will be negative when the net heat balance is exothermic.
In water calorimeters, the main source of a heat defect is the chain of chem-
ical reactions after the radiolysis of water. The reactions after the production
of so-called primary species (which are present about 10
−7
s after passage of
the ionizing particle) are well known and documented (5, 6), and together
with values of the chemical yields of primary species and the heats of forma-
tion of the six stable chemical species after irradiation (7), the chemical heat
defect can be calculated by solving the coupled set of linear differential equa-
tions describing all chemical reactions. The production of primary species,
however, is LET dependent, and this dependence is not very well known.
The most comprehensive information comes from References 7 and 8, and
based on this, calculations of the chemical heat defect for proton beams have
been performed and discussed in various publications (9–15), leading to the
following observations:
• For high-energy (low-LET) protons, pure water saturated with a
chemically inert gas like argon or nitrogen (the argon or nitrogen
system) exhibit a small (<0.1%) initial heat defect, reaching a steady
state after a modest irradiation just as it does in photon beams. For
high-LET protons, however, a steady increase of the chemical energy
in the aqueous system is observed because of a higher production of
hydrogen peroxide than what is decomposed, resulting in a nonzero
endothermic heat defect.
• Pure water saturated with hydrogen (the hydrogen system) exhibits
a zero heat defect over the entire LET range, which can be explained
by an enhanced decomposition of hydrogen peroxide compared
with the nitrogen system.
• When initial oxygen concentrations are present, the hydrogen sys-
tem exhibits an initial exothermic heat defect that increases until
depletion of oxygen after which the heat defect drops abruptly to
zero. This is an attractive system because this phenomenon offers a
way of monitoring when the steady-state, zero-heat-defect condition
is reached.
194 Proton Therapy Physics
• For water with a known quantity of sodium formate as a deliber-
ate impurity saturated with oxygen (the formate system), the exo-
thermic heat defect in a modulated beam is only about half of that
in a
60
Co beam with the same dose rate. This was explained by the
lower chemical yields for certain species at high LET as well as the
time structure of the formation of chemical species due to the beam
modulation.
Two types of experiments can be distinguished that provide support for
the theoretical observations above:
1. Comparison of the heat defect of water with that of a metal for which
the heat defect is assumed to be zero (e.g., aluminium or copper).
The experiment consists of measuring the thermal heating of a dual
water/metal absorber, which forms one thermal body, by totally
absorbing the same number of protons in either the water component
or the metal component. Using such a setup, it was experimentally
confrmed that the endothermic heat defect in pure water increases
with LET from a value close to zero for protons to a value of about
+4% for 100 keV μm
−1
helium ions (16). A weighted least-squares ft of
an exponential function to the data including an uncertainty of 0.3%
for the assumption that the heat defect is zero at low-LET (3) gives
the following:

h e
LET
= ± ( ) ⋅ − ±
− ± ( )⋅
4 1 0 4 1 000 0 001
0 035 0 010
. . . .
. .
(( )
( )
. (7.3)
Figure 7.1 shows the experimental data points as well as the ft with
the standard uncertainty as a function of LET.
2. Relative comparison of the heat defect of different aqueous systems
by comparing their relative response to the same dose. This way
the initial exothermicity of the hydrogen system in the presence of
trace oxygen concentrations was demonstrated for protons as well
as the relative agreement of the hydrogen system with the nitrogen
or argon system after a steady state was reached (9, 10, 14). Also the
lower heat defect of the formate system in protons compared with
photons in a modulated proton beam was demonstrated experimen-
tally (9, 10, 14).
A chemical heat defect can also occur in solid calorimeters. In graphite as
well as plastic calorimeters (A150 tissue equivalent plastic and polystyrene),
reaction of the medium with dissolved oxygen may result in an exothermic
heat defect. This has been suggested to explain the initial overresponse of cal-
orimeters made of A150 and graphite (more than 10% and 2%, respectively),
which disappears after suffcient preirradiation (17, 18). Another suggested
195 Dosimetry
mechanism for a chemical heat defect is the dissociation of polymers, which
explains the endothermic heat defect of about 4% for A150 obtained from
similar total absorption experiments as described above using a dual A150/
aluminium absorber (19–21).
In solid calorimeters made of a crystalline or polycrystalline material such
as graphite, a physical heat defect is also possible due to the creation and
annihilation of interstitial lattice defects. This is generally assumed to be
small but may be larger in proton beams than in photon beams because of
the higher probability of a suffcient energy transfer to a recoil nucleus. Only
at extremely high doses (order 10
9
Gy) received in nuclear reactors has a heat
defect been demonstrated by measuring the release of the Wigner energy
when annealing the graphite samples by heating it above 250°C (22). It is
not clear if and how these results would translate to radiotherapeutic dose
levels. In a proton total absorption experiment using a graphite/aluminium
absorber, an endothermic heat defect of 0.4% with a standard uncertainty of
0.3% was observed (21), indicating that the physical heat defect in graphite
must be limited to a few tenths of a percent.
The second issue of concern with calorimeters in proton beams is that of
heat conduction, potentially leading away heat from the measurement point
or adding heat from the irradiated surroundings of the measurement point.
For water calorimeters, where the thermal diffusivity is relatively low, ther-
mal conduction is manageable when the steep gradients are kept a suffcient
distance away from the point of measurement. The same criterion as in pho-
ton beams could be used that corrections for heat losses are negligibly small
when the distance from the measurement point to steep edges such as the
penumbrae and the Bragg peak or to the distal edge of the spread-out Bragg
–1
0
1
2
3
4
5
6
7
C
h
e
m
i
c
a
l

h
e
a
t

d
e
f
e
c
t

/

%
LET / keV µm
–1
0 20 40 60 80 100
H-1
H-2
C-12
He-4
120 140
FIGURE 7.1
Chemical heat defect of pure water as a function of LET measured for various ions (16). The
middle line represents an exponential ft and the two outer lines the one standard deviation
interval based on the uncertainties from the least-square ft parameters and a standard uncer-
tainty of 0.3% for the assumption that the heat defect is zero at low-LET. (From Brede et al.,
Phys Med Biol, 51(15), 3667, 2006. With permission.)
196 Proton Therapy Physics
peak is at least 3 cm (23). In scanned proton beams, an additional complica-
tion is that when a pencil beam hits the measurement point the instantaneous
gradients are always substantial, but it has been demonstrated theoretically
(11) and experimentally confrmed (24) that if the painting of a target vol-
ume takes not more than 2–3 min, the correction for heat conduction and its
uncertainty are very similar to that of passively scattered broad proton beam
irradiation of the same duration. Also the excess heat due to the presence of
nonwater materials (the glass vessels to contain the high-purity water and
the thermistors probes) has been found to cause only minor differences com-
pared with that of photon beams (24).
In solid calorimeters and in particular graphite calorimeters, the phenome-
non of heat conduction is very different given the higher thermal diffusivity.
In graphite the thermal diffusivity is three orders of magnitude higher than
in water, meaning that temperature profles within an irradiated sample
redistribute within a time interval much shorter than the irradiation time
itself. This is traditionally dealt with by introducing gaps and so-called jack-
ets around the core, a graphite sample with known mass over which the
average dose is measured by comparing the temperature increase during
irradiation with the temperature increase resulting from known electrical
energy dissipation. In photon beams advantage is taken from the almost
linear attenuation curve; by thermally connecting equal-sized parts of the
jackets in front and to the back of the core, the average heating of the jackets
is almost equal to that of the core, thus minimizing radiative heat transfer.
In proton beams, because of the Bragg peak or the distal edge this is more
diffcult to achieve, and the steep gradients need to be either shielded by
inducing more thermal barriers or by matching the size of graphite parts
beyond the core such that the energy per unit mass of those parts equals the
dose in the core (25). For scanned proton beams, the only option is to work in
isothermal operation mode, in which all graphite parts are kept to a constant
temperature and the changes in electrical energy dissipation required dur-
ing irradiation provide a way of measuring of how much energy is deposited
in the core.
Finally, for nonwater calorimeters there is the issue of converting dose to
the calorimeter medium to the quantity of interest: dose-to-water. For graph-
ite calorimeters, the conversion from dose-to-graphite to dose-to-water is one
of the main uncertainties on the dose-to-water determination in a proton
beam (14). If the charged particle spectra at equivalent depths in water and
graphite (related by the CSDA [continuous slowing down approximation]
ranges) are identical, then the dose conversion is adequately described by
the mass stopping power ratio water-to-graphite for the charged particle
spectrum. However, differences in the absorption of primary protons in
nonelastic nuclear interactions and differences in the production of second-
ary charged particles in both target materials are likely to result in unequal
charged particle spectra at equivalent depths. The absorption of primary
protons can be approximated by a simple analytical calculation. Using
197 Dosimetry
nuclear interaction data from the International Commission on Radiation
Units and Measurements (ICRU) Report 63 (26), it is found that the number
of primary protons absorbed over the entire range in graphite is different
from that in water by 2% for 60-MeV protons and 8% for 200-MeV protons
(27). MCNPX (Monte Carlo N-Particle eXtended) Monte Carlo simulations,
on the other hand, indicate that this is largely compensated by the difference
in secondary particle production leading to dose conversion corrections that
are limited to 0.4% at 60 MeV and 0.6% at 200 MeV.
7.1.2 Fluence-Based Measurements
In a broad proton beam, dose-to-water at a shallow depth, z, can in principle
be derived from the proton fuence at the surface, Φ, as follows:

D
S z
k
w
w
w
( )
( )
z
i
= ⋅ ⋅ φ
ρ
Π

(7.4)
where S
w
(z) is the stopping power of the proton spectrum at depth z and Πk
i

is the product of correction factors for beam divergence, scatter, feld nonuni-
formity, beam contamination, and secondary particle build-up. It is obvious
that this method relies on accurate values of the proton stopping power in
water for which the uncertainty is estimated to be 1–2% according to ICRU
Report 49 (28).
The main instrument in use to measure the incident particle fuence is
the Faraday cup, which enables an accurate measurement of the number of
protons, provided it is well designed (Figure 7.2). For broad beams an addi-
tional major uncertainty is due to the determination of the feld area. For
pencil beams this uncertainty vanishes when the derived quantity is a later-
ally integrated dose. A major concern is the infuence of electrons generated
in the entrance window that reach the collecting electrode (and thus reduce
the signal) as well as electrons liberated in and escaping from the collecting
electrode (which enhance the signal). Both sources of perturbation to the
measurement are usually suppressed by a guard electrode with a negative
potential with respect to the electrode and casing, and sometimes with addi-
tion of a magnetic feld.
An alternative method for determining the fuence is to measure the
induced activation of a sample (29). If the number, N, of
12
C atoms in a sample
is known as well as the cross section of the
12
C(p,pn)
11
C reaction, the mea-
surement of
11
C activity, A
0
, immediately after an irradiation time τ can be
used to derive the proton fuence in the center of the broad beam that hits the
sample using the following equation:

φ
σ λ
λ τ
=
⋅
⋅ ⋅
⋅
A e
N
0
2

(7.5)
198 Proton Therapy Physics
where λ is the decay constant of
11
C. The activity is usually measured using
4π βγ-coincidence counting, and it is estimated that the fuence can be derived
with a standard uncertainty of 3%. Advantages of this method are that no
determination of the beam area is needed and that it can be used without
much loss of accuracy in high dose-per-pulse beams such as from synchro-
trons or laser-induced beams.
7.1.3 Ionization Chambers
Ionization chambers are the backbone for reference dosimetry in radiother-
apy. With an ionization chamber, dose-to-water, D
w,Q
, in a proton beam of
beam quality, Q, is related to the average dose-to-air in the air cavity volume,
D
air,Q
, via Bragg-Gray cavity theory:

D D s p
w,Q air Q w air Q Q
= ⋅ ⋅
, ,
( ) ,

(7.6)
where (s
w,air
)
Q
is the Bragg-Gray or Spencer-Attix mass collision stopping
power ratio water-over-air for the charged particle spectrum at the measure-
ment point in water and p
Q
is a correction factor to account for any deviation
from the conditions under which Bragg-Gray cavity theory is valid.
The average dose-to-air can in principle be obtained from the measured
ionization in the cavity, M
Q
, and knowledge of the mass of air in the cavity
(m
air
= ρ
air
·V
cav
) and the mean energy required to produce an ion pair in air,
(W
air
/e)
Q

D
M W e
V
air Q
Q air Q
air cav
,
( )
. =
⋅
⋅ ρ

(7.7)
Protons
Entrance
window
Housing Collecting electrode
Guard
Winding
B
FIGURE 7.2
Schematic diagram of a reference dosimetry level Faraday cup with internal vacuum. Shown
are the collecting electrode, the guard electrode (which is at negative potential with respect to
the collecting electrode), the entrance window, and the windings creating a magnetic feld, B, to
suppress the loss of electrons generated in the collecting electrode. (Reproduced from Palmans
et al., Hadron Dosimetry. In: Clinical Dosimetry Measurements in Radiotherapy (Rogers and
Cygler eds.), Medical Physics Publishing, Madison WI, 2009, previously printed in Palmans
and Vynckier, Reference Dosimetry for Clinical Proton Beams, In: Recent Developments
in Accurate Radiation Dosimetry (Seuntjens and Mobit eds.) Medical Physics Publishing,
Madison WI, 2002. With permission.)
199 Dosimetry
In practice, however, the volume of commercial ionization chambers is not
known with the required precision, and one has to rely on a calibration
in a reference beam to estimate the volume or bypass the requirement of
knowing the volume. It is worthwhile to mention, however, that if an accu-
rate estimate of the volume is available independently of a calibration, for
example, from the manufacturer’s blueprints or measured dimensions (as
in primary standards of air kerma), dosimetry using an ionization chamber
could be based on frst principles using Equations 7.6 and 7.7. It has been
shown that this can provide a reliable way of a monitor unit calibration for
a transmission ionization chamber to link with a Monte Carlo–based plan-
ning system (30).
To facilitate later the discussion of contributions to differences in dosim-
etry protocols, the overall expression to derive dose-to-water from the ion-
ization measurements can be split into three factors as follows:

D M
V
W e s
w Q Q
air cav
air Q w a , ,
( ) ( = 



⋅
⋅






⋅ ⋅
1
ρ
iir Q Q
) . ⋅ 



p

(7.8)
All protocols for dosimetry of proton beams using ionization chambers and
calculated data can be reduced to this factorization in which the second fac-
tor, representing an estimate of the ionization chamber volume, is solely
related to the calibration conditions, whereas the third factor is solely related
to the proton beam.
For example, with the formalism from the International Atomic Energy
Agency (IAEA) TRS-398 (1) using calculated k
Q
values the second factor is
given by

1
0
0
ρ
air cav
D w Q
air Q w air Q
⋅






=
⋅ V
N
W e s
, ,
,
( ) ( )
00 0
⋅








p
Q

(7.9)
where N
D w Q , ,
0
is the absorbed dose-to-water calibration coeffcient in the cali-
bration beam with quality, Q
0
, and the quantities in the denominator have
the same meaning as quoted above but now for the calibration beam quality.
The third factor is identical to the one in Equation 7.8 given that the notations
used are consistent with those in IAEA TRS-398.
If we take the European Charged Heavy Particle Dosimetry (ECHED) pro-
tocol (31, 32) as an example, then the second factor becomes

1 1
ρ
air cav
K wall m
air
c
⋅






=
⋅ − ⋅ ⋅
( )

V
N g A k
W e
( )








(7.10)
where N
K
is the air kerma calibration coeffcient in
60
Co, g is the correction
for radiative losses, A
wall
is the correction factor for absorption and scatter in
200 Proton Therapy Physics
the chamber wall and build-up cap in
60
Co, k
m
is the correction factor for the
nonair equivalence of the chamber’s construction materials, and (W
air
/e)
c
is
the mean energy required to produce an ion pair in dry air in the calibration
beam quality. The third factor is very similar as in IAEA TRS-398 with the
exception that there is no explicit mention of an ionization chamber pertur-
bation correction factor. This is not a de facto difference because in IAEA
TRS-398 the assumption is made that p
Q
equals unity.
Interesting to note is that there may not be a great difference in uncer-
tainty on the chamber volume as derived by this factor from air kerma or
absorbed dose calibrations. However, in the absorbed dose–based protocols,
the quantities occurring in the denominator of Equation 7.9 and those in the
third factor in Equation 7.8 are the same except for the difference in beam
quality and thus are expected to be more strongly correlated than those in
the air kerma–based approach where the factors A
wall
and k
m
refer to very
different conditions as well as to the build-up cap, which is not present with
in-phantom measurements. This shows that this factorization is only for
illustrative purposes but that the factors two and three cannot be considered
independently.
Although it is interesting and necessary to study the infuence of the sec-
ond factor in Equation 7.8 on dosimetry using different dosimetry formal-
isms, it is not related to the proton beam. Differences in dosimetry related to
that factor have been reviewed at length in Huq and Andreo (33 and refer-
ences therein) and will not be further discussed. Concerning the third factor,
each of the constituting quantities deserves separate attention:
• Mean energy required to produce an ion pair in dry air, (W
air
/e)
Q
:
Although often denoted with a capital W, sometimes a small w is
used to clarify that it should be the differential value for the local
charged particle spectrum because protons lose only a fraction of
their energy in the ionization chamber cavity (as opposed to photon
and electron beams, where the integral value accounts for all energy
losses during the complete slowing down of secondary electrons).
The W
air
/e value for protons has been the subject of controversy
since the ICRU Report 31 (34) recommended a value of 35.18 J C
−1
,
adopted by the ECHED (31, 32), whereas the American Association
of Physicists in Medicine (AAPM) Task Group 20 (35) recommended
a value of 34.3 J C
−1
. This discrepancy of 2.6% remained the source
of differences in dosimetry recommendations until the publica-
tion of ICRU Report 78 (36), which adopted the same value as IAEA
TRS-398. There are essentially two ways of measuring this quantity:
(1) a simultaneous measurement of the energy loss over an air col-
umn and the ionization produced per proton and (2) by comparing
the dose response of an ionization chamber and a calorimeter. The
frst method is cumbersome and requires a correction for electron
losses, which is diffcult to determine. The second method has the
201 Dosimetry
disadvantage that it provides not a direct measurement of W
air
/e, but
the pragmatic advantage is that if ionization chamber dosimetry is
based on a value derived from calorimetry, it provides consistency
with the dosimetry in high-energy photon beams. Noteworthy is
also that the W
air
/e value in protons is energy dependent but that
this energy dependence is not very well known (37).
• Water-to-air mass collision stopping power ratio, (s
w,air
)
Q
: The stop-
ping power for protons is governed by the same physics as for elec-
trons and positrons, and the theoretical models for calculations at
high energies are based on the same Bethe-Bloch formulas with a
series of correction terms. For consistency with photon and electron
dosimetry, ICRU Report 49 (38) recommended proton stopping pow-
ers using the same values for the mean excitation energy, I, as used
in the electron and positron stopping power tables of ICRU Report
37 (39). An important difference is that, compared with electrons, the
clinically relevant range of proton energies is at much lower (non-
relativistic) velocities where the density effect is of no importance
but where there is a strong energy (v
−2
) dependence of the stopping
powers (14). The result is that the water-to-air collision stopping
power ratios is fairly constant over the entire clinical energy range.
The most recent recommended values of s
w,air
are Spencer-Attix stop-
ping power ratios, including the contributions of secondary protons
and electrons (40), and are given as a function of the residual range
R
res
by the following (1):

s a b R
c
R
, w air res
res
= + +

(7.11)
where a = 1.137, b = −4.3 × 10
−5
, and c = 1.84 × 10
−3
.
• Ionization chamber perturbation factor, p
Q
: The ionization chamber
perturbation factor corrects for deviations from Bragg-Gray condi-
tions and can according to IAEA TRS-398 be described as the prod-
uct of four factors:
(i) a displacement correction factor, p
dis
, for the deviation of the
effective point of measurement from reference point of the ion-
ization chamber
(ii) a cavity perturbation correction factor, p
cav
, for the perturbation
of the charged particle fuence distribution due to the presence
of the air cavity
(iii) a wall perturbation factor, p
wall
, for the nonwater equivalence of
the ionization chamber’s wall, and
(iv) a central electrode correction factor for the presence of the cen-
tral electrode
202 Proton Therapy Physics
The frst one can alternatively be dealt with by positioning the
effective point of measurement at the required measurement
depth. For proton beams it is slightly easier to determine an effec-
tive point of measurement than for photon beams given the small
lateral defections that protons undergo. A reasonable approxima-
tion is thus to regard protons as traveling along straight lines once
they enter the ionization chamber geometry and integrate their
dose contributions over the cavity volume. For a cylindrical air
cavity with radius R
cyl
in water, it is easy to show that this results
in an effective point of measurement that is relative to the center
of the cavity positioned a distance ∆z
cyl
= 8R
cyl
/3π ≈ 0.85·R
cyl
closer
to the phantom surface (41). For Farmer-type chambers, the higher
density of the wall and central electrode materials brings this
slightly toward the center of the chamber and closer to the value
of ∆z
cyl
= 0.75·R
cyl
recommended in IAEA TRS-398 for ion beams
(42) but this is not the case for other cylindrical chambers with
a thick wall or central electrode for which substantial deviations
from this rule may occur. Regarding the other perturbation fac-
tors, all the evidence points to corrections of less than 1% (14, 15),
and relative correction factors of 1.005 have been demonstrated
both experimentally, by cavity theory and by Monte Carlo simula-
tion for A150 walled ionization chambers compared with graphite
walled chambers (43, 44, 45).
7.1.4 Detectors for Profile Measurements
A range of detectors can be used for lateral or depth–dose profle measure-
ments in proton beams and as for photon beams one can distinguish small,
point-like detectors that are used for scanning one-dimensional profles and
continuous or matrix detectors that form rigid structures and that can mea-
sure two- (2D) or three-dimensional (3D) profles in one exposure with a
high or relevant resolution. Lateral profles are usually not problematic given
that the spectral variations over the feld area are modest. Volume averag-
ing may be of concern in steep penumbrae and small-feld profles occur-
ring in stereotactic treatments and scanned beams. For the measurement
of depth–dose profles, the main issue is that many detectors exhibit a pro-
nounced LET dependence often resulting in a substantial underresponse in
the Bragg peak.
As we have seen, even water calorimeters exhibit an LET-dependent dose
response due to the chemical heat defect, apart from the fact that they are
impractical instruments for measuring depth–dose data. Ionization cham-
bers remain the instrument of choice for depth–dose measurements because
they exhibit a rather modest LET-dependent dose response that is usually
ignored. The third factor in Equation 7.7 clarifes the reasons for this LET
dependence.
203 Dosimetry
First, the water-to-air mass collision stopping power ratio, s
w,air
, is energy
dependent, resulting in the beam quality dependence of Equation 7.11. For
mono-energetic protons of energy E, s
w,air
can be calculated as follows:

s
S E
S E
w air
c
w
c
air
,
( )
( )
=
( )
( )
ρ
ρ

(7.12)
where S E
c
med
( ) ρ
( ) is the restricted mass collision stopping power in the
medium, med, for protons of energy, E. For protons with a spectral energy
distribution, the numerator and denominator in Equation 7.12 become a con-
volution of proton fuence and restricted stopping powers. The restricted
mass collision stopping power can be calculated from the unrestricted mass
collision stopping power

S
c
med
ρ ( ) for example, as tabulated in ICRU Report
49, by (44):

S S
K Z
A
W
c
med
c
med
 med
ρ ρ
β
( )
= ( ) −
⋅
⋅






⋅
2
2
ln
maxx







(7.13)
where the constant K = 0.307075 MeV cm
2
g
−1
and W
max
is the maximum
energy that a secondary electron can obtain from a proton-electron collision.
For energies from 1 to 300 MeV, restricted mass collision stopping power
ratios water-to-air with cutoff energy ∆ = 10 keV, derived from ICRU Report
49 using Equations 7.12 and 7.13, can be approximated by the following:

s E
a E
E b
n
w air ,
( )
( )
=
⋅
−
+ 1

(7.14)
where the constants are a = 1.1425, b = 0.025, and n = 0.0012.
Second, the mean energy required to produce an ion pair in dry air depends
on proton energy (37, 46, 47), and a model for energies above 1 MeV, based on
the assumption that for high-energy protons the value should evolve asymp-
totically to the value for high-energy electrons, is given by the following (46):

W E e
W e E
E k
air
p
e
( ) ( ) =
( ) ⋅
−

(7.15)
where W
e
/e = 33.97 J C
−1
is the mean energy required to produce an ion pair
in high-energy electron and photon beams and k is a constant that equals
k = 0.08513 derived from Dennis’ data (46, 47), whereas a ft to the data from
Grosswendt (37) results in k = 0.05264. These two values for k represent quite
a large difference in the variation of (W
air
/e)
p
with energy (9.3% and 5.5%
from 1 to 300 MeV, respectively), mainly due to the structure of the func-
tional dependence at lower energies; however, this variation is mainly of
signifcance for proton energies under 10 MeV (hence the last couple of mil-
limeters of the proton range).
204 Proton Therapy Physics
Third, the wall perturbation factor for ionization chambers has equally
been demonstrated to be energy dependent (44, 45) and can be calculated
based on cavity theory as follows (44):

p
s s
s
SA
wall
w wall
BG
wall air
SA
w air
=
⋅
, ,
,

(7.16)
where the super indices BG and SA have been introduced to indicate Bragg-
Gray stopping power ratios (using unrestricted stopping powers in Equation
7.12) and Spencer-Attix stopping power ratios, respectively.
The energy dependence of the three contributions is illustrated in Figure 7.3
for graphite- and A150-walled ionization chambers using the W
air
/e variation
from the Dennis data. All contributions were normalized to unity at 100 MeV.
Convolving this with proton spectra and dose contributions as a func-
tion of depth, this leads to a reduction of the peak to entrance ratio of about
1.5% to 2% for air-flled ionization chambers in high-energy proton beams
and 3% to 4% for low-energy beams typically used for the treatment of eye
melanoma, where the lower numbers are obtained using the Grosswendt
data and the higher numbers using the Dennis data. If no variation of the
W
air
/e value for protons with energy is assumed, the reduction of the peak
to entrance ratio is about 0.7% for high-energy beams and 1.2% for low-
energy beams.
For other devices typically used for measuring depth–dose curves, the
underresponse in the Bragg peak is usually worse than for ionization
1
0.99
1.00
1.01
R
e
l
a
t
i
v
e

q
u
a
n
t
i
t
y

n
o
r
m
a
l
i
z
e
d

a
t

1
0
0

M
e
V
1.02
1.03
1.04
Total A150-walled
Total graphite-walled
W
air
/e
s
w,air
p
wall-graphite
p
wall-A150
1.05
10 100
E / MeV
1000
FIGURE 7.3
Relative variation as a function of proton energy of the mean energy required to produce and
ion pair in dry air, the mass collision stopping power ratio water-to-air, and the ionization
chamber wall perturbation correction factor due to secondary electron effects for two wall
materials according to the data and expressions discussed in the text as well as the product of
the three.
205 Dosimetry
chambers. Figure 7.4 shows the underresponse compared with the response
of an ionization chamber in a 60-MeV proton beam for two types of radio-
chromic flm using a model based on experimental data (48) and for ala-
nine using a model based on experimental data from the literature (49).
Note that only the last couple of millimeters of the Bragg curve is shown.
Other dosimeters such as diamond detectors, silicon diodes, MOSFETs
(metal-oxide-semiconductor feld-effect transistors), thermoluminescent
devices, optically stimulated luminescence devices, scintillators, gel dosim-
eters, radiochromic plastics, and photographic flm usually show this Bragg
peak quenching (14), often to a much worse level than in Figure 7.4. Various
explanations have been given for this energy-dependent response such as
single-hit theory (saturation of the sensitive site with one ionization) in, for
example, alanine and radiochromic flm; interradical recombination in, for
example, gel dosimeters; and charge recombination in, for example, dia-
mond and more complex theoretical models including charge transport and
trapping such as in thermoluminescent devices. In addition, several of these
devices are less water equivalent in terms of stopping power variation with
energy as can be seen in Figure 7.5.
On the other hand, some have reported about diodes that over-respond
or highly doped p-type diodes that give good agreement with ioniza-
tion chambers (50), but given the variability of the response of diodes
of the same types, this needs to be verifed for each individual diode. A
gel dosimeter that is less prone to Bragg peak quenching has also been
reported recently, the improvement being explained by the mixing in of a
compound that results in smaller radiation-induced polymers and a higher
viscosity of the gel (51). A gas electron multiplication detector, mainly used
24
0.0
1.0
2.0
3.0
4.0
5.0
6.0
26 28
Depth / mm
Alanine
Markus ionization chamber
GafChromic EBT film
GafChromic MD-55 film
N
o
r
m
a
l
i
z
e
d

d
e
t
e
c
t
o
r

s
i
g
n
a
l
30 32
FIGURE 7.4
Underresponse of two types of radiochromic flm and alanine compared with an ioniza-
tion chamber in the Bragg peak of a 60-MeV proton beam as expected from model functions
derived from experimental data.
206 Proton Therapy Physics
for 2D lateral profle measurements, has also been demonstrated to exhibit
only a small quenching effect in the Bragg peak (52). Another interesting
method to overcome this energy dependence was reported on scintillat-
ing plastics after observing that some scintillating mixtures exhibit an
underresponse, whereas others exhibit an overresponse. By choosing an
appropriate mixture, a scintillator giving the same depth-dependent dose
response as an ionization chamber was established (53), the disadvantage
still being that the result applies only to the one particular energy where
it was matched.
Although with any of the above-mentioned detectors dose distributions
can be obtained by scanning, effcient systems exist that allow measure-
ment of distributions in a single exposure. Multilayer ionization chambers
have been developed (54) containing absorbing material between neighbor-
ing chambers, enabling the measurement of a depth–dose distribution and
range in a single exposure. For 2D and 3D dose distributions ionization
chambers have been confgured in pixel arrays, strips, and multiple-layer
strip arrays extending these possibilities. A multilayer Faraday cup can
also be used for range verifcation (55). Further devices for 2D and 3D mea-
surements to mention are radiochromic flm (48), radiographic flm (56), gel
dosimeters (51), radiochromic plastics (57), scintillating screens (58), scintil-
lating liquids (59), gas electron multiplication detectors (52), and amorphous
silicon fat-panel detectors (60). A more extensive review is given in Karger
et al. (15).
1
0.95
1.00
1.05
s
w
,

m
e
d
1.10
1.15
Air
Diamond
Si
LiF
Al
2
O
3
Alanine
Photographic
emulsion
MD-V2-55
EBT
1.20
1.20
1.30
1.40
s
w
,

m
e
d
1.50
1.60
1.70
10 100
E / MeV
1000
FIGURE 7.5
Mass collision stopping power ratios water-to-medium for a variety of detector materials. The
black curves for air, diamond, alanine, GafChromic EBT flm, and GafChromic MD-V2-55
flm are represented on the left-hand side vertical axis; the gray curves for silicon, aluminium
oxide, lithium fuoride, and photographic emulsion are represented on the right-hand side ver-
tical axis.
207 Dosimetry
7.2 ReferenceDosimetry
Reference dosimetry in clinical beams is usually based on national or
international reports providing protocols or codes of practice. This section
gives frst a historical view followed by a subsection on the most recent
recommendation.
7.2.1 History of Reference Dosimetry for Protons
The frst codes of practice for heavy charged particle dosimetry emerged
in the 1980s and early 1990s from the AAPM (AAPM Report 16 [35]) and
by the ECHED group (31, 32). They all had in common that the frst recom-
mendation was to use a calorimeter for reference dosimetry. If not avail-
able, a Faraday cup could be used as reference instrument (35) or calibrated
against a calorimeter (31, 32), or an ionization chamber calibrated in terms
of exposure in air or air kerma in a
60
Co calibration beam could be used.
In AAPM Report 16 (35) and the original ECHED code of practice (31),
the quantity of interest was defned as dose-to-tissue so that in the third
factor of Equation 7.8, a stopping power ratio tissue-to-air (tissue-to-gas
in AAPM Report 16 because ionization chambers flled with other gas-
ses than air were considered) would occur rather than a stopping power
ratio water-to-air. For those two protocols, the second factor in Equation
7.8 was, apart from a few details, similar to that used in AAPM TG-21 for
photon and electron dosimetry (61), although no consideration was given
to the fact that in the
60
Co calibration beam, part of the electron spectrum
in the air cavity is not generated in the wall. Both also used the stopping
power tables of Janni (62). In the Supplement to the ECHED protocol (32)
dose-to-water was defned as the quantity of interest and in addition, the
stopping powers of ICRU Report 49 (38) were recommended, which was
a step in bringing proton dosimetry in better harmony with high-energy
photon and electron dosimetry. One of the more substantial differences
between the recommendations of the AAPM and the ECHED was, as dis-
cussed before, the substantial discrepancy of about 2.6% in the W
air
/e value
for proton beams.
ICRU Report 59 (63) provided a new recommendation that covered both
the air kerma and the absorbed dose routes for dosimetry, but in the lat-
ter a number of defciencies of the procedures and data were pointed out
(65), including the undocumented derivation of the W
air
/e value for proton
beams based on published data, the recommendation of using a W
air
/e in
ambient air rather than dry air, and the omission of a perturbation factor for
the ionization chamber in the calibration beam (as in the denominator on the
right-hand side of Equation 7.9). IAEA TRS-398 improved on this and pro-
vided a recommendation covering ionization chamber dosimetry based on
absorbed dose-to-water calibrations for all external beams except neutrons.
208 Proton Therapy Physics
For protons, the value of W
air
/e was obtained from a robust statistical analy-
sis of the available data and Spencer-Attix mass collision stopping power
water-to-air ratios (40) were used for the frst time. Other advantages were
better estimates of the uncertainties and better consistency with other exter-
nal beam modalities regarding the measurement of infuence quantities such
as recombination and polarity effects. The most recent recommendation in
ICRU Report 78 (36) integrally adopts the concepts and data from TRS-398.
One of the achievements of ICRU Report 78 was to readdress all the published
W
air
/e data, correcting a few inconsistencies in earlier used data by ICRU
Report 59 and IAEA TRS-398, and to add new data published since 2000. It
was decided that for consistency with calorimetry-based data in high-energy
photon and electron beams, only the data obtained by calorimetry would be
used for a reevaluation (64), resulting in a weighted mean value of 34.15 ±
0.13 J C
−1
and a weighted median value of 34.23 ± 0.13 J C
−1
, both consistent
with the value recommended in IAEA TRS-398. All the calorimetric data and
the quoted mean and median values are shown in Figure 7.6.
With the latter three protocols mentioned, the idea of recommending calo-
rimeters in a clinical environment was abandoned given that calorimeters
are too cumbersome and time consuming to operate for routine dosimetry.
Nevertheless, the frst recommendation of IAEA TRS-398 remains that k
Q

values are measured for each individual ionization chamber in each indi-
vidual beam they are used. A number of published articles have reported
k
Q
values in proton beams by comparing ionization chambers with water
calorimeters both in passively scattered proton beams as in scanned proton
0
33.0
33.5
34.0
34.5
35.0
35.5
36.0
50
(
W
a
i
r
/
e
)
p

/

e
V
100
Weighted
mean
Weighted
median
Schulz et al. 1992
Palmans et al. 1996
Palmans et al. 2004
Brede et al. 1999
Siebers et al. 1995
Delacroix et al. 1997
Medins et al. 2006
Hashemian et al. 2003
150 200
Energy / MeV
FIGURE 7.6
Calorimetric determinations of the mean energy required to produce an ion pair in dry air and
weighted mean and median values as determined in Jones (64). (From Palmans et al., Hadron
Dosimetry. In: Clinical Dosimetry Measurements in Radiotherapy (Rogers and Cygler eds.),
Medical Physics Publishing, Madison WI, 2009, and Jones, Rad Phys Chem, 75(5), 541, 2006.
With permission.)
209 Dosimetry
beams (12, 24, 66–68). Figure 7.7 compares those experimental values with
the calculated values recommended in IAEA TRS-398.
7.2.2 Recommendations of IAEA TRS-398 and ICRU Report 78
It is not the aim here to give a comprehensive overview of the code of prac-
tice for proton dosimetry in IAEA TRS-398 (1), which has been integrally
adopted in ICRU Report 78 (36). For all details the reader is referred to those
reports. The main steps in the dose determination using ionization cham-
bers calibrated in terms of absorbed dose-to-water will be briefy outlined
and some import points to pay attention to concerning proton dosimetry
will be discussed.
The formalism for determination of absorbed dose-to-water, D
w,Q
, in a pro-
ton beam with quality Q is

D M N k
w, Q Q D, w, Q Q Q
0 0
= ⋅ ⋅
,

(7.17)
where M
Q
is the ionization chamber reading corrected for infuence quanti-
ties, N
D w Q , ,
0
, the absorbed dose-to-water calibration coeffcient of the ioniza-
tion chamber in a calibration beam of quality Q
0
and k
Q Q ,
0
the beam quality
correction factor accounting for the use of the calibration coeffcient in a dif-
ferent beam quality Q.
0.96
0.98
1.00
k
Q
1.02
1.04
1.06
1.08
V
a
t
n
i
t
s
k
y

1
9
9
6
P
T
W
3
0
0
0
1

2
5
0

M
e
V
V
a
t
n
i
t
s
k
y

1
9
9
6
P
T
W
3
0
0
0
1

1
5
5

M
e
V
V
a
t
n
i
t
s
k
y

1
9
9
6
C
a
p
i
n
t
e
c

P
R
0
6

2
5
0

M
e
V
V
a
t
n
i
t
s
k
y

1
9
9
6
C
a
p
i
n
t
e
c

P
R
0
6


2
5
0

M
e
V
M
e
d
i
n

2
0
0
6
N
E
2
5
7
1

1
8
0

M
e
V
M
e
d
i
n

2
0
1
0
N
E
2
5
7
1

1
8
0

M
e
V
S
a
r
f
e
h
n
i
a

2
0
1
0
E
x
r
a
d
i
n

T
1

2
3
5

M
e
V
S
a
r
f
e
h
n
i
a

2
0
1
0
E
x
r
a
d
i
n

T
1

2
3
5

M
e
V
G
a
g
n
e
b
i
h

2
0
1
0
E
x
r
a
d
i
n

T
2

1
7
0

M
e
V
FIGURE 7.7
k
Q
values for various ionization chambers derived from water calorimetry (data points) com-
pared with values from TRS-398 (black horizontal lines with gray boxes defning a 1.7%
standard relative uncertainty interval). The three data points on the right-hand side are for
scanned proton beams.
210 Proton Therapy Physics
Because of the limited availability of experimental k
Q Q ,
0
data, their values
are in practice calculated from

k
W e s p
W e s
Q Q
air
Q
w,air
Q
Q
air
Q
w,air
0
,
0
=
( ) ⋅
( )
⋅
( ) ⋅
(( )
⋅
Q
Q
0
0
p

(7.18)
in which all quantities have been defned before. The combination of
Equations 7.17 and 7.18 leads to the factorization in Equations 7.8 and 7.9 as
discussed above.
k
Q Q ,
0
values are calculated with Equation 7.18 as a function of the beam
quality index, R
res
, defned as

R R z
res p
= −

(7.19)
where R
p
is the practical range, defned as the depth distal to the Bragg peak
at which the dose is reduced to 10% of its maximum value and z is the depth
of measurement. R
res
is related to the most probable energy of the highest
proton energy peak in the spectrum.
Concerning the correction for infuence quantities of the ionization cham-
ber reading, the corrections for atmospheric conditions (deviations from
normal pressure, temperature, and relative humidity at which the calibra-
tion coeffcient is valid) and electrometer calibration are the same as in all
modern protocols for high-energy photon and electron beams and will not
be discussed here. The correction for polarity effects and ion recombination
are measured in the same way as well, but an important issue to be consid-
ered is if a proton beam should be regarded as pulsed or continuous with
respect to ion recombination because this makes a difference in deriving
the correction factor from the traditional two-voltage method. IAEA TRS-398
mentions that beams extracted from a synchrotron may have to be regarded
as continuous. However, it has been demonstrated that proton beams from a
cyclotron, which are inherently pulsed, should be regarded as continuous as
well for this purpose given the short time interval between pulses compared
with the ion collection time (69). In high dose rate beams like those used in
ocular treatments, the error on the ion recombination factor could be up to
2% when applying the two-voltage method with the inappropriate assump-
tion that the beam is pulsed.
The calibration coeffcient N
D,w,Q
0
is usually obtained in a
60
Co calibration
beam at a standards laboratory, and in that case IAEA TRS-398 omits the
index Q
0
for both the calibration coeffcient and the beam quality correction
factor: N
D,w
and k
Q
.
k
Q
values for all commonly used ionization chambers have been tabulated
as a function of R
res
in IAEA TRS-398 and are for a selection shown in Figure
7.8. It is clear that the variation with beam quality is rather limited. The dif-
ferences between ionization chamber types is solely due to differences in the
perturbation correction factors for
60
Co.
211 Dosimetry
The ideal situation, however, would be that the ionization chamber is cal-
ibrated against a calorimeter in a proton beam that would then form the
calibration quality Q
0
. k
Q Q ,
0
can then be obtained from the tabulated data as
follows:

k
k
k
Q Q
Q
Q
0
,
0
=

(7.20)
where both Q and Q
0
refer to a proton beam quality. A similar case is that in
which a plane-parallel ionization chamber needs to be used, for example, in
a spread-out Bragg peak in a low-energy beam with very limited extension.
IAEA TRS-398 discourages the use of plane-parallel chambers with
60
Co cali-
bration coeffcients because the perturbation correction factors in the
60
Co
calibration photon beams have a large uncertainty. It has therefore been sug-
gested to cross-calibrate a plane-parallel ion chamber against a cylindrical
chamber in a high-energy proton beam and subsequently use the chamber
in other proton beams by using Equation 7.20 for k
Q Q ,
0
.
7.3 Microdosimetry
Although radiotherapy prescription is based on the macroscopic quantity
absorbed dose-to-water, multiplied with a quality factor, the effect of radia-
tion on individual cells is governed by the local energy deposition within
0.98
0.1 1 10
R
res
/ g cm
–2
100
0.99
1.00
k
Q
1.01
1.02
1.03
1.04
Capintec PR06C
(Farmer - C552)
NE2571
(Farmer - graphite)
IBA FC65P
(Farmer - Delrin)
PTW 30014
(PinPoint)
FWT IC-18
Roos
NACP02
PTW 3001
(Farmer - PMMA)
NE2581
(Farmer - A150)
Markus
1.05
FIGURE 7.8
Calculated k
Q
data as a function of the proton beam quality R
res
for a selection of ionization
chambers taken from IAEA TRS-398.
212 Proton Therapy Physics
the cell or parts of the cell. Microdosimetry concerns the study of the spatial
and temporal distribution of energy deposition accounting with the stochas-
tic nature of energy losses and track structure and therefore provides the
physical information that is more directly linked with the biological effects
of radiation.
7.3.1 Microdosimetric Quantities
Microdosimetry uses quantities that are the stochastic equivalents of
absorbed dose and LET. The specifc energy, z, in a miscroscopic volume, V,
is defned as z = ε/ρV, where ε is the energy imparted in the volume and ρ
the mass density of the medium. The energy imparted is defned as the sum
of all kinetic energy carried by ionizing particles into the volume minus the
sum of all kinetic energy carried by ionizing particles out of the volume plus
the energetic value of any reduction of rest mass taking place within the
volume. The lineal energy, y, is defned as y = ε
1
/ l , where ε
1
is the energy
imparted in the volume in a single event and l is the mean chord length
of the volume. For any concave volume the mean chord length is given by
l V S = 4 , where S is the surface area.
Radiation effects that are stochastic such as the biological response depend
on the probability distributions of the microdosimetric quantities, f(z) and
f(y), and can in principle be derived from those (71, 72). The distribution of
lineal energy is usually represented graphically as y · f(y) plotted against log
(y) or y
2
· f(y) plotted against log (y). In the former representation, the area
under the curve delimited by two values of y is proportional to the fraction
of events between those two values of y, whereas in the latter representa-
tion the area under the curve delimited by two values of y is proportional
to the fraction of dose delivered by events with lineal energy between those
two values. Figure 7.9 gives an example of the second representation of a
microdosimetric spectrum of a proton beam compared with that of a
60
Co
beam (73) together with a biological weighting function for the acute effects
in the intestinal crypt cells of mice as an end point (74) as a function of lineal
energy, indicating why the biological effect of protons is slightly enhanced
compared with
60
Co (see Chapter 19).
7.3.2 Experimental Microdosimetry
A distinction has to be made between regional microdosimetry, the most
common focus of experimental microdosimetry, which aims at measuring
f(y) and f(z) for a particular site of interest, and structural microdosimetry,
which aims at deriving microdosimetric quantities and actions from detailed
3D distributions of energy transfer points.
The most commonly used detectors for regional microdosimetry are tissue
equivalent proportional counters (TEPCs). In its most simple form a TEPC is
a walled ionization chamber operated at high-voltage such that an avalanche
213 Dosimetry
takes place. The number of ion pairs produced is assumed to be proportional
to the energy transferred. By operating at low pressure, the energy deposi-
tion of a small site of tissue density is mimicked (e.g., a 2.5-cm sphere at
pressure of 2.3 kPa is approximately equivalent to a 1-μm-diameter sphere
of density 1 g cm
−3
). If the gas has the same atomic composition as the wall
material, the fuence of secondary charged particles should be independent
of density variations apart from the infuence of the density effect on the
stopping power. For proton beams, the energy deposition in a single event
can be overestimated due to the following three effects (71, 75):
1. The delta-ray effect (a secondary electron that would normally not
cross the same site as the primary proton does enter the volume
because of the larger dimensions),
2. The V-effect (a secondary proton or heavier particle from a nuclear
interaction that would normally not cross the same site as the pri-
mary proton does enter the volume because of the larger dimen-
sions), and
3. The reentry effect (after leaving the collecting volume a secondary
electron following a strongly curved path that would normally not
reenter the measurement volume does reenter because of the larger
dimensions).
For this reason, more sophisticated TEPCs are wall-less, either by using spe-
cial electrodes to shape the feld and that way defne the measurement vol-
ume without the presence of a wall or by using a grid wall, thus minimizing
10
–2
0.0
0.2
0.4
0.6
0.8
1.0
Co-60
p 200 MeV 17.6 cm
r(y)
10
–1
10
0
10
1
y / keV mm
–1
y
2
f
(
y
)r
(
y
)
10
2
10
3
0
1
2
3
4
5
FIGURE 7.9
Microdosimetric spectrum of a 200-MeV proton beam at a depth of 17.6 cm (squares), micro-
dosimetric spectrum of a
60
Co beam (triangles), and a biological weighting function (line).
(Replotted from Coutrakon et al., Med Phys, 24(9), 1499, 1997. With permission.)
214 Proton Therapy Physics
the amount of wall material. Another problem with TEPCs is their size,
which limits the achievable resolution, which is especially a problem in the
Bragg peak, and makes them more vulnerable to pile-up effects in radiother-
apy level dose rates due to the occurrence of simultaneous multiple events
(76). Mini-TEPCs (77) and gas microstrip detectors (consisting of alternating
anode and cathode metallic strips on a substrate and a drift electrode defn-
ing the gas volume) (78) have been developed to overcome these problems for
proton microdosimetry.
Calibration of a TEPC consists of establishing a relation between pulse
height and energy deposition and is done using either a source of particles
with known energy that are completely absorbed in the detector volume
or by making use of the proton edge. The latter exploits the fact that near
the end of the range the proton energy deposition is highest and the lineal
energy distribution has a sharp edge (which is, however, blurred by energy
and range straggling and by the contaminant presence of heavier recoils).
The edge lineal energy for protons was determined as y
edge
= 136 keV μm
−1

for a water sphere of 2 μm in diameter (79) (and should be scaled for the
size and the operational gas density of the TEPC). Knowledge of the mean
energy required to produce an ion pair in the gas, W
gas
, is another source
of uncertainty. W
gas
is known to decrease with energy for a given particle
mass and increases with particle mass for a given energy and is assumed to
add about 5% uncertainty to the energy absorption measured with a propor-
tional counter.
Silicon-based devices for microdosimetry also measure ionization, via
electron-hole pair creation in a depletion layer, but have as a main advantage
compared with a TEPC that their size is much closer to the site of interest in
water or tissue. For radiotherapy this results in both a higher spatial resolu-
tion and a reduction of the delta-ray effect, V-effect, reentry effect, and pile-
up effect. Disadvantages are that the collecting volume is poorly defned,
that they are prone to radiation damage, and that they are not exactly tis-
sue equivalent so that a conversion (with a scaling factor of about 0.63) is
still needed (75). The mean energy required to produce an electron-hole pair,
W
Si
, is about a factor 10 lower than W
gas
in TEPCs. The same problem of the
dependence of W
Si
on particle energy and particle type exists, but a value of
W
Si
= 3.62 eV is often used.
Application of an array of p-n junctions with a pixel area of 0.04 cm
2
to two
therapeutic proton beams revealed that in large beams even with a silicon
diode, pile-up effects can occur (75), but silicon devices can be further minia-
turized. Another interesting feature of silicon technology is that a construc-
tion integrating more than one detector with different functions is possible.
For example, a ∆E-E silicon telescope has been described (80) consisting of
two layers of silicon detectors sharing the same p
+
electrode, the upper one
being very thin (1 μm) and the lower one being 500 μm thick. When a par-
ticle passes through both layers, the signal from the upper layer provides the
energy loss over 1 μm of silicon, whereas the sum of both signals provides
215 Dosimetry
the total energy of the particle (under the condition that it is stopped within
the thick lower layer). This coincidence measurement allows resolving the
particle type that hits the detector because different particle types will
occupy different regions in a ∆E-E map and is thus of interest in mixed par-
ticle felds. Application of the detector to protons showed that contributions
of other ion species in the radiation feld are marginal.
Besides the experimental methods for regional microdosimetry, some
track structure measurement devices have been used in proton beams,
which are mentioned here but of which a more extended overview can be
found in Bradley (75). In cloud chamber microdosimetry, a low-pressure
super-cooled gas is used in which the individual ionizations of the pro-
ton and its secondary particles create a 3D pattern of droplets that can be
resolved by stereoscopic photography, providing extremely high-resolution
detail on the location of individual ionizations within the gas. In an opti-
cal ionization chamber electrons in the particle track are made to oscillate
rapidly by the application of an external, short duration, high-voltage elec-
tric feld. The excited electrons produce additional ionization and electronic
excitation of the gas molecules in their immediate vicinity, leading to fuo-
rescent light emission from the gas that allows the location of the electrons
to be determined with a resolution of 10 nm. In 3D optical random access
memories the energy deposited along the proton track changes a bi-stable
photochromic material from the stable nonfuorescent form to a quasi-stable
fuorescent form. The location of the fuorescent sites can be read out by
confocal laser microscopy.
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8
Quality Assurance and Commissioning
ZuofengLi,RoelfSlopsema,StellaFlampouri,andDanielK.Yeung
CONTENTS
8.1 Standards and Recommendations on External Beam Radiation
Therapy QA and Commissioning ........................................................... 222
8.2 Components of a Clinical Proton Therapy System ............................... 223
8.2.1 Beam Production and Transport System .................................... 223
8.2.2 Beam Delivery Techniques/Nozzles ........................................... 224
8.2.3 Mechanical Gantry or Fixed Beam Line ..................................... 227
8.2.4 Patient-Positioning System ........................................................... 227
8.2.5 Image-Guided Patient-Alignment System ................................. 227
8.2.6 Computed Tomography Scanners for Proton Therapy ............ 228
8.2.7 Patient Immobilization Devices ................................................... 228
8.3 Design of Acceptance Testing and Commissioning Plan for a
Proton Therapy System ............................................................................. 229
8.3.1 Acceptance Testing of Proton Therapy Systems........................ 229
8.3.1.1 Radiation, Mechanical, and Electrical
Safety Issues ............................................................... 229
8.3.1.2 Gantry, Snout, Patient-Positioning, and
Patient-Alignment Systems ............................................ 231
8.3.1.3 Proton Beam Characteristics ......................................... 233
8.3.1.4 Dose-Monitoring System ............................................... 238
8.3.2 Commissioning of Proton Therapy Systems ............................. 239
8.3.2.1 CT HU-to-Stopping Power Calibration ........................ 240
8.3.2.2 Treatment-Planning System Commissioning ............. 240
8.3.2.3 MU Calculations ............................................................. 242
8.3.2.4 Beam-Modifying Accessories ........................................ 243
8.3.2.5 Patient Immobilization Devices .................................... 243
8.3.2.6 R&V System ...................................................................... 245
8.4 Design of a Periodic QA Program for a Proton Therapy System .......... 245
8.5 Dosimetry Instrumentation for Proton Therapy
Commissioning and QA ........................................................................... 251
8.6 Conclusions ................................................................................................. 259
References ............................................................................................................. 260
222 Proton Therapy Physics
Clinical proton therapy is delivered using proton beams produced by either
synchrotron- or cyclotron-based accelerator systems, which differ signif-
cantly in operating details and beam controls (see Chapter 3). The mechani-
cal and electronic components for formation of spread-out Bragg peaks
(SOPBs) from pristine Bragg peaks may differ between different proton ther-
apy systems as well (see Chapters 4–6). Such differences lead to signifcant
diffculties in developing general, comprehensive recommendations for the
commissioning and quality assurance (QA) programs of clinical proton ther-
apy. It is therefore important that practitioners of proton therapy, especially
the medical physicists, develop a machine-commissioning and QA process
before initiation of patient treatment and continue to monitor system perfor-
mance and improve the periodic QA program as more experience is gained
over time with a particular proton therapy system.
8.1 StandardsandRecommendationsonExternalBeam
RadiationTherapyQAandCommissioning
Unlike the case of conventional photon-based external beam radiation ther-
apy, standards of practice for proton therapy system commissioning and
periodic QA programs have not been developed. The American Association
of Physicists in Medicine (AAPM) has developed a number of recommen-
dations for the commissioning and periodic QA of linear accelerator–based
radiotherapy, as embodied in its task group reports (1–3). These reports out-
line detailed, specifc, sometimes prescriptive recommendations of QA tests,
together with acceptable performance tolerances, for the commissioning and
periodic QA of linear accelerators. The AAPM TG45 report (1) provided step-
by-step instructions on the acceptance testing and commissioning of linear
accelerators. The commissioning of a linear accelerator follows successful
acceptance testing of the unit and aims at the accurate collection and model-
ing of beam and nondosimetric machine data for treatment planning. AAPM
TG40 and TG142 reports (2, 3) provide detailed guidelines on the periodic
QA tests to be performed for radiotherapy equipment with test frequency
and tolerance values.
Although the overall structure of a proton therapy system acceptance
testing, commissioning, and periodic QA program will be similar to those
described in these reports, the specifc recommendations of these standards
of practice do not apply well to proton therapy systems in general. A pro-
ton therapy system, for example, will be capable of providing a continu-
ously variable range of beam energies from a minimum value (e.g., 90 MeV)
to a maximum energy of 230–250 MeV at the nozzle entrance. Depending
on the system design, the system may subdivide this continuous span of
beam energy into spans of beam energy or options. Proton therapy systems
223 Quality Assurance and Commissioning
differ from conventional linear accelerator–based radiotherapy in additional
details, including the production and delivery of treatment beams; the use
of image guidance (currently provided by daily or feld-by-feld orthogonal
x-ray imaging); the use of range compensators; and the use of 6 degrees of
freedom (DOF) patient positioners, some with corrections for gantry sags.
The acceptance testing, commissioning, and periodic QA tests will need to
be carefully designed to customize to these differences.
The International Commission on Radiation Units and Measurements
(ICRU) has published a report (4), ICRU Report 78, on prescribing, recording,
and reporting proton therapy. A chapter of this report is dedicated to QA
of proton therapy systems, with discussions on the individual subsystems
of proton delivery, patient positioning and immobilization, and treatment
planning. The report provides two tables as examples for the periodic QA
of passive-scattering beams and active scanning beams. These tables would
serve well as the foundation in building a periodic QA program for a proton
therapy institution; however, revisions and specifcations of tolerances will be
necessary to tailor to the requirements of individual proton therapy systems.
8.2 ComponentsofaClinicalProtonTherapySystem
A modern clinical proton therapy system is designed to include multiple sub-
systems, such that they function collectively as an integrated unit to provide
accurate patient treatment simulation, planning, and delivery. Many of these
subsystems have the same functionalities as their counterparts in traditional
radiation therapy and are different only in specifc confgurations when
adapted for proton therapy applications. Guidelines for their commissioning
and QA tests, whenever applicable, should follow the established standards.
8.2.1 Beam Production and Transport System
An accelerator, either a cyclotron or a synchrotron, is used to produce the
proton beam (see Chapter 3). Cyclotrons produce a nearly continuous beam
of constant beam energy of up to 250 MeV, with adjustable beam current.
The high-energy beam leaving a cyclotron is then reduced or “degraded” to
a lower-energy beam as required for patient treatment, by use of an energy
degrader of tissue equivalent materials of variable thicknesses. The insertion
of an energy degrader, however, also degrades the beam quality by increas-
ing beam emittance or angular spread, as well as the beam energy spread.
An Energy Selection System (ESS) using collimators, slits, and magnets is
then used to restore beam quality. Synchrotrons produce spills of a proton
beam of variable energy, with each several-seconds-long spill consisting of a
beam-on fat top and a beam-off bottom. No energy degrader and selection
224 Proton Therapy Physics
system is required for a synchrotron-based system because of the nearly con-
tinuous adjustability (in beam energy) of the accelerator.
The proton beam, after exiting the ESS for a cyclotron-based system, or the
accelerator in case of a synchrotron, then follows a beam transport system in
vacuum to be directed to individual treatment rooms. Multiple magnets are
used along the beam line for focusing and centering, so that beam quality
is maintained at the highest level possible. Such beam quality parameters
include average beam energy, energy spread, emittance (angular spread),
spot size, and beam current intensity. These physical beam characteristics
may have a signifcant impact on the quality of patient dosimetry. The con-
stancy of these beam characteristics over the lifetime of the proton therapy
system, therefore, needs to be considered carefully in the design of a proton
therapy system commissioning and QA program.
8.2.2 Beam Delivery Techniques/Nozzles
Proton delivery techniques, both passive scattering and active scanning, are
ultimately implemented in the nozzle. The proton beam exiting the beam
transport system is a narrow beam, with a nearly uniform energy spectrum.
This beam produces a narrow pristine peak in water, whereas for clinical
cancer therapy, the beam needs to create a dose distribution that conforms
to the three-dimensional (3D) volume of a target. The nozzle receives the
input of a narrow pencil beam, outputs a beam spread pattern suitable for
delivery of a 3D dose distribution, through either the use of physical scatter-
ers (Chapter 5) or active magnet-driven scanning of the pencil beam in the
beam’s lateral direction (Chapter 6), and creates a depth–dose profle with a
fat (SOBP) or customized shape in the beam axis direction.
Figure 8.1 shows the components of a typical passive-scattering nozzle (5).
The proton pencil beam enters the nozzle through IC1 (ion chamber 1), which
monitors beam centering upon entrance into the nozzle. The frst scatterer
serves to expand the narrow pencil beam into a wide, Gaussian-shaped pro-
ton beam, and the second scatterer subsequently fattens the wide Gaussian
beam into a fat proton beam to allow delivery of 3D conformal proton ther-
apy treatments. Such use of two consecutive scatterers, similar to the use of
scattering foils in conventional linear accelerators for electron beam produc-
tion, is referred to as the double-scattering technique. The second scatterer
may be removed, however, to achieve the single-scattering technique, which
produces a beam with dome-shaped profle but avoids the scattering of pro-
tons in the second scatterer, thereby improving beam quality in lateral pen-
umbra and distal falloff. Moveable collimators/jaws are used to eliminate
scattered protons outside the intended treatment volume. Two ion chambers
(IC2 and IC3) are used for dose and beam profle monitoring and control.
The fnal feld shape is defned by a treatment-feld-specifc aperture (block),
mounted on a moveable snout so as to minimize the distance of the range
compensator/bolus to patient skin and hence reduce in-air proton scattering.
225 Quality Assurance and Commissioning
The creation of SOBP is performed by use of modulation wheels in this
nozzle. In the example of the nozzle by IBA (Ion Beam Applications, Louvain-
la-Neuve, Belgium) each of the three modulation wheels contains three cir-
cular tracks of step-wise increasing thicknesses, which allows step-by-step
pullback of pristine peaks. The proton beam current is modulated based on
precalibrated tables to maintain the fatness of the SOBP and is turned off to
achieve a prescribed SOBP width (6, 7). Accuracy of beam current modula-
tion directly impacts fatness of the delivered SOBP, as well as the absolute
dose value in the middle of this SOBP (7) (see Chapter 5). The presence of
scatterers and modulation wheels in the proton beam path should be of par-
ticular concern in the implementation of a periodic QA program, as they are
the subject of signifcant mechanical wear and tear and over time may suffer
radiation damage.
The nozzle of Figure 8.1, in addition to providing single- and double-
scattering techniques, also supports an active scanning technique, the
“wobbling” or “uniform-scanning” technique (8). The first-scattered
beam is scanned laterally using the two magnets in the nozzle to create
a large lateral beam spread. One of the tracks in a modulation wheel is
used for pristine peak pullbacks, with the wheel set in the indexing mode
and the steps of the track serving as “range shifters.” The proton dose
is therefore delivered in a layer-stacking fashion, with the modulation
Range modulator wheels
Magnet 2
Jaws (X and Y)
(& range verifier)
Snout retraction area
Water phantom
Snout IC2 and IC3
Second scatterers
First
scatterers
Magnet 1
IC1
FIGURE 8.1
Schematics of a passive-scattering nozzle (IBA Universal Nozzle, Louvain-la-Neuve, Belgium).
The beam enters from the right. (Adapted from Paganetti et  al., Med Phys, 2004, 31(7), 2107,
2004.)
226 Proton Therapy Physics
wheel indexed to a new position after completion of dose delivery to a
given layer.
Both scattering and wobbling techniques require the use of high-Z feld-
defning apertures and range compensators, which are mounted on the
snout. Apertures used in proton therapy are typically fabricated out of
brass alloy or low-melting-temperature alloy such as Cerrobend™ (Cerro,
Vineyard, UT). Range compensators may be similarly milled out of PMMA
or high-impact wax. Accuracy of aperture milling affects treated feld size.
The range compensator material composition consistency, as well as its fab-
rication, directly affects dose distribution distal and proximal to the target.
Figure 8.2 shows an active scanning nozzle (9). The insertion of an He
chamber in the beam pathway, as well as removal of scatterers used in pas-
sive-scattering techniques, allows a minimal spot size of the pencil beam at
the exit of the nozzle. Focusing magnets may, in addition, be installed in the
nozzle to further reduce the beam spot size (10). The absence of modulation
wheels and scatterers within a scanning nozzle eliminates concerns of their
mechanical wear and tear and general degradation. The monitor chambers
in scanning nozzles, however, must be able to measure the spot position and
the cumulative doses quickly (10).
For nozzles equipped with snouts that translate along the beam axis to
allow minimal distance of apertures/range compensators to the patient’s
skin, the accuracy of snout movement needs to be verifed, because deviations
from theoretic values would change the projected feld size. The co- linearity
of snout travel to beam axis needs to be verifed and tested at several gantry
angles in a gantry treatment room.
Window; Ti
Profile monitor
Scanning magnet (Y)
Scanning magnet (X)
Scattering device
X-ray tube
Dose-monitor #2
Dose-monitor #1
Spot position monitor
Energy filter
Snout moving device
Energy absorber
Aperture
0 – 0.38 m
Iso - center
3
.
2
4

m
He chamber
He chamber
FIGURE 8.2
Schematics of a scanning beam nozzle. (Adapted from Gillin et al., Med Phys, 2010, 37(1), 154.)
227 Quality Assurance and Commissioning
8.2.3 Mechanical Gantry or Fixed Beam Line
The nozzle is mounted on a mechanical gantry or at the end of a fxed beam
line. The mechanical isocenter accuracy of a proton gantry and the agreement
of radiation and mechanical isocenters need to be calibrated and verifed
periodically in a manner similar to conventional linear accelerator gantry
systems. Techniques including the pointer-tip-matching test and the star-
shot flm test are suitable for this purpose. Moyers and Lesyna (11) described
an extricate test of gantry mechanical isocentricity using theodolites and
demonstrated that the isocenter movement of a proton gantry is similar to
that of a linear accelerator of similar mechanical design. For a fxed beam
line, either vertical or horizontal, an isocenter is defned as the intersection
of beam axis to the patient treatment table rotation axis, and its verifcation
simplifes to verifcation of that agreement.
8.2.4 Patient-Positioning System
Although patient-positioning systems of proton therapy serve the same pur-
pose of treatment tables of traditional radiotherapy units, they may provide
additional capabilities compared with a conventional treatment couch of lin-
ear accelerators, including the following:
• Ability of providing a limited range of patient pitch-and-roll correc-
tions, in addition to the traditional three translational and one rota-
tional DOF;
• Absence of co-linear rotational axis. The table top and base may have
different centers of rotation, such that a table rotation is achieved by
a combination of table translations as well as separate rotations of
the table top and base;
• Ability to compensate for gantry sags using precalibrated lookup
tables;
• Capability of preprogrammed and stored automatic motion maneu-
vers, such as moving to predefned locations for the purposes of
loading/unloading patients or for setting up QA devices such as a
3D scanning water tank.
The QA tests of a proton therapy patient-positioning system need to be
designed to explore and confrm the correct and accurate functioning of the
device in these aspects.
8.2.5 Image-Guided Patient-Alignment System
At the current time, all commercially available proton therapy systems
are installed with orthogonal x-ray-based patient-alignment systems. The
228 Proton Therapy Physics
x-ray tubes may be installed at ±45
o
offsets from the beam axis or having
a moveable x-ray tube inside the nozzle paired with a second tube at 90
o

from the beam axis. For the latter confguration, the x-ray tube in the nozzle
is inserted into the beam path during imaging and is moved out of beam
path during proton beam tuning and delivery. Software packages are gener-
ally used to align precalculated digitally reconstructed radiographs (DRRs)
of setup and treatment felds to corresponding x-ray images of the patient.
Geometric accuracy of such imaging systems relative to the proton beam
isocenter and in various gantry rotation angles, as well as the accuracy and
application of patient shifts calculated by the software package, need to be
verifed. Quality of images of these systems should be evaluated at the time
of system commissioning and subsequently should be tested periodically
for consistency. The radiation doses delivered by such imaging systems
should be evaluated following the recommendations of the AAPM TG75
report (12).
8.2.6 Computed Tomography Scanners for Proton Therapy
Proton therapy dose calculations rely on computed tomography (CT) images
of the patient in the treatment position. The CT numbers (Hounsfeld unit
[HU]) of CT pixels are converted into relative stopping power values for
proton range calculations. It has been demonstrated that, for photon dose
calculations, dose calculation accuracy is relatively insensitive to uncertain-
ties of HU-to-electron density conversions, with 2% to 5% HU value changes
corresponding to 1% dose change, depending on beam energy and tissue
type (13). Uncertainties in the CT HU-value-to-stopping-power conversion,
however, are linearly transferred to uncertainties in proton range calcula-
tions. Accurate and careful calibration of the CT HU-to-stopping-power con-
version is therefore an important and critical part of proton therapy system
commissioning and QA processes.
Other aspects of CT simulations, including geometric accuracy and
image quality, require the same rigor in commissioning and periodic QA
tests. The AAPM Task Group 66 report (14) provides detailed descriptions
of these tests.
8.2.7 Patient Immobilization Devices
Dosimetric effects of patient immobilization devices on proton dose distri-
butions, both in range accuracy and in proton scattering, need to be care-
fully considered and investigated. Sharp variations of thicknesses in these
devices increase dose distribution inhomogeneity, in addition to increasing
uncertainties in the delivered beam ranges. The material composition of
such devices should be homogeneous, because signifcant variations of their
water equivalent thickness within treatment felds would compromise the
delivered dose distributions if left uncompensated for.
229 Quality Assurance and Commissioning
8.3 DesignofAcceptanceTestingandCommissioning
PlanforaProtonTherapySystem
The acceptance testing and commissioning of clinical proton therapy sys-
tems, in principle, will include a similar fow of actions as those for linear
accelerators detailed in the AAPM TG45 report (1).
8.3.1 Acceptance Testing of Proton Therapy Systems
The acceptance testing of a proton therapy system includes demonstration of
the system meeting specifcations in the following aspects:
• Radiation, mechanical, and electrical safety issues
• Gantry, snout, and patient-positioning system mechanical, imaging,
and therapy beam alignments
• Proton beam characteristics
• Dose-monitoring system
Differences between a proton therapy system and linear accelerators, from
facility construction and equipment installation, to the availability of a
practically infnite number of beams, require that such a fow be modifed.
Acceptance testing procedures (ATPs) for linear accelerators, although ven-
dor specifc, have been long established and typically require only minor
revisions specifc to user requirements. Proton therapy system ATPs, how-
ever, are still evolving and would require detailed negotiations and discus-
sions with system vendors as part of the purchasing agreement.
8.3.1.1 Radiation, Mechanical, and Electrical Safety Issues
Radiation safety concerns in a proton therapy facility differ from traditional
linear accelerator facilities primarily in the signifcant neutron exposure
present around the proton accelerator, beam line, and treatment rooms,
as well as the activation of system components. Ipe et  al. (15) discussed in
detail the mechanisms and methods of radiation production and interaction,
shielding, and monitoring requirements, as well as personnel and patient
safety considerations of charged particle therapy facilities (see Chapter 17).
As soon as the accelerator is able to produce proton beams, radiation safety
measures must be taken to ensure that the neutron exposure outside the
accelerator and beam line vault is at a level meeting local regulatory require-
ments. Such a radiation survey must be performed at the highest beam
energy and current to adequately refect the maximum neutron exposure
that the installation engineers, construction workers, and facility personnel
may receive during the subsequent construction, installation, and accep-
tance phases. An x-ray exposure survey should be taken at the same time.
230 Proton Therapy Physics
The presence of activated materials, such as accelerator circulating cooling
water, oil, and replacement parts must be carefully evaluated. Such materials
need to be located in areas considered safe and adequate for radiation protec-
tion and must be posted as radioactive material storage areas as demanded
by local safety requirements.
Radiation safety concerns for a proton therapy facility also differ from a
linear accelerator facility in that facility construction is often ongoing when
beam testing starts. A particular scenario may be that vendor engineers work
overnight to perform beam testing in a given treatment room, and then the
room is turned over to construction workers to complete room furnishing
and ancillary equipment installation. Construction workers are typically not
radiation workers. A daily room survey will therefore need to be performed,
to measure the ambient radiation exposure of the room due to activated mate-
rials. Potentially activated components, such as brass blocks, should be col-
lected and removed from the room before it is turned over to construction
workers. Completion of these radiation safety measures must be documented
in a daily room radiation survey form posted at the entrance to the room.
Training on these procedures needs to be provided to construction workers.
Proton accelerator and beam line vault and treatment rooms are equipped
with beam status indicator lights, crash buttons, door interlocks, and area
radiation-monitoring devices. The accelerator and beam line vault, as well
as treatment rooms, are also installed with search switches and alarms that
disable beam production, transport, and delivery in these areas until manu-
ally cleared. As personnel evacuate these areas in preparation for beam-on
operations, these switches are sequentially enabled, and alarms are sounded
to warn any other persons of the pending start of irradiation sessions, such
that no person is left behind and receives irradiation accidentally. Correct
functioning of these devices must be validated.
Moving subsystems in a proton therapy treatment, including the gantry,
snout, treatment table, and imaging panels, may be equipped with proximity
and collision sensors. The proximity sensors alert operators when a mov-
ing system, including gantry, snout, or treatment table, moves to within a
predefned distance of another subsystem and may automatically slow the
speed of a moving system. The collision sensors detect pressure above a pre-
defned threshold on a given system and stop the moving system. The func-
tioning status of such sensors should be verifed during acceptance testing
to operate according to specifcations. In addition, recovery from a collision,
using either electrical or manual power, should be tested and included in
user training.
Leakage radiation, as well as scattered radiation dose to patient outside
treated volume, should be evaluated during the acceptance testing process.
There should be no leakage of primary protons through the nozzle and
snouts. Radiographic or radiochromic flms may be wrapped around the
nozzle and snout to identify the presence of any such leakage spots, and ion
chambers used for quantitative measurement of absolute dose levels at any
231 Quality Assurance and Commissioning
hot spots that are identifed on the flm. These measurements need to be
performed for all snouts available. The scattered radiation exposure levels
outside treatment feld, both of photons and of neutrons, should be evaluated
and documented (16–20).
8.3.1.2 Gantry, Snout, Patient-Positioning, and Patient-Alignment Systems
The mechanical isocentricity of the gantry and treatment table should be
verifed during acceptance testing. A traditional method, such as “pointer
matching” may be used. Moyers and Lesyna (11) described a method for
measuring the axial as well as radial isocenter walks of a proton gantry
using custom-fabricated gantry-mounted measuring blocks, theodolite, and
a dial indicator (Figures 8.3 and 8.4). Note that, for systems equipped with
removable snouts, such tests can only be performed after verifcation that the
snouts are correctly aligned.
Alignment of each available snout in the gantry radial and the axial direc-
tions, as a function of snout translation distance and of gantry angles, needs
to be verifed to within specifcations. This can be tested by either mechani-
cal means of measuring the position of a fxed point on the snout as it trans-
lates or by scanning the proton beam dose profles in air and verifying their
symmetry for different snout positions. Accuracy of snout translation dis-
tances should be measured and compared to its digital display values. The
snout interlocks for detecting presence of apertures and range compensators
should be tested to work as designed.
The radiation isocenter of a proton gantry may be tested in the same man-
ner as for a traditional linear accelerator using “star-shot” flms. Such tests
FIGURE 8.3
Gantry isocentricity measurement using a theodolite. (Adapted from Moyers and Lesyna, Int J
Radiat Oncol Biol Phys, 60(5), 1622, 2004.)
232 Proton Therapy Physics
should be performed for all snouts to be used on the gantry. Custom aper-
tures need to be fabricated for such tests.
Acceptance testing of the patient-positioning system includes verifcation
of the accuracy and reproducibility of table movements and their limits.
Mechanical measurements using calibrated rulers and levels are suffcient
for these tests. Barkhof et al. (21) described a scintillation screen–based sys-
tem for such tests. Table rotation isocentricity may be tested using the star-
shot flm technique as well. Treatment tables with roll and pitch correction
capabilities should be tested with a small value of such corrections intro-
duced during isocentricity tests. When the patient treatment table is used to
compensate for gantry sags, the accuracy of such corrections must be vali-
dated for a wide range of gantry angles. The maximum values of such cor-
rections should be identifed and compared to measured gantry mechanical
and radiation isocenter walks, as excessively large correction values during
patient treatments may indicate malfunction of the system. Functioning of
motion limit switches, of both software and hardware varieties, needs to be
tested. Activation of these limits should stop movement of the relevant sub-
system and should be readily recoverable.
Acceptance testing of orthogonal x-ray patient-alignment systems used in
proton therapy includes image quality evaluation in terms of low and high
contrast and resolution, the accuracy of radiation exposure parameters of
kVp (kilovolt potential) and mAs (milliampere seconds) x-ray tube leakage
radiation, and radiation exposure measurements. Geometric accuracy of the
patient-alignment system is critically important for accurate delivery of pro-
ton therapy and must be extensively tested. The central axis of the x-ray beam
produced by the nozzle-mounted x-ray tube needs to agree with the treatment
beam and also with the light feld if so equipped. Such agreement needs to be
tested for a number of gantry angles to assure that it is not affected by gantry
sag. For systems using a hardware crosswire, this test is easily performed
using double-exposure flms and a commercial light- and radiation-feld
agreement testing device, illustrated in Figure 8.5. In systems with crosswires
FIGURE 8.4
Measurement of gantry walk in axial direction using a dial indicator. (From Moyers and
Lesyna, Int J Radiat Oncol Biol Phys, 60(5), 1622, 2004. With permission.)
233 Quality Assurance and Commissioning
mounted on interchangeable snouts, all available snouts must be tested. The
second x-ray tube may be similarly tested for agreement of its crosswire to the
gantry isocenter through a number of gantry rotation angles.
8.3.1.3 Proton Beam Characteristics
Proton beam dosimetric parameters to be validated during acceptance test-
ing include beam range, distal falloff, SOBP or beam modulation width,
SOBP fatness, and entrance doses in the depth direction. These measure-
ments may be performed using a scanning water phantom and a parallel
plate chamber as the feld dosimeter. The lateral dose distribution profles
may be measured, again using scanning phantoms with a small diameter
ionization chamber as feld dosimeter, and the beam fatness, symmetry, and
penumbra values at several depths are extracted. Figure 8.6 shows a defni-
tion of these depth–dose beam quality parameters as follows:
Range: depth in water (g/cm
2
) from skin to distal 90% of depth dose
SOBP width: distance in water from proximal 90% to distal 90% of
depth dose
Distal falloff: distance in water from distal 80% to distal 20% of depth
dose
Note that the defnitions listed above use their historical values. The specifc
defnitions of these parameters may be customized, as agreed upon with
the system vendor and installation engineering team, to meet the clinical
requirements of a given proton therapy facility. For example, Engelsman
FIGURE 8.5
Daily QA. Laser/x-ray agreement test.
234 Proton Therapy Physics
et al. (6)

described an alternative defnition of SOBP width to be from proxi-
mal 98% to distal 90% of the depth dose, due to the steeper gradient of the
depth dose at proximal 98% than 90%, a better ft for the output factor predic-
tive model used, and a closer correlation of SOBP width to target thickness
when the target is covered by 100% (mid-SOBP) of the depth dose.
Additional beam parameters to be measured include range and SOBP
width resolution. These measurements may be performed for a single gan-
try angle using a scanning water phantom and a parallel plate chamber as
the feld dosimeter, for beams with varying beam ranges and SOBP widths,
typically at resolutions of 0.1 g/cm
2
for the former and 0.5–1 g/cm
2
for the
latter. The off-axis range uniformity and off-axis SOBP width and fatness of
the beams need to be verifed to be within design specifcations as well by
acquiring a set of depth–dose scans at a number of off-axis points. Lastly,
the dependence of beam quality parameters on snout, dose rate, and gantry
angle needs to be tested.
The characterization of proton beams is one of the more diffcult aspects
of acceptance testing of a proton therapy system, because of the availabil-
ity of beams with nearly continuous beam energy. Direct measurements of
all available beams are intractable and in practice are unnecessary. A thor-
ough understanding of the hardware and software controls that provide
all the available proton beams is therefore a prerequisite in designing an
acceptance testing procedure for a proton therapy system. The following dis-
cussions illustrate this process using the IBA Universal Nozzle (Ion Beam
Applications) as an example. This nozzle, shown in Figure 8.1, is capable of
delivering proton therapy treatment using two scattering techniques:
1. Single scattering: The pencil beam exiting the beam transport line
is expanded through a frst scatterer, such that the narrow Gaussian
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
0 5 10 15 20 25 30 35
Depth (g/cm
2
)
Distal falloff
SOBP width
Proximal depth dose
Range
Proton spread-out-Bragg-peak
%
D
D
FIGURE 8.6
Proton beam depth–dose parameters.
235 Quality Assurance and Commissioning
beam becomes a wider Gaussian beam. The outer parts of the beam
at lower than 95% of the central axis value are blocked by the vari-
able collimators, so that only the center part of the beam is used for
treatment. SOBPs of specifc widths are formed by use of step-wise
thickening range modulator wheel tracks and are controlled by
turning the beam off at the step corresponding to the prescribed
SOBP width, or beam current modulation, created in tabulated fles
during system installation. There are a total of fve single-scattering
options, with all beams in each option sharing common frst scat-
terers and modulation wheel tracks. Beam energy is selected by the
energy selection system (ESS) comprised of an energy degrader at
the accelerator exit followed by energy selection slits and magnets.
2. Double scattering: The single-scattered beam is fattened by a down-
stream second scatterer and then collimated by the variable colli-
mators. The same beam modulation wheel tracks are used, together
with beam current modulation fles. A number of second scatterers
are available that, working jointly with the frst scatterers, form eight
double-scattering options, again with each option sharing second
scatterer and range modulation wheel tracks. The frst scatterers are
selected from a combination of up to eight Al or Pb foils, as cali-
brated at time of system installation.
In addition to the scattering beam options, the IBA Universal Nozzle is
also capable of delivering active scanning beams in two forms: (1) a uniform
scanning beam, which scans a frst-scattered beam laterally to deliver the
dose to a given layer with uniform intensity, before inserting a range shifter
(implemented using a step of a range modulation wheel track) and changing
beam intensity to scan a subsequent, shallower layer, and (2) a scanning pen-
cil beam, which scans an unscattered, prefocused pencil beam with variable
intensity in a given layer before pulling the range back to deliver an inten-
sity-modulated scanning beam to subsequent layers (22). The subsequent
discussions will be limited to the passive-scattering beam options in the IBA
Universal Nozzle. Table 8.1 lists the clinical range and modulation limits of
the double-scattering beams in this nozzle, together with their use of sec-
ond scatterers and range modulation wheel tracks. Note that each option is
further subdivided into three suboptions, and the beam current modulation
fles are custom-designed for each suboption. Acceptance testing of these
options therefore should, at the minimum, verify that a representative beam
within each suboption, corresponding to a distinct beam current modulation
fle, meets design specifcations. The number of measurements required for
acceptance testing is further estimated by an analysis of the dependence of
clinical beam quality parameters, such as beam range and SOBP fatness,
on how they are produced, including the scatterers and modulation wheel
tracks used, as well as snouts and beam gantry angles. As an example, the
beam range is considered to be dependent on the suboption used to generate
236 Proton Therapy Physics
T
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237 Quality Assurance and Commissioning
the beam, but less likely on the gantry angle. Beam range dependence on
the gantry angle can therefore be verifed for two beams out of all avail-
able options: one with a large range and one with a small range. The lateral
dose profle may have large dependence on beam gantry angle and should
therefore be verifed for each option, at prime gantry angles. Lastly, these
measurements should be selected such that they may be used for subsequent
treatment-planning system commissioning validations.
The acceptance testing of active scanning beams is discussed by Farr et al.
for the uniform scanning technique (8), and by Gillin et  al. for the pencil
beam scanning technique (9). These delivery techniques use a signifcantly
reduced number of nozzle hardware components, but rely on magnetic
scanning of the beam to achieve a desired dose distribution in the lateral
direction and use range shifters for pullback of the individual layers of
pristine peaks.
The uniform scanning technique aims to produce a cumulative dose distri-
bution identical to that produced by a passive-scattering beam, with depth-
dose curve characterized by an SOBP, and lateral profles described by beam
fatness, symmetry, and lateral penumbra. Its acceptance testing is therefore
in principle similar to that of scattering beams. The fact that a large-diameter
beam spot is scanned laterally invariably introduces ripples in the lateral
dose profles; and the layer-by-layer delivery of dose in the depth direction,
using a limited number of range shifters, also introduces ripples in the SOBP.
Multiple repainting of the distal layer, up to 100 times (8), is used in typical
uniform scanning schemes to minimize the effect of random beam intensity
fuctuations. The reproducibility of delivered dose distribution of a repre-
sentative feld should be tested. The effect of beam spot size change as the
dose layers are changed should be evaluated by acquiring the lateral dose
profles at several depths of a feld. The depth–dose curve measurement for
such scanning beams is complicated by the layer-by-layer delivery scheme,
and special dosimetry equipment, such as a multilayer ionization chamber
(MLIC) or a multipad ionization chamber (MPIC) (8), can be used to signif-
cantly improve the effciency of data collection.
Pencil beam scanning systems, or spot scanning, on the other hand, con-
struct a desired dose distribution by summation of “spot doses,” each deliv-
ered by a narrow pencil beam with a narrow pristine peak (see Chapter 6).
Each spot of such a composite dose distribution would correspond to a voxel
of the patient’s anatomy, and the total dose delivered to each spot is calcu-
lated to achieve an intensity-modulated dose distribution. The acceptance
testing of a pencil beam scanning system, therefore, will concentrate on the
characteristics of the individual spots. Gillin et  al. described their experi-
ence in acceptance testing and commissioning of such a system (9). Each
pencil beam is characterized by its depth–dose curve and lateral profles.
The widths of the pristine peaks, as a function of beam range, vary signif-
cantly, as refected by the pullback values between neighboring layers. A
large diameter ionization chamber (Bragg peak chamber, PTW-Freiburg,
238 Proton Therapy Physics
Freiburg, Germany) is used to perform point-by-point measurements of
these pristine peaks.
The lateral dose profles of individual pencil beams in such a system are
generally described by Gaussian distributions. However, the lateral low-
dose tails extend to a large distance away from the beam central axis and
need to be verifed for accurate description by the treatment-planning
system. Sawakuchi et  al. (23, 24) performed Monte Carlo calculations and
experimental measurements of the lateral low-dose envelopes of such pen-
cil beams. Such lateral low-dose tails originate from particle interactions
both with the nozzle components and in phantom, contribute signifcant
doses to points as far as 10 cm away from the pencil beam, and can cause
signifcant dose calculation deviations for felds up to 20 × 20 cm
2
if left
unaccounted for.
Pencil beam spot characteristics, including spot-positioning accuracy and
reproducibility, spot shape, and spot diameters, as a function of beam energy
and gantry angle, should be verifed. Gillin et  al. used radiochromic flms
and pinpoint ion chambers for such measurements (9). Spot shapes for a vari-
ety of beam energies were measured at two different gantry angles.
For facilities with multiple treatment rooms, it would be desirable to have
beams in identically equipped treatment rooms to be “matched,” or dosimet-
rically interchangeable, to facilitate future clinical operations when patients
may be treated without being limited to a specifc treatment room. Such
requirements should be discussed in detail with the vendor’s installation
engineers, and measured data from the matched treatment rooms should be
reviewed for agreement.
8.3.1.4 Dose-Monitoring System
Monitor chambers in proton therapy measure the absolute dose delivered, as
well as providing measurement and feedback for beam symmetry control,
using a primary and a secondary backup monitor chamber. Their tests during
acceptance testing are similar to those for linear accelerator monitor cham-
bers, including preliminary calibration, reproducibility, and adjustability.
The linearity and end-effect tests of proton therapy monitor chambers may
be complicated by the fractional doses delivered during beam tuning. For
scattering beam techniques, several pulses of a beam are sent through the
monitor chambers to provide fnal beam tuning and beam range measure-
ments. Although these pulses are synchronized with the beam modulation
technique and delivered to the treatment target during patient treatments,
the total monitor units (MUs) delivered during beam tuning may vary ran-
domly. The monitor chamber linearity and end-effect tests, being a charac-
terization of monitor chamber response, should therefore be evaluated with
these tuning MUs excluded.
The delivered dose rate in proton therapy systems depends on the type
of accelerators used: cyclotrons can typically produce a large beam current,
239 Quality Assurance and Commissioning
allowing high dose rates for larger treatment felds, whereas synchrotrons
are often more limited in their ability to deliver higher dose rates (25). Dose
rate measurements to be performed during acceptance testing therefore
should start with verifcation of the vendor-stated achievable dose rate, typi-
cally under conditions of a set of reference felds. Additional tests include
determination of the average dose rates available, as a function of both feld
sizes and beam energy, for a set of representative beam ranges and modu-
lation widths. Monitor chamber dependence on dose rates is determined
through these measurements as well.
Temperature and pressure correction for monitor chambers used in proton
therapy may be achieved in two manners: automatic compensation based
on chamber-integrated temperature and pressure-sensor measurements or
manually entered temperature and pressure correction values. The tempera-
ture and pressure compensation of the former design can be evaluated by
measuring the output of a reference feld over days and establishing that the
chamber response does not track temperature and pressure variations over
these days. For the latter design, a range of temperature and pressure values
may be entered into the system, and the beam output may be measured to
demonstrate the correctness of system compensation calculations.
Additional monitor chambers may be used in the pencil beam–scanning
technique, as described by Gillin et  al. (9). These monitor chambers per-
form the functions of beam profle and spot position monitoring and trigger
interlocks when the delivered beams deviate from prescribed values. The
primary and secondary (or backup) monitor chambers also interlock on min-
imum and maximum MUs per spot. These interlocks need to be tested dur-
ing acceptance testing, with support of the vendor’s installation engineers.
8.3.2 Commissioning of Proton Therapy Systems
Commissioning of a proton therapy system includes calibration of the CT
scanner to establish the CT HU number-to-proton stopping power conver-
sion curves and acquisition of beam data for treatment-planning system
beam modeling, as required by the selected proton therapy treatment-
planning system. In addition, system commissioning will necessarily
include evaluation of performance of integrated systems, from image acqui-
sition to treatment delivery, using an electronic record and verify (R&V)
system as appropriate. An end-to-end test should be performed at the end
of system commissioning to ensure that the entire integrated system func-
tions as expected. Disease site–specifc operating procedures, especially in
patient immobilization, imaging, treatment planning, and treatment deliv-
ery, should be developed as part of system commissioning. Training should
be provided to radiation oncologists, physicists, dosimetrists, and radiation
therapists on all procedures thus developed. Lastly, a periodic system QA
program, based on the data acquired in the commissioning process, should
be implemented, to ensure constant system performance over time.
240 Proton Therapy Physics
8.3.2.1 CT HU-to-Stopping Power Calibration
The beam range required for patient treatment in proton therapy is calcu-
lated from CT images of the patient, with the CT HU numbers converted to
proton stopping power values using a calibration curve determined at time
of system commissioning. Errors and uncertainties in the HU-to-stopping
power calibration curve translate directly into those of beam range calcula-
tions and need to be minimized. Schneider, Pedroni, and Lomax (26) pro-
posed the stoichiometric method for obtaining this calibration curve. The
HU values of a number of tissue equivalent materials are measured on the
CT scanner, and their stopping power values are then calculated based on
the known chemical compositions and may be confrmed by direct measure-
ment in proton beams. These HU-to-stopping power correlations are then
used to obtain ftting parameters of a HU calculation model describing the
photoelectric, coherent-scattering, and Compton-scattering interactions of
x-rays in the materials. Stopping power values of soft tissues, using chemical
compositions of ICRU Report 49, are then calculated to obtain the complete
HU-to-stopping power calibration curve. Schaffner and Pedroni (27) demon-
strated the accuracy of this method for a number of tissue types.
The tissue equivalent materials used for establishing the HU-stopping
power calibration curve need to be verifed to allow accurate stopping power
calculations. Commercially available tissue equivalent materials, such as
those used for photon CT-electron density calibrations, may not have chemi-
cal compositions of adequate accuracy and consistency for stopping power
calculations. It is therefore important that the materials used in establishing
the CT calibration curve for proton therapy are measured in proton beams to
confrm the agreement of calculated and measured stopping power values.
Additional uncertainties in HU-stopping power calibration include the beam-
hardening effect of CT scanning. High-density materials may produce signif-
cantly different HU values as a function of geometric locations at the center or
peripheral regions of the phantom. The same materials placed in phantoms of
different diameters will produce different HU values as well, further increas-
ing the uncertainties of HU-to-stopping power conversions. The CT scanning
technique used for imaging the phantom needs to include identical techni-
cal parameters, including kilovolts, collimator opening, and reconstruction
algorithms. Variations of these parameters have the potential of signifcantly
increasing the uncertainties in HU-to-stopping power conversion as well.
Commissioning of a CT scanner for proton therapy should therefore include
scanning of the phantom using various techniques, for phantoms of different
diameters, and with the tissue equivalent materials in various locations within
the phantom, so that estimates of these uncertainties may be documented.
8.3.2.2 Treatment-Planning System Commissioning
Commissioning of a proton therapy treatment-planning system includes
collecting the data required by the system for accurate in-phantom dose
241 Quality Assurance and Commissioning
calculations. For systems using the pencil beam dose calculation model
(28–30), these input parameters include the following:
• Beam energy spread, which may be estimated from pristine peak
measurements. A large enough number of pristine peaks should be
measured for each available beam option as required by the plan-
ning system.
• Source size, extracted from in-air measurements of half-beam dose
profles.
• Virtual source-to-axis distance (SAD), describing beam divergence
in air and extracted from in-air measurement of dose profles at
several different distances from the isocenter for a feld of fxed
diameter.
• Effective SAD, describing variation of beam output as a function of
source-to-calculation point distance, or the inverse square law.
Additional parameters may be required for dose calculation using the pencil
beam model, including the nozzle equivalent thickness (NET) of all nozzle
components within the beam path and the description of range modulation
wheel-step widths and thicknesses.
In-phantom dose distributions, both depth doses and lateral profles, are
required for validation of the treatment-planning system as well. Many of
these have been obtained during system acceptance testing. Additionally,
the variation of depth doses, lateral profles, and output factors as a function
of the source-to-skin distance (SSD), snout position/air gap, snout size, and
feld size should be tested using measured beam data. Such data, although
not part of typical vendor performance specifcations and therefore not part
of acceptance testing, are important considerations in clinical proton ther-
apy treatment planning. Figure 8.7 illustrates the SOBP fatness changes as a
function of SSD variations. The “tilt” of the SOBP part of depth–dose curve
deteriorates as the measuring phantom is shifted toward or away from the
B5 - data
B5 - trend
B7 - data
B7 - trend
–10
–0.05
0
0.05
T
i
l
t

S
O
B
P

[
%

/

c
m
]
0.1
0.15
0.2
–8 –6 –4 –2 0
Shift in SSD [cm]
2 4 6 8 10
FIGURE 8.7
SOBP fatness, or tilt change as SSD changes. Solid line; B5 option (see Table 8.1). Dashed line:
B7 option.
242 Proton Therapy Physics
source. Beam penumbra variations as a function of air gap, or the effect of
proton in-air scattering on beam penumbra, is shown in Figure 8.8. A 10-cm
increase in air gap degrades beam penumbra by approximately 2 mm for the
scenarios illustrated.
The accuracy of planning system dose calculation in inhomogeneous
media should be verifed. A phantom consisting of various tissue equiva-
lent materials, such as lung, soft tissue, and bone, may be constructed and
imaged. Calculated dose distributions in the phantom may be compared to
their measurement counterparts.
The slit-scattering effect (31), or protons scattering off the walls of aper-
tures, should be confrmed and documented. Such increases in skin doses
are typically not modeled by pencil beam dose calculation algorithms, but
are important in treatment planning and patient treatment considerations.
Figure 8.9 shows the variations of slit-scattering effect as the air gap varies.
8.3.2.3 MU Calculations
Although a common formalism for the MU calculations of proton therapy
does not exist, system-specifc algorithms have been developed and imple-
mented (32–34). These algorithms are customized to the specifc nozzle
design and beam modulation techniques, and each has its own requirements
of input parameters. Where applicable, the beam data required for the MU
calculation schemes should be measured during the commissioning process,
and calculated output factors should also be verifed.
0.0
0.00
0.20
0.40
0.60
8
0
%
–
2
0
%

L
a
t
e
r
a
l

p
e
n
u
m
b
r
a

[
c
m
]
0.80
1.00
1.20
1.40
1.60
@ 0.5 cm depth @ 9.9 cm depth
Range = 15.1 cm, SOBP width = 10.4 cm (Option B5)
@ 14.1 cm depth
5.0 10.0 15.0 20.0
Air gap [cm]
25.0 30.0 35.0
FIGURE 8.8
Beam lateral penumbra change as function of air gap for a B5 option feld.
243 Quality Assurance and Commissioning
8.3.2.4 Beam-Modifying Accessories
Apertures and range compensators are typically used for scattering and
uniform-scanning techniques, with the former to shape the treatment feld
portals and the latter to provide distal conformance to the target by pull-
ing back the beam ranges locally. The geometric and dosimetric accuracies
of these accessories, as modeled and calculated by the treatment-planning
system, need to be validated by in-water measurements. The aperture thick-
ness required to stop proton beams of a given range should be determined.
Stopping power value of the material used for range compensator fabrica-
tion, typically acrylic, needs to be confrmed as well. A range compensator of
relatively simply geometry may be fabricated, and the measured dose distri-
bution through the compensator should be compared to the calculated one,
such that dose calculation errors and inadequacies of the treatment-planning
system may be identifed. Figure 8.10 shows such a comparison, where dif-
ferences between planned and measured dose distributions are the greatest
near sharp edges of the compensator. A procedure for QA testing of patient-
specifc apertures and compensators should be developed based on these
measurements.
8.3.2.5 Patient Immobilization Devices
Patient immobilization devices used for proton therapy should be evaluated
for their dosimetric properties. A CT scan of each device should be obtained
and imported into treatment-planning system. The dose distribution for a
–10
0
0.2
0.4
R
e
l
a
t
i
v
e

d
o
s
e

[
-
]
0.6
0.8
1
–5 0
Radial position [cm]
5 cm air gap
13 cm air gap
30 cm air gap
5 10
FIGURE 8.9
Dose profle at 0.5-cm depth for three different air gaps. The slit-scattering effect, or the horns
in the profles, is maximum with a small air gap and reduces as the air gap increases.
244 Proton Therapy Physics
beam through the device is calculated and compared to the measured dose
distribution for agreement. In particular, the device is evaluated for the
following:
• Average range pullback: The range reduction, caused by the pres-
ence of the immobilization device, needs to be measured and com-
pared to the value predicted by the treatment-planning system.
Disagreements between the measured and calculated range pull-
backs need to be investigated, and the device may be deemed unac-
ceptable for proton therapy applications.
• Range pullback uniformity: The device should in addition pro-
vide acceptable uniformity in its range pullback within the treat-
ment feld. Because of the multiple Coulomb scattering of protons
in patients, such uniformity will vary as a function of measurement
depth. The evaluation of range pullback uniformity will therefore
need to be performed at several depths as appropriate, based on the
expected beam ranges for the intended clinical disease sites.
• Mechanical integrity: The device, if unsupported by the patient
treatment table during clinical use, needs to be evaluated for sags.
A weight approximating an expected clinical patient weight can be
placed on the device, and the device sag values should be recorded.
Uncertainties in the range pullback of a patient immobilization device that
cannot be resolved may be considered as part of the overall beam range uncer-
tainty. Such uncertainties should therefore be included in the calculation of
2
4
6
8
10
12
14
16
–10 –5 0
Y [cm]
Measurement Eclipse Difference eclipse - measurement
5 10
–10
–5
0
Y [cm]
5
10
–10 –5 0
Y [cm]
5 10
–10 –5 0
Y [cm]
5 10
D
e
p
t
h

[
c
m
.
H
2
O
]
2
4
6
8
10
12
14
16
D
e
p
t
h

[
c
m
.
H
2
O
]
2
4
6
8
10
12
14
16
D
e
p
t
h

[
c
m
.
H
2
O
]
120
100
80
60
40
20
120
100
80
60
40
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
20
0
20
10
Depth
[cm.H
2
O]
0
–10
–5
0
Y [cm]
5
10
120
100
80
60
40
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
20
0
20
–40
–20
20
40
0
10
Depth
[cm.H
2
O]
0
–10
–5
0
Y [cm]
5
10
20
10
Depth
[cm.H
2
O]
0
120
100
80
60
40
20
30
20
10
0
–10
–20
FIGURE 8.10
(Seecolorinsert.) Comparison of calculated and measured dose distribution through a range
compensator with sharp gradients.
245 Quality Assurance and Commissioning
beam range uncertainties for clinical treatment planning and be included in
the facility’s site-specifc treatment-planning procedures.
8.3.2.6 R&V System
The use of an R&V system signifcantly improves the clinical fow of pro-
ton therapy and can help minimize occurrence of treatment delivery errors.
These systems should be tested for data import accuracy, using treatment
plans that use all parameters to be monitored by the R&V system. In addi-
tion to dosimetric parameters including range, SOBP width, and MUs, the
recording and verifcation of geometric parameters (e.g., gantry angle, table
rotation, pitch, roll, and translations) need to be thoroughly tested for a wide
range of clinical scenarios. A set of initial patient setup parameters, deter-
mined by use of orthogonal x-ray imaging, and the table corrections thus
deduced, need to be applied to all subsequent treatment felds accurately.
Treatment plans used for commissioning of R&V systems should therefore
include diffcult treatment cases with table rotation and translation offsets
away from the initial setup locations.
The installation of a multiroom proton therapy system is in general a pro-
longed process lasting for months. It is likely that system acceptance installa-
tion, acceptance testing, and commissioning will occur concurrently among
different treatment rooms and will compete for available accelerator beam
time. The scheduling of such activities in a multiroom installation must
therefore be carefully considered for maximum utilization of beam time and
quickest facility startup.
8.4 DesignofaPeriodicQAProgramfor
aProtonTherapySystem
A periodic QA program for proton therapy is designed to assure that the
system continuously performs as it does at the time of acceptance testing
and commissioning. The failure modes of a proton therapy system can be
signifcantly different from those of a linear accelerator system. In addi-
tion, a proton therapy facility is often expected to provide a large num-
ber of daily patient treatments, with clinical operations extending up to
16 hours per day. Additional times must be allocated for periodic machine
QA as well as patient-specifc QA measurements. A periodic QA program
for proton therapy, especially the tests to be performed, must therefore be
designed with high effciency. Measures to improve QA effciency include
design of specifc tests that refect performance of multiple system compo-
nents, design of test tools that allow quick setup and removal from treat-
ment rooms, and careful scheduling of tests such that the more extensive
246 Proton Therapy Physics
and comprehensive tests are performed on days without scheduled patient
treatments, such as the weekends.
A periodic QA program for proton therapy also needs to be designed to
refect the facility’s experience and confdence with the system. Although
some reproducibility tests are performed during system acceptance test-
ing, those do not represent the long-term stability of the system, espe-
cially mechanical wear-and-tear concerns that may take months or years to
develop. The QA program will therefore necessarily be more complex and
comprehensive in the initial stages of a facility’s clinical operations, while
patient treatment volume is ramping up. QA test results need to be analyzed
and reviewed frequently, and the QA program must be revised to reduce the
frequency of some tests, while potentially increasing the frequency of tests
on components that are identifed to have higher than expected failure rates.
Finally, selection of test frequencies in a proton therapy periodic QA pro-
gram should be done with considerations of the criticality of system failures.
Some tests, such as output measurement, refect catastrophic failures of mul-
tiple system components and must be performed on a daily basis, whereas
small variations in beam centering below those detected by the system’s
built-in beam fatness and symmetry interlocks (as measured by dose pro-
fle measurements) would contribute to small errors in overall dose delivery
accuracy and could be tested on a less frequent basis.
The basic QA tests of a proton therapy system include periodic measure-
ments of machine outputs at the middle of SOBP, beam ranges, SOBP widths
and fatness, and dose profles for reference felds. Depending on the system
design and implementation, the variations of these parameters from baseline
values may indicate potential failures and/or degradation of different sys-
tem components. An understanding of the basic system design therefore is
crucial in determining the frequency at which these measurements are per-
formed. The following discussion illustrates this process using a cyclotron-
based proton therapy system. Arjomandy et al. (35) described a QA program
for a synchrotron-based proton therapy system, with test schedules and tol-
erances customized for that particular system.
After extraction of the beam out of a cyclotron, an ion chamber is used
to measure beam current. As beam current is modulated during delivery
of a scattered beam treatment, deviations of the beam current away from
expected values will lead to beam output, as well as SOBP fatness changes.
Lu et al. (7) show that when the beam current offset is a large percentage of
the prescribed beam current, the effect on SOBP fatness can be signifcant
(Figure 8.11). Such changes are more signifcant for felds with large ranges,
as the prescribed beam currents for such treatments are much smaller than
for shorter ranges. It is therefore important that depth–dose measurements
should be performed for felds with larger ranges in order to detect drifts of
the ion chamber at cyclotron exit.
The proton beam exiting from the cyclotron proceeds through the ESS.
Subsequently, beam line magnets control the beam focusing and alignment
247 Quality Assurance and Commissioning
until the beam enters the treatment nozzle. Drifts in energy degrader and
magnet settings cause range errors, as well as changes in beam energy spread,
spot size, and angular spread. Paganetti et  al. (5) performed Monte Carlo
calculations to evaluate the effects of beam energy spread, spot size, and
angular spread changes on pristine peak distributions, shown in Figure 8.12.
Beam misalignment within the nozzle, for scattering beams, causes pris-
tine peak changes, as well as fatness and symmetry deviations. These
effects were investigated by Paganetti et al. as well (5). Figure 8.13 shows the
effect of a misaligned beam interacting with the frames of the frst scatter-
ers on pristine peak curve. The scattered protons off the frst scatterer frame
create a hump in the entrance dose region of the pristine peak. Effects of
Depth [cm]
(a)
(b)
(c)
0
D
o
s
e

[
%
]
86
88
90
92
94
96
98
100
102
104
106
108
110
5 10 15 20 25 30
FIGURE 8.11
Effect of beam intensity offset away from requested values on shape of SOBP: trace a: with current
modulation and an offset; trace b: with current modulation and no offset; and trace c: without
beam modulation. (Adapted from Lu et al., Med Phys, 2007, 34(10), 3844, 2007.)
0
20
40
60
80
100
20 0 40 60
Depth [mm]
D
o
s
e

[
%
]
80 100
20
30
40
50
60
40 60 80 100
120
FIGURE 8.12
Effect of changes in energy spread, spot size, and angular energy spread on pristine peak. The
dashed lines show the effects of 0.2% change in energy spread, the dotted lines of beam spot
size change by up to 0.25 cm, and dashed-dotted lines of angular energy spread of 2 mm-mrad.
(Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)
248 Proton Therapy Physics
beam misalignment relative to the second scatterer are shown in Figure 8.14.
Changes in SOBP fatness, distal falloff gradient, and proximal depth–dose
shape, as well as lateral fatness and symmetry are easily identifed.
The frst scatterers in this nozzle design contain a set of fat aluminum
or lead foils and are moved in and out of the beam pneumatically. The
0
0.0
R
e
l
a
t
i
v
e

d
o
s
e
0.2
0.4
0.6
0.8
1.0
2 4 6
Depth [cm]
Total dose
Total dose minus scraping
Dose from scraping
frames of the scatterers
8 10 12
FIGURE 8.13
Effect of beam scattering off the frst scatterer frame due to beam misalignment in nozzle on
pristine peak. (Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)
0
0 40 80
Depth [mm]
Second scatterer aligned
Second scatterer tilted by 5°
Second scatterer tilted by 10°
120 160
20
D
o
s
e

[
%
]
40
60
80
100
0
–80 –40 0
Lateral distance to isocenter [mm]
40 80
20
D
o
s
e

[
%
]
40
60
80
100
0
0 40 80
Depth [mm]
120 160
20
D
o
s
e

[
%
]
40
60
80
100
0
–80 –40 0
Lateral distance to isocenter [mm]
40 80
20
D
o
s
e

[
%
]
40
60
80
100
0
0 40 80
Depth [mm]
120 160
20
D
o
s
e

[
%
]
40
60
80
100
0
–80 –40 0
Lateral distance to isocenter [mm]
40 80
20
D
o
s
e

[
%
]
40
60
80
100
FIGURE 8.14
Sensitivity of depth–dose and lateral profles on beam alignment on second scatterers.
(Adapted from Paganetti et al., Med Phys, 2004, 31(7), 2107, 2004.)
249 Quality Assurance and Commissioning
mechanical stress on the frst scatterers, over time, may cause them to deform.
Output variations up to 5%, as well as SOBP changes, have been observed
to associate with such mechanical failures. Visual inspection of such devices
periodically, as well as routine output and SOBP measurements, serve well
to detect such failures.
The formation of SOBPs, using rotating range modulation wheels, relies
on the correct starting and stopping of the beam relative to wheel rotation
angles. Paganetti et  al. (5) showed that misalignment of range modulation
wheels may cause signifcant changes in the SOBP delivered (Figure 8.15).
Lu et al. (7) also investigated the effects of losing beam current modulation
completely and/or timing errors in beam current modulation signals and
demonstrated signifcant changes in SOBP fatness (Figure 8.16).
These fndings of potential system component failures and their effects
on beam parameters are summarized in Table 8.2. Daily, weekly, and
monthly beam QA tests may be selected out of the tests. In the beginning of
0
0 20 40 60 80
Depth [mm]
100 120 140 160
20
D
o
s
e

[
%
]
40
60
80
100
FIGURE 8.15
Sensitivity of SOBP to range modulation wheel alignment. The solid line shows the result for a
correct alignment and the dashed line for a 4% misalignment. (Adapted from Paganetti et al.,
Med Phys, 2004, 31(7), 2107, 2004.)
0
65
70
75
80
85
6τ
4τ
2τ
–τ –2τ
–4τ
–6τ
τ
90
95
100
105
2 4 6 8
Depth [cm]
D
o
s
e

[
%
]
10 12 14 16
FIGURE 8.16
Effect of beam current modulation timing error on shape of SOBP. Dark line represents the
desired SOBP with no timing errors. Others show SOBP with multiples of timing errors of
2 ms. (Adapted from Lu et al., Med Phys, 2007, 34(10), 3844, 2007.)
250 Proton Therapy Physics
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251 Quality Assurance and Commissioning
operations, the SOBP scans were performed daily, until high confdence in
the system’s beam delivery accuracy was established. Subsequently, these
tests were moved to weekly measurements for two reference felds: one for
the standard calibration feld and an additional feld with large (25 cm) range.
Daily output measurements were performed using a custom-made Lucite
output phantom mounted on the snout, to minimize setup errors and time
(Figure  8.17). A light-/x-ray/proton beam agreement test was included, ini-
tially at weekly intervals, rotating through all available snouts (Figure 8.18).
After accumulation of a large amount of data demonstrating excellent agree-
ment (Figure 8.19), this test was moved to monthly intervals. Gantry, treatment
table, and imaging system accuracy tests were included as well. Of particular
interest were the treatment table accuracy tests, initially at monthly intervals,
which were changed to weekly intervals after episodes of sudden table drive
potentiometer failures. Tables 8.3–8.6 show the current daily, weekly, monthly,
and annual QA tests at the University of Florida Proton Therapy Institute
(UFPTI). The cumulative system performance data, illustrated in Figures
8.20–8.23, are periodically reviewed for identifcation of potential system per-
formance drifts, as well as continued improvement of the QA program.
8.5 DosimetryInstrumentationforProton
TherapyCommissioningandQA
Many types of dosimeters have been used for proton therapy (Chapter 7), for
both absolute and relative dose measurements (36). This section is limited
FIGURE 8.17
Daily QA. Output check using a custom-fabricated phantom.
252 Proton Therapy Physics
FIGURE 8.18
Double-exposure flm test of x-ray and proton beam radiation feld agreement. A commercial
light-feld and radiation-feld agreement testing device (Iso-Align, Civco, Kalona, IA) may be
used for such a test.
P
e
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c
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f

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[
%
]
100% crossline inline
80%
60%
40%
20%
0%
distance center proton field to x-ray crosshair [mm]
≤0.25 mm ≤0.50 mm ≤0.75 mm ≤1.00 mm ≤1.25 mm ≤1.50 mm ≤1.75 mm ≤2.00 mm
FIGURE 8.19
Results of light-/x-ray/proton beam feld agreement tests.
253 Quality Assurance and Commissioning
to discussions of common, commercially available dosimeters, including
ionization chambers and diode detectors, including their multidetector con-
fgurations; as well as radiographic and radiochromic flms and TLD (ther-
moluminescent dosimeter) detectors.
Ionization chambers remain the single most important dosimeter for pro-
ton therapy. For absolute dose measurements, the ICRU and the International
Atomic Energy Agency (IAEA) provide the K
Q
values of a large number of
common ion chambers (4, 37). Their use for proton therapy absolute dose
measurements is discussed in Chapter 7. This section therefore concentrates
on discussion of dosimeters for relative dose measurements.
TABLE 8.3
Daily QA for Scattering and Uniform Scanning Beams
Test Tolerance/Comments
Review operator’s cyclotron and gantry startup
checklists
Operator checks machine operating
parameters daily.
Safety interlocks, indicator lights, neutron
detector, A/V systems
 
Output constancy check for scattering and
uniform scanning reference felds
2%. Output measurements in plastic
phantom.
Dose rate measurement 30% tolerance.
kV imaging and laser accuracy 1 mm. Orthogonal x-ray crosshair and laser
agreement.
Range verifer measurements of scattering and
uniform scanning felds
1 mm.
Range modulation wheel control signal timing 0.2 ms. Review of system reported timing
values compared to baseline data.
Scan feld size length and width 3 mm. Compare system reported values to
expected values for uniform scanning
reference feld.
TABLE 8.4
Weekly QA for Scattering and Uniform Scanning Beams
Test Tolerance/Comments
Review daily QA results Review for system performance trends.
MLIC calibration MLIC calibration performed prior to use for
PDD measurements.
Output constancy check for two scattering
and two uniform scanning reference felds
2%. Output measurements using MLIC. Fields
measured include intermediate and large
range felds.
Range measurements of above felds 1.5 mm. Measurements performed using
MLIC.
SOBP width measurements of above felds 2 mm. Measurements performed using MLIC.
SOBP uniformity measurements of above
felds
2%. Measurements performed using MLIC.
254 Proton Therapy Physics
Parallel chambers are suitable for depth–dose measurements. The effec-
tive measurement point is taken to be the inside surface of the front elec-
trode. However, attention should be paid to chamber design: parallel plate
chambers with front windows made of foils may change geometry and thus
may have uncertainties in effective point of measurements, as are cham-
bers with inadequate guard ring-to-electrode spacing ratios (38). Although
a small-diameter parallel plate chamber is adequate for scattering beam
depth–dose scans, depth–dose profles of pencil beams for pencil beam–
scanning technique need to include all scattered particles away from the
beam’s central axis. A large-diameter (8.2 cm) parallel plate chamber (Bragg
peak chamber) has been used for such measurements, although there may
remain a signifcant amount of scattered doses outside the diameter of this
chamber (23, 24). Such missing doses, if not modeled in treatment-planning
systems, may have a signifcant impact on the accuracy of MU calculations
of pencil beam–scanning treatments. Additional measurements, using two-
dimensional (2D) dosimeter instruments, including radiochromic flms and/
or 2D ion chamber arrays, should be performed to evaluate the magnitude of
scattered doses outside the diameter of such chambers.
Depth–dose measurements of scanning beams, if performed using a single-
channel ionization chamber, can be very ineffcient. A complete delivery of
TABLE 8.5
Monthly QA for Scattering and Uniform Scanning Beams
Test Tolerance/Comments
Review daily/weekly QA results Review for system performance trends.
Output constancy check for two scattering
and two uniform scanning reference felds
plus random patient feld
2%. Output measurements performed in water.
Fields measured include intermediate and
large range felds. Patient feld measured to
support MU calculation accuracy.
Range measurements of above felds 1.5 mm. Measurements performed using
in-water scans.
SOBP width measurements of above felds 2 mm. Measurements performed using
in-water scans.
SOBP uniformity measurements of above
felds
2%. Measurements performed using in-water
scans.
Lateral dose profle measurements of two
scattering and two uniform scanning
reference felds
3% fatness; 1.5% symmetry; 2-mm feld size.
Measurements performed using MatriXX ion
chamber array.
Range verifer reading of pristine peak ranges
with and without frst scatterers in beam
1 mm. First scatterer integrity tested.
X-ray/light feld/proton beam feld
agreement
1 mm. Double-exposure flm measurements.
Rotating through snouts.
Patient-positioning system/gantry accuracy 1 mm/1°. Tests include isocentric table
rotation.
Digital imaging positioning system 1 mm in calculated vs. set shifts. Tests
performed for two gantry angles.
255 Quality Assurance and Commissioning
the measured feld needs to be performed for each point of measurement,
because of the layer-by-layer nature of scanning beam delivery. A multi-
channel chamber system, such as the MLIC or MPIC (8), would signifcantly
improve the effciency of such measurements. A prototype system of a com-
mercial version of this design (Figure 8.24) (Zebra, IBA, LLN, Belgium) has
been in use at UFPTI for more than a year for the daily measurement of scan-
ning beam depth–dose curves of reference felds, has proven to be reliable,
and allows daily uniform scanning SOBP measurements without extending
QA time. Multichannel ion chamber arrays in 2D planar confgurations are
especially useful for periodic QA measurements of dose profles. Arjomandy
TABLE 8.6
Annual QA for Scattering and Uniform Scanning Beams
Test Tolerance/Comments
Review daily/weekly/monthly QA results Review for system performance trends.
Dosimetry system intercomparisons All dosimetry systems used for daily,
weekly, and monthly QA tests are
compared to ADCL-calibrated dosimetry
system and calibration factors determined.
Output calibration 1.5%. Scattering and uniform scanning
reference feld outputs calibrated using
ADCL-calibrated dosimetry system.
MU chamber linearity 0.5%
MU chamber dependence on dose rate 1% from 1 to 3 Gy/min
Dose rate accuracy 25% for scattering and uniform scanning
reference felds.
Output factors 2%. Performed for each option.
Output dependence on gantry angles 0.5%. Output of reference felds measured at
prime gantry angles.
Depth–dose scans 1 mm for range, 3 mm for SOBP width, 2%
for SOBP uniformity. Measurements
performed for each option. Off axis scans
performed for 1 feld.
Lateral dose profle scans 2% for fatness and symmetry.
Measurements performed for each option.
Lateral dose profle dependence on gantry
angle
0.5% variations.
Gantry accuracy and isocentricity 0.5° and -mm diameter.
Patient-positioning system translation,
rotation accuracy, and isocentricity
0.5 mm, 0.2°, and 1-mm diameter.
Snout position accuracy and alignment 5 mm in snout position accuracy; 0.5 mm in
alignment in both in-plane and cross-plane
directions.
Imaging system accuracy Within 1 mm for all snouts in both in-plane
and cross-plane directions.
Safety interlocks and radiation monitors A number of safety interlocks and in-room
neutron monitors are tested.
256 Proton Therapy Physics
et al. (39) reported use of such a system (MatriXX, IBA, LLN, Belgium). The
beam’s lateral penumbra measured with such systems will depend on the
distances between detectors and should be done with caution. However, for
beam fatness and symmetry measurements, they found the system to agree
with pin-point type ionization chambers to within 0.5%.
M
e
a
s
u
r
e
d

-

N
o
m
i
n
a
l

O
u
t
p
u
t

[
%
]
5.0
4.0
3.0
2.0
1.0
0.0
–1.0
–2.0
–3.0
–4.0
–5.0
Date
Jan-07 Jan-08 Jan-09 Jan-10 Jan-11
FIGURE 8.20
Daily output measurement results.
15.3
15.2
15.1
15.0
M
e
a
s
u
r
e
d

R
a
n
g
e

[
g
/
c
m
2
]
14.9
14.8
15.4
14.7
Date
Jan-07 Jan-08 Jan-09 Jan-10 Jan-11
FIGURE 8.21
Daily range verifer reading results.
257 Quality Assurance and Commissioning
14.90
08/1
4/06
10/1
4/06
12/1
4/06
02/1
3/07
04/1
5/07
06/1
5/07
08/1
5/07
10/1
5/07
12/1
5/07
02/1
4/08
04/1
5/08
Date
06/1
5/08
08/1
5/08
10/1
5/08
12/1
5/08
02/1
4/09
04/1
6/09
06/1
6/09
08/1
6/09
10/1
6/09
12/1
6/09
14.95
15.00
15.05
R
a
n
g
e

[
c
m
]
15.10
15.15
15.20
15.25
15.30
Field 1 (R = 15.1, M = 1.4)
FIGURE 8.22
Weekly range measurement results from in-water depth–dose scans.
9.80
08/1
4/06
10/1
4/06
12/1
4/06
02/1
3/07
04/1
5/07
06/1
5/07
08/1
5/07
10/1
5/07
12/1
5/07
02/1
4/08
04/1
5/08
Date
06/1
5/08
08/1
5/08
10/1
5/08
12/1
5/08
02/1
4/09
04/1
6/09
06/1
6/09
08/1
6/09
10/1
6/09
12/1
6/09
10.00
10.20
10.40
M
o
d

[
c
m
]
10.60
10.80
11.00
11.20
11.40
Field 1 (R = 15.1, M = 1.4)
FIGURE 8.23
Weekly SOBP width measurement results.
258 Proton Therapy Physics
Films, both the radiographic and radiochromic types, have been used for
proton beam dosimetry measurements. Both types of flms have signifcant
beam energy dependence in proton felds, as has been demonstrated by vari-
ous investigators (40–47). In particular, such energy dependence is demon-
strated by signifcant underresponse in high-LET regions of proton depth
doses or near the end of range, as demonstrated by Vatnitsky (41) (Figure 8.25).
FIGURE 8.24
A prototypical MLIC system being used for uniform scanning beam depth–dose curve
measurements.
0
0
1
2
R
e
l
a
t
i
v
e

d
o
s
e
3
4
1 2 3 4 5
Water equivalent depth, cm
MD-55 film, calibration at peak
MD-55 film, calibration at SOBP
Parallel plate ionization chamber
FIGURE 8.25
Comparison of pristine peak measurements using radiochromic flm and parallel plate cham-
ber. (Adapted from Vatnitsky, Appl Radiat Isot, 1997, 48, 643, 1997.)
259 Quality Assurance and Commissioning
Their use for lateral dose profle measurements, however, have been common.
Farr et al. used radiographic flms to evaluate the feld matching accuracy of
a robotic patient-positioning system and found the results to agree with ion
chamber measurements to within 2–5% (48).
Diode detectors have been evaluated for use in proton therapy dosimetry.
Of the various types of diode detectors, only the hi-p-type ones have been
found to be suitable for proton dosimetry, including both depth–dose and lat-
eral profle measurements (46, 49). Figure 8.26 shows a comparison of pristine
peaks measured by a high-p-doped diode detector, diamond detector, and a
parallel plate chamber. The agreement of the diode-measured curve to that of
the parallel plate chamber is excellent. Diode detectors of small active volumes
are especially suitable for the relative measurements of depth doses and lateral
profles, due to the minimal volume-averaging effect on measurement results.
Their use for absolute dose measurements, even for output constancy checks,
is plagued by response changes relative to the detectors’ radiation history.
Diode detectors may suffer signifcantly higher radiation damage, causing the
detector responses to decrease as the cumulative doses they receive increase.
8.6 Conclusions
Because of the great variations of available beam options and the methods
adopted to produce those among existing proton therapy systems, accep-
tance testing, commissioning, and periodic QA of proton therapy systems
require detailed analysis and understanding of individual systems. Such
analysis needs to include the sensitivity of beam quality parameters to sys-
tem-operating conditions and performance changes, and in particular the
different system failure modes and its consequent beam quality degrada-
tions. Monte Carlo methods (Chapter 9) have proven to be a powerful tool in
supporting this analysis. Although the fundamental principles of designing
0
20 40 60 80 100
Diamond detector
Si detector
Markus ionisation chamber
Diamond detector
Si detector
Markus ionisation chamber
120
Depth [mm]
140 160 180 200 220 174 176 178 180 182 184
Depth [mm]
186 188 190 192
50
R
e
l
a
t
i
v
e

d
o
s
e

i
n

%
100
150
200
250
170
180
R
e
l
a
t
i
v
e

d
o
s
e

i
n

%
190
200
210
220
230
240
250
FIGURE 8.26
Comparison of high-p-doped diode detector and parallel plate chamber for proton depth–dose
measurements. (Adapted from Mumot et al., Phys Med, 25(3),105, 2009.)
260 Proton Therapy Physics
such procedures and programs for proton therapy are no different from
those of conventional linear accelerator–based radiotherapy programs, addi-
tional and/or alternative tests must be identifed through such analysis and
understanding.
Continuous review and improvement of periodic QA programs are an
integral part of the overall QA measures for proton therapy systems. The
QA program may start with comprehensive measurement-based tests at
high, for example, daily frequencies. Through such enhanced QA tests in the
initial stages of a facility’s operations, additional knowledge, insights, and
confdence in the performance of the system are acquired. The QA program
should be revised on the basis of such experiences.
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265
9
Monte Carlo Simulations
HaraldPaganetti
CONTENTS
9.1 Introduction ................................................................................................ 266
9.2 Monte Carlo Particle Transport Algorithms and Codes ...................... 266
9.2.1 The Monte Carlo Method.............................................................. 266
9.2.2 Particle Tracking Using Monte Carlo .......................................... 267
9.2.3 Handling of Secondary Particles ................................................. 268
9.2.4 Proton Physics Defnition ............................................................. 270
9.2.5 User Input/Output in Monte Carlo Simulations ....................... 271
9.2.6 Monte Carlo Codes ........................................................................ 272
9.3 Monte Carlo Code Validation ................................................................... 273
9.3.1 Uncertainties Due to Physics Models ......................................... 273
9.3.2 Uncertainties Due to Material Constants ................................... 273
9.3.3 Validation Measurements for Proton Dose Calculations ......... 273
9.3.4 Validation Measurements for Proton Nuclear Interactions ..... 274
9.4 The Use of Monte Carlo to Study Proton-Scattering Effects ............... 276
9.5 The Use of Monte Carlo for Beam Line Design ..................................... 277
9.6 The Use of Monte Carlo for Treatment Head Simulations or
Treatment Head Design ............................................................................ 277
9.6.1 Characterizing the Beam Entering the Treatment Head .......... 277
9.6.2 Modeling of Beam-Monitoring Devices ..................................... 279
9.6.3 Modeling of Beam-Shaping Devices in Passive Scattering...... 279
9.6.4 Modeling of Scanned Beam Delivery ......................................... 281
9.6.5 Time-Dependent Geometries ....................................................... 283
9.6.6 Treatment Head Simulation Accuracy ........................................ 283
9.6.7 Phase-Space Distributions ............................................................ 285
9.6.8 Beam Models .................................................................................. 286
9.7 The Use of Monte Carlo for Quality Assurance .................................... 287
9.8 Other Monte Carlo Applications ............................................................. 288
9.8.1 Organ Motion Studies ................................................................... 288
9.8.2 Modeling of Detector Systems ..................................................... 288
9.8.3 Simulating Proton-Induced Photon Emission for Range
Verifcation ...................................................................................... 288
9.8.4 Simulating Secondary Neutron Doses ....................................... 289
9.8.5 The Use of Computational Phantoms ......................................... 289
266 Proton Therapy Physics
9.1 Introduction
Computer simulations are used in many areas of research and development.
Specifcally, Monte Carlo simulations allow the precise simulation of experi-
mental conditions. A properly benchmarked Monte Carlo system can thus
save beam time for experiments or create potential scenarios that are diff-
cult to create experimentally. Computer simulations are particularly impor-
tant in a feld such as radiation therapy because the patient can typically not
be used as the subject of experiments.
One of the main goals of computer simulations in radiation therapy is the
prediction of the delivered dose distribution to the patient. This aspect is cov-
ered in Chapter 12 on dose calculation algorithms. This chapter aims at illus-
trating other applications of computer simulations in proton therapy. One
might use such simulations to study the physics of proton beams (Section
9.4) or for beam line design (Section 9.5). Although proton therapy instal-
lations are commercially available, physicists working at a proton therapy
facility are often involved in treatment head design, which will be covered in
Section 9.6. Other sections cover Monte Carlo for quality assurance (Section
9.7) and other more specifc applications of Monte Carlo in proton research
(Section 9.8). First, however, Sections 9.2 and 9.3 will elaborate on the concept
and the achievable accuracy of Monte Carlo simulations.
9.2 MonteCarloParticleTransportAlgorithmsandCodes
9.2.1 The Monte Carlo Method
Initially, Monte Carlo techniques were developed to solve differential equa-
tions, not necessarily to track particles through a medium. It turns out,
however, that the stochastic process applied to solve differential equations
can be used to simulate physics on a step-by-step basis. Particle transport
is based on cross sections (i.e., interaction probabilities) per unit distance.
Monte Carlo algorithms thus sample from stochastic distributions and the
mathematical basis is governed by the central limit theorem (1).
9.8.6 Simulating LET Distributions for Radiobiological
Considerations ................................................................................ 291
9.8.7 Biology: Track Structure Simulations ......................................... 292
Acknowledgments .............................................................................................. 293
References ............................................................................................................. 293
267 Monte Carlo Simulations
Random numbers are sampled from a probability density function.
Random number generators have a period: that is, the number sequence
repeats itself eventually. However, this period is typically long enough in
modern random number generators not to affect simulations. In a transport
simulation, at each step of the particle through the geometry, the probability
density function is representing the probability of physics interactions and
their outcome. Mathematically, this is equivalent to solving the Boltzmann
transport equation for protons.
9.2.2 Particle Tracking Using Monte Carlo
The Monte Carlo method is the most accurate method of simulating particle
interactions within a medium. A particle history is defned as the knowl-
edge of the trajectory of one particle including potential secondary particles.
Many particles need to be simulated in order to achieve a given accuracy.
The uncertainty of Monte Carlo results depends on the number of histories
N with the error in the simulated quantity being proportional to 1/√(N).
Simulation of particle histories begins by sampling a number of events
from a starting source distribution. This can be a mathematical function or
a parameter list resembling an initial particle source, such as the fux from
an accelerator. One then simulates the passage of particles through a well-
defned geometry, one particle at a time, one small step at a time, randomly
sampling from one or more probability distributions at each step in order
to choose how the particle might interact (be absorbed, be annihilated,
change direction, or change energy) consistent with the laws of physics. This
is known as tracking. The tracking geometry is a well-defned geometrical
model, such as a treatment head or a patient geometry. Materials are charac-
terized by their physical properties, such as elemental composition, electron
density, mass density, or mean excitation energy.
The outcome of Monte Carlo simulations depends on the chosen step size.
The step size chosen should be small, so that the difference of the cross sec-
tions at the beginning and the end of the step is small. On the other hand, a
large step size decreases the computing time. Monte Carlo codes often use
various methods to ensure proper step sizes particularly near boundaries
(changes in material) (2–4). Depending on the fexibility of the code, the user
may be allowed to defne the maximum permitted step size.
For uncharged particles it is feasible to simulate all physics interactions.
However, for charged particles, like protons, this would be computation-
ally ineffective because they interact so frequently. For example, the simu-
lation of each elastic Coulomb interaction would cause a huge number of
small-angle scattering events. This observation lead to the development
of so-called class  II condensed history algorithms (5). Energy losses and
directional changes are condensed (or summed) into a single step. For pro-
ton scattering, the defection angle of single-scattering events is very small.
Multiple-scattering theories provide probability density functions that
268 Proton Therapy Physics
represent the net result of several single-scattering events (see Chapter 2).
Therefore, one can sample these distributions to determine the scatter-
ing angle at the end of a simulation step. Furthermore, one might defne
a threshold for the production of δ-electrons. Above an energy threshold
δ-electrons are produced explicitly, but below the threshold continuous
energy loss of the primary particle is assumed. Typically, a maximum step
size is defned, up to which continuous energy loss and a certain multiple-
scattering angle is assumed, unless a so-called catastrophic event occurs.
The latter might include high-energy δ-electrons or nuclear interactions.
The switch from continuous to discrete process considerations might be a
user variable in some codes. Typically, Monte Carlo methods use a combi-
nation of continuous processes based on condensed history and discrete
processes based on an explicit model of each interaction. In proton therapy,
discrete processes are typically nuclear interactions, secondary particle
production (including δ-electrons), and large angle Coulomb scattering.
Figure 9.1 illustrates a particle being tracked through a medium. To save
time specifcally with small effects of low energy particles, particle trans-
port is terminated based on a user-defned particle energy or particle range
threshold.
9.2.3 Handling of Secondary Particles
Secondary particles are typically saved on a memory stack and tracked after
the primary particle is fnished. Production cuts for secondary particles can
infuence energy loss and thus the simulation results (4). To improve compu-
tational effciency, one might decide not to track all particles. Particles not
being tracked should deposit their energy locally in order to ensure energy
conservation.
Figure 9.2 shows the primary and secondary proton fuence as a func-
tion of depth for a 160-MeV beam. For proton dose calculation, primary and
Scattering at an angle
Creation of a second particle
FIGURE 9.1
Schematic illustration of a particle tracking using Monte Carlo. The particle is being scattered
at certain angles for the frst fve steps, before a physics interaction causes a second particle to
be created (dashed line). Consequently, afterwards two particles need to be tracked indepen-
dently. Each step (straight line) might resemble several interactions in the condensed history
method.
269 Monte Carlo Simulations
secondary protons account for roughly 98% of the dose, depending on the
beam energy (6). This includes the energy lost via secondary electrons cre-
ated by ionizations. The δ-electron energy, E
δ
, can be calculated assuming
maximum energy transfer, which a point-charge particle can impart to a sta-
tionary unbound electron (masses of the proton and electron denoted as m
p

and m
e
, respectively):

E m c
m
m
m
m
e
e
p
e
p
δ
β
β
θ
β

−
⋅ +
−
+
¸
¸

2
1
1
2
1
2
2
2
2
2
( )
cos
( )
__
,


¸


1
]
1
1
−
2
1
.
(9.1)
For protons, the maximum energy of the δ-rays can be approximated as a
function of the proton energy, E
p
,

E
m
m
E
E
e
p
p
p
δ
max
. ≅ ≅ 4
500
(9.2)
This corresponds to a maximum range of the delta electrons of about 2.5 mm
for a 250-MeV proton. The highest energy electrons are preferentially ejected
in a forward direction. The energy of most electrons in a proton beam is
much less than 300 keV, which corresponds to a range of 1 mm in water.
Thus, explicit tracking of electrons is not necessarily required for dose calcu-
lations on a typical computed tomography (CT) grid. The tracking of second-
ary electrons is certainly required for microscopic simulations, for example,
to study radiobiological properties, for microdosimetry, or for absolute dose
simulations (7). The explicit tracking of secondary electrons should not be
100
80
60
40
20
0
0 50 100 150 200
P
r
o
t
o
n

fl
u
e
n
c
e

[
%

i
n
i
t
i
a
l

fl
u
e
n
c
e
]
D
o
s
e

[
r
e
l
a
t
i
v
e

u
n
i
t
s
]
Depth in water [mm]
FIGURE 9.2
Monte Carlo–simulated proton fuence as a function of depth for a 160-MeV proton beam. The
dose is shown as a dashed line, and the solid and dotted lines illustrate the primary proton and
the total (primary and secondary) proton fuence, respectively.
270 Proton Therapy Physics
neglected for ion chamber simulations (7–9). For applications other than dose
calculation, additional particles might need to be considered, such as neu-
trons (see Chapters 17 and 19).
9.2.4 Proton Physics Definition
The reason for the increased accuracy of Monte Carlo simulations compared
to analytical algorithms lies in the way the underlying physics is modeled.
Monte Carlo simulations are able to take into account the physics of interac-
tions on a particle-by-particle basis. This is done using theoretical models,
parameterizations, and/or experimental cross section data for electromag-
netic and nuclear interactions. Monte Carlo accuracy thus depends on the
detailed knowledge of physics for a particular particle, energy region, and
material.
Typically, the energy loss of protons is calculated by the Bethe-Bloch equa-
tion down to 2 MeV. Below 2 MeV a parameterization based on stopping
power formalism, for example, based on the International Commission on
Radiation Units and Measurements (ICRU) (10), might be used. Multiple
scattering is realized in condensed history class II implementations (11). The
Moliere theory (see Chapter 2) predicts the scattering angle distribution but
does not give information about the spatial displacement of the particle. The
Lewis method (12) allows calculation of moments of lateral displacement,
angular defection, and correlations of these quantities. Multiple-scattering
algorithms used in Monte Carlo codes may differ but are typically variations
of Lewis’s theory.
Typically, all possible interaction types need to be considered, such as
ionization, excitation, multiple Coulomb scattering, and nuclear interac-
tions. Although nuclear interactions are not responsible for the shape of
the Bragg peak (the majority of dose is deposited via electromagnetic ion-
ization and excitation), they do have a signifcant impact on the depth–
dose distribution (see Chapter 2) because they cause a reduction in the
proton fuence as a function of depth (about 1% of the primary protons
undergo a nuclear interaction per centimeter range of the beam) (6).
Multiple Coulomb scattering causes broadening of the beam, that is, a soft-
ening of the penumbra.
An interaction between the projectile and the nucleus can be modeled as
an intranuclear cascade with the probability of secondary particle emission.
Once the energy of the particles in a cascade has reached a lower limit, a
pre-equilibrium model can be applied. To accurately account for secondary
particles from nuclear interactions, the nuclear interaction probability and
the secondary particle emission characteristics must be known.
Nuclear interactions are typically parameterized using cross sections,
that is, interaction probabilities. Cross sections as a function of proton
energy may not be available for all reaction channels. In these cases, mod-
els, parameterizations, or a combination of models, parameterizations,
271 Monte Carlo Simulations
and experimental data must be used. The specifc choice may depend not
only on the particle or energy region, but also on the required accuracy
(vs. effciency) of a particular application. The cross section for a specifc
atomic or nuclear interaction caused by an incident particle is defned as
the probability for the occurrence of the event for one target nucleus, P,
divided by the particle fuence. With the fuence defned as the number of
particles, N, incident on a sphere of cross-sectional area, A, a cross section
is defned as

σ =
P
dN dA
.
(9.3)
Cross sections are divided into elastic cross sections (scattering of the inci-
dent particle of the nucleus with conservation of kinetic energy) and non-
elastic cross sections (nuclear excitation with potential creation of secondary
particles and no conservation of kinetic energy).
Cross sections can be single differential or double differential. The lat-
ter would describe the probability for energy loss with the primary par-
ticle defected under a specifc angle. Cross sections for proton-nucleus
interactions for applications in proton beam therapy are summarized by
the ICRU  (13). Treatment head simulations require accurate cross sections
in particular for steel (beam scatterers, collimator housing, magnet hous-
ing, detector housing), Lexan (beam scatterers, modulators, compensators),
lead (beam scatterers, modulators), aluminum (beam scatterers, modulators,
collimator housing, ion chambers), carbon (modulators), brass (collimators,
apertures, magnets), nickel (collimators), copper (magnets), PVC (ion cham-
bers), Mylar (ion chambers), and many others. The importance of accurate
double- differential cross sections may depend on whether these materials
are used in either beam-shaping or beam-modifying devices and on what
their typical position in the treatment head is.
For pencil beam scanning, small uncertainties in the “nuclear halo” (sec-
ondary particles emitted in nuclear interactions surrounding the primary
beam) or multiple Coulomb scattering can cause large uncertainties when
adding multiple pencils (14). The dose distribution is small for each pencil
but can be signifcant for a set of pencils delivering a dose to the target vol-
ume or in the sharp dose gradient at the distal falloff, as has been studied
using Monte Carlo (15).
9.2.5 User Input/Output in Monte Carlo Simulations
When designing a Monte Carlo simulation, one needs to defne the follow-
ing: the tracking geometry, the materials involved, the particles of interest,
the generation of primary events, the tracking of particles through materials
and electromagnetic felds, the physics processes governing particle interac-
tions, the response of sensitive detector components, the generation of event
272 Proton Therapy Physics
data, the storage of events and tracks, the visualization of the detector and
particle trajectories, and the analysis of simulation data at different levels of
detail. Depending on the code, some of these tasks may be taken care of by
default settings.
If one uses an existing executable that is already tailored to a specifc
application, input parameters might be limited to defning, for example, the
proton beam energy and the settings of a specifc device in a bigger geom-
etry assembly. The specifc defnition of these devices depends on the Monte
Carlo code in use. Most Monte Carlo codes would expect a more or less com-
plex defnition of geometries in an input fle, whereas others might expect a
defnition of geometry using a programming language.
The results of Monte Carlo simulations are typically analyzed from one-,
two-, or three-dimensional (1D, 2D, or 3D) histograms. Some Monte Carlo
codes designate such histograms as tallies. These are flled during the simu-
lation if certain conditions for a histogram bin are fulflled (e.g., a particle
has deposited a specifc amount of energy in a specifc area of the geometry).
One can also store entire particle histories for retrospective analysis. Caution
is warranted when dealing with dose scoring in a Monte Carlo system. A
Monte Carlo system typically provides information about the status of a
tracked particle either at the beginning or at the end of an individual step.
Typically, Monte Carlo systems require a particle to stop at a geometrical
boundary in order to adjust for the change in physics. It needs to be under-
stood whether the Monte Carlo defnes the post-step point as within the vol-
ume to be entered. Thus, one has to make sure that energy is deposited in
the volume according to the path of the particle track to avoid dosimetric
artifacts at boundary crossings.
9.2.6 Monte Carlo Codes
There are various Monte Carlo codes for use in proton therapy, for example,
FLUKA (16, 17), Geant4 (18, 19), MCNPX (20, 21), VMCpro (22), and Shield-
Hit (23). Typically, a Monte Carlo program is a software executable for which
the user has to write an input fle depending on the specifc problem. There
are also other approaches, such as Geant4, where the code provides only an
assembly of object-oriented toolkit libraries with the functionality to simu-
late different processes organized in different functions within a C++ class
structure. The ability to program is prerequisite for designing simulations
using these types of codes. Monte Carlo codes also differ in the level of con-
trol over tracking parameters. The ability to control every parameter (e.g.,
physics settings, step sizes, and material constants) adds fexibility but may
also make the code diffcult to use and prone to inaccurate results due to
user error.
In addition to the codes mentioned above, there are also programs that
serve as interfaces to Monte Carlo codes, for example, user platforms for spe-
cifc tasks (24–26).
273 Monte Carlo Simulations
9.3 MonteCarloCodeValidation
9.3.1 Uncertainties Due to Physics Models
The accuracy of Monte Carlo simulations depends on tracking parameters,
such as the step size (see above). Obviously, it also depends on the accuracy
of the implemented physics. Some codes were originally developed for high-
energy physics applications and therefore span a wide range of particles and
energy domains. A Monte Carlo code might allow different physics settings
from which the user can choose. There might even be different settings for
different energy domains. Models might not be tailored for proton therapy
simulations because they were originally designed for high-energy physics
applications and therefore require adjustment (27–29).
For example, there are different parameterizations for multiple-scattering
models and although the physics might be reasonably well understood, dif-
ferent Monte Carlo implementations can result in discrepancies. The imple-
mentation of the multiple-scattering theory can differ slightly from Molière
theory (30, 31), for example, for multiple scattering, the code Geant4 uses a
condensed history algorithm that utilizes functions to calculate the angular
and spatial distributions of the scattered particle implementations (32).
The signifcance of uncertainties in nuclear interaction cross sections
depends on the application. For example, for shielding calculations, accu-
rate double-differential cross sections (in energy and emission angle) for
proton-neutron interactions are important. According to the ICRU (13),
angle-integrated emission spectra for neutron and proton interactions are
known only to within 20–30% uncertainty. Total nonelastic and elastic cross
sections have uncertainties of <10%.
9.3.2 Uncertainties Due to Material Constants
Uncertainties in stopping power parameters also infuence calculation
uncertainties, specifcally the proton beam range (see Chapter 13) (4, 33, 34).
Values for the mean excitation energy might have uncertainties on the order
of 5–15%. Such an uncertainty for beam-shaping materials can lead to more
than 1-mm uncertainty in the predicted beam range in water (31). It is impor-
tant to consider this uncertainty when simulating energy loss in thick tar-
gets (4, 35). Typically, mean excitation energies are adjusted to agree with
measurement for elements where data exist and are interpolated, based on
theory, where data do not exist. Note that the exact density for some materi-
als (e.g., carbon) used in scattering system is often not known.
9.3.3 Validation Measurements for Proton Dose Calculations
Monte Carlo code validation for the settings of different physics parameters
(e.g., cross-section data, model parameterizations, cutoff values for particle
274 Proton Therapy Physics
production, and consideration of secondary particles) is typically done by
code developers. If the code is used for applications not anticipated by the
developers, benchmarking and validation have to be performed by the user.
Direct experimental validation of cross sections is often not feasible in proton
therapy institutions where the main users are located. Here, benchmarking
is mostly based on Monte Carlo simulations of less fundamental quantities,
such as dose. Benchmarking studies should not be too complicated in terms
of the underlying geometry so that discrepancies can be attributed to differ-
ences in physics and not to shortcoming in simulating the geometry.
Three of the most commonly used codes in proton therapy (Geant4,
FLUKA, and MCNPX) were compared with each other and with measure-
ments by Kimstrand et al (2). The physics settings within the codes were
varied. The study aimed at the simulation of the scattering contribution at
aperture edges where protons scatter at inner surfaces of apertures at very
small angles (i.e., a situation where small uncertainties in scattering power
would be measurable). The particle distribution was measured with a fuo-
rescent screen and a CCD camera. Signifcant impact of user-defned param-
eters was found. Others have analyzed the multiple-scattering algorithm
and beam profles in water downstream of inhomogeneous targets and com-
pensators for validation (28). For dose calculation, Monte Carlo benchmark-
ing studies are typically done using heterogeneous geometries consisting of
various materials (36, 37).
Benchmarking studies comparing experimental depth–dose distributions
and beam profles have been conducted for complex treatment heads
(34, 36, 37). Figures 9.3 and 9.4 show a comparison of Monte Carlo simulations
using the Geant4 code with experimental data measured with an ionization
chamber at the Francis H. Burr Proton Therapy Center at MGH. Studying
heterogeneous half-beam blocks and measuring/simulating the dose down-
stream can be a valuable test of scattering models.
9.3.4 Validation Measurements for Proton Nuclear Interactions
The correct modeling of nuclear interactions is important for dose calcula-
tion, especially if Monte Carlo is used for absolute or relative dosimetry (7).
Although the comparison of dose distributions is a valuable benchmark
for electromagnetic interactions, nuclear interaction components cannot be
studied separately in an experiment solely measuring dose. An experimen-
tal tool particularly useful for testing proton nuclear interaction data is the
multilayer Faraday cup (see Chapter 2) (40, 41). It is sensitive to electromag-
netic and nuclear inelastic reactions and measures the longitudinal charge
distribution of primary and secondary particles. Because it relies on charge
rather than dose, it is capable of separating the nuclear interaction compo-
nent from the electromagnetic component. This is because nuclear stop-
ping of protons takes place predominantly in the plateau region of a Bragg
peak, whereas electromagnetic stopping takes place around the Bragg peak.
275 Monte Carlo Simulations
Various Monte Carlo physics models for the simulation of electromagnetic
and nuclear interactions were validated against the measured charge distri-
bution from a Faraday cup (42).
The Faraday cup can only validate total cross sections. For treatment head
simulations and beam characterization, total and differential cross sections
for materials of beam-shaping devices are required to compensate for fu-
ence loss due to nuclear interactions. For primary standards and reference
dosimetry, these cross sections with high accuracy are needed for a limited
set of detector materials. Another example is the simulation of nuclear activa-
tion of tissues relying on isotope production cross sections for human tissues
(43–45). The International Atomic Energy Agency (IAEA) has recognized the
need for standardizing the use and modeling of nuclear interactions in pro-
ton and heavy ion radiation therapy (46).
D
o
s
e

[
%
]
80
100
60
40
20
0
D
o
s
e

[
%
]
80
120
100
60
40
20
0
0 50 100
Depth [mm]
150 200
0 50 100
Depth [mm]
150 200
FIGURE 9.3
Measured data (open circles) and Monte Carlo generated data (solid lines) for two depth-
dose curves from the Francis H. Burr Proton Therapy Center at Massachusetts General
Hospital. Top: a Bragg peak with a nominal beam energy at the treatment head entrance
of ~190 MeV. The spread-out Bragg peak (bottom graph) is based on a clinical feld with the
prescription of 17.2-cm range and 6.8-cm modulation width. The Monte Carlo simulation
included the entire treatment head geometry. (From Paganetti et al., Med Phys., 31, 2107,
2004. With permission.)
276 Proton Therapy Physics
There are considerable uncertainties when it comes to simulating neutron
production. A precise modeling of neutron yields is needed when simulat-
ing both scattered neutron doses to assess potential risks for patients (see
Chapter 18) (47, 48) and neutron production for protection and shielding (see
Chapter  17). These simulations require double-differential production cross
sections for tissues, beam-shaping devices, and shielding materials. There
are various nuclear interactions channels for neutron production, as neutron
and secondary charged particle emissions from nuclear interactions can be
the result of complex interactions. There are insuffcient experimental data of
inelastic nuclear cross sections in the energy region of interest in proton ther-
apy. Parameterized models for Monte Carlo transport calculations based on
theory in regions where experimental data do not exist can be diffcult because
of uncertainties in the physics of intranuclear cascade mechanisms. Proper val-
idation of Monte Carlo codes to perform such simulations is required (38, 49).
The agreement in neutron dose simulations is typically not as good as with
photons, electrons, or protons. Agreements of Monte Carlo results and mea-
sured data have been reported to be only between 10% and 340% (38, 50–53).
9.4 TheUseofMonteCarlotoStudy
Proton-ScatteringEffects
Analytical methods might have to estimate complex physics interactions. If
proton beams pass through complex heterogeneous geometries, a phenom-
enon called range degradation occurs (54, 55), which can be simulated using
120
100
80
60
40
20
0
6 8 10 12 14 –10 –8 –6 –4 –2 0
Depth [cm] Distance from beam axis [cm]
1 2
1 2
3
3
D
o
s
e

[
%
]
120
100
80
60
40
20
0
D
o
s
e

[
%
]
FIGURE 9.4
Measured (open circles) and simulated (solid lines) dose distribution. The left panel shows
the experimental setup with the beam impinging on a half-block of bone equivalent mate-
rial (black) into a water phantom (gray). The dashed lines indicate the directions of the scans
shown in the middle and right panels. The beam profle (3) was measured in an SOBP plateau.
(From Paganetti et al., Med Phys., 53(17), 4285, 2008. With permission.)
277 Monte Carlo Simulations
Monte Carlo codes. Another effect that can be studied with Monte Carlo quite
easily is scattering at sharp edges, for example, in apertures (56–58). One might
consider Monte Carlo–calculated kernels that can be used within analytical
methods, for example, simulated scatter kernels with Monte Carlo to incorpo-
rate aperture scatter in the treatment-planning algorithm (56). Multileaf col-
limators to replace patient-specifc apertures have been studied with Monte
Carlo as well, with the aim of improving the beam penumbra (59).
Markers implanted in the patient for setup or motion tracking do have
an impact on dose calculations. They are typically not modeled accurately
in pencil beam algorithms because of their high-Z nature. Monte Carlo has
been used to study the impact of such markers on the dose distribution (60).
9.5 TheUseofMonteCarloforBeamLineDesign
The basic beam line elements between the accelerator and the treatment
room that might be simulated using Monte Carlo are bending magnets and
energy degraders. Energy degraders are needed in cyclotron-based facili-
ties because cyclotrons extract a single energy. Depending on the desired
beam range, the energy has to be reduced using a degrader in the beam line
outside of the treatment room or in the treatment head. The latter is typi-
cally avoided because of the scattering it produces, which broadens the beam
and creates secondary radiation. Degraders are built as single or multiple
wedges that can move in and out of the beam. Monte Carlo beam transport
through carbon and beryllium degraders has been performed with the goal
of improving beam characteristics (4).
A large part of beam line simulations has to do with beam steering through
magnetic felds. Although this can be done with many Monte Carlo codes,
(e.g., Geant4), tracking through magnetic felds is usually quite slow because
it is based on using Runge–Kutta algorithms and parameterized feld maps.
The curved particle in a specifc feld is broken up into linear chord segments.
Beam optics calculations are therefore often done numerically (61), but there
are specialized Monte Carlo codes that simulate magnetic beam steering (62).
9.6 TheUseofMonteCarloforTreatmentHead
SimulationsorTreatmentHeadDesign
9.6.1 Characterizing the Beam Entering the Treatment Head
A parameterization of the phase space at treatment head entrance might in
principle be defned from frst principles, based on the knowledge of the
magnetic beam steering system or by ftting measured data (37). For typical
278 Proton Therapy Physics
Monte Carlo applications in proton therapy, the beam line magnets that steer
the beam into the treatment head would not be modeled, but the simulation
would start at the treatment head entrance. A parameterization of the beam
at the entrance of the treatment head can be done based on beam energy,
energy spread, beam spot size, and beam angular distribution (36,  63).
Measuring some of these parameters directly can be diffcult, and a user
might have to rely on the manufacturer’s information.
The angular spread is not easily measurable and is typically on the order
of 2–5 mm-mrad. It can also be parameterized using the emittance of the
beam, defned as the product of the size and angular divergence of the beam
in a plane perpendicular to the beam direction.
The size of the proton beam spot is well known because a segmented
transmission ionization chamber is typically located at the treatment head
entrance for beam-monitoring purposes. For most facilities, the size of a pro-
ton beam is usually on the order of 2–8 mm (sigma). Using an incorrect spot
size in the simulations can have a signifcant impact on the results, depend-
ing on the design of the treatment head. It has been shown that the exact
knowledge of this parameter might not be signifcant for passive scattering
simulations at least for certain modulator wheel designs (36, 64). The impact
of the beam spot size depends on the width of each step used on the modu-
lator wheel, that is, the number of absorber steps covered by the beam at a
given time. For beam scanning, the exact beam spot size and its shape are, of
course, vital, because it directly infuences the spot size and shape at treat-
ment head exit as prescribed by the planning system.
The initial energy spread and spot size at nozzle entrance might infuence
the fatness of a spread-out Bragg peak (SOBP) because these parameters
infuence the peak-to-plateau ratio of the individual Bragg peaks that form
an SOBP. Clinically, one of the most important parameters is certainly the
beam energy, as felds are prescribed using the beam range in water. The
energy and energy spread can be obtained either directly, using an elastic
scattering technique (65), or indirectly, by measuring the range and shape
of Bragg peaks in water (64). The energy spread of proton beams entering
the treatment head from a cyclotron is typically <1% (ΔE/E), whereas a syn-
chrotron may extract beams with an energy spread two orders of magnitude
smaller.
The parameters listed above are typically correlated. It has been demon-
strated that this correlation is insignifcant when modeling a passive scatter-
ing system, mainly because the amount of scattering material in the beam’s
path uncouples the parameters at the treatment head exit (36). For beam-
scanning simulations such a correlation, for example, between the particle’s
position within the extended beam spot and its angular momentum, needs
to be taken into account, because it might affect the size of the pencil beam
exiting the treatment head. Because of the energy spread of the beam, a
defection in a magnetic feld will lead to a correlation of particle energy and
position.
279 Monte Carlo Simulations
9.6.2 Modeling of Beam-Monitoring Devices
Beam-monitoring devices are typically transmission ionization chambers.
To simulate a realistic dose distribution, simulating these chambers in
detail might not be necessary because they cause only a little scattering and
energy loss of the beam. Simulating plain or segmented ionization chambers
is done for the purpose of designing ionization chambers or studying beam
steering, as well as calculating the absolute dose in machine monitor units.
For a patient’s treatment the prescribed dose is converted into machine
monitor units. A monitor unit typically corresponds to a fxed amount of
charge, collected in a transmission ionization chamber incorporated in the
treatment head. This reading is related to a dose at a reference point in
water (66, 67). Absolute dose can thus be simulated if a detailed model of
the treatment head, including the ionization chamber geometry and read-
out, is available  (7). In a segmented ionization chamber the volume used
for absolute dosimetry can be quite small (e.g., 1–2 cm in diameter). This
causes low statistics when simulating the chamber response (from energy
deposition events) and thus requires a large number of histories to be simu-
lated. Figure 9.5 shows the Monte Carlo model of an ionization chamber. As
an approximate approach, one might simulate the energy deposited in the
ionization chamber without predicting the actual output charge (68), that
is, simulate a relative number that has to be normalized against a reference
charge (27, 69).
9.6.3 Modeling of Beam-Shaping Devices in Passive Scattering
Monte Carlo simulations are extremely valuable in treatment head design
studies, as they can reduce the required number of experiments consider-
ably. Small design changes can be tested computationally before building or
modifying hardware components. Furthermore, for research studies requir-
ing accurate characterization of the radiation feld, treatment heads are mod-
eled to characterize the beam at treatment head exit. Such simulations can
also be useful when commissioning planning systems (70–72). There are
various reports on Monte Carlo treatment head simulations (27, 28, 36, 39, 51,
68, 69, 72–74).
FIGURE 9.5
Monte Carlo model of an ionization chamber at the Francis H. Burr Proton Therapy Center at
the Massachusetts General Hospital. Shown is a vertical cut through the device. The simula-
tion was done with the TOPAS Monte Carlo system.
280 Proton Therapy Physics
Most Monte Carlo models attempt to model machine-specifc compo-
nents in the treatment head using manufacture blueprints (36, 37, 39).
Creating a Monte Carlo model of a treatment head could also be based on
a computer-aided design (CAD) interface to the Monte Carlo code (75). If
Monte Carlo codes only allow the defnition of geometrical objects out of
a library of standard objects, a complex geometry can be represented as a
combination of regular geometrical objects. Some devices can be modeled
easily by using boxes or tubes, whereas others require complex solutions
due to their irregular shapes. The most important beam-shaping devices
to be modeled are the passive scattering system, as well as apertures and
compensators.
Treatment heads in passive scattering proton therapy can be rather com-
plex, and the position or state of certain devices can change depending on
the specifed feld. For example, scattering foils might be inserted or different
modulator wheels evoked for a certain combination of range and modula-
tion width. The Monte Carlo model of a treatment head has to accommodate
all possible variations of geometrical settings. One might generate a generic
treatment head in the Monte Carlo code that is initialized when the code is
set up (or compiled) and then modify the generic geometry using parameters
provided via an input fle. To simulate a specifc feld, one has to defne spe-
cifc treatment head parameters or the range and modulation width, which
can subsequently be converted into the treatment head parameters. The
parameters are provided either by a treatment-planning system (if it pre-
scribes the treatment head settings for a patient feld) or by the treatment-
control system (if the treatment head settings are defned by an interface
to the planning system or manually by an operator), or they can simply be
defned arbitrarily by the user.
The targeted accuracy when modeling the treatment head in a Monte
Carlo system depends on the purpose of the simulation. For calculating
phase-space distributions for dose calculation in the patient, it is probably
suffcient to have only beam-shaping devices included in the simulation.
Passive scattering simulations require the double- or single-scattering sys-
tem, the modulator wheel, aperture, and compensator. For other applications
such as ionization chambers for detector studies for absolute dosimetry or
housing of devices to study scattering or shielding effects, one might need a
more realistic description of other treatment head components. The follow-
ing paragraphs describe the modeling of the most important devices in a
treatment head.
A contoured scatterer typically consists of two components: one made
of a high-Z material and one made of a low-Z material. The thickness
of the high-Z material decreases radially with distance to the feld cen-
ter, whereas the thickness of the low-Z material increases as a function of
radial distance. The bi-material design ensures that the scattering power is
independent of the beam energy. Such a complex geometry might be mod-
eled by combining regular objects, for example, by combining cones (36).
281 Monte Carlo Simulations
A modulator wheel can be simulated by using segments out of a circular
structure. Each of these segments is characterized by thickness, material,
and minimum and maximum radius, as well as the angle covered. Note
that because beam spots often overlap with several wheel steps, it is not
suffcient to use one simulation per absorber step and combine simulations.
Figure 9.6 depicts Monte Carlo models of a contoured scatterer and a mod-
ulator wheel.
The geometries of patient feld-specifc apertures and compensators are
typically provided by the planning system. There can also be hard-coded
versions in the Monte Carlo if standard regular shapes are being used for
commissioning or testing purposes. Apertures are often studied because
of both the secondary radiation they produce (47) and the effects of edge
scattering. An aperture opening might be characterized by a set of points
following the inner shape of the drilled opening. If the Monte Carlo code
can translate this information into a 3D object representing the aperture, the
information can be used directly. Otherwise, different parameterizations
need to be applied (36). For a compensator, the geometry can be described by
a set of points in space defning the position and depth of drill bits for use
in a milling machine. A Monte Carlo code might use these milling machine
fles directly. Using standard regular shapes (such as tubes), the geometry
can then be modeled (36).
9.6.4 Modeling of Scanned Beam Delivery
Treatment heads for beam scanning are, geometrically, less complicated to
model because there are fewer objects in the beam path. Essential to model
might only be the scanning magnets and, perhaps an aperture. Treatment
head simulations for scanned beams have shown good agreement (73).
(A) (B) (C)
FIGURE 9.6
Monte Carlo model of a contoured scatterer used in a double-scattering system (left: mesh
type image) and a modulator wheel based (middle: transparent steps of the wheel; right: actual
simulated proton tracks) at the Francis H. Burr Proton Therapy Center at the Massachusetts
General Hospital. The simulation was done with the TOPAS Monte Carlo system (26).
282 Proton Therapy Physics
Depending on the scanning system, accurate description of the feld lines
compared with binary felds, and accurate beam emittance is important
when simulating dose distributions using Monte Carlo. To fully model a
scanned beam treatment head, the Monte Carlo code has to be able to simu-
late magnetic beam steering. Depending on the beam steering, a scanned
proton beam can be convergent or divergent. Magnetic felds are typically
not modeled physically but rather geometrically by defning an area within
the geometry in which particle tracking is affected by a magnetic force of
certain strength (36). Particle tracking is then performed according to feld
equations. As an approximation, instead of implementing the feld lines,
one might approximate a magnetic feld with a certain strength as simply
on or off as a function of positioning in the geometry (i.e., assume perfect
dipoles). Attention needs to be given to the maximum step size while track-
ing protons through the magnetic feld because large steps lead to consid-
erable uncertainties when simulating the curved path of particles through
the feld. Figure 9.7 shows an example of protons steered through a mag-
netic feld.
If the scanning pattern for a prescribed treatment for pencil beam scan-
ning is simulated, the magnetic feld settings are prescribed by either the
planning system or by a treatment control system, based on information by
the planning system (76). These feld characterizations are typically beam
spot positions at a plane upstream of the patient that are parameterized as
x and y coordinates and spot energy. If the spots are being modeled using
Monte Carlo tracking through the nozzle, this information needs to be trans-
lated into magnetic strengths in Tesla. The relationship is typically known
from results of commissioning measurements.
FIGURE 9.7
Proton tracks steered though a magnet with a specifc feld strength as modeled within Geant4.
The simulation was done with the TOPAS Monte Carlo system (26).
283 Monte Carlo Simulations
9.6.5 Time-Dependent Geometries
For passive scattering (modulator wheel rotation) as well as beam scanning
(changing magnetic feld), the treatment head geometry involves devices
with a time-dependent setting. Considering time-dependent settings by
adding numerous individual runs can be cumbersome because separate
executables or input fles might be needed for each potential setting. The
rotation of the modulator wheel can be simulated by adding individual runs
of pristine Bragg peaks that are subsequently added based on weighting fac-
tors obtained from the wheel geometry (27, 72). One can also use a slab of a
fxed thickness and then change the start position of the beam inside the slab
to modulate different thicknesses (68).
An alternative is to change the geometry dynamically by applying a
four-dimensional (4D) Monte Carlo technique (77). Although still discrete,
the technique is basically continuous, as it allows geometry changes after
each particle history. In a simulation of passive scattered delivery, the wheel
position was changed in steps of 0.7°. The resolution of the simulation had
little infuence on the speed of the calculation, because motion was handled
by simply changing pointers within the computer memory (36). To simu-
late a beam-scanning pattern, 4D Monte Carlo techniques can be used to
constantly update the magnetic feld strength (76, 77). This allows studying
beam-scanning delivery parameters (73, 76, 78).
Another time-dependent feature in beam delivery might be the modula-
tion of the beam current in passive scattering systems (see Chapter 6) (79).
Because each patient feld is unique in terms of range and modulation width,
there needs to be a unique wheel design for each feld (each range and modu-
lation width). Because this is impractical, one uses a fnite set of modulator
wheels, each resembling a unique step design to create full modulation to
the patient’s skin. To deliver a certain modulation width, as well as meet
specifcations for SOBP fatness, the beam current might be regulated at the
accelerator (beam source) level to fne-tune the shape of the SOBP depth-
dose distribution (see Chapter 6) (79). Thus, the beam current is continuously
modulated as a function of rotation angle. This can be incorporated into the
Monte Carlo code by using a fnite set of look-up tables correlated to the
rotating wheel in 4D Monte Carlo.
9.6.6 Treatment Head Simulation Accuracy
Figure 9.8 shows the simulated geometry of a proton therapy treatment head.
The accuracy has to be validated experimentally, for example, by compar-
ing the fatness of the SOBP and the shape of the lateral beam profle (see
Figures 9.3 and 9.4). For beam scanning one might validate the simulation by
analyzing the beam spot size and Bragg peak width.
For a passive scattering treatment head having many beam -shaping
devices, the accuracy of the simulation depends on the available information
284 Proton Therapy Physics
regarding the geometry of treatment head elements, for example, whether
drawings of geometries are provided by the vendor (36). In addition, it
might depend on our knowledge of exact material compositions and mate-
rial properties (64). Thus, the desired accuracy might not be reachable
based on frst principles, depending on the complexity of the treatment
head or beam settings or the geometry information. Certain parameters
describing material compositions may not be known to suffcient preci-
sion. The SOBP range might be very sensitive (up to 1–2-mm range varia-
tions) to changes in the density of materials in the modulator wheel or
scatterers (64). Materials commonly used for these devices are polyethyl-
ene (Lexan), lead, and carbon. Specifcally, in the case of carbon, the nomi-
nal density as specifed by the manufacturer can vary substantially from
the actual density because carbon is available in various specifcations.
The knowledge of material constants affects not only the range but also
the modulation width.
The question arises: how precisely can one simulate beam delivery
with a Monte Carlo treatment head model if one has to rely on specifica-
tions given in the manufacturer’s blueprints? Good agreement might be
found based on first principles (36, 64), but in certain cases the results of
a Monte Carlo–based passive scattering proton beam system might show
discrepancies when compared with experiments. If the simulations differ
from experimental data, adjusting parameters might be difficult because
FIGURE 9.8
Monte Carlo model of one of the treatment heads at the Francis H. Burr Proton Therapy Center
at Massachusetts General Hospital. The simulation was done with the TOPAS Monte Carlo
system (26).
285 Monte Carlo Simulations
of the complexity of proton therapy treatment heads. For example,
adjusting nozzle geometries to improve a slight tilt in an SOBP will cor-
respondingly affect the modulation width (64). Additional experimental
information might be needed to adjust settings of material characteristics
within the Monte Carlo. An alternative solution is the simulation of the
treatment head based on the available geometrical and initial beam infor-
mation and then fine-tuning if the outcome in terms of range and modu-
lation width does not exactly match the experimental data. Beam current
modulation (beam weight as a function of modulator wheel angle) can be
used to correct the Monte Carlo simulations if the desired SOBP flatness
can not be reached based on first principles (64). Any “tuning” should be
done with caution and only for small corrections, because it might affect
the beam characteristics or might even point to a problem in the Monte
Carlo settings.
9.6.7 Phase-Space Distributions
The results of particle tracking through a treatment head are typically stored
in a phase-space distribution to be used for further simulations. A phase-
space distribution is a fle containing the parameters for a large set (typically
tens or hundreds of millions) of particles. It is generated when protons are
tracked through the treatment head and the kinetic parameters are recorded
for each particle. Thus, a phase space is a fle where each particle is repre-
sented as a point in space with some of its characteristics. It can be defned at
a particular surface of any given shape recording all particles that cross this
surface (e.g., particles that enter a particular device). For dose calculations the
phase space is normally defned at a plane perpendicular to the beam axis
between the treatment head and the patient or phantom.
The aim is to minimize calculation time due to reusing the phase space
if multiple scenarios with the same feld characteristics are to be studied.
Phase-space fles may only contain the most relevant parameters, such as
the energy, directional cosine, and particle type. However, for specifc stud-
ies one is often interested in the history of particles (e.g., if the particle is a
secondary or primary particle or if the particle was scattered at a specifc
device). In this case the phase space may contain additional parameters or
binary fags to allow partial reconstruction of a particle’s history. The IAEA
has suggested a standardized phase-space format.
In photon therapy, phase-space distributions play a big role in dose cal-
culation. For dose calculations in passive scattered proton therapy, phase
spaces are less useful because each feld typically has a unique setting of
the treatment head and beam energy, thus making it unlikely that the phase
space can be reused. This is true in particular if the patient-specifc aperture
and compensator are included in the treatment head simulation. For beam
scanning one might be able to fnd a beam parameterization as will be dis-
cussed in the next section.
286 Proton Therapy Physics
Typically, protons, neutrons, electrons, and photons are included in phase-
space distributions. For beam scanning, the contribution of secondary par-
ticles in the phase space can often be entirely neglected. However, even for
passive scattered proton beams, the contribution of secondary protons from
the treatment head reaching the patient is quite small. Secondary protons
generated upstream of the fnal collimator are typically emitted at an angle
that prevents them from passing through the patient-specifc collimator. In
addition, those generated within the collimator will most likely be stopped
in it. For a very small aperture (diameter of the opening just 3 cm), the treat-
ment head effciency (protons exiting versus protons entering the treatment
head) at the Francis H. Burr Proton Therapy Center was simulated to be just
0.7%, whereas for a bigger aperture opening (15-cm diameter) it increased to
17.7%. The yield of secondary protons per primary proton in the phase-space
fles was just 0.5% and 0.6%, respectively (i.e., almost independent of the feld
size). However, nuclear interactions do play a role in the yield of the prima-
ries, as they cause a loss of primary protons along the beam path through
the treatment head. Figure 9.9 shows energy distributions of protons and
neutrons at the exit of a treatment head.
9.6.8 Beam Models
Beam models are a mathematical parameterization of a radiation feld exit-
ing the treatment head. They are a standard feature in Monte Carlo simula-
tions for conventional photon or electron beams (80). As we have described
above, proton therapy treatment head settings are highly feld dependent,
and thus beam models are more diffcult to defne.
2e+6
2e+6
1e+6
P
a
r
t
i
c
l
e
s

/

M
e
V
P
a
r
t
i
c
l
e
s

/

M
e
V
MeV MeV
5e+5
0
100 120 140 160 180 200 200 150 100 50 0
1e+5
1e+4
1e+3
1e+2
1e+1
FIGURE 9.9
Energy distribution at the exit of the treatment head for a feld with a range of 20 cm in water
and a modulation width of 6 cm at the Francis H. Burr Proton Therapy Center at Massachusetts
Genera Hospital (left: primary protons; right: secondary protons from nuclear interactions
[dashed] and neutrons from nuclear interactions [dotted]).
287 Monte Carlo Simulations
It is possible to deconvolve an SOBP into its pristine peak contributions for
optimizing beam current modulation (79). This method, in combination with
assumptions about the angular spread of the feld, could also serve to con-
struct a beam model depending on the complexity of the double-scattering
system. Whether such a beam model is realistic depends on the purpose of
the study. It might be fne for dose calculation purposes but not for studies
where the underlying energy distribution of the beam needs to be known
exactly. Note that similar dose distributions can be delivered with different
underlying proton energy distributions (but different fuences). The creation
of a given SOBP might not be unique in terms of the underlying pristine
Bragg peaks.
The situation is different for beam scanning. Here, beam models are fea-
sible because a feld can be characterized by a fuence map of pencil beams
(x, y, beam energy, weight, divergence, and angular spread). The parameters
can be obtained by Monte Carlo simulations of the entire treatment head
including the magnetic felds (34) or by experiments, for example, fuence
distributions of pencil beams in air and depth–dose distribution measured
in water (81). For some scanned beam deliveries one might want to use an
aperture to reduce the beam penumbra. In this case, it is essential to consider
aperture scattering in the beam model.
The fact that realistic beam models can be constructed for pencil beam
scanning has important implications when using Monte Carlo for clinical
dose calculation. For passive scattering simulations, the majority of calcu-
lation time is spent tracking particles through the treatment head due to
the low effciency of proton therapy treatment heads for passive scattering
(typically between 2% and 40%, depending on the feld). The use of beam
models allows the use of fast Monte Carlo routinely in the clinic for beam
scanning (37).
9.7 TheUseofMonteCarloforQualityAssurance
Monte Carlo simulations are very helpful for designing a new facility, for
quality assurance (QA), and for supporting everyday operation (e.g., cal-
culating tolerances on the appropriate beam delivery parameters; see
Chapter  8). QA is based on routine measurements. Monte Carlo simula-
tions can assist clinical QA procedures. By simulating dose distributions
and varying beam input parameters, tolerance levels for beam parameters
can be defned (36). Monte Carlo simulations are particularly valuable for
studying scenarios that cannot be created easily in reality, (e.g., slight uncer-
tainties or misalignments in the treatment head geometry that might occur
over time).
288 Proton Therapy Physics
9.8 OtherMonteCarloApplications
9.8.1 Organ Motion Studies
Monte Carlo simulations in radiation therapy are mainly used for dose calcu-
lation (as will be described in Chapter 12). Given its accuracy, especially for
low-density materials and in the presence of heterogeneities, Monte Carlo dose
calculation is attractive for studying motion effects in lung dosimetry (82, 83).
For studying dosimetric effects in time-dependent geometries, the results
of individual 3D calculations are usually combined. This method can poten-
tially become cumbersome, in particular when assessing double-dynamic
systems, for example, investigating the infuence of time-dependent beam
delivery (i.e., magnetically moving beam spots in proton beam scanning) on
the dose deposition in a moving target. In 4D Monte Carlo simulations, the
time parameter is translated into the number of histories per updated geom-
etry. The use of this technique when modeling time-dependent structures in
the treatment head has been described above. It has also been used to model
respiratory patient motion (77, 83) and to study interplay effects between
respiratory motion and beam-scanning (76).
If the dose is to be calculated based on a time-dependent patient geometry,
it cannot be accumulated based on a fxed voxel grid. It was therefore sug-
gested to track points in the geometry based on voxel displacement maps
generated via deformable image registration (83). The local dose is calculated
as a function of well-defned, moving subvolumes and not as a function of
position in a fxed coordinate system. It has also been shown that deformed
voxels might be used within Monte Carlo dose calculation (84).
9.8.2 Modeling of Detector Systems
One of the frst applications of Monte Carlo methods in radiation therapy
was the simulation of detector systems. For example, Monte Carlo simula-
tions have been performed to design a prompt gamma detector for QA (85).
Another example is the use of Monte Carlo simulations to optimize image
reconstruction for proton CT (86, 87).
9.8.3 Simulating Proton-Induced Photon
Emission for Range Verification
Protons undergo nuclear interactions in the patient, which can lead to the for-
mation of positron emitters. Because the patient is “active” after being irradi-
ated for therapy, one can use a positron emission tomography (PET) image for
in vivo verifcation of treatment delivery and, in particular, beam range (see
Chapter 16). Monte Carlo simulations play a vital role for this purpose and are
used to generate a theoretical PET image based on the prescribed radiation
289 Monte Carlo Simulations
feld, which can then be compared to the measured PET distribution for treat-
ment verifcation (44, 45). The problem when simulating these images is the
low statistics due to the relatively low cross section for generating a posi-
tron emitter. Fluence-to-yield conversion methods are therefore being used
where positron emitter distributions are calculated by internally combining
the proton fuence at a given voxel with experimental and evaluated cross
sections for yielding
11
C,
15
O, and other positron emitters (43). Lack of detailed
cross sections data is currently limiting the accuracy of in vivo range verifca-
tion (88). Similarly, the emission of gamma rays from excited nuclear states,
so-called prompt gammas, can be simulated using Monte Carlo (89).
9.8.4 Simulating Secondary Neutron Doses
Monte Carlo simulations have been used for shielding design studies (see
Chapter 17) (90–92). Secondary neutrons reaching the patient are of concern
because of potential side effects (see Chapter 18). The neutron-generated dose
can not be calculated using an analytical dose calculation method imple-
mented in a treatment-planning system because the dose calculation is not
commissioned for low doses. Neutron doses are very low (typically <0.1% of
the target dose) and are thus negligible for treatment planning. Furthermore,
secondary neutron doses are diffcult to measure because neutrons are
indirectly ionizing and interact sparsely. Monte Carlo simulations are very
valuable for assessing neutron dose in patients (47, 93, 96) or studying the
infuence of treatment head devices and their design on neutron produc-
tion (97, 98). The MCNPX code was used to assess neutron and photon doses
in proton beams (51–53, 72, 93, 104). Further, FLUKA (50, 103) and Geant4
(47, 94, 96) were applied to assess secondary doses in proton beams. Neutron
production in proton beams was also studied using the Shield-Hit (105, 106)
and PHITS codes (107).
For uncharged particles, like neutrons, interacting less frequently, Monte
Carlo simulations might be time consuming because more histories are
required to achieve a reasonable statistical accuracy. One approach to over-
coming this problem is the use of tabulated energy-dependent fuence-
to-equivalent dose conversion coeffcients (108–115) in combination with
calculating particle fuences at the surface of a region of interest (organ)
(51, 102, 116). This approach avoids the time-consuming simulation of each
energy deposition event. Radiation weighting factors (see Chapter 18) can be
applied on an average basis or during the simulation at each energy deposi-
tion event (47, 48). Different dose-scoring methods when simulating neutron
equivalent doses have been compared (48).
9.8.5 The Use of Computational Phantoms
Organs not directly considered in the treatment-planning process are typi-
cally not imaged. Consequently, whole-body computational phantoms can
290 Proton Therapy Physics
play an important role when combined with Monte Carlo dose calculations
to simulate scattered or secondary doses (e.g., neutron doses) to organs far
away from the target region (117). Initially, the radiation protection commu-
nity had defned stylized phantoms that are based on simple geometrical
shapes (e.g., an elliptical cylinder representing the arm, torso, and hips, a
truncated elliptical cone representing the legs and feet, and an elliptical cyl-
inder representing the head and neck). Human anatomy is too complex to be
realistically modeled with simple geometrical shapes. A more realistic repre-
sentation of the human body can be achieved using voxel phantoms, where
each voxel is identifed in terms of tissue type (soft tissue, hard bone, etc.) and
organ identifcation (lungs, skin, etc.) (118). In a Monte Carlo environment
each phantom voxel is usually tagged with a specifc material composition
and density. Voxel phantoms are largely based on CT images and manually
segmented organ contours. For each organ and model and age- and gender-
dependent densities, as well as age-dependent material compositions, can be
adopted based on ICRU (119) and organ-specifc material composition as a
function of age can be based on individuals at the International Commission
on Radiological Protection (ICRP) reference ages (120, 121). Dosimetric differ-
ences between the use of stylized phantoms and the use of voxel phantoms
can be up to 150% (110, 122–126). In addition to standard adult male or female
models, models of pregnant patients (127, 128) and the pediatric population
have been designed (129–137).
To match a particular patient as closely as possible using a voxel phan-
tom in a Monte Carlo simulation, one might have to interpolate between
two different phantoms doing uniform scaling. There is also the prob-
lem of differences in the distribution of subcutaneous fat when trying to
create an individual from a reference phantom. The latest developments
in whole-body computational phantoms for Monte Carlo simulations are
hybrid phantoms (138, 139). These phantoms are typically based on com-
binations of polygon mesh and nonuniform rational B-spline (NURBS)
surfaces. They provide the fexibility to model thin tissue layers and allow
for free-form phantom deformations for selected body regions and inter-
nal organs. Each organ can be adjusted to the desired shape and volume
using patient-specifc images and deformable image registration (140–144).
Patient body weight can be accommodated through adjustments in adi-
pose tissue distribution (145–147). A series of reference (i.e., 50th height/
weight percentile) pediatric hybrid models has been developed (136).
Figure 9.10 shows a hybrid phantom and how it can be shaped to resemble
a specifc patient. Details regarding source images, developmental pro-
cedure, modeling issues, and resulting hybrid phantoms can be found
elsewhere (138).
Phantoms have been implemented in many Monte Carlo codes to assess
neutron doses in proton therapy (47, 94–96, 101, 103). For example, work has
been done on neutron dose contamination in proton therapy in pediatric
patient anatomies (47) based on computational phantoms (134, 137).
291 Monte Carlo Simulations
9.8.6 Simulating LET Distributions for Radiobiological Considerations
Prescription doses to cancerous tissue as well as dose constraints to organs
at risk are based on clinical experience with photon beams. Proton doses
are related to photon doses using the relative biological effectiveness (see
Chapter 19). Biophysical modeling is far from being able to simulate all radia-
tion effects in subcellular structures. The physics, however, can be simulated
reasonably well. To interpret biological experiments one needs to know the
characteristics of the radiation beam. The absorbed dose can be described
as the integral of the particle fuence times the total mass stopping power
over the particle energy distributions (148, 149). One parameter that is being
used to interpret biological effectiveness of proton beams is the linear energy
transfer (LET). One might simulate dose-averaged LET distributions in a
patient geometry to identify potential hot spots of biological effectiveness
(see Chapter 19) (150).
When calculating the dose-average LET during a Monte Carlo run, one
needs to record each energy loss, dE, of a particle and the length of the par-
ticle step that leads to the energy deposition event, dx. In a CT geometry, all
values can be scored voxel by voxel (v):

LET
dE
dE
dx
dE
d
events
events
( ) v =
⋅
( )
⋅
∑
∑
1
ρ
. (9.4)
Note that when simulating LET
d
using Monte Carlo simulations, the cut-
off defned to stop further tracking of the proton can have a signifcant
infuence (151).
FIGURE 9.10
Frontal views of patient-dependent pediatric female phantoms at a specifc targeted standing
height and at their 10th, 25th, 50th, 75th, and 90th percentile body masses. Also shown are
lateral views for different targeted standing heights. (From Johnson et al., Proc IEEE, 97(12),
2060, 2009. With permission.)
292 Proton Therapy Physics
9.8.7 Biology: Track Structure Simulations
To understand the biological effect of radiation, Monte Carlo simulations
can be used to study the interactions of particles with biological struc-
tures, like the DNA (152–170). More accurately than by using the LET, one
might analyze proton track structure to gain insight into biological effects
(see Chapter 19) (165). The particle track structure describes the pattern of
energy deposition events of proton tracks, including the secondary elec-
trons, on nanometer scale. At a given LET, smaller tracks are most likely to
produce more signifcant DNA damage. Simulations are based on energy
depositions and/or simulation of ionization frequencies. Considering
energy depositions is more accurate because excitations play a role in radia-
tion damage as well.
In Monte Carlo codes DNA damage can be associated with a specifc
energy amount imparted per track length or per assumed subcellular vol-
ume (171). Simulations have been used to predict the passage of proton
tracks through DNA and to correlate the energy deposition events to dif-
ferent types of strand breaks (164). The production of very small DNA frag-
ments is the result of energy depositions within the nanometer scale and is
due to correlated events from the same track (156). Simulations may assume
a certain proportionality between ionization frequency and lesion type in
the DNA, which might be further refned by modeling subvolumes of the
DNA that can have different geometrical shapes (172). Predictions can be
made on the likelihood of DNA damage and damage clustering, which in
turn can be used to make assumptions about repair probability for certain
DNA damages. Analyzing the distance of two energy deposition events on a
nanometer scale can give insight into lesion complexity (173).
Track structure can be simulated with the same codes that are used for
macroscopic dose simulations. However, many specifc codes have been
developed, particularly to deal with low-energy particle tracks and with
the δ-electrons produced by proton tracks (174, 175). For example, the code
PARTRAC includes an accurate representation of the chromatin and of the
physical and physiochemical processes associated with the energy deposi-
tion by radiation (157, 158, 161). The code is based on an extension of MOCA14
(176, 177). Another example is the MCDS code (169, 170), a code applicable to
a variety of different particles. Accurate single and double-differential cross
sections for inelastic and elastic interactions, including ionization, leading
to δ-electron emission are needed (173, 174, 178, 179). Specifc Monte Carlo
models based on clustered DNA damage, taking into account the stochastic
aspects of δ-electron emission, have been developed (171, 180–182).
Currently, Monte Carlo simulations are not able to fully simulate radiation
action and radiation effects on living cells. Although Monte Carlo codes have
been used successfully for predicting DNA damages (183), the link to cellular
response, including repair mechanisms, has not yet been fully established.
To model cellular radiation effects, it is necessary to predict the relationship
293 Monte Carlo Simulations
between the lesion distribution and the kinetics of damage processing. There
are approaches combining the Monte Carlo simulation of microdosimetric
quantities with biological models. For example, the Monte Carlo code PHITS
has been modifed to allow the simulation of radiolysis (184) to be com-
bined with the MKM model (see Chapter 19) in order to predict biological
effects (107).
Acknowledgments
The author thanks Dr. Bryan Bednarz and Jocelyn Woods for proofreading
and Dr. Jan Schuemann and Clemens Grassberger for their help with some
of the fgures.
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305
10
Physics of Treatment Planning for
Single-Field Uniform Dose
MartijnEngelsman
10.1 Introduction
Radiation therapy is a multidisciplinary science. It requires continuous
and accurate communication between physicians, clinical physicists, treat-
ment planners, therapists, and nurses. Arguably the most important step in
the radiation treatment of a cancer patient is the act of treatment planning.
Treatment planning combines the available clinical information about the
CONTENTS
10.1 Introduction ................................................................................................ 305
10.2 Prerequisites for Treatment Planning ..................................................... 307
10.2.1 Clinical Information ...................................................................... 307
10.2.2 Treatment-Planning System ......................................................... 308
10.3 The Tools of Treatment Planning ............................................................ 309
10.3.1 Beam-Specifc Choices ................................................................... 309
10.3.1.1 Lateral Safety Margins ................................................... 309
10.3.1.2 Distal and Proximal Safety Margins ............................ 312
10.3.1.3 Beam Direction ................................................................ 317
10.3.1.4 Patching ............................................................................ 318
10.4.1 Treatment-Plan-Specifc Choices ................................................. 320
10.5 SFUD with Pencil Beam Scanning .......................................................... 321
10.6 Specialized Treatments ............................................................................. 322
10.6.1 Eye Treatments ............................................................................... 323
10.6.2 Proton-SRS ...................................................................................... 324
10.6.3 Proton-SBRT .................................................................................... 326
10.7 Patient Treatment-Planning Examples ................................................... 326
10.7.1 C-Spine Tumor ................................................................................ 326
10.7.2 Lung ................................................................................................. 329
10.8 Future Perspectives of SFUD ................................................................... 332
References ............................................................................................................. 332
306 Proton Therapy Physics
patient with the physics aspects of proton therapy and the proton therapy
equipment (Figure 10.1). For optimal treatment plan design it is important
that both physicians and clinical physicists have at least a rudimentary
understanding of each other’s specialization.
The goal of treatment planning is to design the best possible treatment
given the limitations of the radiation therapy equipment available (1–3). A
good treatment plan ensures the delivery of the desired dose to the tumor
while delivering the lowest possible dose to surrounding normal tissues.
This requires elaborate tweaking of many beam properties, such as beam
direction, feld shape, and beam weight. Treatment planning allows those
responsible for the radiation treatment of a patient (i.e., the radiation oncol-
ogist and clinical physicist) to determine the three-dimensional (3D) dose
distribution that will be delivered to the patient. With the dosimetric con-
sequences of each tweaking visualized before actual treatment delivery, it
Clinical Physics
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FIGURE 10.1
Treatment planning is the act of combining clinical information and physics information in
order to design the best possible radiation delivery.
307 Physics of Treatment Planning for Single-Field Uniform Dose
is possible to design the treatment that best satisfes the wishes of the radia-
tion oncologist, that is deliverable with the equipment available, and that is
robust under typical radiotherapy uncertainties.
This chapter will discuss treatment planning of proton radiotherapy
for single-feld uniform dose (SFUD), in which each proton radiotherapy
beam delivers a homogeneous dose to the tumor. SFUD proton therapy can
be delivered with passively scattered proton therapy (PSPT) as well as by
means of pencil beam scanning. Most of this chapter will be focused on
PSPT. The notable differences between SFUD using pencil beam scanning
and SFUD using PSPT will be discussed in the section “SFUD with Pencil
Beam Scanning.”
Though discussed in detail in Chapters 13 and 14, touching on aspects of
the uncertainties in a proton treatment plan cannot be avoided completely
because the physicist and the radiation oncologist have to be intimately
aware of these uncertainties at the time of treatment plan design.
10.2 PrerequisitesforTreatmentPlanning
The prerequisites for proton treatment planning are clinical information and
a treatment-planning system (TPS).
10.2.1 Clinical Information
Clinical information consists of imaging data and the radiation oncologist’s
intent (i.e., a dose prescription for the target and dose limits for surrounding
healthy tissues [OAR, organs at risk]). Even in routine proton therapy treat-
ment planning an abundance of imaging data, over multiple imaging modal-
ities, is used by the physician to determine the exact location(s) of cancer
within the patient. Without going into detail, the minimum amount of imag-
ing information is the treatment-planning CT (computed tomography) scan.
On this CT scan, the target and OAR are delineated. Outlining the target in
proton therapy follows the guidelines of the International Commission on
Radiation Units and Measurements (ICRU) (4–6). Briefy, the physician delin-
eates the visible tumor (visible on any imaging modality), which is denoted
the gross tumor volume (GTV). On the basis of clinical experience, the physi-
cian can expand the GTV into a clinical target volume (CTV) to account for
suspected invisible spread of the cancer.
The physician also provides a prescription, in dose to be delivered to the
target and dose constraints for the OAR. In prescribing the dose to the target
it is common for the GTV to have a higher prescription dose than the CTV.
A prescription for the target consists of a fraction dose and the total number
of treatment fractions. For the target the goal of treatment planning is to sat-
isfy the prescription as accurately as possible. Overdosing and underdosing
308 Proton Therapy Physics
(parts of) the target is undesired. Prescriptions for the OAR are an upper
limit and can be expressed in many different ways: for example, a maxi-
mum dose to any point, a maximum volume that cannot receive more than
a certain dose, and the mean dose. For the OAR, the goal is not to exactly
meet the constraint but to, if possible, further minimize the dose while still
satisfying the dose prescription of the target. Prescriptions for the target and
one or more OAR are, however, frequently mutually exclusive. Treatment
planning is therefore a balancing act between maximizing the probability
of curing the patient (TCP, tumor control probability) and minimizing the
probability of serious adverse side effects (NTCP, normal tissue complication
probability).
The last clinical, and clinical physics, input into the design of the treatment
plan is an estimate of target motion and the expected setup accuracy of the
patient in the treatment room. This information is used to expand the CTV
with a safety margin into a planning target volume (PTV), or it can other-
wise be taken into account in the design of the treatment plan. For a more
detailed discussion on the use of the PTV in proton therapy, see Chapter 11.
Chapter 15 discusses a more advanced method of taking uncertainties into
account in the treatment-planning process.
From here on in this chapter, when we refer to the “target,” we will be
referring to any delineation of the tumor; i.e., the GTV or the CTV. Also,
in this chapter uncertainties in the target location are directly taken into
account in the beam-specifc parameters rather than using a PTV as an inter-
mediary step.
10.2.2 Treatment-Planning System
The clinical information serves as input for the TPS. Within the TPS the plan-
ning CT scan is a virtual representation of the patient at the moment of treat-
ment delivery. For uncertainties related to the treatment-planning CT scan,
see Chapter 13. The TPS also, as much as possible, provides a representation
of the capabilities of the treatment delivery system (e.g., gantry angles, aper-
ture shapes, available proton energies, and beam penumbra) (Figure 10.1).
The treatment planner uses the TPS to defne all treatment beam-specifc
information such that the treatment prescription is satisfed to the maximum
possible extent. At completion of the treatment plan the output of the TPS
consists of all data to be used for actual treatment delivery. This not only
includes dosimetric data such as the prescribed range and modulation width
of each treatment feld, but also imaging information to be used for accurate
patient alignment at the time of treatment, such as digitally reconstructed
radiographs. It is of great importance for the clinical physicist and the physi-
cian to understand the limitations of the TPS. Especially the dose calculation
algorithm, which is at the heart of the TPS, is an approximation, albeit one
that has acceptable accuracy for the vast majority of treatment scenarios. For
details on dose calculation algorithms, see Chapter 12.
309 Physics of Treatment Planning for Single-Field Uniform Dose
10.3 TheToolsofTreatmentPlanning
Table 10.1 shows the many attributes under control of the treatment plan-
ner during proton radiotherapy treatment planning. For ease of discussion
they have been subdivided into beam-specifc and treatment plan–specifc
parameters. Also indicated is what safety margin is affected by which beam-
specifc parameter. The order of discussion of each of these parameters
may at times appear somewhat arbitrary. For example, in clinical practice
the treatment planner will frst choose the beam direction before deciding
on the more detailed aspects such as aperture shape and beam range. The
choice of beam angle is, however, easier to understand with details regard-
ing the choice of range and modulation already explained.
10.3.1 Beam-Specific Choices
10.3.1.1 Lateral Safety Margins
For each beam direction the aim during treatment planning is to conform
the dose closely to the target, both laterally and in the depth direction. In
the lateral direction this conformality is achieved by using a custom-milled
aperture or a multileaf collimator (MLC) (Chapter 5). For simplicity this
chapter will use the word “aperture” to denote either. A target can have a
very complex 3D shape and the optimal shape of the aperture can therefore
TABLE 10.1
The Many Attributes under Control of the Treatment Planner in
Designing a Passively Scattered Proton Therapy Treatment Plan
Parameters SafetyMargin
Beam specifc
Range (R) Distal
Modulation (M) Proximal
Aperture shape (AP) Lateral
Range compensator shape (RC) Distal
Smearing Distal
Air gap/snout extension Lateral
Isocenter location
Beam direction (gantry angle, couch rotation)
Patching
Treatment plan specifc
Number of beams
Relative beam weights
Beam combinations per treatment fraction (“fraction groups”)
Use of photon beams
310 Proton Therapy Physics
best be determined in the beam’s eye view (BEV). The two aspects affecting
the lateral safety margin are the penumbra of the proton beam at the depth
of the target (dosimetric margin) and the expected uncertainty in the target
position due to setup errors and intrafractional tumor motion (setup margin)
(see Figure 10.2a). The penumbra depends on the proton beam-line specifcs
100
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FIGURE 10.2
(a) The lateral margin between aperture edge (50% isodose level) and target edge consists of
a dosimetric margin and a setup margin. The central white area indicates the target, which,
in this example, needed to be covered with the 95% isodose level assuming a 5-mm setup
margin. (b) Beam’s eye view of a single feld for the treatment of an intracranial tumor. The
dashed white circle indicates the maximum available aperture size. The dark structure indi-
cates the target, whereas the thick solid white line indicates the aperture shape that was used.
A uniform margin of 7 mm was needed to ensure target coverage. To remain within the dose
tolerance of the brainstem, a reduced margin was needed. An even smaller margin toward the
optical nerves and chiasm was needed to suffciently spare these OAR.
311 Physics of Treatment Planning for Single-Field Uniform Dose
and varies with range and depth in the patient (Chapter 4). The dosimetric
margin is the distance between the 50% isodose level (the feld edge) and the
desired isodose coverage (typically the 95% isodose level). Expected setup
errors are part of the clinical input by the physician and clinical physicist.
The setup margin can vary from 1–2 mm for intracranial radiosurgery treat-
ments to about 10 mm for prostate treatments.
To frst order, the shape of the aperture will be a simple geometric expan-
sion of the shape of the target in the BEV (Figure 10.2b). Just as in photon
radiotherapy, the magnitude of the lateral safety margin can be based on clin-
ical experience, but also on a margin recipe; for example, van Herk et al. (7).
Frequently, the treatment planner has to locally alter the shape of an aper-
ture. Because of multiple Coulomb scattering within the range compensator
(RC) and within the patient, a uniform margin between target and aperture
edge will typically not result in a uniform margin between the prescription
isodose level and the target. This requires local expansion and shrinking of
the aperture. Furthermore, dose limits to adjacent OAR may also require the
treatment planner to manually alter the aperture shape. In Figure 10.2b, the
lateral margin between aperture and target has been reduced in the direc-
tion of the brainstem and is even more reduced toward the optic nerves.
The achievable shape of an aperture furthermore depends on the limitations
of the milling machine (e.g., diameter of the drill) that creates the physical
aperture, and the TPS has to mimic these limitations accurately. If an MLC
is used, the aperture shape is limited by the width of the MLC leafs. Dose
calculation within the TPS provides feedback to the treatment planner as to
the adequacy of the shape of the aperture.
Typically, passively scattered proton therapy beam lines allow motion
of the aperture and RC combination along the beam axis by means of
snout translation. This allows the treatment planner a choice of air gap
(Figure  10.3), defned as the distance between the downstream side of the
RC and the patient skin. The TPS has to be able to model the choice of air
gap and the consequences for the shape of the aperture. An increase in air
gap increases the penumbra in the patient, and this should be modeled by
the dose calculation algorithm (Chapter 12). More important, an aperture
projection discrepancy may occur in the treatment room if the aperture has
been created for a specifc air gap that cannot be reproduced at the moment
of actual treatment. The patient’s shoulder may, for example, not be part of
the CT scan and limit snout translation. The increased air gap results in more
dose to normal tissues because it leads to an increase in feld size and to a
softening of the lateral penumbra. Especially when an aperture edge is used
to exactly control the dose to an OAR, every millimeter can be important. At
the time of treatment planning an air gap of a few centimeters is typically
chosen to allow for some wiggle room at the time of treatment. For patient
treatments that require abutting felds, an intentional increase in the air gap
and related increase in penumbra can be benefcial as it reduces underdos-
age and overdosage at the match line.
312 Proton Therapy Physics
10.3.1.2 Distal and Proximal Safety Margins
The largest beneft of protons for sparing OAR is the fnite range of protons. The
many uncertainties in the calculated range in the patient of protons at the time
of treatment planning and in the required proton range at the time of treatment
delivery, necessitate the use of safety margins both distally and proximally to
the target. Proximal safety margins can be larger than distal safety margins
because of smearing of the RC (see below). The distal safety margin is, however,
certainly more important. Keeping the spread-out Bragg peak (SOBP) depth-
dose distribution in mind, an error in the range of a proton feld can be the dif-
ference between 0% and 100% of the beam dose to the target (and to an OAR),
whereas an error in the modulation width has more moderate consequences.
The prescribed range is chosen to ensure distal target coverage with the
prescribed dose for that beam direction. Typically, the range of a SOBP is
defned by the water equivalent depth of the distal 90% isodose level. The
required range to cover the target is determined by ray-tracing the water
equivalent depth (more precisely; the proton stopping power) over the extent
of the target in BEV. The rays emanate from the virtual source position, and
accumulation of water equivalent depth will take place from the location
where the ray enters the patient geometry to the distal edge of the target.
The uncertainty applied to this required range is 3.5% of the range plus an
additional millimeter (see Chapter 13), but this may differ slightly between
institutions. The prescribed range R, in cm, therefore, is

R R
i
= ⋅ + 1 035 0 1 . max( ) .
, (10.1)
with R
i
the range for each ray i.
S
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io
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AirGap
FIGURE 10.3
The snout can be translated along the beam direction to bring the feld-specifc hardware
(aperture and RC) as closely as possible to the patient. Minimizing the air gap reduces the
lateral penumbra of the dose distribution.
313 Physics of Treatment Planning for Single-Field Uniform Dose
If a RC has a minimum thickness (e.g., 1–2 mm, for milling purposes), then
this minimum thickness is taken into account for each ray as well. Defning
the range by the distal 90% isodose level means that a small part of the target
will receive a dose down to 90% rather than 100% of the prescribed dose for
that beam direction if these range uncertainties are actual (see Chapter 13).
The volume of the target receiving a too low dose will be limited as distal
conformality in a typical patient scenario is never submillimeter tight. Also,
the typical use of multiple beam directions mitigates the magnitude of the
possible underdosage.
The prescribed modulation width is chosen to ensure proximal coverage
of the target with the prescribed dose. The required modulation width of a
beam is also determined by means of ray-tracing, but with range uncertain-
ties (3.5% plus 1 mm) applied both at the distal end and the proximal end:

M R P
i i
= ⋅ − ⋅ + max( . . ) . 1 035 0 965 0 2 , (10.2)
where P
i
is the water equivalent depth of the proximal edge of the target
along each ray. This modulation width may need to be altered as a function
of the amount of smearing applied to the RC (see below). For a treatment
plan that consists of multiple beams, one could in principle achieve adequate
target coverage even when not all beams individually ensure proximal and
distal target coverage. However, in clinical practice such detailed tweaking
of a treatment plan is very labor intensive and is not performed.
The RC ensures tight distal target coverage. It allows increased sparing of
OAR and normal tissues distal to the target by locally pulling back the SOBP
as much as possible without affecting target coverage. The TPS provides a
method to determine the 3D shape of the RC and can model the presence of
the RC and its effect on the beam-specifc dose distribution in the patient. As
mentioned, the minimum thickness of an RC has to be taken into account in
the prescribed range.
A typical method to determine the RC thickness as a function of the BEV
position is ray tracing to the distal edge of the target. Along each ray, the
thickness of the RC is then determined by

RC R R
i i i
= − max( ) . (10.3)
This method of RC design, however, ignores the effect of multiple Coulomb
scattering in the patient that is taken into account when performing the dose
calculation based on this RC. The result may be that distal dose conformal-
ity is inadequate, with location-specifc overshoot and undershoot depend-
ing on the patient geometry. The worst-case scenario is that an additional
“RC volume” has to be manually drawn in the CT scan to which the RC
will be designed, thus “faking” the TPS into designing an adequate RC. This
is extremely labor intensive, but better methodologies are currently not yet
314 Proton Therapy Physics
available in commercial TPSs. An improvement would be, for example, to
allow the treatment planner to virtually “pull” isodose lines, thereby locally
affecting the RC thickness. Best is to have an algorithm that automatically
optimizes the RC based on the actual dose calculation algorithm (i.e., a dosi-
metric rather than a radiologic/geometric determination). The thickness of
the RC lateral to the target, but within the aperture circumference, is unde-
fned and typically is set to the nearest still-defned thickness.
An important aspect affecting distal conformality is RC smearing (e.g.,
[6,  8]). Smearing is best explained by assuming that the only uncertainties
are setup errors (e.g., no range uncertainties or patient density changes). In
this case, the RC could be designed to tightly conform the distal falloff of the
SOBP to the target (Figure 10.4a). This is accurate as long as point p in the
patient is aligned with point r in the RC. At the time of delivery of a treat-
ment fraction, however, the patient may be slightly misplaced with respect to
the beam-specifc hardware. A typical setup error could be up to a few mil-
limeters, and such a setup error is mimicked in Figure 10.4b. Point p is under-
dosed because protons traveling to this point have to pass through too thick
RC
p
p
r
r
p
r
p r
Beam
T
a
r
g
e
t
T
a
r
g
e
t
T
a
r
g
e
t
T
a
r
g
e
t
skin
Beam
a) b)
c) d)
FIGURE 10.4
Schematic diagrams explaining smearing in a 2D geometry. In reality, smearing is applied to
a 3D range compensator (RC). The dark circle indicates a high-density structure. (a) No smear-
ing applied, patient and RC aligned. (b) No smearing applied, patient misaligned. (c) Smearing
applied, patient and RC aligned. Also indicated is the shape of the RC prior to smearing. (d)
Smearing applied, patient misaligned.
315 Physics of Treatment Planning for Single-Field Uniform Dose
a part of the RC (points p and r are no longer aligned). The process of smear-
ing is effectively a “hollowing out” of the 3D RC. The thickness at a specifc
location of the RC after smearing is the minimum thickness of the unsmeared
RC as found within a certain distance (i.e., the “smearing radius”) from this
point. Figure 10.4c shows the dose distribution in the patient for the smeared
RC as observed in the treatment-planning geometry (i.e., without any patient
alignment error). Smearing the RC results in regional overshoot of the pro-
ton beam. This overshoot is necessary to ensure target coverage in case of
a patient alignment error (Figure 10.4d). Smearing does not affect the pre-
scribed range, but it may affect the prescribed modulation; see the numerical
example below. In fact, the large modulation chosen in Figure 10.4 is neces-
sary to ensure proximal target coverage under setup errors and smearing.
Please note that no material is taken away at any point on the RC that already
has the minimum thickness prior to smearing.
Proper patient alignment minimizes the necessary smearing and the unde-
sired overshoot, and undershoot of protons into healthy tissue. Although
the smearing process does not take into account secondary effects such as
altered multiple Coulomb scattering inside the RC and patient, the smearing
process is a good method to ensure target coverage for setup errors (shifts
of the entire patient) with a magnitude up to the smearing radius. Smearing
is not a fail-safe method to deal with relative changes in the patient density
distribution, such as an upstream high-density structure moving to a dif-
ferent relative location with respect to the target, but it may have some merit
even in those cases. Smearing has also been suggested as a non-fail-safe
method of handling breathing motion for lung cancer (see section “Patient
examples”).
Because smearing and its application in the TPS are not intuitive, a numer-
ical example follows using a two-dimensional (2D) geometry. Figure 10.5
shows a hypothetical tumor in a, mainly, unit-density phantom. Each voxel
is 1 cm × 1 cm, and the dark area in the bottom right corner has a density of
twice unit-density. The proton beam enters from below, lateral target cover-
age is not taken into consideration, and a 1-cm smearing radius is assumed.
Table 10.2 shows the steps in the design of the beam focusing on the rays
aimed at positions A–E in Figure 10.5. The required range to cover the distal
edge of the tumor in the case of no uncertainties (D
r
) is largest for ray E (i.e.,
12 cm). Taking into account range uncertainties of 3.5% + 1 mm (D
u
), the pre-
scribed range (R) is 12.52 cm. A RC has to be designed to pull back the distal
falloff where necessary (column RC
r
). The RC thickness after smearing is
shown in column RC
sm
, leading to a depth of the distal falloff along each ray
as according to column D
u,sm
. Especially for rays B and D smearing increases
the proton beam penetration inside the patient. The required modulation
along each ray, to ensure proximal target coverage, requires calculation of
the water equivalent depth of the proximal tumor edge (P
r
) corrected for the
same range uncertainties of 3.5 % + 1 mm (P
u
). The difference between D
u,sm

and P
u
provides the required local modulation width (M
sm
), the maximum of
316 Proton Therapy Physics
which is the prescribed modulation width (M). For this phantom, the larg-
est water equivalent tumor thickness was 4 cm, but the prescribed modula-
tion taking into account range uncertainties and smearing (setup errors) is
almost 7 cm. Counterintuitively, in this example this modulation is needed
to cover the target at its thinnest water equivalent thickness (ray B).
A B C D E
BEAM
FIGURE 10.5
Stylized unit-density 10 × 12-cm
2
phantom irradiated with a proton beam incident from below.
The thick black line indicates the target. The dark gray area indicates a high-density structure.
TABLE 10.2
Steps in Determining, for a Passively Scattered Proton Therapy Field, the
Beam-Specifc Range, Modulation Width, and Range Compensator Thickness
Distal,Range Proximal,Modulation
D
r
D
u
RC
r
RC
sm
D
u, sm
P
r
P
u
M
sm
A 8.00 8.38 4.14 4.14 8.38 5.00 4.73 3.65
B 8.00 8.38 4.14 1.03 11.49 5.00 4.73 6.76
C 11.00 11.49 1.03 1.03 11.49 7.00 6.66 4.83
D 11.00 11.49 1.03 0.00 12.52 7.00 6.66 5.86
E 12.00 12.52 0.00 0.00 12.52 8.00 7.62 4.90
The values represented take into account range uncertainties and setup errors, for the
situation depicted in Figure 10.5. The underlined numbers designate the prescribed
range (R) and modulation width (M).
317 Physics of Treatment Planning for Single-Field Uniform Dose
10.3.1.3 Beam Direction
Now that we have a detailed understanding of how certain beam-specifc
parameters are chosen and, more importantly, how they affect target cover-
age and dose to normal tissues, we can discuss the choice of beam directions.
Gantries and robotic treatment couches allow the choice of almost any inci-
dent beam direction over a 4π solid angle. For isocentric gantries the beam is
always aimed at isocenter, which is, simply put, the point at which the cen-
tral beam axes for any gantry angle coincide. The choice of isocenter location
inside the patient is an important aspect of treatment planning. Typically
it will be near the center of the target; however, it is always chosen to be
at a location that can be accurately reproduced at the time of patient treat-
ment, based on imaging information provided by the TPS and as acquired
by means of imaging on any treatment day. It is important to realize that the
isocenter location is “fxed” in the treatment room, and one aligns the patient
such that the anatomical location of the isocenter as chosen during treat-
ment planning corresponds with the location of the room isocenter. Once the
patient is aligned with the room isocenter, the treatment couch allows rota-
tion of the patient around the room isocenter while maintaining alignment
between the anatomical and room isocenter.
Many of the considerations in choosing beam directions also play a role in
conformal photon radiotherapy, but they are much more important in proton
therapy because of the fnite range of protons. An obvious consideration is
to geometrically avoid OAR. One tries to prevent multiple beams to over-
lap on the patient skin because the skin is a very sensitive OAR and proton
therapy beams do not have the skin-sparing effect of photon beams. The lack
of a build-up effect at the patient skin for proton beams on the other hand
allows a choice of beam directions through the immobilization devices used
without signifcantly increasing the skin dose. Bulky immobilization devices
may, however, require an increase in snout extension, thus increasing the
lateral penumbra and the dose to normal tissues. Furthermore, immobiliza-
tion devices may lead to abrupt variations in water equivalent path length,
not only at the edge of the immobilization device but also within the device
itself, increasing dose to normal tissues due to smearing.
In general, beam directions should avoid “skimming” steep density gra-
dients, for example by preferring angles of beam incidence that are near-
perpendicular to the patient skin, and by not aiming a beam parallel to the
mediastinum-lung interface or diaphragm-lung interface. Beam directions
parallel to the auditory canal and the base of the skull should also be avoided
because these may challenge the accuracy of the dose calculation algorithm.
High-density material in the patient, such as titanium rods used for stabiliz-
ing the spinal column after tumor resection, are avoided as much as possible
due to range uncertainties and dose shadowing effects. If it is unavoidable
to treat through these high-density materials, one aims to use multiple beam
directions to mitigate the possible dosimetric consequences.
318 Proton Therapy Physics
To prevent aperture projection errors (see section “Lateral Safety Margins”)
the treatment planner needs to be aware of the exact geometry of treatment
nozzle and treatment couch, choosing a safe beam direction if necessary. In
general, treating obliquely through the treatment couch (less than 45° angles)
is avoided. Such a beam direction would increase the penumbra because
of the increased snout extension and because of the increase in prescribed
range for that beam angle.
A fnal point of consideration is range variations that occur if the treatment-
planning CT is an incorrect representation of the patient geometry at the time
of treatment delivery. These interfractional variations in the 3D density distri-
bution of the patient make, for example, the following beam directions unfa-
vorable: skimming a patient breast fold, treating through the diaphragm, and
treating through an air-flled rectum.
10.3.1.4 Patching
In principle, the choice to do patching is also beam direction related, but it
is such a specialized issue in proton therapy that it will be treated indepen-
dently. Patching is used if no single feld direction can be chosen that would
allow delivery of the required dose to the entire target without running the
risk of severely overdosing an OAR very close to this target. Patching is typi-
cally considered if the target wraps closely around an OAR, with the toler-
ance dose of the OAR smaller than the prescribed target dose. To deliver
the (remaining) dose to such a target with a single feld, one would have to,
partially or fully, irradiate through the OAR, thereby overdosing it, or one
has to aim the beam directly at the OAR while trying to spare it by means
of proton range. Because of range uncertainties, this latter solution is not
favored unless there is a suffcient gap (e.g., >2-cm water equivalent path
length) between the distal target edge and the OAR. Rather, the choice is to
stay-off the OAR by means of the much more certain lateral aperture edge.
A typical example case for patching is shown in Figure 10.6. The “through”-
feld treats a part of the target volume from the proximal to distal edge. The
aperture is designed to cover as much of the target as possible while staying
off the OAR. The OAR in this example are the spinal cord and the brain-
stem. Figure 10.6, d and e, show the beam’s eye view for the through feld
with the target volume and patch volume, respectively. The patch volume
is that part of the target volume that is not captured within the aperture
outline of the through feld. The aperture of the “patch” feld is subsequently
designed to this patch volume. The proton range for the patch feld is cho-
sen such that the distal dose falloff matches on the lateral penumbra of the
through feld along the patch line. Figure 10.6, f and g, show the beam’s eye
view for the patch feld. Both the through feld and patch feld stay off the
OAR by means of aperture edge. The combined dose distribution, as cal-
culated by the TPS, is shown in Figure 10.6c. Unless special measures are
taken (9), the distal and lateral SOBP dose gradient are dissimilar enough
319 Physics of Treatment Planning for Single-Field Uniform Dose
that dose homogeneity along the patch line is in the order of ±10% even in
the absence of any range uncertainties. Furthermore, any subsequent mil-
limeter of overshoot or undershoot of the patch feld varies the local dose
variation by about another 10%. Some proton therapy institutes will apply
105 %
95 %
50 %
20 %
rough
Patch

r
o
u
g
h

b
e
a
m

Target Volume
P
a
t
c
h

b
e
a
m

Target Volume
Patch Volume

r
o
u
g
h

b
e
a
m

Patch Volume
P
a
t
c
h

b
e
a
m

d)
a)
f )
g)
e)
b)
c)
105 %
95 %
50 %
20 %
105 %
95 %
50 %
20 %
FIGURE 10.6
(Seecolorinsert.) Example of a patch combination in proton therapy. (a and b) The beam direc-
tion and relative dose distribution of the through feld and patch feld, respectively. The red
area indicates the target, and the blue area indicates the spinal cord. (c) The relative dose distri-
bution for the patch combination. (d–g) The beam’s eye view of the patch felds with either the
entire target volume (in red) or only the patch volume (in purple).
320 Proton Therapy Physics
smearing to the RC of the patch feld; others do not. In either case, tissues
near the patch line can get a considerable overdosage or underdosage on a
per treatment fraction basis depending on the setup error and the uncer-
tainty in the range calculation. For this reason, the total dose delivered by
any single patch combination is limited. For targets that need to receive a
large (remaining) dose by means of patching, the treatment planner will try
to fnd multiple patch combinations, limiting the use of each patch combi-
nation to 3–5 fractions. This substantially averages out the uncertainty in
absolute dose along the patch lines. The aim is to have patch lines not cross,
but sometimes this is unavoidable.
10.4.1 Treatment-Plan-Specific Choices
As a single proton feld can deliver a homogeneous dose to the target, it is
possible to deliver the entire prescribed dose with only a single feld. For
some tumors such as lacrimal gland tumors this is indeed clinical practice.
More frequently, however, multiple beams are used to spread out the dose
to normal tissues, just as in photon radiotherapy. A very complex head-and-
neck treatment, with for example a large CTV requiring the use of abutting
felds and multiple boost regions, can consist of 10–15 unique treatment felds.
The fact that each proton feld (or patch combination) delivers a homogeneous
dose to the target allows the treatment planner great fexibility in choosing
individual beam weights. This can help spare certain OAR. Homogenous
dose delivery per feld also allows treatment of only a limited number of felds
for each treatment delivery fraction, instead of treating all felds every day.
Many proton therapy centers pursue this strategy of treating fraction groups
at some cost in biologically corrected dose to the healthy tissues (10). For this
strategy to be safely and effectively applied, one needs to confrm at the time
of treatment planning that target coverage is not only achieved by delivery of
all felds over the entire treatment course, but for each fraction group.
Once the total dose delivered by a feld and the number of fractions this
feld will use are known, the output of the feld (dose per monitor unit,
MU) can be determined. As there are only a very limited number of proton
therapy centers and as the proton therapy beam-line layouts are still in the
process of “normalizing,” current commercially available TPSs are typically
not able to calculate the expected number of MUs for a treatment feld. This
important characteristic, MU, is therefore at the moment often determined
by an in-house-developed output prediction model or by individual feld
measurements (Chapters 8 and 12).
It is possible that photon felds are intermixed into what is mainly a pro-
ton therapy treatment plan. The reason would be one of the following: (1) to
decrease skin dose, (2) to allow a patient treatment to start even though no
proton treatment slots are yet available, and (3) to allow patient treatments
to continue in case of unexpected unavailability (downtime) of the proton
treatment machine.
321 Physics of Treatment Planning for Single-Field Uniform Dose
10.5 SFUDwithPencilBeamScanning
In many respects SFUD treatment planning with pencil beam scanning is
the same as intensity-modulated proton therapy (IMPT) treatment planning.
The main difference is that automatic optimization of the spot weights in
SFUD is performed on a per-beam basis, ensuring that a homogeneous dose
is delivered to the target by every feld individually. In IMPT, spot weight
optimization is performed over all felds in parallel. Each individual feld
can deliver a highly inhomogeneous dose distribution to the target, with all
felds combined ensuring the desired (homogeneous) target dose coverage.
For details as to the implementation of pencil beam scanning into the TPS
and the use in everyday clinical practice (e.g., choice of spot locations and
representation of range shifters), we refer the reader to Chapter 11. This sec-
tion is limited to comparing SFUD using pencil beam scanning and PSPT.
SFUD treatment planning with pencil beam scanning has the same goal
as PSPT: each treatment feld ensures a homogeneous dose to the target
volume under setup errors and range uncertainties. There are a few nota-
ble differences, however, most of which are benefts. The main dosimetric
beneft of pencil beam scanning is that it allows both distal and proximal
conformality for a single beam (Figure 10.7). Although not an accurate
description of how spot weights are chosen in pencil beam scanning, one
way of looking at it is that it allows the range and modulation width to be
set on a per-proton-ray-beam (source to distal target edge) basis. Range
uncertainties and setup uncertainties (smearing) and their effect on the
Photons PSPT PBS
Skin Skin
FIGURE 10.7
Schematic diagram showing the lateral conformality of a photon beam (left), the lateral and
distal conformality of a passively scattered proton beam (middle), and the lateral, distal, and
proximal conformality of SFUD using pencil beam scanning (right). (Courtesy of Benjamin
Clasie.)
322 Proton Therapy Physics
location-specifc required range and modulation width will be taken into
account for each individual ray beam, thereby sparing normal tissues prox-
imal and distal to the target. The exact choice of range and modulation
along any ray beam is, however, limited by the step size between range-
energy layers. In other words, without the use of a RC, distal conformality
will probably be slightly worse compared to PSPT. Proximal conformality
will also not be perfect, even without range uncertainties, but both effects
are expected to be clinically insignifcant, especially in a multiple-feld
treatment plan.
Another advantage of pencil beam scanning may be the possibility to
allow for improved dose homogeneity along patch lines under range uncer-
tainties by intentionally softening both the lateral penumbra of the through
feld and the distal penumbra of the patch feld. Just as a wedged feld com-
bination in photon therapy is not considered intensity-modulated radiother-
apy (IMRT), use of this patch-line smoothing should be considered SFUD
instead of IMPT. At the time of this writing it is unsure if commercially
available TPSs have the capability to automatically design such smoothed
patch combinations.
The main practical beneft of pencil beam scanning is that design and
fabrication of feld-specifc RCs and apertures is no longer necessary or at
least substantially reduced. This improves the workfow considerably and
reduces the time between treatment plan completion and the frst treatment.
For example, rather than a laborious manual tweaking of a RC, the dose dis-
tribution for a feld can be automatically optimized (Chapter 15).
Adaptive treatment planning in proton therapy using apertures and RCs
(i.e., PSPT), is very resource intensive both in manpower and materials. The
improved workfow of pencil beam scanning allows faster treatment adapta-
tion to a changing patient geometry over the course of radiotherapy treat-
ment. Treatment adaptation in proton therapy is not as widely applied as in
photon therapy, but the increased availability of pencil beam scanning may
close this gap.
Two possible downsides of pencil beam scanning over PSPT are interplay
effects (discussed in Chapter 14) and the achievable lateral penumbra, espe-
cially for shallow ranges (see Chapter 4).
10.6 SpecializedTreatments
This section discusses three proton therapy treatments that are a bit less
mainstream: eye treatments, proton stereotactic radiosurgery (proton-SRS),
and proton stereotactic body radiotherapy (proton-SBRT). In this chapter,
SRS denotes a high-precision single-fraction (or occasionally double-fraction)
treatment of a target within the patient’s skull. SBRT is used to describe a
323 Physics of Treatment Planning for Single-Field Uniform Dose
high-precision treatment of a target lesion within the patient’s body over at
most a handful of treatment fractions.
10.6.1 Eye Treatments
With a local control rate of well over 95% after 5 years of follow-up (e.g., [11]),
treatment of ocular tumors is one of the success stories of proton radiother-
apy. Depending on the tumor type, a typical prescription is fve fractions
of either 10 or 14 Gy each, delivered in fve consecutive treatment days. The
main OAR are the lens, the macula, and the optic nerve.
Treatment planning is typically based on a recreated geometry rather
than on CT-imaging information (Figure 10.8). Briefy, a model of the eye
and tumor is created in the TPS based on ultrasound measurements and
orthogonal x-rays. The ultrasound provides information regarding the axial
length of the eye, lens thickness, and the thickness (“height”) of the tumor.
The base of the tumor is reconstructed based on the location of four or more
tantalum clips, visible on x-rays, that are sutured near the edge of the tumor
during a surgical procedure. These clips also help guide patient setup at the
moment of treatment. For a detailed description of the target-localization
procedure for treatment planning and treatment delivery, see Delaney and
Kooy or Albert et al. (2, 12).
The model in the TPS accurately reproduces the location of the OAR for the
gaze direction that is preferred for treatment. Apertures are used to tightly
a)
1 mm
2
3
1
Disp. Width: +29.7 mm
Center: (+3.1, +9.1)
Disp. Width: +36.8 mm
Center: (-2.2, +6.7)
1 mm
1
4
3
2
Dose %
100
90
70
50
30
10
Scale: 5.389 : 1 Scale: 4.345 : 1
b)
FIGURE 10.8
(Seecolorinsert.) Model of the eye as created within EYEPLAN (version 3.05, Martin Sheen,
Clatterbridge Centre for Oncology, Bebington, UK). (a) Beam’s eye view. The thick magenta line
indicates the aperture outline. Also indicated are the optic nerve (yellow cone), the lens (green
and blue circles), the optic axis (blue line), the macula (magenta cross), and some of the clips
(thin magenta ellipses, labeled 1–4). (b) Dose distribution in the vertical beam plane in a slice
through the center of the tumor.
324 Proton Therapy Physics
conform the dose distribution to the tumor in the lateral direction. If patient
setup is based on orthogonal x-rays of the tantalum clips, the aperture mar-
gin is typically 3 mm. Half of this distance (1.5 mm) is to account for the
lateral dose gradient between feld edge and 90% isodose level. The other
1.5 mm is to take into account target delineation and setup uncertainties.
If patient setup is based on the beam-line light feld rather than orthogo-
nal x-rays, the aperture margin is increased by 0.5 to 1.0 mm because of the
additional setup uncertainty. The aperture outline can be locally adjusted to
spare OAR. With few exceptions, a typical aperture has an area of less than
a few square centimeters. The use of RCs in ocular proton therapy is uncom-
mon. Range and modulation width are chosen to ensure target coverage in
the depth direction. Range uncertainties vary between 2.5 and 4.0 mm for
anterior to posterior tumors, respectively. An extra millimeter of range may
be added if the location of the tumor brings the proton beam in close proxim-
ity to the eyelid. The proximal margin is 3.0 mm unless the target extends all
the way toward the surface of the eye.
Every millimeter of functioning retina can mean an improvement in the
quality of life of the patient. Ocular proton beam lines therefore are opti-
mized to have a very sharp lateral falloff to allow maximum sparing of the
OAR. The beam-line layout of the worldwide available ocular treatment
beam lines varies greatly. Depending on the dosimetric characteristics of the
beam line, there may be a large effect of aperture shape and size on the out-
put (in cGy/MU) (13). However, in general the ocular TPS is not able to pre-
dict this output, and felds need to be individually calibrated to determine
the required MUs to deliver the prescribed dose.
10.6.2 Proton-SRS
In proton-SRS a very high dose, typically 10–20 Gy, is delivered in only a
single fraction (sporadically: two fractions) to a small tumor. The healthy tis-
sues tolerate the high-fraction dose because of the small irradiated volume.
Compared to photon therapy, the characteristic depth–dose distribution of
protons can certainly beneft the sparing of healthy tissues (14).
The main diffculty with proton-SRS treatments is that there is no mitiga-
tion of setup and range uncertainties by averaging out of the dosimetric con-
sequences over multiple fractions. All dose is delivered in a single fraction,
which means that any setup error and range uncertainties have a maximum
negative impact. To ensure target coverage, one would like to apply wide
safety margins. The necessity to limit the dose to, and the volume of, irradi-
ated healthy tissues, however, implies a strong need for applying small dis-
tal, proximal, and lateral safety margins.
SFUD treatment planning for proton-SRS to a large extent is the same as
for normally fractionated treatments, except that there is even more empha-
sis on high-accuracy treatment delivery. Extra measures are taken in patient
immobilization (bite-block or invasive stereotactic frame), target and OAR
325 Physics of Treatment Planning for Single-Field Uniform Dose
delineation by means of additional imaging (e.g., high-resolution MRI or CT
angiography), and patient position verifcation (use of fducial markers) (2, 6).
Typically the dose is prescribed to the 90% isodose level relative to the dose
in the center of the target. This ensures a steep dose falloff (lateral, distal,
and proximal) at the cost of increased target dose inhomogeneity. It also
makes the minimum dose within the target insensitive to the few-percent
dose variations that can be present in the depth direction of the SOBP. The
altered prescription isodose level only slightly affects the choice of range,
modulation width, and target-to-aperture margin, when compared to stan-
dard fractionation in which the aim typically is to ensure coverage of the
target with the 95% or even 98% isodose level.
For same-day treatments (CT scanning, treatment planning, and treat-
ment) one may have insuffcient time to create patient-specifc hardware,
and therefore one may have to choose to use standard aperture shapes and
no RC. The increased convenience for the patient then has to be balanced
against the increased dose to healthy tissues and risk of complications.
Compared to normal fractionation schedules, it is even more important
to choose beam directions that minimize density variations (e.g., avoiding
sinuses), especially if the CT scan and patient treatment are not on the same
day. It is also important to minimize the dose delivered by beam directions
that are challenging for accurate dose calculation (e.g., bony anatomy mixed
with air-flled cavities such as the auditory canal). Even in the absence of
much tissue inhomogeneity, the dose algorithm has to accurately represent
the dose distribution for a single beam, which is challenging for very small
felds (see Chapter 13).
Standardized beam arrangements can be used for standard indications
such as the treatment of pituitary tumors. The number of treatment felds
for a lesion can vary between 2 and 6, with more beams allowing more
spreading out of the dose to the healthy tissues and also providing some
dose- averaging effect in case one beam inadvertently underdoses the target.
The small target sizes make patching (see section “The Tools of Treatment
Planning”) an unnecessary technique. If it were benefcial in a rare case to
spare an OAR, dose uncertainty on the patch line in combination with the
very high fraction dose contraindicates its use.
Designing a treatment plan for a patient with multiple spatially separated
intracranial lesions is an especially complicated process, as any overlap
between treatment felds for different targets will double the dose to local
healthy tissue. The fact that proton beams have no exit dose helps in pre-
venting such beam overlap. It is possible to perform proton-SRS treatments
with (SFUD using) pencil beam scanning as long as the achievable lateral
penumbra is sharp enough to provide suffcient sparing of healthy tissues
lateral to each feld. Especially for small targets the distance between spot
positions also has to be small enough to allow tight lateral, proximal, and
distal coverage. For more information on proton-SRS, see Delaney and Kooy
or Chin and Regine (2, 15).
326 Proton Therapy Physics
10.6.3 Proton-SBRT
Typical treatment sites for proton-SBRT are pancreas, liver, and lung. Just
as with proton-SRS treatments, proton-SBRT treatments are characterized
by a high dose per fraction. The number of treatment fractions, however, is
increased and can vary between three fractions of about 20 Gy and 15 frac-
tions of about 5 Gy. Compared with a single-fraction radiosurgery treatment,
the use of multiple fractions will result in some averaging out of the dosimet-
ric consequences of setup errors and range uncertainties. There are, however,
a number of additional uncertainties that indicate a need for increased safety
margins (also Chapters 13 and 14). Setup accuracy in general is compromised,
which indicates a need for increased safety margins. It is harder to align the
target laterally with respect to the beam because the target itself may not
be visible by means of in-room imaging modalities, and it may move with
respect to the more clearly visible bony anatomy. The movability of surround-
ing organs and the target due to, for example, breathing, heartbeat, and flling
of the gastrointestinal tract, can result in large intra- and interfractional range
variations. This aside from the “automatic” increase in range uncertainty due
to the increased ranges that will be needed to treat these deep-seated targets.
Because the number of treatment fractions is still quite limited, it is impor-
tant for the data used for treatment planning (CT scan) to closely represent
the patient density distribution at the time of treatment. For this, one should
minimize the time between planning CT scan acquisition and the frst day
of treatment, as well as to minimize the time of the overall treatment course.
One can also acquire more than one CT scan on different days before treat-
ment to ensure overall reproducibility of the patient geometry, for example,
the level of the patient’s breathing.
10.7 PatientTreatment-PlanningExamples
Proton radiotherapy nowadays is applied to treat almost any tumor site. This
section will, however, be limited to two examples for passively scattered pro-
ton therapy only. The section “SFUD with Pencil Beam Scanning” provides
details as to how these plans would be different if pencil beam scanning
were applied. The C-spine tumor example highlights treatment planning in
a geometry without (much) density variation but which requires patching.
The lung cancer example highlights the diffculties of proton therapy plan-
ning in a time-varying density geometry.
10.7.1 C-Spine Tumor
The patient shown in Figure 10.9a has a tumor within the neck region,
wrapped around the spinal cord and the inferior aspect of the brainstem. The
327 Physics of Treatment Planning for Single-Field Uniform Dose
450
400
200
100
f )
rough

r
o
u
g
h

P
a
t
c
h

r
o
u
g
h
P
a
t
c
h
P
a
t
c
h
P
a
t
c
h
5200
100
90
80
70
60
50
V
o
l
u
m
e

(
%
)
Dose (cGy * RBE)
0
5
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0
1
0
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5
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6
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g)
a)
1 2
3 3
b)
h)
2250
2200
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c)
Anterior
Posterior
R
i
g
h
t
L
e
f
t

1100
1000
900
400
d)
1100
1000
900
400
e)
Spinal Cord
GTV
Brainstem
FIGURE 10.9
(See color insert.) Treatment planning of a C-spine tumor for a prescribed dose of of 50 Gy
(5000 cGy). (a) Single slice indicating the target (red) and spinal cord (blue). (b) Multiple patch
lines (yellow) for multiple patch combinations. (c) Absolute dose delivered by a left- and a right-
lateral feld. Beam directions are indicated by white arrows. (d) Dose distribution of the frst
patch combination. (e) Dose distribution of the second patch combination. (f) Dose distribution
of the third patch combination, when using the right-lateral through feld. (g) Cumulative dose
distribution taking into account all treatment felds. (h) Dose-volume histogram of the CTV,
spinal cord, and brainstem. The vertical dashed lines indicate 95% and 107% of the prescription
dose. The solid red areas indicate underdosing and overdosing of the CTV.
328 Proton Therapy Physics
challenge for this particular patient and radiotherapy treatment course was
to deliver the prescribed dose of 50 Gy to the target in 25 fractions of 2 Gy,
while limiting the maximum dose in the spinal cord and brainstem to 30 Gy.
This example highlights two other aspects that are especially of concern
for proton therapy and that are related to range uncertainties (Chapter 13).
Dental fllings resulted in artifacts in the CT. The density around the fll-
ing was, however, not overridden because the preferred beam directions
for this treatment are lateral to posterior. The large density variations in the
mouth (high-density teeth, air cavities, and tongue repositioning accuracy)
as well as the sensitivity of the oral mucosa to radiation contraindicate use
of anterior beam directions. Titanium screws and other hardware are pres-
ent near the posterior border of the target. Care was taken to ensure that the
observed electron density of this hardware was converted into the correct
relative proton stopping power. Beam directions for this patient were chosen
to minimize the extent of titanium hardware within the BEV, while allowing
a proper choice of beam angles for the multiple patch combinations.
The choice of which beam angles to use for what part of the treatment
is driven by the need for multiple patch combinations. Limiting the use of
each patch combination to 3–5 fractions, at least two patch combinations are
needed to deliver the fnal 20 Gy on top of 30 Gy with conformal felds. Use
of only two patch combinations would, however, allow no more dose to be
delivered to the spinal cord with any of the patch felds. This then requires
each of these felds to have a substantial margin between the aperture edge
and the spinal cord, thereby compromising target coverage near the spinal
cord. Rather, the choice is to have the conformal felds deliver a reduced dose
of, in this case, only 22 Gy, permitting the patch felds to have tighter mar-
gins to the spinal cord. This allows treatment of almost the entire target to
the prescribed dose, at the cost of fnding a third patch combination. The
three patch lines are indicated in Figure 10.9b, and the treatment planner
has this in mind when designing the conformal felds and subsequent patch
combinations. In other words, the entire treatment is mapped out before the
frst beam is designed within the TPS.
Treatment planning was started with a right lateral feld and a left lateral
feld delivering a homogeneous target dose of 22 Gy(RBE) (relative biologi-
cal effectiveness). As indicated in Figure 10.9c, these felds did not attempt
to spare the spinal cord, and this OAR gets 100% of the dose delivered with
these felds. As the subsequent patch felds have intended right-posterior
and left-posterior beam directions, the conformal felds were chosen to be
right- and left-lateral in order to spread out the dose to the healthy tissues.
Figure 10.8, d and e, show the frst two patch combinations, each delivering
10 Gy(RBE) to the target and using lateral-oblique felds. The isodose lines
show some underdosage and overdosage along the patch lines. The third
patch combination uses two patch felds and alternating right-lateral and left-
lateral through felds to deliver 8 Gy(RBE) to the target. Figure 10.9f shows the
patch combination using the right-lateral through feld. The cumulative dose
329 Physics of Treatment Planning for Single-Field Uniform Dose
distribution for the entire treatment plan is shown in Figure 10.9g. The corre-
sponding dose-volume histograms of the target, spinal cord, and brainstem
are shown in Figure 10.9h. The vertical dotted lines indicate 95% and 107% of
the prescribed dose, which are the ICRU tolerance levels for dose inhomoge-
neity (4, 5). Underdosage occurs in the region of the target closest to the OAR
and is unavoidable because this OAR has to be spared. Overdosage occurs
on the patch lines. Overdosage and underdosage is very limited, as indicated
by the red-flled areas in Figure 10.9h, this despite the close proximity of the
OAR to the target and a low dose-constraint for these OAR.
10.7.2 Lung
Proton radiotherapy of a near unit-density tumor that is moving within
low-density lung tissue is a major challenge. Variation in the density geom-
etry can occur within the fraction, between fractions and over the whole
course of the treatment. Details regarding these uncertainties are provided
in Chapters 13 and 14; this section will be limited to describe a “forward”
planning approach. “Forward” in this context means a treatment planning
approach that mimics classical conformal photon treatment planning as
much as possible (i.e., use of a single CT scan and manual individual beam
design).
A number of such approaches for forward planning have been discussed
in the literature (16–19). Moyers et al. already pointed out the difference
from classical treatment planning in which the aim is to ensure dose cover-
age of the CTV by conforming the prescribed dose to the PTV (16). In their
approach, the PTV is only used for determining lateral (aperture) margins,
whereas range, modulation, and RC smearing are chosen on a per-feld basis
to ensure target coverage under range uncertainties.
Engelsman and Kooy use a two-step approach frst choosing parameters
of each individual beam to ensure tight dosimetric coverage of the CTV on
the mid exhale representative CT scan (17). This is followed by the applica-
tion of lateral, distal, and proximal margins on a per-feld basis to ensure
target coverage under setup errors and range uncertainties. Their simula-
tions show that the magnitude of both the lateral aperture margin and distal
smearing margin can be less than the sum of the expected maximal setup
error and breathing amplitude. This approach works for the stylized phan-
tom used in their study because the required range to cover the most distal
target edge does not vary over the breathing cycle. For at least some patients
underdosage of the target can occur if motion of the tumor relative to other
densities in the patient requires an increase of range, something that the
simple approach of smearing the RC can not provide.
An improved approach is described by Engelsman, Rietzel, and Kooy (18),
in which feld-specifc apertures and RCs are an aggregate of the required
aperture and the RC for all phases (or at least the most important phases)
of the four-dimensional (4D) CT scan. This approach is, however, labor
330 Proton Therapy Physics
intensive and requires automation before it can be routinely applied. Even
then it would guarantee tumor coverage over all phases of the planning
4D CT scan, but not necessarily under variations in patient geometry with
respect to this planning 4D CT scan.
Kang et al. (19) describe an internal target volume (ITV) approach (5) with
density override of the iGTV (internal GTV) to ensure target coverage in
every phase of the breathing cycle. As they defne the iGTV to be the enve-
lope of all GTVs over the breathing cycle, target delineation requires a 4D CT
scan. Treatment planning uses only a single CT scan: the density-averaged
CT scan. Individual beams can, but do not have to, be designed using the
previously mentioned two-step approach. The density override simulates
the tumor to be at all possible locations at once and more than ensures target
coverage over all phases of the 4D CT scan. It also provides a “buffer” for
density variations over the course of the treatment, such as tumor growth
or a moderate change in breathing motion. During any treatment delivery,
however, the tumor will be only in one location at a time and the “loss” of
density will result in an increased dose to normal tissues distal to the target
compared to what is displayed at the time of treatment planning.
In general, and especially for lung tumors, the price of ensuring target cov-
erage, for example, under density variations, range uncertainties, and setup
errors, is an increased dose to surrounding normal tissues. Even the most
conservative of the lung tumor treatment-planning approaches described
(19) does not guarantee target coverage for all patients and all possible den-
sity variations with respect to the treatment-planning CT. The aim is there-
fore to use more than two beam directions such that target regions that may
be underdosed by a single beam receive full dose from at least two other
beam directions, thus mitigating the possible negative clinical consequences.
Figure 10.10 shows an example of a lung tumor treatment plan, according
to the treatment planning protocol as described in Engelsman and Kooy (17).
The fractionation is 70 Gy in 35 fractions of 2 Gy each.
Treatment planning is performed on the mid-exhale CT scan, and beams
are designed in two steps. In step 1 the high-dose region of each beam sep-
arately is conformed tightly to the target. Step 2 takes range uncertainties,
setup uncertainties, and breathing motion into account by increasing the
range, modulation, and smearing distance and by expanding the apertures.
The treatment plan avoids beam directions that are parallel to density gradi-
ents. This serves two purposes. First, it minimizes overshoot due to smearing
(see section “Distal and Proximal Safety Margins”), and second, it reduces
the probability of target underdosage should the breathing motion vary from
treatment planning CT to fractions of treatment delivery. Figure 10.10, a–c,
shows the dose distribution for each of three individual beam directions after
step 1. The overshoot of a few millimeters is deemed acceptable on a multifeld
treatment plan, and tweaking this is very time consuming because our TPS
does not allow automatic dosimetric optimization of the RC. The overshoot is
also a consequence of the need to cover the target in more superior or inferior
331 Physics of Treatment Planning for Single-Field Uniform Dose
a)
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
b)
c)
d)
e)
f )
g)
h)
FIGURE 10.10
(See color insert.) Treatment planning of a lung tumor. (a–c) Relative dose distribution for
each of three individual felds when conforming the high-dose region tightly to the target
volume (indicated in red). (d) Cumulative dose distribution for all three felds combined. The
right-hand panels (e–h) show the same information but now for the planning stage when tak-
ing into account range uncertainties, breathing motion, and setup errors.
332 Proton Therapy Physics
CT slices. The modulation width appears too large for the same reason. The
undershoot is only about 5 mm water equivalent but appears especially large
because it is in low-density lung tissue. Figure 10.10d shows the cumulative
dose distributions for all beams combined, with each feld having an equal
weight. Figure 10.10, e–h, shows similar dose distributions, but after step 2. It is
obvious that for any single beam the high-dose region (95% isodose level) does
not conform to a geometric expansion of the target. This means that, for pro-
ton therapy planning in nonuniform geometries, a PTV-based approach has
limited merit. The cumulative dose distribution for step 2 is shown in Figure
10.10h. A similar cumulative dose distribution could have been designed
using a PTV-based planning approach. It is, however, very important to keep
in mind that such an approach would not result in the beam-specifc dose dis-
tributions (Figure 10.10, e–g) that are necessary to guarantee target coverage
under range uncertainties, setup errors, and target motion.
10.8 FuturePerspectivesofSFUD
For most tumor sites SFUD treatment plan design is straightforward. SFUD
proton therapy is a very powerful tool. It allows conformality of the pre-
scribed isodose to the target nearing what is achievable with IMRT, while
reducing the (integral) dose to surrounding normal tissues by up to a factor
of three. It is, however, of vital importance that the detrimental effects of
range uncertainties and patient density variations are adequately taken into
account in the treatment planning process. The treatment planner, physician,
and medical physicist have to be continuously aware that the fnite range of
protons is not only a blessing but also a risk.
For many patients IMPT may be able to make only modest improvements to
the treatment plans as the application of SFUD proton therapy already allows
high conformality of the high-dose region to the target. SFUD proton therapy
is likely to continue to be applied for many patients, or at least for a substan-
tial fraction of the prescribed dose to many patients. Full-scale clinical use of
IMPT (Chapter 11) may have to wait until the proton therapy community has
minimized range uncertainties or is able to take the remaining uncertainties
effectively into account by means of, for example, robust optimization.
References
1. Meyer JL. IMRT, IGRT, SBRT: advances in the treatment planning and delivery
of radiotherapy. Basel, Switzerland: S. Karger AG; 2007.
2. Delaney TF, Kooy HM. Proton and charged particle radiotherapy. Philadelphia
(PA): Lippincott, Williams & Wilkins; 2008.
333 Physics of Treatment Planning for Single-Field Uniform Dose
3. Goitein M. Radiation oncology: a physicist’s-eye view. New York (NY): Springer;
2008.
4. ICRU Report 50: Prescribing, recording and reporting photon beam therapy.
International Commission on Radiation Units and Measurements, 1993.
5. ICRU Report 62: Prescribing, recording and reporting photon beam therapy.
International Commission on Radiation Units and Measurements, 1999.
6. ICRU Report 78: Prescribing, recording, and reporting proton beam therapy.
International Commission on Radiation Units and Measurements, 2007.
7. van Herk M, Remeijer P, Rasch C, Lebesque JV. The probability of correct target
dosage: dose-population histograms for deriving treatment margins in radio-
therapy. Int J Radiat Oncol Biol Phys. 2000 Jul 1;47(4):1121–35.
8. Urie M, Goitein M, Wagner M. Compensating for heterogeneities in proton radi-
ation therapy. Phys Med Biol. 1984 May;29(5):553–66.
9. Li Y, Zhang X, Dong L, Mohan R. A novel patch-feld design using an opti-
mized grid flter for passively scattered proton beams. Phys Med Biol.
2007;52(12):N265–75.
10. Engelsman M, Delaney TF, Hong TS. Proton radiotherapy: the biological effect
of treating alternating subsets of felds for different treatment fractions. Int
J Radiat Oncol Biol Phys. 2011 Feb 1;79(2)616–22.
11. Egger E, Schalenbourg A, Zografos L, Bercher L, Boehringer T, Chamot L, et al.
Maximizing local tumor control and survival after proton beam radiotherapy of
uveal melanoma. Int J Radiat Oncol Biol Phys. 2001 Sep 1;51(1):138–47.
12. Albert D, Miller J, Azar D, Blodi B. Albert & Jakobiec’s principles & practice of
ophthalmology. 3rd ed. Orlando (FL): Saunders Elsevier; 2008.
13. Daartz J, Engelsman M, Paganetti H, Bussière MR. Field size dependence of the
output factor in passively scattered proton therapy: infuence of range, modula-
tion, air gap, and machine settings. Med Phys. 2009 Jul;36(7):3205–10.
14. Bolsi A, Fogliata A, Cozzi L. Radiotherapy of small intracranial tumours with
different advanced techniques using photon and proton beams: a treatment
planning study. Radiother Oncol. 2003 Jul;68(1):1–14.
15. Chin LS, Regine WF. Principles and practice of stereotactic radiosurgery. New
York (NY): Springer Science+Business Media; 2008.
16. Moyers MF, Miller DW, Bush DA, Slater JD. Methodologies and tools for
proton beam design for lung tumors. Int J Radiat Oncol Biol Phys. 2001 Apr
1;49(5):1429–38.
17. Engelsman M, Kooy HM. Target volume dose considerations in proton beam
treatment planning for lung tumors. Med Phys. 2005 Dec;32(12):3549–57.
18. Engelsman M, Rietzel E, Kooy HM. Four-dimensional proton treatment plan-
ning for lung tumors. Int J Radiat Oncol Biol Phys. 2006 Apr 1;64(5):1589–95.
19. Kang Y, Zhang X, Chang JY, Wang H, Wei X, Liao Z, et al. 4D proton treatment
planning strategy for mobile lung tumors. Int J Radiat Oncol Biol Phys. 2007
Mar 1;67(3):906–14.
335
11
Physics of Treatment Planning
Using Scanned Beams
AntonyLomax
CONTENTS
11.1 Introduction ................................................................................................ 336
11.2 Basic Principles ........................................................................................... 336
11.2.1 The Power of Modulation ............................................................. 336
11.2.2 There Is No Spread-Out Bragg Peak ........................................... 337
11.2.3 There Are No Collimators and Compensators .......................... 339
11.2.4 Field Design and the Need for Optimization ............................ 339
11.2.5 Dose Calculations for Scanning and IMPT................................ 342
11.2.6 The Impact of Secondary Particles .............................................. 344
11.2.7 The Problem of Superfcial Bragg Peaks ..................................... 347
11.3 SFUD or IMPT ............................................................................................ 349
11.3.1 SFUD Planning .............................................................................. 349
11.3.2 Intensity Modulated Proton Therapy (IMPT) Planning .......... 351
11.3.3 Normalizing IMPT Plans.............................................................. 352
11.4 Optimization Strategies for IMPT ........................................................... 353
11.4.1 Degeneracy in IMPT Optimization ............................................. 353
11.4.2 When Less Is More: Field Numbers in IMPT Planning ........... 355
11.4.3 Bragg Peak Numbers, Beam Sizes, and Bragg Peak
Placement ........................................................................................ 356
11.4.4 The Importance of Starting Conditions in IMPT
Optimization .................................................................................. 360
11.5 Dealing with Uncertainties ...................................................................... 364
11.5.1 Magritte’s Apple ............................................................................. 364
11.5.2 Sources of Delivery Uncertainties ............................................... 364
11.5.3 To PTV or Not to PTV? That Is the Question ............................. 365
11.5.4 Robust Optimization ..................................................................... 368
11.5.5 Tools for Evaluating Plan Robustness ......................................... 369
11.6 Case Studies ................................................................................................ 372
11.6.1 Case 1: Nasopharynx Carcinoma ................................................ 372
11.6.2 Case 2: Sacral Chordoma .............................................................. 373
11.7 Summary ..................................................................................................... 375
References ............................................................................................................. 376
336 Proton Therapy Physics
11.1 Introduction
It is becoming increasingly clear that the most fexible method of delivering
proton therapy (or particle therapy generally) is by the use of active scanning.
In this approach, narrow pencil beams of the selected particles are scanned
across the target volume in three dimensions, using defector magnets in
the directions orthogonal to the beam direction, and some form of energy
modulation for positioning of the Bragg peak in depth. In its most fexible
form, such delivery systems are capable of complete control of the dose
delivered by each such pencil beam, resulting in a true fuence modulation
in three dimensions from each individual incident feld direction; see for
example, Webb and Lomax (1). This is truly the particle therapy equivalent of
intensity-modulated radiotherapy (IMRT) with photons, and brings similar
(if somewhat more) advantages and potential disadvantages. In this chapter,
we will look into both the physics and methods of treatment planning for
scanned particle beams, starting with the similarities to conventional IMRT
and the main dissimilarities to passive scattering proton therapy. In addi-
tion, we will look at different modes of optimizing scanned proton therapy
treatments and look into how possible delivery uncertainties can be dealt
with. Finally, case studies will be presented to indicate the potential power
of these techniques.
11.2 BasicPrinciples
11.2.1 The Power of Modulation
The introduction of intensity-modulated methods into conventional radio-
therapy with photons can truly be described as a revolution. Although the
more advanced (and computer aided) three-dimensional (3D) planning tech-
niques developed in the 1980s were capable of producing extremely complex
and conformal treatments, it was the introduction of optimization algo-
rithms, together with the development of hardware for the delivery of more
or less arbitrary fuence profles, that really opened up the world of highly
conformal radiotherapy to clinics large and small. The secret of IMRT’s suc-
cess lies in its ability to fully exploit a degree of freedom that had hitherto
only been manipulated in a rather limited way. This degree of freedom is the
manipulation of the cross-feld fuence profle of the delivered feld.
Cross-feld fuence had, of course, been modulated for many years in con-
ventional planning, through the use of collimators (essentially a binary fu-
ence modulation of the delivered feld) and by the use of wedges, either fxed
or dynamic. Indeed, somewhat more sophisticated fuence modulation could
(and was) achieved using compensators to compensate for missing tissues.
337 Physics of Treatment Planning Using Scanned Beams
However, all these methods were limited in their extent. Nevertheless, they
indicated the power of fuence modulation, and it was only a matter of time
before a number of breakthroughs were made that could provide both the
calculational techniques necessary for fully exploiting this approach and the
hardware necessary to deliver it, which were the implementation of optimi-
zation techniques to radiotherapy (sometimes called inverse planning) and
the development of computer-controlled, dynamic multileaf collimators,
respectively. Although it is somewhat overstated to say that this combina-
tion turned radiotherapy from a predominantly palliative discipline to a pre-
dominantly curative therapy, there is no doubting that the introduction of
IMRT helped transform radiotherapy into the precise and accurate therapy
that we know today.
Consequently, intensity modulation has been shown to be an extremely
powerful tool for conforming radiation to the target volume. Imagine what
could be achieved if not just the cross-feld fuence could be modulated, but
also the depth–dose curve of the radiation as well? This is what essentially
can be achieved with active scanned proton (particle) therapy.
11.2.2 There Is No Spread-Out Bragg Peak
Conventional (passive scattering) proton therapy is based very much on the
concept of the spread-out Bragg peak (SOBP) (see Chapter 10). This is the
basic deliverable depth–dose element, produced by either a continuously
rotating range modulator wheel or a ridge flter (see, e.g., Koehler et al. [2]).
As described in more detail in Chapter 5, the SOBP is constructed generally
before the beam has been spread laterally and before the laterally scattered
beam is subsequently shaped using collimators and compensators. This is
an important limitation of this technique. As the SOBP is constructed on the
narrow, unbroadened beam, the width of the SOBP along the beam direction
is invariable across the feld. Put another way, although the length of the
SOBP (and in principle its shape) can be varied from feld to feld, within a
single feld, the SOBP depth–dose curve is constant across the feld.
The consequence of this is shown in Figure 11.1, which shows a single
slice of a large Ewing’s sarcoma and the calculated dose distribution from
a single, passively scattered proton feld incident from the posterior aspect.
Although this feld direction may not be optimal for this particular case, it
has been chosen deliberately in order to show the limitations of the SOBP
technique. Indicated in the fgure is the “length” of the SOBP that must be
produced in order to fully cover the target volume. For this case, the SOBP
must be about the same length as the thickest portion of the target volume
along the beam direction, as indicated by the solid white line in the fgure, in
this case about 10 cm. However, the target thickness varies extensively across
the target and in this slice is considerably narrower in the portion directly
posterior to the femoral head. Thus, the same SOBP delivered here will be far
too wide (as shown by the broken line), with the consequence that the whole
338 Proton Therapy Physics
femoral head, although proximal to the target volume, will receive the full
dose. In addition, at the lateral border of the target, as the distal edge comes
closer to the surface and the thickness of the target narrows, the SOBP dose
can extend well beyond the proximal border of the target to the surface of
the patient.
Once again, it should be pointed out that this is an extremely poor feld
direction for treating such a target, but it nicely illustrates the problem of
passive scattering delivery and the use of a feld-invariant SOBP depth-
dose curve. Indeed, due to this limitation, passive scattering can be directly
compared to the delivery of open felds with photons. The depth–dose
curve is invariant (a fxed extent SOBP in the proton case), and the fuence
of particles across the feld is also uniform. Therefore, proton therapy using
passive scattering is essentially the direct equivalent of open-feld therapy
with photons.
However, this chapter is about beam scanning, so why all the discussion
about passive scattering and SOBPs? Because one of the most important dif-
ferences between beam scanning and passive scattering, particularly when
we get to intensity-modulated proton therapy (IMPT), is that the effective
depth–dose curve for the proton feld can vary across the feld. During
the delivery, the treatment planning (and the delivery machine) has com-
plete control over the fuence delivered by each Bragg peak delivered to the
patient, with the consequence that, in the most general case, Bragg peaks
can be distributed in three dimensions throughout the target volume (see
Section 11.2.4). Thus, the effective depth–dose curve (that resulting from
the superposition of all energy/range-shifted Bragg peaks along one pencil
Dose %
104
90
80
70
60
50
40
30
0
FIGURE 11.1
(See color insert.) The dose distribution for a single, passively scattered proton beam (indi-
cated by the green arrow) incident from the anterior aspect of a large and complex Ewing’s car-
cinoma. The white double-headed arrows show the minimum SOBP length necessary to cover
the whole target, and how, due to the irregularity of the distal edge of the target, such fxed
SOBPs can extend well into the normal tissue areas even when the target is quite deep seated.
339 Physics of Treatment Planning Using Scanned Beams
beam direction) can also be varied. In other words, and as we will see in
more detail later, there is no SOBP in pencil beam scanning.
11.2.3 There Are No Collimators and Compensators
Now let’s look at differences between scanning and passive scattering when
conforming the dose to the target volume. Again, there are two major dif-
ferences: how the dose is conformed to the distal edge of the target and how
lateral dose conformation is achieved. As described elsewhere, for passive
scattering, such conformation is achieved through the use of feld-specifc
compensators (for distal edge conformation) and feld-specifc collimators/
apertures (for lateral dose conformation). With pencil beam scanning, these
devices are no longer necessary. Because the Bragg peaks lateral to the beam
direction can be freely chosen (and delivered) at the treatment-planning stage,
then it is a feature of the planning process to identify those Bragg peaks that
intersect with the target volume and to deliver only these. As we will see
below, this preselection process as part of the treatment planning effectively
acts as a 3D aperture, simultaneously cutting out Bragg peaks that are outside
the volume laterally as well as distally and, crucially, proximally as well. Thus,
for pencil beam scanning, there is no need for collimators and compensators.
However, in order not to propagate a misunderstanding around this point,
this is not the same as saying that collimators and compensators cannot be
used. Of course, as long as the delivery nozzle supports the mounting of such
devices, there is actually no reason why collimators/compensators cannot be
used as well with scanning, and particularly for the treatment of superfcial
tumors these devices can provide a valuable method for sharpening the lat-
eral penumbra over and above that resulting from the pencil beam size itself.
I will return to this issue in Section 11.2.7.
11.2.4 Field Design and the Need for Optimization
So let’s now look in a little more detail into feld design for pencil beam–
scanning treatments. I do not mean here the selection of feld angles. In this
context, by feld design I want to describe in more detail exactly the steps that
are required for designing a single, scanned proton beam feld, assuming that
the feld direction has already been defned. The description given here is
mainly based on the process used for planning at the Paul Scherrer Institute
(PSI), but the general principles will be the same for any scanning feld.
The main steps of the feld-design process for scanned proton felds are
shown in Figure 11.2. Once a feld direction has been defned, the frst step
is to determine the possible set of all deliverable Bragg peaks within the
patient. This set of Bragg peaks will clearly be dependent on the physical
characteristics of the delivery machine. For instance, the resolution of the
energy selection (i.e., is it continuous or discretized?), the maximum deliv-
erable energy, the minimum deliverable energy, and the maximum extent
340 Proton Therapy Physics
of the feld size, which will generally be defned by the scanning range of
the defector magnets used for scanning. For the case shown in Figure 11.2,
these parameters are as follows. A maximum proton energy of 138 MeV was
selected for the feld, minimum energy is close to zero due to the fact that
the energy is modulated at our facility by the insertion of range shifter plates
into the beam directly before the patient (see, e.g., Pedroni et  al. [3]), and
for an energy of 138 MeV, our delivery system has enough such plates to
%
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FIGURE 11.2
(Seecolorinsert.) The main steps in the feld-design process for a single SFUD (Single Field,
Uniform Dose) feld irradiating a meningioma (a). (b) All possible Bragg peaks that can be
delivered from the selected feld direction and with the feld geometry parameters as described
in the text. (c) The subset of Bragg peaks automatically selected for subsequent optimization
based on their position in relation to the surface of the selected target volume. (d) The initial
dose distribution resulting from the preselection process and initial set of Bragg peak fuences
(starting conditions) shown by the colors in (c). (e) Bragg peak fuences after the optimization
process, displayed using the same color scale as in (c). (f) The dose distribution resulting from
the set of optimized Bragg peak fuences shown in (e).
341 Physics of Treatment Planning Using Scanned Beams
bring the Bragg peaks right to the surface of the patient. In addition, spacing
between the Bragg peaks in depth is defned by the thickness of these plates,
which are 4.6 mm water equivalent. Finally, orthogonal to the beam direc-
tion, each pencil beam can be defected ±10 cm from the central axis and with
a user-defned pencil beam separation. For the case shown in Figure 11.2,
pencil beam spacing orthogonal to the beam direction was defned as 5 mm.
Figure 11.2b therefore shows, for one slice of this patient, all the possible
Bragg peaks that could be delivered using the parameters defned above.
Each red cross is a possible Bragg peak position, now converted from water
equivalent range to depth in the patient, which is obviously different due to
the varying density of tissues within the patient. This transformation (from
a uniform spacing of Bragg peaks in water equivalent space to an irregular
spacing of Bragg peaks within the patient) can clearly be seen from the spac-
ing of the Bragg peak in the air of the nasal cavities, as well the irregular
shape of the maximum Bragg peak penetration distal to the target volume.
To reiterate, the Bragg peaks range out on this side simply because the maxi-
mum energy selected for this feld (138 MeV) has a maximum range in water
of about 13 cm, and the irregular end-of-range line in the patient is therefore
essentially the 138-MeV isodepth line. That this is irregular in shape is sim-
ply due to the different tissue densities within the patient.
Step two in the feld-design process should be relatively obvious. Clearly, we
do not need to understand too much about physics or Bragg peaks to realize
that if we want to only irradiate the outlined target, we do not need to deliver
Bragg peaks (and therefore dose) in tissues a long way outside of the target, so
we can easily preselect the Bragg peaks that we will need for delivery based
on this distribution. Simply put, all Bragg peaks outside of the target can be
removed (switched off), whereas all Bragg peaks within the target volume
are retained. In fact, it is not quite that simple. As can be seen in Figure 11.2c,
which shows the subset of selected Bragg peak positions that will be used
subsequently in the feld-design process, Bragg peaks a little distance outside
the target have also been preserved. This is necessary because of the discrete
spacing of the Bragg peaks. If only peaks within the target are selected and
because the pencil beams are defned on a 5-mm grid, in the worst case, the
most superfcial Bragg peaks could be up to 5 mm inside the target volume,
leading to potential problems of target coverage at the edge of the target. To
avoid this, for the example shown in the fgure, all Bragg peaks up to 5 mm
outside have also been selected for the subsequent steps of the calculation.
The reader will have noticed that in Figure 11.2c, the subset of selected Bragg
peaks are now also color coded to represent the relative fuence of each Bragg
peak. That is, we have assigned an initial set of relative weights to all Bragg peaks
that will be used for input into the subsequent optimization process. The impor-
tance of this step will be considered in more detail in Section 11.4.4. Suffce it to
say that these are what we call the initial starting conditions for the optimization.
Figure 11.2d shows the dose distribution resulting from the set of
weighted Bragg peaks shown in Figure 11.2c after the application of an
342 Proton Therapy Physics
analytical dose calculation (outlined below). What is immediately clear is
that, based on the initial guess for the starting beam weights, the dose in
the target is anything but homogenous. In the middle of the target there
is generally too much dose, whereas at the edges, there is too little. This is
mostly an effect of the irregular shape of the target, as well as the large size
and substantial overlapping of neighboring pencil beams. That is, where
there is overlapping of many different pencil beams (in the center of the
target), there is suffcient (even too much) dose, whereas at the edges, where
inevitably there are fewer overlapping pencil beams, the dose is too low. To
improve dose homogeneity across the target then, an optimization proce-
dure needs to be applied in order to fnd a set of Bragg peak beam weights
that satisfes this condition.
The result of this optimization process is shown fnally in Figure 11.2e, with
the resultant dose distribution in Figure 11.2f. What is interesting in Figure
11.2e is the quite different distribution of Bragg peak weights after optimiza-
tion compared with the initial weights. Although the Bragg peaks at the dis-
tal end generally have higher weights, the internal Bragg peaks (those within
the target volume) have very low weights (<5% of the maximum weight in
the feld indicated by the white crosses in the fgure). Figure 11.2f, however,
shows that the optimization was necessary and successful. The fnal dose
distribution conforms quite well to the target contour at the 95% dose level
(red area) and also provides a relatively homogenous dose across the whole
target. It is also important to note that this is the result of the feld design, as
well as the optimization, for a single feld only.
Before moving on, some remarks need to be made about the Bragg peak
preselection process. In principle, if the optimization algorithm is good
enough, the preselection of Bragg peaks is not absolutely necessary. In this
case, the optimization would automatically switch off the Bragg peaks out-
side the target volume, at least when a zero dose constraint is assigned to all
surrounding normal tissues. However, this would inevitably slow down the
optimization process as, for each iteration, the dose contribution from every
pencil beam shown in Figure 11.2a will have to be calculated. In contrast,
by using a preselection process, the number of Bragg peaks for which the
calculation needs to be performed can be reduced substantially. By a similar
argument, the dose calculation matrix can also be signifcantly reduced in
size if we restrict this to the region of the target. In short, the preselection
process described above is essentially an effciency measure, using a priori
knowledge of the Bragg peaks that will make a signifcant contribution to the
target dose in order to make the subsequent optimization quicker.
11.2.5 Dose Calculations for Scanning and IMPT
To get from Figure 11.2e to 11.2f, requires a dose calculation, the intricacies of
which will be covered more in Chapter 12. I will therefore only very briefy
review these from the point of view of pencil beam scanning.
343 Physics of Treatment Planning Using Scanned Beams
As with other forms of proton therapy, there are basically three classes of
dose calculations that can be used for scanned proton therapy; ray casting,
pencil beam (both analytical approaches), and Monte Carlo, which have been
nicely reviewed and described by Schaffner, Pedroni, and Lomax (4). With
the ray casting (as still used at our institute), the physical pencil beam inci-
dent on the patient is modeled as the smallest element in the dose calculation,
with density heterogeneities being dealt with by a simple scaling of the water
equivalent depth of each dose grid calculation point along the feld direction
(4). In contrast, for the pencil beam approach, the physical pencil beam is fur-
ther subdivided into a number of smaller beam elements per physical pencil
beam (typically 4–64, depending on the calculation accuracy required), with
each beam element being weighted such that the resultant dose envelope
approximates to the lateral spread of the physical beam in air. This concept
is shown in Figure 11.3a. Such an approach has been described in detail by
Soukup et  al. (5). An alternative to this approach was earlier described by
Schaffner, Pedroni, and Lomax (4), where instead of modeling a single physi-
cal pencil beam, the total fuence from all applied pencil beams is frst calcu-
lated and then modeled by the appropriately weighted set of beam elements
(see Figure 11.3b). This approach has the advantage of speed in the calcula-
tion, because fewer beam elements need to be calculated over the whole feld,
whereas the frst approach (Figure 11.3a) has obvious advantages during the
optimization procedure, where the weights of the physical pencil beams (and
therefore the total fuence) is changing iteration-by-iteration. In practice, most
commercial treatment-planning systems for pencil beam scanning are essen-
tially similar to that shown in Figure 11.3a. Finally, Monte Carlo techniques
can also be used (6–8), whereby the physical pencil beams are each repre-
sented by many thousands of individual protons tracked through the patient
a
b
FIGURE 11.3
Analytical calculations using the pencil beam model. (a) The decomposition of an individual
Gaussian physical pencil beam into a subset of (Gaussian) beamlets for calculation, showing
how a discrete set of such beamlets can be weighted in order to model the shape of the actual
physical pencil beam. (b) The composition of a total fuence (sum of all individual physical
pencil beams into a single composite fuence) and its decomposition into beamlets for the cal-
culation. (After Schaffner et al., Phys Med Biol., 44, 27, 1999.)
344 Proton Therapy Physics
geometry, the number of protons per pencil beam then being proportional to
the relative fuence (weight) of that pencil beam. As with other areas of radio-
therapy, Monte Carlo calculations provide by far the most accurate results,
but at considerable calculational expense. On the other hand, Monte Carlo
calculations for scanned felds can, in principle, be considerably faster than
for passive scattering, because the incident pencil beams can be more easily
modeled without necessarily transporting particles through the treatment
nozzle, and the lack of collimators and compensators means that the tracking
process can start directly in the patient (see Chapter 9).
11.2.6 The Impact of Secondary Particles
As described in Chapter 2, protons traversing a medium undergo a num-
ber of different processes: energy loss, scatter, and interactions with atomic
nuclei (9, 10). In the latter process, about 1% of the incident protons are lost
per centimeter of traversed matter through interactions with nuclei. These
proton losses are not without consequence, however, and although the pro-
ton may be lost from the primary beam, a spectrum of secondary particles
are produced (11). Although these include heavier and extremely low-range
particles such as deuterium and tritium, secondary protons and neutrons are
the most predominant.
Let’s frst consider the neutron contribution (see Chapter 18). This has been
the subject of much controversy and discussion in the last few years. In an
article published in 2006, Hall estimated the risk of secondary cancer induc-
tion as a result of radiotherapy using IMRT, passive scattered and active
scanned protons (12). In that article he claimed that the neutron background
resulting from passive scattering could be extremely high and if one takes
into account the potential relative biological effectiveness (RBE) for neu-
trons, could potentially more than cancel out the signifcant reduced (pri-
mary) integral dose resulting from proton therapy. Although the article had
a positive effect on highlighting the neutron contamination as a potentially
important issue, subsequent work and more detailed analysis indicated that
the problem is much smaller than initially estimated (13–18) . Nevertheless,
Hall pointed out an important issue relative to active scanning: that in any
case, the neutron contamination is considerably smaller than that for pas-
sive scattering. This is due to the fact that for scanning, the beam exiting the
treatment nozzle can be very clean (there are very few beam-line elements
that intersect with the beam close to the patient) and that no collimators are
required, which are a primary source of neutron contamination for passive
scattering (13). Indeed, a few years earlier, measurements made at our insti-
tute with scanned proton beams indicated that the neutron contamination
lateral to the feld direction was of the same order of magnitude (as in fact,
somewhat lower than) the neutron contribution from a 15-MV photon feld
of similar size and dose (19). This is one of the major advantages of the scan-
ning approach
345 Physics of Treatment Planning Using Scanned Beams
Perhaps more of an issue for active scanning, and in particular IMPT, is the
secondary proton contribution. Although the fuence of secondary protons
is only a few percent of the fuence of the primary beam, secondary protons
have a much wider angular distribution, leading to a long, low dose tail to
the lateral dose profle of the beam—the so-called halo effect. The effects of
this halo on dosimetry and an analytical model for estimating its effect has
previously been published by Pedroni et al. (20). If this effect is ignored in the
dose calculation, it has been found that errors in absolute dose of up to 9–10%
can be observed for small felds. This is due to the secondary protons essen-
tially removing the dose from the primary feld and into the tissues outside
of the irradiated volume. Figure 11.4 shows this effect. In Figure 11.4, a and
b, calculated profles through a Single Field, Uniform Dose (SFUD) active
scanned feld (see Section 11.3.1) are shown, together with second profles
(shown as closed circles) showing the same feld, but this time calculated
taking into account the secondary proton halo. There is a clear (and systematic)
reduction of about 2% in the dose level throughout the high-dose region and
a small, but just visible, increase in dose in the tails of the profle. Figure 11.4,
c and d, shows the same profles, but this time with the full dose profle
0.00
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Position (cm)
T-axis profiles
a b
c d
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T-axis profiles
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U-axis profiles
5
0
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D
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(
%
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60
80
100
0.10
0.20
D
o
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(
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0.30
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–5 0
Position (cm)
U-axis profiles
5
0
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(
%
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o
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(
G
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0.30
0.40
FIGURE 11.4
Effect of the secondary particle “halo” dose associated with scanned proton beams on the abso-
lute dosimetry of homogenous felds. (a and b) Orthogonal dose profles through a homogenous
(SFUD) scanned proton feld calculated using primary particle contributions only (solid line)
and with the additional effect of the secondary halo dose (closed circles). The dose halo essen-
tially removes dose from the primary feld and adds dose to the tails of the profle. (c and d) The
same profles, but with the primary and halo dose profle (closed circles) globally increased by
2% such as to correct for the effect.
346 Proton Therapy Physics
(primary and halo dose) increased in dose globally by 2%. Although there
is a slight rounding in the full dose profle in comparison to the primary
dose profle, after a global increase in dose, a much improved agreement
between the two is found. It is through this global scaling of absolute dose
that such effects are currently dealt with at our clinic, although clearly, the
best approach is to incorporate the halo effect into the dose calculation dur-
ing the optimization process, an approach that is now being adopted by most
proton treatment–planning manufacturers.
Perhaps more signifcant, however, is the potential effect of this halo dose on
IMPT (Intensity Modulated Proton Therapy, see Section 11.3.2) plans. Figure
11.5 shows lateral profles through an example IMPT feld. Again, Figure 11.5,
–4
0.0
0.2
0.4
0.6
–2 0
Position (cm)
T-axis profiles a b
c d
e f
U-axis profiles
2 4 6
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%
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(
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Position (cm)
0
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Position (cm)
T-axis profiles
2 4 6
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–14
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Position (cm)
8 16
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U-axis profiles
With NI halo
IC measurements
With NI halo
IC measurements
–10
0.0
0.5
1.0
1.5
–5 0
Position (cm)
5 10
0
50
100
150
D
o
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(
%
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D
o
s
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(
G
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U-axis profiles
T-axis profiles
–5
0.0
0.2
0 5
Position (cm)
0
20
40
D
o
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(
%
)
D
o
s
e

(
G
y
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FIGURE 11.5
Similar profles as for Figure 11.4, but this time for a more complex, intensity-modulated proton
therapy (IMPT) feld. (a and b) Primary and primary+halo profles before the dose correction.
(c and d) After correction by 4% dose. Note the improved agreement in the dose peaks, but the
subsequent “collection” of dose in the dose valleys due to the accumulation of halo doses in
these areas. (e and f) Ionization-based measurements for two more profles through the same
feld, this time showing the good agreement of measurement to the primary+halo model.
347 Physics of Treatment Planning Using Scanned Beams
a and b, shows the primary only profles compared with the primary plus
halo profles. As with the SFUD example above, there is a clear and system-
atic underdosage throughout the profle for the primary and halo calculation,
particularly in the sharp peaks of dose. Figure 11.5, c and d, then show the
two profles compared after the primary and halo dose has again been glob-
ally corrected as described above. An interesting effect can now be seen in the
valleys of the dose profle. Although the corrected profle improves the cor-
respondence between measurement and calculation in the high dose regions,
the halo dose effectively collects in the valleys of the dose distribution, locally
increasing the dose in these regions. As these valleys are often the result of
the IMPT optimization attempting to reduce the dose into critical structures,
it is important to understand this effect. In the worst case, if the halo dose is
not taken into account at the optimization stage, the actual delivered dose in
the low-dose valleys could be in reality a few percent higher than anticipated.
Figure 11.5, e and f, shows the resulting ionization chamber measurements
for both profles, clearly showing that the effect estimated from the analytical
halo model of Pedroni et  al. (20) is quite accurate and reiterates the impor-
tance of the halo effect on scanned proton therapy dose distributions.
11.2.7 The Problem of Superficial Bragg Peaks
Before leaving this section, one additional point needs to be made about feld
design (and delivery) for active scanned proton therapy: the problem of deliv-
ering superfcial (low energy) Bragg peaks. This is a problem that occurs sur-
prisingly often, is not trivial, and unfortunately is often overlooked. So what
exactly is the problem? As should be clear to the reader by now, the depth of a
Bragg peak in the patient is determined by the energy of the incident beam, so,
if it is necessary to deliver Bragg peaks close to the surface of the patient, then
proton beams of very low energy are required. Indeed, if Bragg peaks need to
be delivered exactly at the surface of the patient, essentially a proton beam of
close to zero energy is required. Here lies the problem. It is extremely diffcult
to produce low-energy proton beams from accelerators that are designed to
operate at energies of 200 MeV or more. Even with synchrotrons (with which
the energy can be changed pulse-to-pulse) it is diffcult to extract beams with
energies much less than 70–100 MeV. With cyclotrons it is even more diffcult.
Being fxed energy machines, the only way to reduce energy is to introduce
material into the beam. This in turn causes the beam to diverge (due to mul-
tiple Coulomb scattering in the degrading material); consequently, to obtain a
narrow beam after the degradation process, the beam needs to be collimated
with an inevitable loss of beam fuence. This process can be horribly ineff-
cient. As an example, at PSI, in order to degrade the 250-MeV beam produced
by our super-conducting cyclotron down to 70 MeV for eye irradiations, 99.7%
of the protons exiting the accelerator will be lost in this degradation process!
The next question then is how often do we require such Bragg peaks? After
all, when looking at the standard SOBP curve and the relative weights of the
348 Proton Therapy Physics
Bragg peaks required to produce such a curve, the low-range (and therefore
low-energy) Bragg peaks have extremely low weights. Nevertheless, in many
circumstances, low-range Bragg peaks can be very important.
Figure 11.6a shows a slice through a large sacral chordoma, with the
planning target volume (PTV) shown in yellow. Also shown are the Bragg
peaks that can be delivered to this tumor from a single lateral beam, assum-
ing a maximum energy of 177 MeV and a minimum energy of 70 MeV. As
with Figure 11.2e, the colors of the crosses show the relative weights of each
Bragg peak after optimization. There is a clear absence of Bragg peaks at the
most proximal part of the tumor for all positions within about 3 cm of the
patient surface. However, for this slice, this is not a great problem, because
the tumor is thick enough along the feld direction that there are at least 37
Bragg peaks stacked from the distal end; for the last few energy layers, the
Bragg peaks will have extremely low weights (white crosses in the fgure).
%
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FIGURE 11.6
(See color insert.) An example of the importance of superfcial Bragg peak positions. (a) An
example slice through the PTV of a large chondrosarcoma in the pelvis region. The PTV is
shown in green, and the colored crosses show the deliverable Bragg peaks if a minimum deliv-
erable energy of about 70 MeV is assumed (3-cm range). Because of this minimum deliverable
limit, there is a 3-cm strip of the PTV close to the patient surface where no Bragg peaks can
be applied. (b) A second slice through the same PTV, 5 cm more superior. Here the PTV is
extremely narrow and superfcial, and with the minimum 3-cm range, this portion of the PTV
cannot be suffciently covered with Bragg peaks to ensure a homogenous coverage of the PTV
at this level. (c and d) The resulting dose distributions at the two levels after optimization.
Although the coverage at the frst level is suffcient, there is a clear problem at the more supe-
rior level due to the lack of Bragg peaks in the proximal aspect of the PTV.
349 Physics of Treatment Planning Using Scanned Beams
Thus, the inability to deliver Bragg peaks closer to the patient surface will
not be a problem at this level, because they are not required. Figure 11.6b is
another slice through the same CT set and target volume, but about 5 cm
more superior. Now the PTV has a completely different form, being rather
narrow and very superfcial. Again, the Bragg peaks for the same feld are
shown, assuming once again that the minimum energy that can be delivered
is 70 MeV. Because of the very superfcial position of the PTV at this level and
the limit on the lowest energy of Bragg peaks that can be delivered, there is
a signifcant problem in covering the target suffciently. Indeed, by looking
at the resulting dose distribution at this level (Figure 11.6d), it has not been
possible to obtain a homogenous dose across the PTV because of the lack of
superfcial Bragg peaks. Consequently, it will be very diffcult to treat such
a target volume from the selected feld direction without being able (in the
same feld) to deliver both high- and extremely low-energy beams of high
fuences. For instance, taking Figure 11.6 as an example, in order to cover the
PTV at all depths and all levels, it would be necessary to insert a preabsorber
to deliver Bragg peaks to the last 3 cm of the target (e.g., for the portion of
the feld covering the target at the level shown in Figure 11.6b), but it would
be unfortunate to always have the preabsorber in the beam for delivering
the more deeply applied Bragg peaks (e.g., the majority at the level shown
in Figure 11.6a), as it will inevitably degrade the lateral characteristics of the
beam.
Ideally then, from the delivery machine point of view, one wants a preab-
sorber that can be automatically inserted into the beam when low penetra-
tion Bragg peaks are required and a treatment-planning system that supports
this feature. In addition, it would be of great advantage in such cases to be
able to use feld-specifc collimators in combination with scanning in order
to sharpen up the lateral penumbra after the inevitable degradation result-
ing from the preabsorber for the superfcially applied pencil beams. At the
time of writing, all these requirements are, sadly, lacking in most commer-
cial scanning proton systems.
11.3SFUDorIMPT
11.3.1 SFUD Planning
In the previous section, the importance of optimization for active scanning
was described, using the example of a single feld. The result of this optimiza-
tion process was a dose distribution in which the dose throughout the target
volume was more or less homogenous (at least within ±10% of the prescrip-
tion dose). Although it could be argued that one may want to have a some-
what more homogenous dose across the target for a compete plan, the result
of the optimization process is nevertheless impressive and provides a result
350 Proton Therapy Physics
that is already close to a clinically acceptable dose distribution. Nevertheless,
as with conventional photon treatment planning and passive scattered proton
therapy, it is extremely rare that single-feld plans are planned or delivered
(the treatment of uveal melanomas and craniospinal axis irradiations being
the exceptions). The reasons for this are twofold. First, additional felds can
improve the overall dose homogeneity across the target volume and second,
the robustness of the delivered plan can be improved. When one or more indi-
vidually optimized and homogenous dose distributions are added together to
make a composite plan, we call this a Single Field, Uniform Dose (SFUD) plan
(21). An example of such a plan is shown in Figure 11.7, where the four indi-
vidual feld dose distributions are shown together with the combined dose of
all these felds added together. As is clear from the individual felds, the dose
across the target for each feld is close to uniform, whereas the combination
of all the felds improves both the dose homogeneity and dose conformation.
The SFUD approach then, although involving an optimization and modu-
lation of the fuence of each individual pencil beam of each feld, ensures a
smooth dose across the target from each feld and can therefore be consid-
ered to be the scanning equivalent of treating with open felds in photon
therapy, as well as passively scattered proton therapy. Indeed, although to
the author’s knowledge nobody is pursuing this approach, there is no reason
to believe that SFUD-type delivery with an active scanning system could
not be combined with compensators and collimators in order to construct
patched plans as performed routinely with passive scattering. As noted
above, the use of scanning does not necessarily exclude the use of collima-
tors and compensators, and the SFUD approach could provide a method by
which, if desired, patched-feld techniques could be delivered with an active
scanning system.
Dose %
Combined distribution
F3
F1 F2
F4
107
90
80
70
60
50
40
30
0
FIGURE 11.7
(Seecolorinsert.) A frst-course SFUD (single-feld uniform dose) plan to a large and complex
skull-base chordoma, together with the individual feld dose distributions making up the total
plan (F1–F4). Note that for each feld, the dose across the target volume is more or less homogenous.
351 Physics of Treatment Planning Using Scanned Beams
11.3.2 Intensity Modulated Proton Therapy (IMPT) Planning
One reason perhaps that scanning and feld patching are often thought
to be mutually exclusive is because scanning provides the possibility to
deliver IMPT.
When one thinks about optimization in radiotherapy, one immediately
thinks about IMRT. Although this name is somewhat unfortunate in many
ways (1), it has become ubiquitous to describe the process of simultaneously
optimizing the cross-feld fuences of many, angularly separated photon
felds, such as to conform the high dose to the defned target volume while
additionally selectively sparing neighboring critical structures. The key to
our discussions here is the phrase “simultaneously optimizing” the fuence
from different felds. This is patently not what we are doing with SFUD plan-
ning where the optimization process was restricted to each feld individu-
ally. However, there is no reason why the optimization process for active
scanning cannot also be performed in a similar way to IMRT, that is, that
the fuences of all proton pencil beams from multiple felds are optimized
together in the same process. When the planning and optimization process
is performed in this way, we term such treatments IMPT, simply because this
is then the exact proton equivalent of IMRT with photons (21, 22). Also, as
with IMRT, in IMPT planning the optimization can also be driven, not just
by the requirement of delivering a therapeutically relevant dose across the
tumor, but also such that selected critical structures are spared through the
defnition of dose constraints.
An example of an IMPT plan, with its component individual feld dose
distributions is shown in Figure 11.8, which shows a complex (and large)
skull base chordoma that is close to the brainstem, shown in red. For this
plan, the optimization has been asked to cover the PTV as much as possible,
Dose %
Combined distribution
F3
F1 F2
F4
122
90
80
70
60
50
40
30
0
FIGURE 11.8
(Seecolorinsert.) The second-course IMPT (intensity-modulated proton therapy) plan for the
same case as in Figure 11.7. This time, IMPT has been used to cover the PTV as much as pos-
sible, while also setting a dose constraint on the brainstem, which partially overlaps with the
PTV. The individual feld dose distributions are also shown (F1–F4).
352 Proton Therapy Physics
while sparing the brainstem at about the 60–70% level. The difference from
the corresponding SFUD plan shown in Figure 11.7 should be clear. Now, the
individual feld dose distributions are anything but homogenous; indeed,
they are highly complex and irregular in form and individually are useless
for ensuring a homogenous coverage of the target volume. However, when
all these felds are combined into the fnal plan (shown in the center of the
fgure), the target is homogenously covered, while simultaneously sparing
the brainstem. By carefully reviewing the individual feld dose distribu-
tions, it is also possible to see how the optimization process has achieved this
result. The proton pencil beams passing through the brainstem have been
selectively reduced in weight for all felds, with the missing dose resulting
from this process being compensated for by the other felds. This is of course
the power of IMPT. As the optimization is performed simultaneously for all
felds, then missing doses from one feld can be easily compensated for by
the other felds, a possibility that is missing in SFUD planning. However,
the individual feld distributions also show the potential problem of IMPT
planning. The distributions are extremely irregular and complex, which can
have consequences on the robustness of the plan, as we will discuss in more
detail later.
In this section I have deliberately made a clear distinction between SFUD
and IMPT planning, and this is a distinction that we adhere to clinically at
our institute. Where possible, SFUD planning is used for as many cases as
possible, and IMPT plans are only used when the geometry of the case is so
complex that SFUD planning becomes limited. Even in such cases, SFUD
planning will be used for the frst course of treatment, with an IMPT plan
being used as a second or third course in order to “pull-off” the critical
structures. However, there is no reason why SFUD- and IMPT-type felds
could not be used in the same plan or treatment course. Although this is
not something we have yet pursued (and to the author’s knowledge has
not been investigated anywhere), one can imagine that a single plan could
consists of one or two SFUD felds and one or two IMPT-type felds, in
which the IMPT optimization takes into account the dose resulting from
the SFUD feld or felds. In particular, such an approach could be very
interesting for simultaneous integrated boost (SIB)-type treatments, with
the low dose per fraction part of the treatment delivered using SFUD and
the higher dose-per-fraction boost portion being delivered using IMPT-
type felds.
11.3.3 Normalizing IMPT Plans
A few words need to be said about normalizing and prescribing the dose
to SFUD and in particular, IMPT plans. For SFUD plans, although the dose
for the full plan can be quite uniform across the target, it can nevertheless
vary by at least ±5%, sometimes even more when using small numbers of
felds or in anatomical areas with complex density heterogeneities (which
353 Physics of Treatment Planning Using Scanned Beams
can signifcantly distort the Bragg peak shape). Thus, normalizing/prescrib-
ing to a single point of such a plan could, in the worse case, lead to quite sig-
nifcant changes in the overall dose to the tumor. Given that complex IMPT
plans (i.e., those in which many critical structures maybe spared through the
use of constraints in the optimization process) can be even more inhomo-
geneous, the problem in this case can be even more severe. For this reason,
we strongly recommend the recommendations of International Commission
on Radiation Units and Measurements (ICRU) Report 78 (23) be followed,
which states that such plans should be normalized to the median or mean
dose to the prescribed target. This is certainly suffcient for SFUD plans, but
there can still be a problem with IMPT plans, particularly when normalizing
to the mean dose because IMPT is most often used in cases where there are
neighboring, dose limiting structures.
The selected target dose is often inevitably compromised in order to attain
the constraint dose in the critical structures. A good example of this is shown
in Figure 11.8. For this reason, at our institute, we normalize IMPT plans by
calculating the mean (or median) dose to the defned target minus all over-
lapping critical structures. Indeed, given that there is always a fnite dose
gradient between the organs at risk (OAR) and the target, we actually defne
an expansion of 2–3 mm around each OAR for which a dose constraint has
been defned and use this as the structure for which the dose is subtracted
during the normalization process.
11.4 OptimizationStrategiesforIMPT
11.4.1 Degeneracy in IMPT Optimization
It will be left to Chapter 15 to deal with optimization theory for proton treat-
ment planning. Nevertheless, a chapter about treatment planning for scan-
ning and IMPT cannot be complete without a discussion about the problem,
and potential, of degeneracy in the optimization process. In basic terms,
degeneracy simply means that there can be many, sometimes quite different
solutions to the specifc optimization problem being solved. In general terms,
degeneracy will decrease as the number of goals and constraints defned in
the optimization process increase. Thus, if the only goal of the optimization
process is to achieve a uniform dose to the target volume, the problem will
be highly degenerate, whereas if the problem is to achieve a suffcient tar-
get coverage while also sparing dose to multiple neighboring critical organs
while also minimizing the total dose to all normal tissues, then clearly, the
degree of degeneracy will rapidly decrease. Indeed, degeneracy has been
recognized for many years in the optimization of IMRT plans (24–27). Given
that for a typical active scanning feld, many thousands of individual Bragg
peaks are available to the optimization process, in most clinical situations,
354 Proton Therapy Physics
the optimization process for IMPT will generally be much more degenerate
than the corresponding IMRT problem.
The concept of degeneracy has led some investigators to propose alterna-
tive methods of planning, and delivering, IMPT-type treatments. For exam-
ple, in Section 11.3.2, the process described for optimizing IMPT plans can be
considered to be the most general approach, as it has the largest number of
Bragg peaks available to the optimization process. Indeed, it has been previ-
ously categorized as 3D-IMPT by Lomax (22), in that the initial Bragg peaks
available to the optimization routine are distributed throughout the target
volume in three dimensions for each feld. In the same publication, however,
three alternative approaches to IMPT were also described, namely 2D, 2.5D,
and distal edge tracking (DET).
The 2D and 2.5D approaches are rather similar in concept and can be dif-
ferentiated simply by the fact that the 2D approach (in which fxed extent
SOBP pencil beams are modulated in the two dimensions orthogonal to
the feld direction) was mainly proposed as a possible method that could
be implemented on existing passive scattering machines. On the other
hand, 2.5D is a special case of the full 3D approach, with the difference
being that the relative fuence of Bragg peaks along the feld direction is
predefned and is not varied as part of the optimization process. Thus, the
2.5D approach is also essentially a 2D modulation, with the main difference
to the 2D approach being that for each pencil beam, mini-SOBPs are defned
that match to the thickness of the target in that position (22). Although to
the author’s knowledge no facility is using or planning to use the 2.5D
approach, it should perhaps not be forgotten, as it could possibly have some
advantages, lying as this technique does somewhere between SFUD and
full 3D-IMPT in complexity.
The last approach is DET, and next to 3D-IMPT it is the IMPT “favor”
that has attracted the most interest in the literature and even by some pro-
ton therapy manufacturers. This approach was frst proposed by Deasy
et al. (28), and the idea is quite simple. Instead of distributing Bragg peaks
throughout the target volume from each direction, each feld only delivers
single Bragg peaks to the distal end of the selected target volume. Through
the application of a number of such felds, the optimization algorithm then
modulates the individual pencil beams (in two dimensions) such that a
homogenous dose across the target can be achieved, even with a surpris-
ingly small number of felds. Indeed, this is the nearest equivalent to IMRT
with photons that is possible with protons. Although it has been suggested
that the DET approach can be very sensitive to delivery uncertainties (29,
30), more recently the opposite has been shown for certain types of cases
(31). In any case, DET has potentially a number of advantages in that of
all the techniques, it uses the smallest number of Bragg peaks/pencil
beams and, at least for centrally positioned tumors, it has been shown to
minimize the delivered integral dose in comparison to the other IMPT
approaches (28, 32).
355 Physics of Treatment Planning Using Scanned Beams
11.4.2 When Less Is More: Field Numbers in IMPT Planning
A special consequence of the degeneracy of the IMPT optimization problem
is its consequence on the selection of feld arrangements and in particular
the number of felds necessary to achieve a clinically acceptable solution.
This has been studied by Stenecker et  al. (33) for a simple head and neck
case. In this work, photon IMRT and IMPT plans were calculated using 3–9
equally spaced felds. In addition, for each feld arrangement and delivery
type, the dose constraints on both parotid glands were successively reduced
for different plans, and the resultant mean dose to these structures then was
plotted against the resulting dose inhomogeneity in the PTV. Such curves
were produced for 5- and 9-feld IMRT plans, and 3-, 5-, and 9-feld IMPT
arrangements. An example of such a plot for one case is shown in Figure
11.9. For IMRT, it is quite clear that, as the number of felds available to the
optimizer increases, the quality of the plans improves. That is, the curve of
parotid dose against PTV dose inhomogeneity moves toward the bottom left
(indicating lower parotid dose and a lower dose heterogeneity in the PTV).
However, it also clearly shows that there is always a “play-off” between
parotid dose and PTV coverage. Even for the nine feld plans, as parotid dose
is reduced, dose heterogeneity in the PTV increases.
For the IMPT plans, however, the results are quite different. To begin
with, for all IMPT plans, the doses to the parotids are always substantially
lower than the IMRT plans for the same (or better) dose homogeneity in the
PTV. More interestingly, and also more relevant to the discussion here, there
seems to be little advantage in moving from 3- to 5- or 9-feld plans. Indeed,
the curves relating parotid and PTV dose are more or less superimposed on
one another, indicating that, at least from the point of view of parotid spar-
ing, 3-feld IMPT plans are just as effective as 9-feld IMPT plans.
As stated at the beginning of this section, this is also a result of the degen-
eracy factor available to 3D-IMPT plans and after a little thought should not
come as a great surprise. After all, we know from SFUD planning that for
not too complex cases, a single actively scanned feld direction can be opti-
mized such that it delivers a more-or-less homogenous dose to the target.
Although the addition of more felds improves dose homogeneity and con-
formation, the gain factor is still only relatively small. The same is true for
the IMPT plans represented in Figure 11.9. The problem for the optimizer in
this case was not too complex (as homogenous a dose as possible across the
PTV while sparing both parotid glands) and thus, as we add in felds, the
problem becomes more and more degenerate. For the case shown, it appears
that just three equally spaced proton feld directions provide enough Bragg
peaks to the optimizer to provide equally good results compared with those
resulting from many more feld directions. This is borne out in clinical prac-
tice at our institute. In the 14 years we have been treating patients using both
SFUD- and IMPT-based proton treatments, we have not yet found it neces-
sary to deliver any more than four felds per plan (34).
356 Proton Therapy Physics
11.4.3 Bragg Peak Numbers, Beam Sizes, and Bragg Peak Placement
For completeness when talking about degeneracy, we should also mention
that, in addition to the position and relative fuence of individual Bragg
peaks, other parameters can potentially be modulated as part of the opti-
mization process. Examples include the number of Bragg peaks, the size of
the pencil beam, and the placement of Bragg peaks in relation to the target
volume. These issues will be briefy reviewed here.
Given that, at least for not too complex treatments, 3D-IMPT and DET
(almost the two extremes of the IMPT spectrum, but see below) can provide
extremely similar dose distributions, there is clearly a whole spectrum of
solutions in between. Searching this solution space could be quite interest-
ing, particularly when only a limited number of feld directions are available
Dose %
a b
c
10%
2
0
.
0
%
2
5
.
0
%
3
0
.
0
%
3
5
.
0
%
4
0
.
0
%
4
5
.
0
%
5
0
.
0
%
5
5
.
0
%
12%
D
1
0
5
-
D
9
5

(
P
T
V

a
t

l
e
v
e
l

o
f

p
a
r
o
t
i
d
s
)
14%
16%
18%
20%
22%
24%
26%
117
110
90
80
70
60
50
30
0
Dose %
123
110
90
80
70
60
50
30
0
Mean bilateral parotid dose
IMRT - 5 Fields
IMRT - 9 Fields
IMPT - 3 Fields
IMPT - 5 Fields
IMPT - 9 Fields
FIGURE 11.9
(Seecolorinsert.)(a and b) Example IMPT (three-feld) and IMRT (nine-feld) plans to a simple
head and neck case. (c) Plots of target dose homogeneity plotted against mean dose to both
parotid glands for different IMRT and IMPT plans. Each point on the plot corresponds to one
plan, consisting of different numbers of felds (indicated by the lines) and decreasing con-
straints on the parotid glands. With IMPT, similar (if not better) target dose homogeneity can
be achieved for much lower doses to the parotids than for any of the IMRT plans, and little
difference is observed between three-, fve-, and nine-feld IMPT plans.
357 Physics of Treatment Planning Using Scanned Beams
or desired (remember that to obtain a uniform dose across the target volume
with the DET approach, a number of angularly spaced felds are required,
because a single DET-type feld can never provide a uniform dose across the
target). For instance, even for an SFUD feld, do we need to have Bragg peaks
distributed completely over the whole target volume? Figure 11.2e shows an
example. After the optimization, the majority of Bragg peaks within the tar-
get have very low relative weights (the white crosses in Figure 11.2e). Do we
need to deliver all these, or are many redundant?
In a study we performed a few years ago, it was found that by building a
spot-reduction option into the optimization algorithm (35, 36) the number of
delivered Bragg peaks could be reduced by up to 85%. When using the same
approach for IMPT (multiple-feld) optimization, the number of Bragg peaks
could be reduced even more, as would be expected perhaps when comparing
the 3D-IMPT and DET approaches. Interestingly however, when applying
the spot reduction approach to a simple cylindrical target volume, it was
even found that DET is not necessarily the optimum approach for reducing
Bragg peak numbers. Figure 11.10 shows the Bragg peak positions resulting
from the spot reduction approach for this case. As can be seen, only dis-
tal Bragg peaks in the central portion of the sphere are actually needed to
ensure a homogenous dose across the target when planning using fve IMPT
felds. The more lateral distal peaks have been successfully removed. For this
solution, 20% fewer Bragg peaks are required than for the DET solution!
a b c
d e
2500 spots per field
IMPHNT_CTO_TO IMPHNT_CTO_TO IMPHNT_CTO_TO
150 spots per field 120 spots per field
f
FIGURE 11.10
(Seecolorinsert.) (a–c) Dose distributions for fve-feld plans to a cylindrical target volume.
(a) 3D-IMPT; (b) DET; (c) using the spot-reduction algorithm explained in the text. (d–f) The
corresponding Bragg peak positions and weights for the posterior feld of each plan only, with
the colors representing the relative weight of the individual Bragg peaks. The correspond-
ing number of non-zero weighted Bragg peaks for each approach is also shown. Using a spot
reduction scheme directly in the optimizer, a substantial reduction in the number of Bragg
peaks required for dose coverage can be achieved, and this approach even fnds a solution
where fewer Bragg peaks than the DET approach are required (120 peaks per feld as opposed
to 150 peaks per feld for the DET approach).
358 Proton Therapy Physics
So, do such methods for reducing the number of Bragg peaks bring any
advantages from the point of view of delivery? Surprisingly, not as much
as one may expect. When the potential reduction in delivery time for these
cases was calculated (and subsequently measured) it was found that the
reduction in delivery time for 80% reduction in the number of delivered
Bragg peaks was only of the order of 6%. When analyzed, this was found to
be due to the fact that, although the total dead time for the feld (the time to
move from Bragg peak to Bragg peak position) was somewhat reduced, this
only accounts for about 40% of the total treatment time (at least on our deliv-
ery system), whereas the total beam-on time (i.e., the total number of protons
that have to be delivered) remains the same. That is, although the number of
Bragg peaks can be signifcantly reduced, the average fuence per delivered
Bragg peak increases. This is of course also the case for DET plans. On the
other hand, reduced numbers of delivered Bragg peaks per feld could have
some indirect advantages from the point-of-view of delivery. As the average
fuence per delivered pencil beam increases, this could allow one to deliver
the treatment using higher beam intensities. This in turn would result in
signifcant reductions in the time required to deliver each feld.
On a similar note, it is often discussed whether there are any advantages
to varying the lateral beam size within a delivered feld, rather than using a
constant beam size. Again, using Figure 11.2d above as an example, the argu-
ment goes as follows. If we have so many low-weighted Bragg peaks flling
in the dose in the central and proximal portion of the target volume, is it
not possible to replace at least some of these with a much smaller number of
larger Bragg peak or pencil beams? In principle the answer is likely to be yes,
at least to a point. However, this author is not convinced that the quality of
the resulting plan can ever be as good as that resulting from the delivery of
many smaller Bragg peaks and is also not completely convinced that such an
approach brings much in the way of advantages. In principle, using varying
beam sizes is similar in concept to the Bragg peak reduction schemes dis-
cussed above. In the end, at least with a constant intensity source, the total
number of protons that need to be delivered will be about the same, with the
only gain coming from a possible reduction in the dead time for the treat-
ment, as less pencil beams need to be delivered. If intensity can be varied
however, then perhaps, as with Bragg peak reduction, some more gains could
be made. Despite some reservations about the usefulness of this approach, it
is nevertheless an undoubtedly interesting area for future research.
Finally in this section, I will discuss Bragg peak placement as a planning
parameter for SFUD and IMPT planning. In Figure 11.2b, the Bragg peaks
(indicated by the crosses) have been calculated and selected based on a regu-
lar (and rectilinear) starting grid. That is, orthogonal to the direction of the
incident feld, the delivered pencil beams are separated by 5 mm in both
directions. Also, in depth, although the Bragg peaks are irregularly spaced
in the patient (due to the differences in densities through different parts of
the patient), they are nevertheless regularly spaced in water equivalent depth
359 Physics of Treatment Planning Using Scanned Beams
(in the case of Figure 11.2d, with a separation of 0.46 cm). As the Bragg peaks
are distributed on such a grid, the consequence is that, in order to cover the
selected target volume completely, Bragg peaks up to 5 mm outside of the
selected target volume have to be selected as well, as are clearly visible in
Figure 11.2d. If these additional external Bragg peaks are not selected, then,
in the worse case, the nearest Bragg peak to the surface of the target volume
could be up to 5 mm inside the target volume, with obvious consequences
for dose coverage of the target (see Figure 11.11a). Thus, although a rectilin-
ear placement of Bragg peaks is certainly the simplest, it is not necessarily
the best.
As an alternative, one can imagine selectively placing Bragg peaks directly
on the surface of the target volume and then flling-in the remaining Bragg
peaks internally to the target as required (in this case on an irregular grid,
see, e.g., Figure 11.11b). Such an approach should certainly improve dose fall-
off outside the target volume and could potentially lead to a more effcient
delivery. However, to achieve this, a fne spatial resolution is required in the
placing of pencil beams both orthogonally to the feld direction (which with
modern magnets should not be too challenging) but also in depth, which
requires a fne resolution in the energy selection system. Nevertheless,
irregular and contour-based Bragg peak positioning will certainly be a
a
b
FIGURE 11.11
A schematic comparison of spot placement on a rectilinear and regular grid (a) and the gain
that could be achieved by “optimizing” Bragg peak/pencil beams such that placement is per-
formed frst on the target surface, and then pencil beams/Bragg peaks are “flled-in” in the
internal region (b). In theory, this should signifcantly improve penumbra around the target
volume.
360 Proton Therapy Physics
requirement and perhaps will even be standard in future active scanning
delivery and treatment-planning systems.
11.4.4 The Importance of Starting Conditions in IMPT Optimization
In the previous sections, we have looked at various consequences of degen-
eracy in IMPT planning. Whether this is forcing the solution to one requiring
fewer delivered Bragg peaks (as in the DET approach) or the fact that in some
circumstances satisfactory plans can be achieved with small number of felds,
I hope that it is clear that there are many different solutions to the IMPT prob-
lem that give similar dose distributions. So how do we search this immense
space of possible solutions, or indeed how do we decide which of the many
similar solutions we actually want for our fnal plan? (See also Chapter 15.)
Hard core optimizers will argue that a comprehensive optimizer will fnd
any of these solutions if suffcient constraints to the optimization algorithm
are defned, and the answer we achieve should be driven by defning the
full problem to the optimizing engine. There is certainly much merit in this
approach. However, one could also ask, why let the optimizer do this (with
the associated time-cost function) when in many cases, it is absolutely clear
that the optimization can be helped by defning starting conditions? The
specifc solution of DET is, after all, achieved by defning the starting condi-
tions as being just those Bragg peaks that are delivered to the distal edge of
the target, and de-selecting (or not selecting at all) the Bragg peaks inter-
nal to the target volume. However, the DET solution is just a special case of
3D-IMPT, and if this is indeed the most optimal result (or the most desired),
then a good optimizer should be able to fnd its way to this solution. Such an
approach was attempted in our example of spot reduction above. By adding
a spot reduction algorithm to the optimization, we could show that the solu-
tion could be driven toward the DET solution, and even beyond (see Figure
11.10). So why is DET still referred to as a particular approach? Because, in
the end, it is much easier to get to the DET solution by defning the start-
ing conditions of the optimization than to start with a full 3D distribution
of Bragg peaks across the target (or why not across the whole patient?) and
then to get the optimizing algorithm to work out that DET is the result that
is required. In other words, the defnition of starting conditions for the IMPT
optimization is a way in which the user (the treatment planner) can already
impart his or her knowledge of the case or of previous similar cases in order
to achieve the desired result.
As in other chapters of this book, the reader will certainly fnd counter
arguments to this, let’s have a look at the starting condition issue in some-
what more detail.
Although many sophisticated optimization algorithms are available
(Chapter 15), it is still very much the case that many of the optimization
algorithms used in commercial and research treatment-planning systems
are rather simple in concept. Although there are certainly exceptions, most
361 Physics of Treatment Planning Using Scanned Beams
algorithms are gradient based and are based on rather simple dose or dose-
volume constraints to the target volume (or volumes) and multiple OAR’s.
Given that the problem for the optimizer is then overdefned (or degener-
ate), such algorithms will inevitably fnd the nearest solution to the starting
conditions that best fts all the constraints. There is no reason for it to do
anything else, as the algorithm will likely fnd the nearest local minimum in
the solution space. Thus, in many systems, a defnition of the starting condi-
tions is a “must” for users if they want to impose other conditions on the
fnal plan.
Take as an example Figure 11.12, which shows a schematic representation of
a simple two-feld, parallel opposed plan to a centrally placed target volume.
Now, let’s assume that the only constraint for this plan is to obtain a homog-
enous dose across the target volume and that we are going to perform an
IMPT plan as defned in Section 11.3.2 (i.e., the Bragg peaks from both felds
will be simultaneously optimized and the only requirement is that the dose
a
b
c
"flat SOBP"
"gradient SOBP"
Individual
Bragg peaks
Individual
Bragg peaks
FIGURE 11.12
A schematic representation of two possible solutions to the defnition of Bragg peak weights
along the beam direction for a simple, parallel opposed feld plan. (a) The resulting dose profle
along the beam direction as a result of the use of a set of preweighted Bragg peaks delivering a
mini-SOBP along the feld direction. (b) The dose profle resulting from the same optimization
of the same felds, but assuming that the frst “guess” for Bragg peak weights along the beam
direction is a constant set of weights. (c) The dose profles from the two solutions superim-
posed on top of each other.
362 Proton Therapy Physics
from both plans combine to deliver a homogenous dose across the target vol-
ume). Figure 11.12a shows one possible solution for this problem. As a starting
condition for both felds, a set of Bragg peaks has been used that is already
weighted such that the resultant dose profle in depth is a mini-SOBP. It is
clear then, that when these two felds combine, the resulting dose will already
be very close to uniform across the target, and the optimizer will perhaps only
have to fne-tune Bragg peak weights in order to achieve the desired result.
In the case of Figure 11.12b, the initial set of Bragg peak weights has been
defned such that the weights are the same regardless of their relative depth
along the beam direction (i.e., all Bragg peaks have the same initial relative
weight). If we calculate the resultant depth–dose curve for such a weight-
ing, then this actually gives a linear wedge profle in depth, with the maxi-
mum dose at the proximal end and the dose reducing toward the distal end.
However, the feld from the opposite side has a similar arrangement, and when
both are combined, similarly to Figure 11.12a, the resultant dose across the
target volume is once again more-or-less uniform. Again, the optimizer has
to do little work in order to obtain a uniform dose across the target. Indeed,
if target dose uniformity is the only criterion for the optimization (as stated
above), the optimizer in the second case has no reason to do anything else.
So in Figure 11.12 we have two possible IMPT solutions for delivering a
uniform dose to the target volume. Are they equivalent? Well, yes and no.
They are equivalent if one is only interested in target dose uniformity, but
not in other aspects. Take for example Figure 11.12c, where we have overlaid
the combined dose profles of the two felds on top of each other and have
normalized them such that the dose to the target is the same. It is now clear
that in the entrance regions of the two felds, there is a clear difference in
dose between the two solutions. Solution A (the predefned SOBP approach)
results in a signifcantly lower dose in the entrance channels than solution
B (the constant weight approach), and I think most readers will agree that
solution A is the more desirable.
If the example shown above appears to be rather artifcial, then consider
Figure 11.13, which shows two plans for a prostate case, using conventional
feld directions (parallel opposed lateral felds) for prostate treatments with
proton therapy (37). The plan in Figure 11.13a and c, has been optimized using
the mini-SOBP starting conditions described above, whereas in Figure 11.13b
and d, the plan uses the constant weight approach, also described above.
Despite similar coverage and dose uniformity in the target, the additional
dose in the entrance channel for the constant weight approach is clearly visi-
ble in comparison to the mini-SOBP approach. Figure 11.13c and d, shows the
single-feld distributions for the right-hand feld of each plan after optimiza-
tion. Because of the irregular nature of the target volume, although there is
some clear variation of dose across the target for both felds, there is never-
theless a clear trend in the two felds. The mini-SOBP approach has resulted
in a relatively uniform coverage of the target from the single feld (similar
to the result one would expect from using the SFUD approach), whereas the
363 Physics of Treatment Planning Using Scanned Beams
constant weight approach results in a single-feld distribution with a clear
dose gradient from the proximal-to-distal end of the target, demonstrating
an in-depth profle similar to that shown in Figure 11.12b.
The dose distributions in Figure 11.13 have been calculated using the opti-
mization algorithm of the PSI planning system (22, 36), which is a gradient-
based method. However, such felds have been calculated by the author on at
least two commercial systems with similar results, indicating that the choice
of starting conditions can be an important issue. Indeed, even if a more
sophisticated optimizer (e.g., one that fnds a global minimum) is used, the
result will be the same if target uniformity is the only defned goal. To get
to solution A (if starting from solution B), one has to defne more parameters
about the dose to the normal tissues. For the example described here, this
would certainly make sense, but the point is, a sophisticated optimization
engine is only as good as the input parameters (constraints) defned for it.
So if we did want to get to a DET solution, what would we defne to the
optimizer? If we wanted to use larger spots in the internal portion of the tar-
get, how would this be expressed? If we only want to use two felds instead
of four, how do we incorporate this into the optimizer? This is not to say that
these cannot be done through optimization alone, but only is to emphasize
%
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FIGURE 11.13
(See color insert.) Dose distributions for the complete plans and one example feld for lat-
eral opposed feld plans for a prostate case, (a and b) calculated using the preweighted, SOBP
approach and (c and d) calculated using the constant weight approach. As in Figure 11.12, the
constant weight approach leads to single-feld distributions with a clear and distinct dose gra-
dient from the proximal to distal end. This in turn leads to a clear increased dose to the normal
tissues lateral to the target volume in comparison to the preweighted approach.
364 Proton Therapy Physics
that for many cases the defnition of starting conditions is a logical and per-
haps somewhat easier approach to achieving the desired result.
11.5 DealingwithUncertainties
Having looked in some detail at some of the characteristics of the optimiza-
tion problem for IMPT, and in particular at the problems, and potential, of
degeneracy, I now move on to a potential area where that degeneracy could
well be utilized to advantage: to help design plans that are robust to poten-
tial delivery errors (see Chapters 13–15).
11.5.1 Magritte’s Apple
A famous painting by Belgian artist Rene Magritte is entitled Ceci n’est
pas une pomme (This Is Not an Apple). Although the image is clearly a very
beautiful painting of an apple, Magritte’s point was exactly that—it is just
a painting of an apple and not a real apple. In many ways, the same can be
said of dose distributions calculated (and displayed) by treatment-planning
systems. Although they are quite accurate representations of the estimated
deposited dose, they are exactly that: just representations and estimates.
What will actually be delivered to the patient will be, at many different lev-
els, inevitably different. Thus, a dose distribution displayed by a treatment-
planning system is just an image of the (to be) delivered dose and is not the
true delivered dose.
This may all seem overly pedantic, but an appreciation of how a treatment
may vary from that calculated by the treatment-planning system is an impor-
tant criteria in designing and evaluating treatment plans, and every type of
treatment will be subject to many, very different treatment uncertainties. In
this section, we will look at different ways of dealing with such uncertain-
ties and how to analyze and display these when analyzing treatment plans.
11.5.2 Sources of Delivery Uncertainties
Before looking at the management of uncertainties, let’s frst look at the pos-
sible uncertainties associated with modern radiotherapy, and in particular,
proton therapy. These can be divided into four categories: clinical, spatial,
calculational, and delivery based.
Clinical uncertainties result from initial diagnosis through to the def-
nition of the target volume to be irradiated. Although certainly one of the
potentially most grave uncertainties would be a complete misdiagnosis of
a tumor, there is little that can be done at the treatment planning/deliv-
ery stage to rectify this, so we will skip over this. The other main clinical
365 Physics of Treatment Planning Using Scanned Beams
uncertainty is uncertainty in the defnition of the target volumes and critical
structures. Again, although it has been well documented that this could be
one of the largest sources of uncertainty in radiotherapy, various tools such
as multimodality imaging and fusion, international standards on the defni-
tion of target volumes (i.e., GTV/CTV concepts) hopefully help to keep these
to a minimum (38, 39). In any case, once the targets and OARs have been
defned, it is the author’s opinion that these have to be accepted as correct,
and then it is the treatment planner’s job to design a plan that best meets the
criteria defned by the responsible clinician.
So let’s move onto the second category of errors: spatial errors. These can
come from errors and uncertainties in the imaging process such as image
distortions (although with modern imaging equipment this is perhaps less
of a problem nowadays than a few years ago); however, more relevant from
the point of view of treatment planning and delivery, is the impossibility of
positioning a patient in exactly the same place every day of a fractionated
treatment and the impossibility of keeping a patient perfectly still for the
duration of each delivered fraction. Depending on the site being treated, the
type of immobilization used, and the patients themselves, these errors can
easily be the order of millimeters to centimeters in magnitude and need to
be seriously considered in the planning process. Although many values can
be found for these errors in the literature, they are largely of little use, as
positioning errors will be very dependent on the working practices of each
individual center. Nevertheless, such errors can (and should) be separated
into random errors (those that vary day to day with a resulting spread of
values over the whole treatment) and systematic errors (those that may be
the same for every fraction). The reason to separate these different types of
uncertainty is simple. Random errors will generally have a blurring effect,
whereas systematic errors can lead to large, constant errors. From the point
of view of uncertainty management, systematic errors are by far the most
important, and particularly for proton therapy, there is an additional spatial
error that needs to be considered, exactly because in most circumstances it
is a systematic error. That is, the uncertainty in the range of protons in the
patient. In other words, the uncertainty in where the Bragg peak actually
stops. The sources and estimated magnitudes of these uncertainties are cov-
ered in detail in Chapter 13, but they can easily reach 3% from imaging and
calibration uncertainties alone (40, 41) and much greater values when taking
into account reconstruction artifacts due to metal implants or changes in
patient anatomy (42, 43).
11.5.3 To PTV or Not to PTV? That Is the Question
Uncertainty management is nothing new in radiotherapy. In the 1980s,
Goitein and coworkers recommended including error estimates as part of the
routine planning process, in the form of maximum and minimum plans in
addition to the nominal distribution, to encapsulate possible variations of the
366 Proton Therapy Physics
dose distribution about the nominal values (44, 45). Unfortunately these ideas
were never successfully incorporated into commercial treatment- planning
systems, and these innovative ideas have not as yet caught on. Instead, uncer-
tainties have been managed using the concept of the PTV as defned in ICRU
reports 50 and 62 (38, 39), where the PTV is defned as a spatial expansion
of the clinical or gross tumor volume, with the margin for the expansion
being defned by the likely uncertainties associated with the treatments.
This has led to the concept of margin recipes, where statistical analysis has
been applied to the PTV expansion concept in order to more precisely defne
(and standardize) margin expansions. The most well known of these is that
defned by van Herk et al. (46), which defnes the margin based on a separa-
tion of the uncertainties into random and systematic components. However,
most of this work has been concentrated on photon-type treatments, and little
work has been published for margin recipes for proton therapy.
However, should there be a difference between PTV defnitions and mar-
gin recipes between proton and photon therapy? The answer is certainly
yes. The problem lies in the additional uncertainty relating to the calculation
of the range. Although the effect of positioning errors on the PTV in proton
therapy are similar to those for conventional therapy (after all, there should
not be any difference in random and systematic positioning uncertainties
between different treatment modalities if the same fxation devices are used),
there is essentially no concept of range uncertainty in photon therapy. As
noted above, range uncertainty is almost certainly systematic in nature, and
there is no reason to believe that the magnitude of uncertainties in range are
the same as (or are even correlated to) the positioning uncertainties orthogo-
nal to the beam direction. Thus, because range uncertainties will be different
from and most likely larger than positional errors, and additionally range
errors are likely to be systematic, a signifcantly different margin expansion
for the PTV will be required at the distal end of the target than lateral to the
feld direction. Consequently, a single PTV expansion for the whole target
that is valid for all felds is not necessarily valid for proton therapy. Much
more likely is that a feld-specifc PTV is required, with a different expan-
sion being used along the beam direction to that laterally. Very few (if any)
planning systems allow for such an expansion. Indeed, most facilities with
passive scattering take a very different approach for exactly this reason. As
described by Moyers et  al. (47), the typical approach to allowing for errors
is to expand the aperture lateral to the feld by an amount determined from
the estimated positional errors, while modifying the compensator by shav-
ing-off a fxed amount of material to ensure a controlled overshoot of Bragg
peaks at the distal end. The amount shaved-off is then determined from the
estimated uncertainties associated with the range. As the two uncertainties
are dealt with differently, and independently, then this approach is equiv-
alent to a feld-specifc PTV, without actually defning a PTV. Indeed, it is
important to realize that when building the margins into the feld-specifc
hardware devices (apertures and compensators), a PTV should not be used,
367 Physics of Treatment Planning Using Scanned Beams
because the uncertainty management is built directly into the feld hardware
rather than being incorporated into a target volume expansion.
For scanning, the approach adopted for passive scattering is not valid
because generally, and as discussed above, scanning does not require feld-
specifc apertures or collimators. Thus, other methods of uncertainty man-
agement need to be adopted. At PSI, we use a single PTV expansion similar
to conventional therapy, with the margin mainly being determined either by
an assessment of the positioning errors or from the range uncertainties (48).
However, this is not necessarily the best approach. For instance, if the PTV
concept is to be used, then it would be more reasonable to defne a PTV per
feld (as described above), as this is the nearest analog to the approach gener-
ally adopted for passive scattering.
Alternatively, it is conceivable that the PTV concept is preserved to deal
with positional errors, and other methods are adopted for the range errors.
We have previously looked into the possibility of building range uncertainty
into the optimization, by simply performing the Bragg peak selection and
optimization on a modifed CT data set in which all CT voxels have an arti-
fcially increased Hounsfeld unit (HU) value (e.g., by +3%, the estimated
uncertainty in the range). When the optimized set of Bragg peaks are then
used to calculate the fnal dose on the nominal, unmodifed CT, this leads to
a systematic overshoot of the dose to the PTV by about 3%. An example of
this approach is shown in Figure 11.14a. This SFUD plan has been calculated
to a PTV expanded by 3 mm around the CTV and with a planned overshoot
of 3%. This can be compared to a plan with an isotropic margin expansion of
5 mm (our typical value for such a case) for which no planned overshoot was
used (Figure 11.14b). The 3-mm expansion with planned overshoot delivers a
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FIGURE 11.14
(Seecolorinsert.) (a) An SFUD plan calculated using an isotropic PTV margin of 5mm, with-
out planned overshoot. (b) The same case calculated using a “planned overshoot” of 3% and an
isotropic margin of 3mm (see text for fuller description of this technique). For plan a, there is a
reduction in the amount of normal tissue irradiated (best seen by comparing the 30% and 40%
isodose edges between the two panels), but the planned-overshoot technique with the 3-mm
margin has also been shown to be at least as robust to potential range uncertainties as using
the larger PTV margin.
368 Proton Therapy Physics
lower dose to the normal tissues than the 5-mm expansion, while being just
as robust to both positional and range errors as the 5-mm expansion. For this
case, the differences are not huge, but this should illustrate that there is still
a lot of work to be done in the development of PTV concepts for scanning
proton therapy.
11.5.4 Robust Optimization
The concept of planned overshoot described above is essentially a “trick” in
the optimization to “fool” the algorithm that all tissue densities are some-
what more dense than in reality. However, would it not be more elegant to
incorporate all delivery uncertainties into the optimization, such that the
degeneracy of the optimization problem can be utilized to generate funda-
mentally “robust” plans? This is an area that is attracting more and more
interest in the literature in the form of robust optimization. There are two
approaches, in analog to the discussion about optimization above. One is by
manipulating the starting conditions of the optimization in order to point
the optimization in the correct direction toward a robust solution; the other
is to incorporate uncertainties directly into the optimization process itself
(49–51). The latter of these is covered in more detail in Chapter 15, and will
not be described further here. We will thus concentrate in this chapter on
robust planning through manipulation of the starting conditions of the opti-
mization process.
In a previous publication, we have shown that, even for extremely simple
cases, IMPT plans can be less robust than SFUD plans for the same case, at
least to range uncertainties (30). However, in the frst IMPT case reported in
the literature, IMPT was actually used to improve plan robustness against that
that could be achieved with a single SFUD feld plan (52). For this case, the full
target volume was split into two subvolumes, with each feld of the three-feld
plan covering a different subvolume. The way in which these subvolumes
were defned resulted in a solution in which no highly weighted Bragg peaks
were delivered against the spinal cord, which lay at the distal end of the PTV.
Consequently, even if range errors of 10% were assumed, the IMPT plan still
kept the spinal cord below the defned tolerance, whereas a single SFUD feld
applied to the same PTV under the same error conditions would overirradiate
the spinal cord signifcantly.
The defnition of these subvolumes was, of course, essentially a defnition
of the starting conditions for the optimization that ensured a robust solution.
Indeed, this approach to robustness is not new. It is exactly the same concept
that is used in feld patching in passive scattering, where many felds are
patched around a critical structure in order to avoid using the steep distal
falloff of the Bragg peak that will be particularly sensitive to range errors.
More recently, we have studied the relative robustness of 3D-IMPT and DET
plans to a number of different uncertainties (29, 30) and found, at least for the
cases studied, that 3D-IMPT was generally more robust than DET and that
369 Physics of Treatment Planning Using Scanned Beams
the more complex the IMPT plan (i.e., the more modulation there is in each
IMPT feld) the more sensitive (less robust) is the plan. This work has been
followed up by Albertini, Hug, and Lomax (31), who have investigated the
relative robustness of different IMPT favors through the manipulation of the
starting conditions for a number of different cases. In that work, it is shown
that clear differences in the robustness of the plans can be demonstrated,
but also that 3D-IMPT is not always necessarily better than DET. Depending
on the geometry of the case, DET could sometimes give a more robust plan
(at least to range uncertainty) because in some cases, neighboring critical
structures are spared only using the lateral edge of delivered pencil beams,
and not the distal edge, as is sometimes the case for the 3D-IMPT approach.
Although this may sound confusing and maybe makes the choice between
different IMPT techniques seem rather diffcult, it is hoped that these studies
can provide pointers to case solutions that, depending on the geometry of the
cases being planned can be defned, will allow the planner to make informed
decisions about the type of IMPT to use in order to make a robust plan.
11.5.5 Tools for Evaluating Plan Robustness
As outlined in the previous section, robust planning and optimization is a
growing area of research in proton therapy. It is therefore interesting to note
that, despite these developments, there is still little in the way of tools for
actually evaluating the robustness of a plan. Given the importance put on
this aspect in this chapter, and in the proton therapy community generally,
this is a rather strange omission. As has already been mentioned, such tools
were suggested by Goitein in the 1980s (44), but have unfortunately not been
generally adopted. However, given the complexity of (in particular) IMPT
plans, it seems to the author that simple tools for evaluating the robustness
of treatment plans should be standard tools in any treatment-planning sys-
tem. Without such tools, how can the effcacy of robust planning techniques
actually be determined? Or how will it be possible, in the degenerate world
of IMPT planning, to differentiate between two IMPT solutions with very
similar resulting dose distributions but for which robustness may be very
different (i.e., between a 3D and DET-type solution)?
In the last few years, we have tried to follow on from the work of Goitein
et  al. (44) and develop tools for representing robustness to the treatment
planner. The worse-case distribution has already been mentioned above
(29, 53). More recently, we have developed the concept of error-bar distribu-
tions, which essentially display as a 3D distribution the width of the two-
sided error bar associated with the nominal dose at every point of the 3D
distribution. The full details of this approach can be found in Albertini, Hug,
and Lomax (54), and just one example will be shown here.
Figure 11.15a and b, shows the nominal dose distributions of two plans
to a paraspinal case; one is an SFUD plan (a and c), the other an IMPT plan
(b  and  d). Field directions for the two cases are the same. Figure 11.15, c
370 Proton Therapy Physics
and  d, shows the resultant error-bar distributions, which here are the so-
called composite distributions that combine the possible random effects of
positional spatial errors with the systematic effects of range errors into a
single error distribution. In these fgures, the colors now show the possible
variation in dose at each point about the nominal value and within a certain
confdence limit (in this case the 85% confdence limit). In a similar way to
dose distributions, cumulative error bar–volume histograms (EVHs) can also
be calculated for any delineated structure, which then indicate the amount
of dose variance that can be anticipated in any structure. These can be inter-
preted like normal tissue DVHs, in that the more the curves are toward the
bottom left-hand corner of the plot, the less dose variance there will be in
that structure and the more robust is the plan for this structure. The cor-
responding EVH plots for the two plans shown in Figure 11.15 are shown in
Figure 11.16.
%
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c d
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FIGURE 11.15
(Seecolorinsert.) Example application of “error-bar” distributions to display potential dose
errors for proton treatment plans. (a) A three-feld (1 lateral and 2 superior lateral obliques)
SFUD plan to a skull base chordoma. (b) A four-feld (right and left lateral anterior and poste-
rior oblique) IMPT plan to the same case with a strict dose constraint on the brainstem. (c and
d) Composite error-bar distributions for the two plans, which combine random and systematic
errors into a single error-bar distribution (see text for a fuller explanation). The potential varia-
tion of dose within the CTV (inner yellow contour) for the IMPT is clearly much higher than
that for the SFUD plan, whereas the opposite is true for the brainstem (spared in the optimiza-
tion process for the IMPT plan).
371 Physics of Treatment Planning Using Scanned Beams
There are some subtle, but maybe signifcant differences in the dose vari-
ance distributions. Directly at the border of the high-dose region with the
brainstem, the dose variance of the IMPT plan is actually somewhat smaller
than that of the SFUD plan, indicating that the IMPT plan could, in this
case, be a little more robust than the SFUD plan when considering dose to
the brainstem. This is confrmed somewhat by the EVHs, where the IMPT
reduces the volume of the brainstem that could experience large dose vari-
ances. Although it could be argued that the differences here are insignif-
cant, this example has been chosen for the following reason. The variance
distributions are clearly different, indicating that there could well be dif-
ferences in the robustness of the two plans to delivery errors and that such
differences can never be inferred from the nominal dose distributions alone.
Only when looking at the variance distributions do some differences become
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FIGURE 11.16
Example error-bar–volume histograms (EVHs) for the CTV (a) and brainstem (b) of the two
plans shown in Figure 11.15. As with conventional DVHs for critical structures, EVHs that are
toward the bottom left-hand corner of the plot are more robust (less dose variation at a given
volume) than EVH curves toward the top right. The EVH plots clearly show that within the
CTV, the SFUD plan is far more robust than the IMPT plan, whereas in the brainstem, the IMPT
plan is a little more robust than the SFUD approach.
372 Proton Therapy Physics
apparent, perhaps then aiding the decision process on which of these two
plans is preferable. In other words, evaluating robustness using tools such as
those suggested here provide an additional criterion by which the planner
can more accurately navigate through the degenerate world of SFUD and
IMPT plans.
11.6 CaseStudies
To fnish this chapter, I will briefy present two typical cases that have been
treated using SFUD and IMPT at PSI, in order to give the reader a favor of
what can be achieved using active scanned proton therapy.
11.6.1 Case 1: Nasopharynx Carcinoma
The frst case is a sinonasal undifferentiated carcinoma. Figure 11.17 shows
two slices through the PTV1 at the level of the eyes and optic structures. The
volume of PTV1 is 300 ml and of PTV2 284 ml. The prescription for the case
was 54Gy(RBE) to PTV1 and 70 Gy(RBE) to PTV2. As with all our plans, a
global RBE value of 1.1 has been assumed. Figure 11.17 shows two of three
series and the composite dose (the combined dose from all plans) delivered to
this patient. Plan 1 is an SFUD plan to PTV1 (delivered from 0 to 30Gy[RBE]),
whereas plan 2 is an IMPT plan to PTV1 with dose constraints defned to
the brainstem, optic structures, and cochleae (30–54Gy[RBE]). Plan 3 (not
shown) is an IMPT plan to PTV2, with the same dose constraints to the same
OARs as for plan 2. Four felds were used for each plan using the same feld
geometry for all plans: right and left lateral beams with a 15° table kick, an
anterior-superior oblique feld, and a posterior-superior oblique feld.
Even for the large and rather complicated PTV1, the SFUD frst series plan
provides a relatively homogenous and conformal plan. The PTV is well
encompassed by the 95% dose level (the red color wash in the fgure), and
there is a good dose homogeneity (absolute maximum dose in the plan is
107%). For the second series plan (Figure 11.17, c and d), an IMPT plan cal-
culated to PTV1 was used to already start pulling dose off the main dose
limiting critical structures (those to which a dose constraint was defned
in the IMPT plan), as can be clearly seen in the slice between the eyes, as
well as somewhat in the region of the brainstem and cochleae. In addition,
because of the selective sparing of the critical structures, the maximum dose
in the plan increased a little (from 108 to 114%), which is typical for such
IMPT plans. This was somewhat more increased in the third series IMPT
plan, despite the fact that the constraints and feld geometry are identical.
However, this is a feature that we often see with our IMPT plans when the
volume reduces somewhat. Nevertheless, this plan is perfectly acceptable.
373 Physics of Treatment Planning Using Scanned Beams
The fnal, composite distribution shown in Figure 11.17, e and f, indicates the
quality of the full treatment, which provides precision, homogeneity, and
conformality to a particularly large and complex tumor situated between a
number of sensitive critical structures.
11.6.2 Case 2: Sacral Chordoma
Figure 11.18 shows the individual series plan and composite treatment for a
relapsing sacral chordoma. The PTV in this case is 1.4 liters, and this volume
was treated to a total of 74 Gy(RBE) using two series. The frst series (Figure
11.18, a and b) is a two-feld SFUD plan using angles of ±15° away from the
%
a b
c d
e f
107
95
90
80
70
60
50
30
0
%
107
95
90
80
70
60
50
30
0
%
114
95
90
80
70
60
50
30
0
%
114
95
90
80
70
60
50
30
0
%
110
95
90
80
70
60
50
30
0
%
110
95
90
80
70
60
50
30
0
FIGURE 11.17
(See color insert.) Case study 1: sinonasal undifferentiated carcinoma. (a and b) Two slices
through the frst series, four-feld SFUD plan (0.0–30.0 Gy). (c and d) The same slices through
the second series, four-feld IMPT plan (30.0–54.0 Gy). (e and f) The composite dose for the com-
plete treatment (up to 70 Gy) including a third series to PTV2 from 54.0 to 70.0 Gy (not shown).
374 Proton Therapy Physics
vertical (posterior) and that was delivered from 0 to 36 Gy(RBE). Again, two
different slices through this complex case are shown, the frst rather more
superior and at the level of the cauda equina, and the second more inferior
and at the level of the rectum. Note the almost total sparing of dose in the
abdominal region and pelvic space.
Figure 11.18, c and d, shows the second series IMPT plan, delivered from
36 to 74 Gy(RBE). This is also a two-feld plan, but with the felds now sepa-
rated from the vertical (posterior) by ±30°. In this case, IMPT has been used
in order to reduce the dose to the cauda and the nerve roots, which are
visible just anterior to the cauda. The ability to form donut-like dose holes
around centrally spaced critical structures from an extremely narrow feld
%
a b
c d
e f
110
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
%
116
95
90
80
70
50
60
30
0
%
116
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
FIGURE 11.18
(See color insert.) Case study 2: a relapsing sacral chordoma. (a and b) Two slices through
the frst series, two-feld SFUD plan (0.0–36.0 Gy[RBE]). (c and d) The same slices through the
second series two-feld IMPT plan (36.0–74.0 Gy[RBE]). (e and f) The composite dose for the
complete treatment (74.0 Gy[RBE]).
375 Physics of Treatment Planning Using Scanned Beams
arrangement is a unique ability of IMPT. Even in this case, the doses to the
abdomen, rectum, and pelvic space are extremely low. Finally, Figure 11.18,
e and f, shows the composite dose distribution for the whole treatment (to 74
Gy[RBE]).
This case graphically illustrates the power of scanned proton therapy
for delivering highly conformal dose distributions to large volumes while
minimizing the integral dose to all normal tissues outside of the target vol-
ume, and its ability to selectively spare smaller critical structures embedded
directly in the target volume with the use of very small numbers of felds.
Indeed, this allows for very large doses to be delivered to large volumes with
little in the way of acute side effects to the patient.
11.7 Summary
Proton therapy is currently experiencing what can only be called a boom
period. Particularly in Europe and the United States, a number of hospital-
based sites are nearing completion, are in a late stage of planning, or are
currently being seriously discussed. In Japan, many centers are already
operational and are well established. Although at the time of writing, the
vast majority of centers are mainly based on the passive scattering approach,
and only four centers worldwide are currently treating with scanned proton
beams (PSI, Villigen, Switzerland; University of Texas MD Anderson Cancer
Treatment Center, Houston, TX; Rinecker Proton Therapy Center, Munich,
Germany; and Massachusetts General Hospital, Boston, MA), of the new cen-
ters currently being planned, many are planning on either treating a substan-
tial number of their patients using scanning or treatment will be exclusively
based on scanning. The reasons for this are clear. As we have tried to outline
in this chapter, scanning provides the most fexible method for delivering
proton therapy, either for achieving improved dose conformation per feld
or, perhaps more importantly, allowing for IMPT. The latter approach truly
allows the treatment planner to fully exploit the advantageous characteris-
tics of protons in ways that are not possible with photon-based techniques or
with passive scattering (see, e.g., case study 2 in Section 11.6.2).
However, as we have also tried to explain here, this fexibility does not
come without consequence. In particular, great attention must be paid to the
characteristics of the delivery device in order to get the most out of scan-
ning. Clearly, because the maximum lateral penumbra that can be achieved
is determined on the scanned pencil beam size, it is imperative that the
delivery machine minimizes this as much as possible. In addition, and
as described in detail in Section 11.2.7, much attention must also be paid
to the problem of the delivery of superfcial Bragg peaks, a problem sadly
overlooked by many manufacturers. Then in treatment planning, given the
376 Proton Therapy Physics
degeneracy of the problem, there is a great potential for either exploiting
this to the maximum or ignoring this and leaving the user frustrated with
suboptimal plans. Although it is tempting to think that existing IMRT opti-
mization methods will suffce for scanned protons, the additional degrees
of freedom available to the optimizer, together with the characteristics of
protons mean that already in the planning system, special care needs to be
paid to these factors, for instance, by the use of multiple-criteria planning
approaches (as described elsewhere in this book) and/or the ability for the
treatment planner to set the starting conditions to drive the result of the opti-
mization in a desired direction (as described in Section 11.4.4 of this chapter).
Finally, although plan robustness is a sadly underevaluated characteristic of
any radiotherapy treatment, it is certainly true that, due to their fnite range,
this aspect is more important for proton therapy than it is for conventional
therapies. Although much of this aspect can be gained through experience
and good training of staff, it is also an aspect that should be more closely
incorporated into the planning and quality assurance aspects of proton
therapy. For this, tools must be provided by both the treatment planning
and delivery machine manufacturers by which the consequences of delivery
uncertainties can be estimated at the time of planning and their magnitudes
determined during treatment. For this, uncertainty analysis tools should
be provided in the treatment-planning systems, as well as advanced imag-
ing and verifcation tools at the treatment machine. As such, there is much
interesting and important technological research and development still to be
done in the feld of scanned proton therapy.
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381
12
Dose Calculation Algorithms
BenjaminClasie,HaraldPaganetti,andHanneM.Kooy
CONTENTS
12.1 Pencil Beam Algorithms ........................................................................... 382
12.1.1 Rationale .......................................................................................... 382
12.1.2 Physics Model ................................................................................. 383
12.1.2.1 Elastic Scatter in Medium .............................................. 383
12.1.2.2 Large Scattering Events .................................................. 386
12.1.3 Dose to Patient ................................................................................ 388
12.1.4 Beam Representation ..................................................................... 389
12.1.4.1 SOBP Beams ..................................................................... 389
12.1.4.2 SOBP Production Model ................................................ 391
12.1.4.3 Scanning Beams .............................................................. 393
12.1.4.4 Implementation ............................................................... 394
12.1.5 A Scatter-Only Monte Carlo ......................................................... 396
12.2 Monte Carlo Algorithms ........................................................................... 398
12.2.1 Statistical Resolution in a Clinical Setting ................................. 398
12.2.2 Improving Monte Carlo Effciency .............................................. 399
12.2.3 CT Conversion ................................................................................ 399
12.2.4 Absolute Dose ................................................................................. 401
12.2.5 Dose-to-Water and Dose-to-Tissue .............................................. 401
12.2.6 Impact of Nuclear Interaction Products on Patient Dose
Distributions ................................................................................... 402
12.2.7 Differences between Proton Monte Carlo and Pencil Beam
Dose Calculation ............................................................................ 403
12.2.8 Clinical Implementation ............................................................... 405
12.2.9 Simplifed Monte Carlo Dose Calculations ................................ 407
Acknowledgments .............................................................................................. 407
References ............................................................................................................. 408
382 Proton Therapy Physics
12.1 PencilBeamAlgorithms
12.1.1 Rationale
Pencil beam dose calculation models are the most pragmatic representation
for empirically modeling dose transport in medium. The pencil beam model
is a convenient representation of a piecewise geometric and physical approx-
imation to the exact model where each pencil beam allows a suffciently
accurate approximation of all dose-depositing processes in the patient by
local effects, those along the axis of the pencil beam. Pencil beam algorithms
use the mathematical concept of a set of narrow beams that, as a composite,
(1) model all the degrees of freedom of the radiation feld, (2) fll the physical
space of the radiation feld, and (3) provide a good approximation of model-
ing the patient as a set of interactions of the pencil beam in a “slab” geometry
around the pencil beam axis. Interactions in laterally infnite slab geometry
are well understood, and its application in pencil beam models is only lim-
ited by the lateral extent of the pencil beam itself. That is, the pencil beam
local model is insensitive to heterogeneities lateral to its bounding envelop.
Pencil beam models introduce the concept of modeling fuence, ϕ, transport
along the pencil beam axis as a function of radiological depth, ρ, combined with
a lateral energy diffusion kernel, K. Energy released in medium, and quantifed
as dose to water, for a set of pencil beams, p, is E x d d K r A
p
( , ) ( ( )) ( , ( ))

=
∑
ρ ρ d ,
where ρ is the radiological depth, r is the distance from the pencil beam axis
to the point at

x, and dA is the “area” of the pencil beam. The kernels, K, are

x
generated by, for example, Monte Carlo as dose-to-water. The kernels are radi-
ally symmetric and spatially invariant in compliance with the slab geometry
assumption. More accurate kernels include polar angular dependencies and
corrections for heterogeneities along the displacement, r. The nature of the
kernel is fundamentally different between photon and charged particle dose
models. For photons, the kernel is superimposed on a point on the pencil
beam axis and transports the energy liberated at that point (i.e. the KERMA,
within the medium). For protons, the kernel quantifes the diffusion of the
pencil beam protons relative to the pencil beam axis.
The pencil beam model was frst applied in electron dose calculations (1).
The electron feld was subdivided in rectangular pencil beams and each
pencil beam modeled the electron fuence diffusion in medium in the pres-
ence of heterogeneities as quantifed on computed tomography (CT) data.
Figure 12.1 shows a simple pseudocode description of a pencil beam model
implementation where the line (1) creates an initialized set of dose calcula-
tion points, containing the position based on the CT data set and accumu-
lates dose at that position; (2) sets up the computation given a decomposition
of the feld into mathematical pencil beams; (3) creates a trace object that
maintains the geometry and state necessary to resolve the physics interac-
tions as a function of depth; (4) places the points in the coordinate system of
383 Dose Calculation Algorithms
the pencil beam with the z-axis along the pencil beam axis and where each
trace is to the depth of the next point sorted in depth, now, along the pencil
beam axis; (5) traces the pencil beam through the volume in increments;
(6) computes the local kernel given the results from the trace and the phys-
ics model; and (7) adds dose as a consequence of the kernel convolution.
The performance of an algorithm implementation is of course of primary
signifcance. The above algorithm scales obviously as O(P), linearly with
the number of pencil beams, but the performance of the super position of
the kernel on the points will be very sensitive to the details of its imple-
mentation. It is of course the evolution of the kernel and its convolution on
the dose point geometry that are the key to the effciency of the algorithm
implementation.
Pencil beam models are well suited to model the transport of protons
through the patient because a narrow beam of protons is itself a pencil beam.
The fact, however, that a physical proton beam is well approximated by a
mathematical pencil beam does require special implementation consider-
ations as described below.
12.1.2 Physics Model
12.1.2.1 Elastic Scatter in Medium
The physical processes involved in traversal of protons through medium are
well understood (see Chapter 2). The primary mode of interaction is through
elastic scatter of the proton in the electric feld of the atoms in the medium.
These numerous scattering events have the statistical consequence that the
density of protons lateral to the mean direction approximates a Gaussian
distribution. The Gaussian approximation is rigorous, according to the cen-
tral limit theorem, if every scattering event occurs at a small angle. The
proton scattering events, however, have an angular distribution governed,
effectively, by the small-angle Rutherford form, dσ/dΩ ≈ 1/θ
4
, which means
that the lateral distribution will be Gaussian for small angles but will trend
1 points = new_matrix(sizeof(CT), bounds);
2 for each pencil-beam P in field F {
3 trace = new_trace(P);
4 points_p = place_and _sort_point_in(trace, points);
while inside(trace, CT) {
5 trace = trace_to_z_of_next_p(trace, CT);
6 kernel = compute_kernel(kernel, trace, physics_model);
7 points_p = compute_dose(kernel, points_p);
}
}
FIGURE 12.1
Pseudocode implementation of a pencil beam algorithm. The algorithm collects the calculation
points (points) and sorts the points along the axis of each pencil beam P (points_p) to permit
direct step-wise tracing to the depth of each point. At each point, the algorithm computes the
extent of the pencil beam and computes the dose to the affected points.
384 Proton Therapy Physics
toward a scattering tail distribution, 1/θ
4
. A complete multiple Coulomb
scattering (MCS) theory was published by Molière in 1947 (2).
We want to derive a model for the evolution of a beam with initially zero
emmittance (i.e., zero lateral width and zero angular spread) in medium
whose stopping power is characterized relative to water. The latter is in
compliance with the defnition of the dose kernels in water that we apply to
the water equivalent representation of the patient. This evolution is largely
described by the Gaussian widening of the proton distribution and the
involved volume in which those protons will interact.
Fermi-Eyges theory (3) describes the evolution of spatial and angular distri-
butions of particles propagating through matter with the assumption that the
particles undergo many small-angle scattering events. It was initially applied
in pencil beam algorithms for electron beams (1) and more recently, although
not in the Fermi-Eyges form, to proton (4) and heavy-ion beams (5). The the-
ory is more accurate for protons and heavy ions because these particles scat-
ter through small angles in interactions with the atoms in the medium.
The Fermi-Eyges theory predicts that the lateral spread of a parallel and
infnitesimally narrow proton beam as a function of depth in water, z (in
centimeters), is Gaussian in shape with width given by (6)

x z z z z T z dz
MCS x MCS
z
2
0
2
( ) ( ) ( ) ( )
,
= = −
∫
σ ′ ′ ′ [
2
  cm
22
]

(12.1)
where x z x N
MCS i
i
N
2 2
1
( ) / =
=
∑
is the lateral variance of the beam (equal to σ
2
x MCS
z
,
( ),
the square of the standard deviation of the Gaussian profle, in the limit of
many events) and T z d dz ( ) / ≡ θ
2
is the scattering power. Gottschalk (7) gives
a parameterization of the scattering power that is accurate almost within
experimental errors for protons in water, thin slabs, and high-Z materials.
The parameterization, called the improved nonlocal formula, is given by
T z T pv p v
dM
( ) [ . . log ( ( / ) ) = = + − + 0 524 0 1975 1 0
10 1 1
2
.. log ( / ))
. log ( / )log
2320
0 0098
10
10
pv MeV
pv MeV −
110 1 1
2
2
1
1
( ( / ) )] −






pv p v
E
pv L
s
R
×

(12.2)
where pv [MeV] is the product of the proton momentum and velocity and is
a function of z, p
1
v
1
is the initial product of momentum and velocity, E
s
= 15.0
MeV, and L
R
is the radiation length (36.1 cm for water).
Most treatment-planning algorithms, however, use the Highland formula
for calculating the spread of proton beams in water, which is accurate within
±5% (4). The Highland scattering angle is integrated along the beam axis,
and the result for the lateral standard deviation at z is (8)

σ
x MCS
R
z
z
L
,
( ) log
. Me
2
10
2
1
1
9
14 1
+
¸
¸

_
,


¸

1
]
1
×
VV
pv
z z
L
dz
z
R
× − ( )
¸
¸

_
,


¸


1
]
1
1
∫
′ ′
0
2
1

(12.3)
385 Dose Calculation Algorithms
where ρ = 1 g/cm
3
is the density of water and where the MCS is multiple
Coulomb scattering. The Highland approximation and Fermi-Eyges theory
with the improved nonlocal formula are given in Figure 12.2 for proton
beams in water and the two parameterizations agree within 7%.
Each pencil beam evolves in water according to σ
x MCS
z
,
( ). At z, the total dis-
tribution is the convolution of two Gaussian functions: the initial or unper-
turbed Gaussian beam shape and the additional spreading from MCS in
medium. The beam spread at z for an initially thick beam with zero angular
spread is therefore

x z x z x
thick MCS thick
2 2 2
0 ( ) ( ) ( ) = +

(12.4)
where x
thick
2
0 ( ) is the initial variance of the thick Gaussian beam. If the initial
beam has nonzero angular spread, then

x z x z x z
thick MCS vac
2 2 2
( ) ( ) ( ) = +

(12.5)
where x z x z x
thick thick thick vac
2 2 2
0 2 0 ( ) ( ) ( ) ( = + ⋅ ⋅ + θ θ 00
2
) ⋅ z is the spread of the beam in
a vacuum at z, x x N
thick i i
i
N
θ θ ( ) / 0
1
=
=
∑
is the initial covariance (6), and
θ
thick
2
0 ( ) =
θ
i
i
N
N
2
1 =
∑
/ is the initial angular variance.
Proton pencil beam dose calculations determine the MCS lateral spread for
each pencil beam in a feld at each depth, and because a typical feld consists
of thousands of pencil beams, corresponding to the spatial and energy sub-
divisions, and hundreds of dose calculation depths, the spread calculation
algorithm must be fast and accurate. The use of a look-up table for the results
0.2
0.2
0
0
0.4
0.4
0.6
0.6
z/R
σ
x
,

M
C
S
(
z
)

/

σ
x
,

M
C
S
(
R
)
0.8
0.8
1
1
0.2
0
0
0.4
20 10
0.6
R [cm]
σ
x
,

M
C
S
(
R
)

[
c
m
]
30
0.8
40
1
FIGURE 12.2
Left: the normalized Gaussian spread in water vs. normalized depth, z/R, where R is the range
of protons to stop in water (cm). This relation is independent of R between 0.1 and 40 cm and is
the same for both Equations 12.1 and 12.3. Right: the Gaussian spread at maximum depth (i.e.,
z = R) for Equation 12.1 (dashed line) and Equation 12.3 (solid line).
386 Proton Therapy Physics
in Figure 12.2 can improve the speed of the dose calculation; see appendices
in Hong et al. (4).
Computational results in water are extended to heterogeneous media by
assuming the media is water-like. That is, the physical depth, z, is converted
to a water equivalent depth along the central ray of the pencil beam, and the
media are assumed to have the radiation length of water. A general purpose
Monte Carlo simulation should be used to check dose calculations for treat-
ment plans in media that are not water-like.
12.1.2.2 Large Scattering Events
Dose deposited outside of the central Gaussian region, from large-angle elas-
tic scattering events and secondary particles, is called the beam halo. This
leads to extended tails in the spatial and angular distributions of the beam.
No correction for this effect is needed for uniform felds typical of those pro-
duced in scattering systems or uniform scanning systems because there is
equilibrium of the lateral scattered dose and the effect is implicitly included
in either measurement or model (9). On the other hand, nonhomogeneous
felds are implicit in proton pencil beam scanning and the beam halo can not
be ignored in the calculation of absolute dose. This effect has been studied
by Pedroni et al (10), Soukup, Fippel, and Alber (11), and Sawakuchi et al. (12,
13), and ignoring the halo in treatment planning can lead to errors on the
order of 5%.
The halo contribution to the proton spread is characterized by a much
larger radial effect. Figure 12.3 shows the buildup of dose measured on the
central axis of square felds for a pencil beam of range 25 cm in water. The
effect extends up to a distance on the order of 7 cm as shown in Figure 12.3
where full build-up is achieved in a square feld of 15 cm.
The halo is not easily described a priori. In practice, however, the halo can
be well parameterized as a second Gaussian pencil beam with a fraction,
f
H
, relative to the total beam. This weight is slowly varying as a function of
depth, d, and range, R, and a simple parameterization is adequate to describe
dose deposited by the halo, such as

1
0 1 2
− = = + + f d R
D R d
D R d
a R a R t a
H
M
T
( , )
( , )
( , )
( ) ( ) (
∞
∞
RR t )
2

(12.6)
where t equals d/R, D R d
M
∞
( , ) is the MCS depth–dose component integrated
over an infnitely broad lateral feld, D R d
T
∞
( , ) is the same for the total mea-
sured depth dose. The fraction, f
H
, is derived from measurement and used,
subsequently, to decompose measured depth doses into MCS depth doses
and halo depth doses (Figure 12.4).
In our implementation, we parameterize the coeffcients in Equation 12.6
for f
H
as

a R b b R b R
i i i i
( )
, , ,
= + +
0 1 2
2

(12.7)
387 Dose Calculation Algorithms
5 10 15
Full width of square (cm)
20
R = 25 g/cm
2
, Depth of water = 17.4 cm
R = 25 g/cm
2
, Depth of water = 22.4 cm
25 30
5
0.96
0.98
1
1.02
10
D
o
s
e

(
a
.
u
.
)
0.96
0.98
1
1.02
D
o
s
e

(
a
.
u
.
)
15
Full width of square (cm)
20 25 30
FIGURE 12.3
Observed dose build-up in the center of a square feld as a function of feld width. The square
feld is delivered by a set of mono-energetic, 25 cm in water, pencil beams that populate
the feld area uniformly. The blue markers are measurement, and the red line is the model
described in the text (Equations 12.6 and 12.7 and Table 12.1). Dose (Y-axis) is normalized to a
10 × 10 square feld central dose.
0
10
–3
10
–2 MCS
2nd p
10
–1
G
y

c
m
2

G
p
–
1
10
0
10
1
2 4 6 8 10
Depth dose R = 16 cm
Depth/cm
12 14 16 18 20
0 5
10
15
20
25
30
R cm water
Fraction of dose due to 2nd p
0.2
0.4
t = d/R
0.6
0.8
1
0
0.02
0.04
f
H
0.06
0.08
0.1
0.12
FIGURE 12.4
The total measured depth dose (left) is decomposed into its component from MCS protons
(top curve) and from secondary scattered halo protons (bottom curve). The decomposition
(Equation 12.6) can be characterized as a second-order polynomial surface as a function of
range-scaled depth t = d/R and Range (right).
388 Proton Therapy Physics
where the values for b are given in Table 12.1. This parameterization is
derived from measurements of dose build-up in, for example, the center of
circular rings of proton pencil beams of increasing radius and as a func-
tion of depth and energy. The parameterization allows a decomposition of
a measured pristine peak depth dose in terms of elastic and inelastic dose
contributions as a function of energy and depth (see Figure 12.4).
Finally, the spread of the halo appears to be suffciently constant (in
the beam at the Massachusetts General Hospital [MGH]) as a function of
depth as

σ
Η
( ) . . . . R R R = − + 6 50 0 34 0 0078
2
(12.8)
The halo model quantifcation is sensitive to the details of the measurements
and beam conditions. The primary concern, however, is to characterize the
energy fow away from our primary dose component characterized by f
H

because the redistribution of this secondary scattered energy is very homo-
geneous compared with the primary energy distribution in the patient.
12.1.3 Dose to Patient
The dose to a point p in the patient from a proton pencil beam can now be
stated as follows:

D p
W
r
D
p
p
( ) exp ( ) = −








∞
2 2
2
πσ σ
ρ
2 2

(12.9)
where W is the dosimetric “weight” of the pencil beam (physically propor-
tional to the number of protons in the pencil beam),
ρ ρ
p W W
M
S t dt =
−
∫
0
( )
is the
water equivalent depth along the pencil beam axis of u to the point p, σ is
the total spread of the pencil beam at depth ρ
p
, and r
p
is the shortest distance
from p to the pencil beam axis. The same mathematical form in Equation
12.9 can be used to model the dose from the primary, multiple Coulomb,
or halo components as defned by the depth dose, D, and the appropriate
spread.
TABLE 12.1
Fit Parameters for Equation 12.7 to Obtain the Coeffcients a
i
for the
Computation of the Depth-Dependent Fraction f
H
in Equation 12.6
a
0
a
1
a
2
b
0, i
1.002 2.128e-03 −2.549e-03
b
1, i
−5.900e-04 −2.044e-02 2.125e-02
b
2, i
0 3.178e-04 −3.788e-04
These values characterize the beam at MGH (2010).
389 Dose Calculation Algorithms
12.1.4 Beam Representation
The dose contribution from a specifc beam must now be represented in
terms of the pencil beam computational units in Equation 12.9. We have two
classes of proton beams: scattered felds (Chapter 5) and pencil beam scan-
ning felds (Chapter 6). These differ, fundamentally, in their means of pro-
ducing dose distributions.
Scattered felds are limited to dose distributions which, by design and
in water, have a uniform dose region between the distal range and proxi-
mal range (defned as the modulation width). These felds are referred to
as spread-out Bragg peak (SOBP) felds as a consequence of the production
method in which a single pristine Bragg peak is modulated in fxed energy
intervals to create the uniform profle. The set of energies, distributed
between a distal-to-proximal range value, of pristine peaks determines the
modulation width, whereas the relative contribution of each pristine peak
produces the uniform dose over the modulation width. SOBP felds were
used from the very beginning of proton radiotherapy as both the energy
interval set and the pristine peak weights could be combined in a mechanical
range modulator, typically constructed as a rotating wheel where an angu-
lar interval encoded both the range and relative contribution by its thickness
and its angular width (Chapter 5). The incoming beam of a given energy
would pass through these intervals, where the interval thickness reduced
the beam energy and the angular width its beam-on time, to produce the
characteristic SOBP dose distribution. SOBP felds require an aperture to
provide lateral conformation of the SOBP feld and a range compensator to
achieve distal conformation, while they always produce a uniform lateral
dose profle, by design, in water defned by the modulation width and the
lateral extent. Scanning felds, in contrast, can achieve any dose distribution
in the patient without the need of such devices, although the use of these
devices could have some beneft. Note that SOBP felds can also be produced
by uniform scanning beams, where the beam intensity is constant during
an energy layer. Functionally, such SOBP felds are equivalent to those pro-
duced in scattered systems.
12.1.4.1 SOBP Beams
Algorithmically, there are some considerations: (1) the apertures and range
compensators need to be modeled, (2) the stacking of the pristine peaks
needs to be accurately modeled, and (3) some properties of the production
system may need to be considered explicitly.
In general, an SOBP feld is produced in a scattering system (see Chapter 5).
The use of a scattering system results in a feld that appears to emanate from
a “virtual” source. Such a feld has an intrinsic inverse square relationship in
its depth–dose distribution. The source position can be inferred by measur-
ing the increase in width of a collimated feld as a function of distance. Thus,
390 Proton Therapy Physics
a decomposition of a scattered feld requires the use of an inverse-square
scaled depth–dose distribution in Equation 12.9.
The scattering system produces a source with a size correlated to the
amount of scattering material in the beam. Thus, there is an intrinsic pen-
umbra associated with the feld analogous to that in electron scattered felds
(1). The penumbra is quantifed by measuring the penumbral edge as a func-
tion of distance (from the source) and projecting the penumbral edge at the
source position. The projected penumbral width is modeled as a Gaussian
spread contribution σ
s
from the “virtual” source to the total pencil beam
width. The source size in a proton scattering system is signifcant and on
the order of 5 cm. This source size effect is mitigated by placing the source
as far away from the patient as possible (and one reason for the large proton
gantry diameter; the other being the signifcant size and mass of the bend-
ing magnet) and to place an aperture as close to the patient as possible. The
source size, and σ
s
, is thus demagnifed by the ratio of distances. The source
size contribution at the calculation point p is

σ σ
s p
A p
A
s
z
z z
SAD z
( ) =
−
−







(12.10)
where z
p
is the z-position (along the central axis of the SOBP feld) of the
point p, z
A
is the z-position of the aperture, and SAD is the distance from the
isocenter to the source.
SOBP felds use, invariably, a range compensator that shifts the initial
range across the feld area to that range necessary to “just” place the distal
edge of the feld beyond the distal target volume surface. The range compen-
sator thus presents various thicknesses of material (typically Lucite) along
the lateral extent of the beam. Protons passing through a particular thickness
t will scatter as a consequence and introduce an additional contribution σ
R
equal to

σ
R p R
L t = θ ( )

(12.11)
where θ
R
(t) can be computed by Equations 12.1 and 12.2, or tabulated as in
Hong et al. (4), and L
p
is the distance from the range compensator intersec-
tion point to the calculation point p along the ray from the source to p.
The total spread of a pencil beam at the depth of point p is (including
Equation 12.3)

σ = σ σ σ
2 2 2 2
T S R MCS
+ +

(12.12)
Thus, for scattered SOBP felds, produced by set of pristine peaks of energies,
R, the dose to a point p becomes

D p
r
D d
SAD
T
R
p
T
R
p
( ) exp ( ) = −








∑ ∞
1
2 2
2
2
2
π π σ σ
−−






z
SAD
p
2

(12.13)
391 Dose Calculation Algorithms
where the inverse square correction accounts for the intrinsic divergence of
the feld and hence each pencil beam. Dose distributions in treatment plan-
ning programs are typically obtained through the application of Equation
12.13. The model holds up well compared to Monte Carlo (14, 15) and fails in
predictable areas of high-Z materials and distal of heterogeneities.
12.1.4.2 SOBP Production Model
There are multiple means of creating SOBP felds. The most common method
is to use a rotating modulator wheel with angular segments of widths and
thicknesses corresponding to the pullback and weight of individual pristine
peaks that comprise an SOBP feld (Figure 12.5). The construction of such
0
%

D
o
s
e
0
20
40
60
80
100
120
20 40 60 80
No BCM modulation
With BCM modulation
Decreased SSD
100 120
Depth/mm
50
95
100
140
180
S
t
o
p

a
n
g
l
e
220
100
105
%

D
o
s
e
55 60
101
0 mm
A
s
Track step
Beam
size
9 mm
Depth/mm
20 40 60 80
Modulation
(90-98%)/mm
FIGURE 12.5
The SOBP is constructed from the weighted superposition of a single pristine peak, pulled
back (shown as the individual pristine peak depth doses) by successively increasing step thick-
ness on a rotating modulator wheel. The wheel weights are adjusted by modulating the beam
current as a function of wheel rotation angle (with BCM modulation curve). In absence of this
modulation, the wheel produces the SOBP (no BCM modulation curve). The SOBP is designed
to be fat at the nominal SSD of SAD-30 mm (proximal of the distal edge); other SSD values
create a slope in the SOBP. The fgure in the top right shows the effect of the source size, where
the 0-mm line is the SOBP proximal falloff for an infnitesimal spot, whereas the 9-mm line
corresponds to the observed softening of the proximal “knee” as a consequence of the source
size. The fgure in the bottom right shows the stop angle (expressed as an 8-bit value) to achieve
the desired modulation. The above SOBP has a range (modulation) equal to 110 (80).
392 Proton Therapy Physics
modulator wheels is an art and, in theory and practice, only achieves a “per-
fect” uniform SOBP plateau for the design energy.
We demonstrate the production and modeling for a rotating modulator
wheel corresponding to the system used by IBA (IBA Ltd, Louvain la Neuve,
Belgium) in their double-scattering system design. This design has a set of
fxed range modulator wheels (implemented as up to three concentric tracks
on a single modulator wheel) where the thickness of a track step is a com-
bination of a high-Z (lead) and low-Z (carbon/Lexan) material such that the
scattering angle remains constant, independent of total (water equivalent)
thickness. The beam subsequently passes through one (of three) scatterer
(see Chapter 5) to produce a uniform feld up to a 25-cm diameter. The clini-
cal range of energies range from 5 to 30 cm in water and require the use of
eight combinations, dubbed options, of track and scatterer. Each of the eight
options is further subdivided into three suboptions. Thus, a suboption cov-
ers about 1 cm of energy interval over which the energy effect on the shape
of the SOBP is assumed negligible. The track rotates at 10 Hz and produces a
full SOBP dose distribution in the patient 10 per second.
In our clinical practice we achieve SOBP plateaus with a ±0.5% unifor-
mity when the isocenter is positioned slightly (~3 cm) from the distal falloff:
SSD = SAD – R + 3, where SSD is source-to-skin difference and Sad is source-
to-axis difference. This requirement is well beyond any theoretical ability
to design the proper track thicknesses and angular intervals. The IBA sys-
tem, however, uses beam current modulation as a function of rotation angle
to modulate the track contributions for each pristine peak produced by the
track. This modulation as a function of rotation angle (i.e., as a function of
position along the track) allows an increase or decrease of current to correct
any design limitations. The track is designed up to a maximum modulation
width (corresponding to the maximum track step thickness). The current
modulation allows any modulation up to the maximum track thickness by
turning the current off before the rotation completes. Thus, modulation is a
function of rotation angle, referred to as the “stop angle” in this context.
The track has discrete steps, and the fnite source size (approximately the
track width) causes incomplete contributions of the pristine peak dose when
the source stops at a junction (see Figure 12.5). Thus an SOBP is not a simple
superposition of discrete energy pristine peaks.
A model for such a track system specifes, for each track, a base pristine
peak depth–dose distribution (defned at a range R equal to the maximum
energy of an option), its current modulation distribution, its source size on
the track, and its thickness and angular width for each track step (typically
on the order of 30 steps). This base pristine peak depth dose is not trivial to
obtain. The scattering system inside the housing of the gantry nozzle pres-
ents a complex geometry in which the scattered beam is not easily, if at all,
characterized. In addition, the measurement has to be done while the mod-
ulator wheel is rotating. A simple approach has been to measure only the
protons that pass through the frst, thinnest step of the track by, essentially,
393 Dose Calculation Algorithms
producing an SOBP of zero modulation. The use of this pristine peak, how-
ever, fails to produce SOBPs that compare well with measurements. Lu and
Kooy (16) describe a rigorous experimental method to measure the pristine
peak while the wheel is rotating. This pristine peak does produce an excel-
lent correspondence between calculations and measurements.
The SOBP is computed as follows:

D d Q P d T BCM A d
i
i
i
i
( ) ( ) ( ) ( , ) = −
−
∫
∑ 0 0
1
θ θ θ
θ
θ
σ
Q

(12.14)
where Q
0
is the total charge delivered in a rotation over the angle θ, P
0
is the
SOBP depth–dose distribution at the maximum range defned for a track
option, BCM is the (relative) beam current modulation over the rotation, and
A(σ
Q
, θ) is the fractional area of the beam spot (relative to the total spot area),
with spread σ
Q
at the rotation angle.
Figure 12.5 shows the result of the model in Equation 12.14 to produce an
SOBP at the design SSD and the relevance of the beam current modulation
and source size modeling. In clinical practice, the SOBP is specifed only
in terms of its distal range, typically the 90% (relative to the plateau) range
R90, the modulation width from R90 to the proximal falloff, and its dose
expressed in monitor units (MUs, the units of the ionization reference cham-
ber). The latter was, by convention, also defned as the 90% value. This, how-
ever, leads to a defnition of modulation values larger than the range. The
latter, in turn, leads (at least in our practice) to issues in beam delivery and
feld output specifcation in terms of Gy/MU (9). Therefore, a more consistent
defnition is the modulation width between the distal R90 and the proximal
98% falloff. This defnition, however, does require an accurate description of
this proximal falloff and the implementation of Equation 12.14. Its absence
can result in a 5-mm error.
12.1.4.3 Scanning Beams
Proton pencil beams scanned by orthogonal dipole magnets can irradiate
arbitrary feld areas without the need for a mechanical collimating aperture.
Variation of the pencil beam energy allows control of the pristine peak posi-
tion within the patient and thus also removes the absolute need for a range
compensator. Finally, varying the intensity (expressed as total charge) of the
pencil beam allows for dose modulation throughout the target volume. Thus,
scanned beams have three degrees of control: energy, position, and charge
(intensity). The size of the beam tends to be fxed in current scanning system
implementation, although there will be an energy dependence. Pencil beam−
scanning systems are generally assumed to deliver their dose in patient
in discrete energy layers as changes in energy may require a mechanical
manipulation of the beam and “slow” changes in beam-line magnetic sys-
tems. Much effort, however, is focused on removing this limitation.
394 Proton Therapy Physics
In a pencil beam−scanning feld, the “pure” pencil beam emerges from
the beam-line transport system and traverses one or more foils that separate
vacuum from air and one or more ionization chambers required for register-
ing current and position. Thus, the overall “thickness” of space between the
beam line and the patient is small, on the order of 4 mm. The pencil beam is
thus little perturbed.
The algorithmic representation of the pencil beam is thus as a “cone” of
protons with an elliptical spread (expressed in (σ
x
, σ
y
) in the reference plane
of the beam). By and large the focusing of the pencil beam is ignored and
the pencil beam is assumed nondivergent. The use of a range compensator
is not excluded and thus the spread will include σ
R
(Equation 12.12). The
effect of including an aperture has not been well studied but is expected to
improve the penumbral edge for “large” spot size. An elliptical spot size may
rotate as a function of gantry angle, which introduces an implementation
requirement.
The dose from a set of proton pencil beams, R, is

D p
r
D d
T
R
p
T
R
p
( ) exp ( ). = −








∑ ∞
1
2 2
2
2
2
πσ σ

(12.15)
Note the absence of the inverse square correction for the depth dose because
the pencil beam is not diverging. The beam will, however, have an inverse
square behavior if one or both axes of the pencil beam pivot around a scan-
ning magnet bending source. This effect manifests itself in the ray-tracing
of the pencil beam axes through the volume and computationally expresses
itself in the computation of r
p
in Equation 12.15. There are beam confgura-
tions where, in fact, one axis is at infnite SAD as a consequence of the beam-
line magnet layout or where the beam is only scanned in a line as in one of
the gantry systems at the Paul Scherrer Institute (PSI, Villigen, Switzerland).
12.1.4.4 Implementation
Physical proton pencil beams have the nice mathematical form of Equation
12.15. This, however, may lead to the assumption to directly model the physi-
cal pencil beams, spots in the discussion below, produced in a proton deliv-
ery system by Equation 12.15. These spots, however, have sizes (3–10 mm
σ) that exceed the computational need for resolution. Instead, the correct
approach is to frst transport infnitesimally narrow mathematical proton
pencil beams through the patient to satisfy the need for spatial accuracy in
patient and subsequently superimpose the spots. We defne these mathemat-
ical pencil beams as bixels and defne the bixel set B, each with unit number
of protons, that covers the required patient volume including targets and
organs-at-risk for each treatment beam. We subsequently superimpose the
spots, deliverable by the equipment for each feld, on top of this bixel space
(see Figure 12.6).
395 Dose Calculation Algorithms
The calculation in patient thus becomes

D x G
S
S
( )

=
∑

(12.16a)

×
σ σ ( , )
exp
( , )
,
1
2 2
2
2
2
π
O S
S K
O S
R z R z
dA −






∫
KK








∑
K

(12.16b)

×
ρ
σ ρ) σ ρ)
2 2
( )
( ,
exp
( )
( ,
D
R
p p
s
∞
−


2 2
2
π R
x
R
s
K
s








(12.16c)
where the frst term (12.16a) is the number of protons G
S
(in units of bil-
lions, or Giga-protons Gp) in a pencil beam spot from the set S, the second
term (12.16b) is the apportionment of these G
S
protons, given the optical
spread σ
O S
R z
2
( , ) of the spot, over the set of computational pencil beams K.
This set of computational pencil beams K in Equation 12.16c is defned at the
highest resolution necessary to accurately represent the dose in the patient.
Equation 12.16c models the diffusion of the number of protons, given by the
product of (12.16a) × (12.16b), in the patient given the scatter spread σ
P
(R
S
, ρ) in
the patient due to MCS. In a pencil beam–scanning system, the spot spread
σ
O S
R z
2
( , ) in Equation 12.16b is determined by the optical properties of the
system and is a function of the spot range R
S
and position z along the pencil
beam spot axis. The parameter Δ
S,K
denotes the position of a point in the
computational pencil beam area A
K
with respect to the spot coordinate sys-
tem. The fnal term (12.16c) follows Pedroni et al. (10), where D z
R
∞
( ) (in units
of Gy·cm
2
·Gp
−1
) is the absolute measured depth dose per proton integrated
over an infnite plane at depth z, σ
P
(R
S
, ρ) is the total pencil beam spread at
radiological depth ρ caused by MCS in the patient (see Hong et al. [4]), and
Xk1 Xk0
Fj(k)
2∆X
j
Yk0
j j+1
k(j)
k(j+1)
Yk1
(xj, yj)
FIGURE 12.6
The transport of spots, physical pencil beams j, through the patient frst transports “small”
bixels (hatch bar in Gaussian, left) through the patient. The bixels have initial 0 spread and thus
only spread as a consequence of in-patient scatter. Each spot j contributes to k(j) bixels pro-
portional to the area of bixel k under the spot j. The subdivision ensures that the transport in
patient is at the highest lateral resolution, limited by the bixel area and the bixel spread at depth,
and removes the dependency on spot spread on the calculation resolution and performance.
396 Proton Therapy Physics
K
x ( )

is the displacement from the calculation point to the K pencil beam
axis. Equation 12.16 is a phenomenological description of the distribution
in patient of protons delivered by the set of spots S. Finally, the product of
(12.16b) and (12.16c) is a convenient computational unit in the pencil beam–
scanning optimization algorithms and maintained as a look-up table, often
dubbed “Dij,” to map the number of protons (12.16a) to dose to a point.
The use of mathematical pencil beam bixels increases the computation per-
formance signifcantly. The main computational burden in a pencil beam algo-
rithm is the part of the algorithm that, at each step along the pencil beam axis,
fnds the points that are within the Gaussian envelop (line 7 in Figure 12.1). This
search time is proportional to the area (i.e., O(σ
2
)). Thus, tracing the narrow-
est possible pencil beams, the bixels, improves computational performance.
An effcient search algorithm will rely on ensuring that points are effciently
ordered with respect to the pencil beam to ensure that points are indexed as a
function of distances along and lateral to the pencil beam axis.
12.1.5 A Scatter-Only Monte Carlo
Pencil beam implementations suffer from the assumption that interactions
along the central axis are representative within the whole Gaussian envelop.
This makes pencil beam models insensitive to heterogeneities near the pen-
cil beam axis, reduces the lateral sensitivity to that of the Gaussian width,
and overemphasizes dosimetric diffusion as a consequence of upstream het-
erogeneities on the pencil beam axis.
The intrinsic physics pencil beam model for primary and secondary scat-
ter of protons suffces for clinical modeling of the dose distribution. This
allows the defnition of a simple Monte Carlo implementation where scatter
is modeled on a voxel basis for a proton traversing the voxel. This imple-
mentation (pseudocode in Figure 12.7) uses two random numbers: one to
select the scattering mechanism based on Equation 12.6 and one to select the
azimuthal angle (0–2 π) of scatter along the direction of the incoming proton.
The polar angle is the mean scattering angle, either from MCS or halo inter-
actions, based on the voxel density. The large number of voxels assures that
this approximation converges to the correct overall scatter in the medium.
The Monte Carlo transports individual protons through a volume repre-
sented by a rectangular 3D grid of voxels. Each voxel has the relative (to water)
stopping power, S
v
, obtained, in practice, from CT Hounsfeld units (17). We
score the dose to a voxel as the sum of energy depositions along the indi-
vidual proton tracks that traverse the voxel and divide by the voxel mass.
A proton, of energy E
S
, enters a voxel on one of its faces and exits on
another. The model computes the (unscattered) exit point along the incom-
ing proton direction (u, v, w) and the distance L between the entrance and
this projected exit point. The mean polar MCS scatter angle in the voxel is θ =
θ
0
(E
S
)√S
v
, whereas the mean polar halo scatter angle is θ = θ
H
(E
S
)√S
v
and the
azimuthal angle is randomly uniform between 0 and 2π. The mean scatter
397 Dose Calculation Algorithms
angle θ
0
(E
s
) is derived and quantifed by Gottschalk (7). The mean scatter
angle θ
H
(E
s
) is ftted to reproduce the observed spread (Equation 12.8). The
fraction of protons that scatter with the halo scatter angle and the azimuthal
angle are the random variables. The proton direction is adjusted to (u’, v’, w’)
given the scattering angles and the actual exit point is computed.
The energy loss of the proton along the mean voxel track length ⟨L⟩ is

= × × ×
< >
∞
λ
ρ
ρ
ρ ( ) ( , ) E T R d
S
S
L
W p
V
V
W
W
V
.
(12.17)
150
Ei
Eo
d = (Ei-Eρ)/pV
(s,ρ,<L>)
(θ,ϕ)
while E > 0 {
1. Compute current voxel position;
2. If outside of volume, exit;
3. Look up MCS or Halo scattering angle;
4. Generate random azimuth angle;
5. Compute new direction;
6. Estimate traversal distance in voxel;
7. Compute energy loss;
8. Deposit energy in voxel;
9. Reduce current energy;
10. Compute voxel exit point;}
100
50
–25 0 25
Lateral/mm
FIGURE 12.7
Top: pseudocode for the transport of protons through a set of voxels. Only MCS and second-
ary scattered protons are considered, each with a mean scattering angle scaled to the voxel
dimension and density. The resultant code implementation is well suited to a GPU architecture
because of its compactness and its lack of secondary particles. Bottom: two pencil beams tra-
versing a medium with alternating high- and low-density regions.
398 Proton Therapy Physics
The use of a mean track length ⟨L⟩ serves solely to reduce computational
overhead.
Computed pristine peak Bragg peaks using ∆
⟨L⟩
(E) and their range com-
pared to the original projected range (from PSTAR from the National
Institute of Standards and Technology) show excellent agreement.
The simplicity of the model offers excellent opportunities for a GPU
(graphics-processing unit) implementation. In our implementation of the
model in CUDA, on an entry-level nVidia FX1700 card, it achieves a perfor-
mance of 2,000,000 protons/100 cm
2
in 10 s in 128
3
voxels. This is compared
to our analytic pencil beam algorithm implementation, which computes the
same distribution in 30 s. Thus, it is clear that at least a simple Monte Carlo,
yet improved compared to a pencil beam model, now outperforms signif-
cantly traditional algorithmic model implementations.
12.2 MonteCarloAlgorithms
The principles of Monte Carlo simulations are outlined in Chapter 9. This
section describes the specifc aspects of using Monte Carlo for dose calcula-
tion purposes.
12.2.1 Statistical Resolution in a Clinical Setting
Other than with analytical methods, the accuracy of the dose calculation
with Monte Carlo depends on the calculation time. The more histories that
are being tracked the lower the statistical uncertainty. For clinical dose cal-
culations it is important to estimate the number of histories needed. This
number depends on the feld parameters, for example, on the beam energy
and treatment volume. If the whole treatment head is being considered (i.e.,
if the simulation is not based on a phase space distribution) the required
number of histories also depends on the effciency of the treatment head.
For pencil beam scanning, the effciency of the treatment head is typically
more than 90%, whereas for passive scattering it is typically in the order
of 3–30%. For passive scattered delivery, a typical number of proton histo-
ries for a given patient feld is ~25 million at the treatment head entrance
to reach ~2% statistical accuracy in the target for a single feld based on
the treatment planning grid resolution (based on the treatment head at the
MGH). This number is quite low compared to photon therapy due to the
higher proton LET. If an analysis is done for the entire plan (i.e., not feld
specifc), fewer protons per feld may be suffcient. Note that a certain statis-
tical accuracy in the target volume does not guarantee the same accuracy in
the organs at risk. However, the impact of statistical defciencies is less for
dose-volume analysis in organs at risk because the dose distribution is less
homogeneous (18, 19).
399 Dose Calculation Algorithms
12.2.2 Improving Monte Carlo Efficiency
There are several techniques to improve the computational effciency of
Monte Carlo for proton beams in patients (20, 21). Furthermore, Monte Carlo
codes have been specifcally designed for fast patient dose calculations using
approximations to improve computational effciency (22–25). One method
is to implement track-repeating algorithms in which precalculated proton
tracks and their interactions in material are tabulated. The changes in loca-
tion, angle, and energy for every transport step and the energy deposition
along the track are recorded for all primary and secondary particles and
reused in subsequent Monte Carlo calculations (26).
Particle tracking in a voxel geometry is computationally ineffcient because
in a standard Monte Carlo code, each particle has to stop when a bound-
ary between two different volumes is crossed. Thus, the maximum step size
is limited. This limitation even occurs when two adjacent voxels have the
same material composition. Algorithms have been developed to tackle this
problem (27, 28). Such algorithms are based on an image segmentation that
compromises the regular voxel geometry. The effciency (and potential com-
promise in accuracy) depends on the CT resolution.
The speed of the Monte Carlo simulation depends on the grid size, but
assuming that a step size above 1 mm is typically not warranted: a larger
grid size does not translate into a huge gain. Nevertheless, to decrease the
statistical uncertainty one might be tempted to interpolate the CT grid to a
larger grid. Furthermore, treatment planning algorithms often present dose
distributions on a more coarse grid than the one provided by the patient’s CT
scan. The problem with resampling the CT grid is that averaging of material
compositions is not well defned. Thus, to avoid resampling, the Monte Carlo
should operate on the actual CT scan, which is typically in the order of 0.5
to 5 mm. That of course also implies that the Monte Carlo simulations might
be required to operate on a nonuniform CT grid as often used clinically (20).
Resampling to improve statistical uncertainty can still be done after the dose
calculation, where weighting of doses that contribute to a given voxel on a
grid can be done accurately based on volume averaging.
To improve the computational effciency smoothing or de-noising algo-
rithms have been suggested to reduce statistical variations in Monte Carlo
dose calculation (29–33). These methods need to be applied with caution
because regions of low signal are, other than in imaging, not noise but valid
information. Some de-noising techniques tend to soften dose falloffs, which
could have a negative impact when used in proton therapy. Furthermore, one
has to keep in mind that, other than in photon therapy, dose is not directly
proportional to particle fuence in proton therapy.
12.2.3 CT Conversion
The patient geometry is typically available as a Digital Imaging and
Communications in Medicine (DICOM) stream (34). The grid under which
400 Proton Therapy Physics
CT data are stored can be regular or with a nonequidistant slice spacing
because regions of greater interest are often scanned with a smaller slice
thickness. With a software interface, Monte Carlo codes can use DICOM
directly (35–37).
Analytical (e.g., pencil beam) dose calculation algorithms in photon ther-
apy use electron density because the dominant energy loss process is interac-
tion with electrons. Protons lose energy by ionizations, MCS, and nonelastic
nuclear reactions. Because each interaction type has a different relationship
with the material characteristics obtained from the CT scan (38, 39), relative
stopping power is being used to defne water equivalent tissue properties in
proton therapy.
Monte Carlo dose calculations are based on a more specifc tissue descrip-
tion, that is, material compositions and mass densities. In addition, mean
excitation energy for each tissue can be obtained by using Bragg’s rule and
the atomic weight of the elements. Mean excitation energies are subject to
uncertainties that might be in the order of 5–15% for tissues, which can lead
to uncertainties in predicting the correct proton beam range (40). Mean
excitation energies for various elements are tabulated by the International
Commission on Radiation Units and Measurements (ICRU) (41). Averaged
values for tissues are also given directly by the ICRU (42, 43).
The accuracy of dose calculations, not only for Monte Carlo methods, is
affected signifcantly by the ability to precisely defne tissues based on CT
scans (44, 45). CT numbers refect the attenuation coeffcient of human tissues
to diagnostic x-rays and may be identical for several combinations of elemen-
tal compositions, elemental weights, and mass densities (46). In CT conver-
sion schemes, tissues are grouped into different tissues that share the same
material properties (i.e., elemental composition and ionization potential),
which are typically between 5 and 30 different tissues (i.e., distinct material
compositions are being used) (20, 44, 47). For better accuracy, independent of
the number of tissues, the number of densities is typically the same as the
number of grey values (CT numbers) (20). Models based on tissue materials
or animal tissues have been used to determine the correspondence between
Hounsfeld numbers and human tissues (45). Stoichiometric calibrations of
Hounsfeld numbers with mass density and elemental weights allow accu-
rate CT conversion (46). Several conversion schemes have been published
(17, 46, 48). A robust division of most soft tissues and skeletal tissues can be
done, but soft tissues in the CT number range between 0 and 100 can only
be poorly distinguished because CT numbers of soft tissues with different
elemental compositions are similar. A conversion table can be extended to
higher Hounsfeld units in order to deal with high-Z implant materials in
the patient (47).
Discrepancies in mass density assignments and assignments in elemental
compositions can lead to dose uncertainties (44). A relationship between a
certain CT number and a combination of materials is not unique, and vari-
ous fts can lead to a feasible result (46, 49). Not only can the absolute dose
401 Dose Calculation Algorithms
vary, but also the proton beam range might depend on the accuracy of the CT
conversion. For head and neck treatments it was shown that CT conversion
schemes can infuence the proton beam range in the order of 1–2 mm (49).
Any conversion scheme is valid only for the CT scanner used for the
underlying measurements. A normalization for the Monte Carlo can be done
by either doing a separate stoichiometric calibration or, as an approximation,
by simulating relative stopping power values in the Monte Carlo based on a
existing CT conversion and then by comparing the results with the planning
system conversion curve that had been validated during the commissioning
process. Based on this a slight correction of material compositions (or even
less cumbersome), mass densities can be done (15, 20, 50).
12.2.4 Absolute Dose
Monte Carlo dose calculation results are often presented as relative doses.
Absolute doses are typically reported as cGy per MU (15, 51). Absolute dose
prediction can be done based on simulations of the ionization chamber
readings (Chapter 9). In a segmented ionization chamber the volume used
for absolute dosimetry can be quite small (e.g., 1–2 cm in diameter). This
causes low statistics when simulating the chamber response (energy deposi-
tion events) and thus requires a large number of histories to be simulated.
The method is thus not effcient for routine use. An alternative method for
simulating absolute doses with Monte Carlo is to simply relate the number
of protons at treatment head entrance to the dose in an SOBP in water for a
given feld specifcation. With an accurate model of the treatment head this
method is equivalent to a direct monitor unit simulation because instead of
relating the dose to the impact of the beam at a given plane in the treatment
head (in an ionization chamber), one relates the dose to a specifc number of
protons at treatment head entrance.
12.2.5 Dose-to-Water and Dose-to-Tissue
Dose in radiation therapy is traditionally reported as dose-to-water. Analytical
dose calculation engines, e.g., pencil beam algorithms, calculate dose by
modeling physics relative to water (using the relative stopping power). There
is an open discussion whether doses in radiation therapy should be reported
as dose-to-water or dose-to-tissue (52). The advent of Monte Carlo is in part
responsible for this question. Arguments in favor of using dose-to-water
include the fact that clinical experience is based on dose-to-water, that qual-
ity assurance and absolute dose measurements are done in water, and that
tumor cells in the human body consist mostly of water. Dose constraints in
treatment planning are based on our experience with dose-to-water.
Monte Carlo dose calculation engines are not based on stopping power
relative to water. Instead, they are based on material properties, which are
converted from CT numbers: material composition, mass density, and mean
402 Proton Therapy Physics
excitation energy. Naturally, Monte Carlo dose calculation does result in
dose-to-tissue. A conversion of Monte Carlo results into dose-to-water thus
disregards one of the advantages of Monte Carlo simulations. Nevertheless,
to allow a proper comparison between Monte Carlo– and pencil beam–
generated dose distributions, one has to convert one dose metric to the other.
This can be done in Monte Carlo simulations based on known relationships
for proton energy–dependent relative stopping powers and on a nuclear
interaction parameterization (53). It has been shown that in most cases it is
suffciently accurate (within ~1%) to do a conversion to dose-to-water retro-
actively by simply multiplying the dose with energy independent relative
stopping powers (53).
Dose-to-water can be higher by ~10–15% compared to dose-to-tissue in
bony anatomy. For soft tissues the differences are typically on the order of
2% (Figure 12.8). Because the difference in mean dose roughly scales lin-
ear with the average CT number, a rough scaling based on the CT numbers
might be suffcient, depending on the desired precision (53).
12.2.6 Impact of Nuclear Interaction Products
on Patient Dose Distributions
Analytical algorithms are typically based on measured dose distributions
and thus include all relevant dose contributions naturally. For Monte Carlo
dose calculation one needs to decide which interactions to include. Protons
lose energy not only via electromagnetic but also via nuclear interactions.
The latter needs to be taken into account, specifcally in the entrance region
of the Bragg curve (39, 54–57), where it can be well over 10% of the total dose.
Monte Carlo simulations need to explicitly generate all secondary particles
in order to ensure proper energy balance. Although generating all secondary
–2
0
2
4
6
8
10
12
200 0 400 600 800 1000
CT number
(
D
w
(
m
e
a
n
)
-
D
m
(
m
e
a
n
)
)
/
D
w
(
m
e
a
n
)

[
%
]
FIGURE 12.8
Percentage difference between dose to water, D
w
, and dose to medium, D
m
, as a function of the
mean Hounsfeld unit, CT number, in the volume. Circles, organs at risk; squares, target struc-
tures. (From Paganetti, Phys Med Biol., 54, 4399, 2009. With permission.)
403 Dose Calculation Algorithms
particles is necessary, it might not be necessary (depending on the applica-
tion) to track them (Chapter 9). If the range of the particles is smaller than the
region of interest (e.g., the size of a voxel in the patient), it might be suffcient
to deposit the energy (dose) locally. For patient-related dose calculations, typ-
ically only secondary protons from nuclear interactions need to be tracked.
Nuclear interaction cross sections show a maximum at a proton energy of
about 20 MeV and decrease sharply if the energy is decreased (Chapter  9).
As a rule of thumb, the average proton energy in the Bragg peak is about
10% of the initial energy. The contribution of dose due to nuclear interactions
becomes negligible close to the Bragg peak position of a pristine Bragg curve
because of the decreasing proton fuence and a sharply decreasing cross sec-
tion. Secondary protons cause a dose build-up in the entrance region of the
Bragg curve because of forward emission of secondary protons from nuclear
interactions.
For an SOBP, nuclear interactions still play a role in the peak because dose
regions proximal to the Bragg peak contribute. This leads to a tilt of the dose
plateau if their contribution is neglected (57). Figure 12.9 shows the dose con-
tribution from secondary protons compared to the total dose for a treatment
feld used to treat a spinal cord astrocytoma.
Consideration of nuclear interactions is particularly important for pencil
beam scanning because each pencil is surrounded by a long-range nuclear
halo (Chapter 11). The dose distribution is small for each pencil, but can be
signifcant for a set of pencils delivering dose to the target volume or in the
sharp dose gradient at the distal falloff (12, 58).
12.2.7 Differences between Proton Monte Carlo
and Pencil Beam Dose Calculation
Differences between Monte Carlo–based dose calculation and analytical
methods in proton therapy have been demonstrated extensively (11, 15, 24,
59–62). Error analysis can be applied when comparing Monte Carlo and ana-
lytical dose calculation and optimization methods (63).
10
30
50
70
90
95
100
102
1
3
5
7
9
9.5
10
FIGURE 12.9
(Seecolorinsert.) Dose distribution for one treatment feld in a patient treated for a spinal cord
astrocytoma. Left: prescribed dose (in %). Right: dose due to secondary protons generated in
nuclear interactions (in % of the prescribed dose).
404 Proton Therapy Physics
Pencil beam algorithms are less sensitive to complex geometries and den-
sity variations: bone–soft tissue, bone–air, or air–soft tissue interfaces (64).
Most pencil beam algorithms project the range based on the water equivalent
depth in the patient calculated for individual beam spots. This neglects the
position of inhomogeneities relative to the Bragg peak depth (59, 65, 66). Even
small discrepancies in local energy deposition can result in changes in range
over the entire beam path (20). If a proton beam passes through complex
heterogeneous geometries a phenomenon called range degradation occurs
(58, 67), which is correctly predicted using Monte Carlo only. Note also that
some pencil beam models do not consider aperture-edge scattering, which
can cause dose errors for the frst few centimeters entering the patient (68).
One of the areas where pencil beam algorithms specifcally show weak-
nesses is in the presence of lateral heterogeneities (11, 60, 61). Figure 12.10
demonstrates the inaccurate consideration of interfaces parallel to the beam
path with a pencil beam algorithm due to the treatment of multiple scatter-
ing in heterogeneous media. It is noteworthy that large density gradients
that can be tangential to the beam do not only occur in the patient but also
in range compensators.
Treatment planners are typically aware of dose calculation uncertainties
and take these into consideration when prescribing felds, for example, by
avoiding pointing a beam toward a critical structure and by applying safety
margins (see Chapter 10). Because of such precautions, differences between
pencil beam algorithms and Monte Carlo dose calculations turn out to be
1 Gy(RBE)
3 Gy(RBE)
5 Gy(RBE)
7 Gy(RBE)
9 Gy(RBE)
11 Gy(RBE)
13 Gy(RBE)
15 Gy(RBE)
17 Gy(RBE)
FIGURE 12.10
(Seecolorinsert.)Axial views of dose distributions calculated using a commercial planning
system based on a pencil beam algorithm (right) and a Monte Carlo system (15) (left). The
patient was treated for a spinal cord astrocytoma with three coplanar felds (same as Figure
12.9). The fgure only shows one of the felds. The Monte Carlo dose calculation was based on a
CT with 176 × 147 × 126 slices with voxel dimensions of 0.932 × 0.932 × 2.5/3.75 mm
3
(variable).
The yellow circle indicates the dosimetric impact of an interface parallel to the beam path.
Doses are in Gy(RBE).
405 Dose Calculation Algorithms
small when analyzing dose volume histograms from carefully designed
plans. It appears that the differences are not always clinically signifcant
(15, 61). More accurate dose calculations might however lead to the reduction
of margins.
A heterogeneity index parameterizes lateral tissue heterogeneities for a
beam spot and might be useful to decide if signifcant differences between
pencil beam algorithm and Monte Carlo algorithm are to be expected
(64). Here, the radiological depth of each voxel is calculated. Next, a disk
of radius 3σ
0
orthogonal to the pencil beam axis around the Bragg peak
position is defned, where σ
0
is the initial lateral spread. The homogene-
ity index is defned as the standard deviation of fuence weighted radio-
logical depths on this disc. A slight variation of this method was used to
analyze proton dose calculations (61). It was shown that the dose error
(variation of the relative mean systematic error) between pencil beam–
and Monte Carlo–generated dose calculation depends on the heterogene-
ity index.
Monte Carlo simulations have been used to benchmark analytical algo-
rithms (11, 15, 69) or to help commissioning planning systems (70, 71). Monte
Carlo is also the method of choice in special geometries. For example, tanta-
lum markers used to stabilize bony anatomy after surgery or as markers for
imaging can lead to signifcant dose perturbations typically not predicted
accurately by pencil beam algorithms (72).
It is likely that the future of dose calculation lies in Monte Carlo. Currently
the computational effciency of most Monte Carlo codes is not optimized
for routine clinical use. Monte Carlo can be used for recalculation of pen-
cil beam–optimized dose distributions (with subsequent fne-tuning) or for
Monte Carlo treatment planning including iterative dose calculation for opti-
mization. If Monte Carlo treatment planning is to be done, it needs to be
incorporated into a framework for treatment plan optimization (61, 73). A
compromise would be to utilize a Monte Carlo dose engine only at a limited
number of checkpoints during the optimization process.
12.2.8 Clinical Implementation
If proton Monte Carlo dose calculation is not part of commercial treatment
planning systems, one might be interested in implementing an in-house
Monte Carlo system in the clinic, which can then be used for routine dose
calculation as well as for research purposes (e.g., the Monte Carlo system
used at MGH (15, 76), see Figure 12.11). To facilitate data fow between
the planning system and the Monte Carlo, the CT information and plan-
ning information needs to be imported from the planning system, and
input fles for the Monte Carlo phase space and dose calculation have to
be created.
Simulations of phase spaces is common practice when using Monte
Carlo in radiation therapy even though in proton therapy it is unlikely that
406 Proton Therapy Physics
identical beam settings are prescribed for different patients and thus reus-
ing a phase space is unlikely. However, the separation of the phase space
calculation from the dose calculation might be done because the treatment
head may overlap with the patient CT volume (depending on the size of the
air gap)  (15). Overlapping geometries can cause ambivalent situations in a
Monte Carlo transport environment and should be avoided. A phase space
distribution can thus be used as a starting point for simulations inside the
CT volume.
If the planning system prescribes the settings of treatment head com-
ponents (e.g., the modulator wheel), the phase space can be simulated
accordingly. If the planning system prescribes solely range and modula-
tion width, the translation into treatment head settings is typically done
by the treatment control software for the actual treatment. Consequently,
this algorithm needs to be incorporated into the Monte Carlo code (15, 74).
Aperture and compensator are also prescribed by the planning systems
and can be modeled in the Monte Carlo using the milling machine fles
(see Chapter 9).
For proton beam scanning, the planning system will most likely provide a
matrix of beam spot energies, beam spot weights, and beam spot positions,
which can be translated into Monte Carlo settings in a straightforward man-
ner. Whether a complex beam model is needed to prescribe the distribution
of these parameters within each spot depends on the delivery system (see
Chapter 9).
The patient’s CT image can be imported in at least two ways, either by
importing a DICOM stream directly in the Monte Carlo (35, 36) or by import-
ing CT information based on a planning system–specifc format (15, 50).
The latter has the advantage that all Monte Carlo related input data can be
imported from the planning system instead of importing patient data as
DICOM from an external database. Within the Monte Carlo the CT image
might be translated into a Monte Carlo–specifc format, and the calculations
can be done on grids identical or different from the CT grid or the grid used
for treatment planning.
FIGURE 12.11
(Forcolorimage,seecover) Protons tracked through a treatment head (left), particle tracks in
a volume-rendered CT (middle), and dose (right) in a volume-rendered CT simulated with the
TOPAS Monte Carlo system (76) combined with the graphics system gMocren (75).
407 Dose Calculation Algorithms
Besides the radiation feld and the patient geometry other vital informa-
tion is needed to simulate a patient treatment. These are the gantry angle, the
patient couch angle, the isocenter position of the CT in the coordinate system
of the planning program, the number of voxels and slice dimensions in the
CT coordinate system, the size of the air gap between treatment head and
patient, and the prescribed dose (15). Also, couch and gantry rotations have
to be applied. The different coordinate systems (treatment control system,
treatment head, planning system, and CT system) have to be converted into
a common simulation coordinate system.
A user interface tailored to the planning system might be needed to facili-
tate the data fow from the planning system to the Monte Carlo system.
Results of the Monte Carlo simulation might be analyzed in the planning
system (if this is agreed upon with the vendor) or using a standalone visu-
alization tool.
12.2.9 Simplified Monte Carlo Dose Calculations
There are hybrid methods that combine aspects of Monte Carlo simulation
and analytical algorithms (see 12.1.5). There are many ways to improve the
accuracy of pencil beam algorithms by adding Monte Carlo components (e.g.,
using spot decomposition), which are often associated with signifcantly
decreased computational effciency (11, 61).
One obvious use of Monte Carlo in dose calculation algorithms without
the disadvantage of long calculation times is the implementation of Monte
Carlo–generated kernels to be used as look-up tables (61). Precalculated
depth–dose curves in water can serve as input for pencil beam algorithms.
Simplifed Monte Carlo methods using measured depth–dose curves in
water or other materials as input have also been proposed (25).
A signifcant speed improvement compared to codes like Geant4 and
FLUKA (see Chapter 9) has been reported for VMCpro (22). Here, vari-
ous approximations were introduced, for example, a simplifed multiple-
scattering algorithm and density-scaling functions instead of actual material
compositions. Nuclear interactions are treated as a correction to electromag-
netic interactions by using parameterizations and distribution sampling,
and it was shown that these are valid for dose calculations, at least for
broad beams.
Acknowledgments
The authors thank Dr. Bryan Bednarz for proofreading parts of the manu-
script and Dr. Jan Schümann for help with the fgures.
408 Proton Therapy Physics
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413
13
Precision and Uncertainties in Proton
Therapy for Nonmoving Targets
JatinderR.PaltaandDanielK.Yeung
CONTENTS
13.1 Introduction ................................................................................................ 414
13.2 Range Uncertainties in Clinical Proton Beams ..................................... 415
13.2.1 Inherent Uncertainties in Linear Stopping Power .................... 415
13.2.2 Uncertainties in the Formation of Broad Clinical Proton
Beams (Laterally and In-Depth) .................................................. 416
13.2.3 Uncertainties in the Determination of Radiological
Thicknesses of Bolus/Compensator Materials and
Accessories ...................................................................................... 417
13.3 Range Degradation in Patients ................................................................ 417
13.3.1 Patient Alignment and Setup in the Treatment Beam ............. 418
13.3.2 Relative Motion of Internal Structures with Respect to the
Target Volume ................................................................................ 418
13.3.3 Misalignment of the Apertures and Compensator
(If Present) with the Target Volume and Critical Organs ........ 419
13.4 Impact of Tissue-Density Heterogeneities ............................................. 419
13.4.1 Bulk Heterogeneities Intersecting the Full Beam ..................... 420
13.4.2 Bulk Heterogeneities Partially Intersecting the Beam ............. 421
13.4.3 Small but Complexly Structured Heterogeneities
Intersecting the Beam.................................................................... 422
13.5 CT Conversion Uncertainties ................................................................... 423
13.6 Planning and Delivery Uncertainties ..................................................... 425
13.6.1 Patient Selection ............................................................................. 425
13.6.2 Beam Delivery Techniques ........................................................... 426
13.6.3 Positioning, Immobilization, and Localization ......................... 426
13.6.4 Imaging for Treatment Planning ................................................. 427
13.6.5 Proton Treatment Planning .......................................................... 427
13.6.6 Uncertainty in Planning and Delivery ....................................... 428
13.7 Considering Uncertainties in Planning and Delivery .......................... 430
13.8 Summary ..................................................................................................... 430
References ............................................................................................................. 432
414 Proton Therapy Physics
13.1 Introduction
Proton therapy allows for conformal dose distributions with sharp dose
falloff for complex target volumes and unprecedented lower doses in nor-
mal tissue as compared to state-of-the-art conventional radiotherapy. Unlike
three-dimensional conformal radiotherapy (3DCRT), the precision and
accuracy of both the treatment planning and delivery of proton therapy are
greatly infuenced by random and systematic uncertainties associated with
the delineation of volumes of interest in 3D imaging, imaging artifacts, tissue
heterogeneities, patient immobilization and setup, inter- and intrafractional
patient and organ motion, physiological changes, and treatment delivery.
Furthermore, the locations, shapes, and sizes of diseased tissue can change
signifcantly because of daily positioning uncertainties and anatomical
changes during the course of radiation treatments. Transient intrafractional
changes, such as rectal and bladder flling status, in the treatment of prostate
cancer, can also introduce uncertainties in dose delivery. Because of these
changes, the 3D computed tomography (CT) images used for radiation treat-
ment planning do not necessarily correspond to the actual position of the
anatomy at the delivery time of each treatment fraction or even to the mean
treatment position. Therefore, the traditional assumption that the anatomy
discerned from 3DCT images acquired for planning purposes is applicable
for every fraction is treated with suspicion in proton therapy.
The published literature concerning acceptable planning and delivery pre-
cision and accuracy in proton therapy is sparse. However, the dose-response
curve in radiation therapy is quite steep in certain cases, and evidence sug-
gests that a 7–10% change in the dose to the target volume may result in
a signifcant change in tumor-control probability (1). Similarly, such a dose
alteration may also result in a sharp change in the incidence and severity of
radiation-induced morbidity.
Surveying the evidence on effective and excessive dose levels, Herring
and Compton (2) concluded that a therapeutic system should be capable of
delivering a dose to the tumor volume within 5% of the dose prescribed. The
International Commission on Radiation Units and Measurements (ICRU)
Report 24 (1) lists several studies in support of this conclusion. Because the
fnite range of protons makes proton therapy more susceptible to tissue-
density uncertainties than photon therapy, achieving the aforementioned
dose accuracy in proton therapy is a challenge. The primary effect of interfrac-
tional variations in the shapes, sizes, and positions of anatomical structures;
tissue heterogeneities; uncertainties in the conversion of CT numbers to rela-
tive electron densities; imaging artifacts; and beam delivery uncertainties in
conventional photon therapy is that they smear dose distribution in a patient
(3–5). On the other hand, similar uncertainties in proton therapy can result
in signifcantly compromised target coverage and/or normal- tissue spar-
ing, which limit the full potential of proton therapy. This chapter describes
415 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
precisions and uncertainties associated with proton therapy for nonmoving
targets; it also provides strategies for mitigating some of these uncertainties.
13.2 RangeUncertaintiesinClinicalProtonBeams
Proton beams are used in radiation therapy because of the physical char-
acteristics of energy loss by protons as they penetrate into matter, namely,
(1) protons have a fnite depth of penetration into material, the magnitude
of which depends on their energy and on the stopping power of irradiated
material; (2) protons exhibit a Bragg peak with negligible dose at the end
of their range; and (3) the dose from a proton beam falls off sharply, both
laterally and distally. Figure 13.1 shows the relationship between the proton-
beam energy and its maximum penetration in water. However, the clinical
proton beams are not mono-energtic and do not exhibit the same relation-
ship as shown in Figure 13.1. Clinical proton beams have energy and angular
spread, which is a result of energy losses and scattering in beam-modifying
devices, in dosimetric equipment in beam line, and in the air gap. Therefore,
the factors that contribute to range uncertainties in clinical proton beams
include the following:
• Inherent uncertainties in linear stopping power
• Uncertainties in the formation of broad clinical proton beams (later-
ally and in-depth)
• Uncertainties in the determination of radiological thicknesses of
bolus/compensator materials and accessories
13.2.1 Inherent Uncertainties in Linear Stopping Power
In a recent publication (6), Andreo explained that the range of I-values for
water and tissue-equivalent materials stated in ICRU reports 37, 49, and
0
20
40
60
80
100
120
100 0 200 300 400 500
Proton energy / MeV
R
a
n
g
e

i
n

w
a
t
e
r

/

c
m
FIGURE 13.1
Proton range in water as a function of energy.
416 Proton Therapy Physics
73 (7–9) for the collision stopping-power formulas, namely 67, 75, and 80 eV,
yield a spread of the Bragg peak’s depth as well as a spread of up to 3 mm
for a 122-MeV proton beam (Figure 13.2). He also found that the uncertainty
in the Bragg peak is energy dependent due to other energy-loss competing-
interaction mechanisms. Although accurate depth–dose distribution mea-
surements in water can be used when empirical dose-calculation models are
developed, the energy dependence of range uncertainties causes substantial
limitations. In the case of in vivo human tissues, where distribution mea-
surements are not feasible, a spread of the Bragg peak’s depth due to the
various soft-tissue compositions is of the same magnitude or more than that
of water. This fnding indicates that the inherent uncertainty in the compu-
tation of linear stopping power of water and tissue equivalent material can
result in an uncertainty of ±1.5%–2.0% in the range calculation of a clinical
proton beam.
13.2.2 Uncertainties in the Formation of Broad Clinical
Proton Beams (Laterally and In-Depth)
A broad proton therapy beam can be formed by passive scattering or by
dynamic scanning of a pencil beam both laterally and in-depth. In passive
scattering, the placement of scattering material in the beam provides a near-
uniform dose within the feld; a variable thickness propeller that rotates in
the beam gives uniform dose in-depth. In beam scanning, lateral and in-
depth uniform dose distribution is achieved by scanning a pencil beam
or a spot both laterally and in-depth (by changing its energy). The lateral
9.5
0
1
2
d
E
/
d
z

(
M
e
V
/
g

c
m
2
)

p
e
r

i
n
c
i
d
e
n
t

p
a
r
t
i
c
l
e
3
4
122 MeV Protons on water: I
w
- dependence
Peak spread is .7 g/cm
2
for 230 MeV protons
P122I
w
= 67eV
P122I
w
= 75eV
P122I
w
= 80eV
0.3 g/cm
2
10.0 10.5
Depth in water (g/cm
2
)
11.0 11.5
FIGURE 13.2
Variation of the depth of Bragg peak for the I-values of water 67, 75, and 80 eV for a 122-MeV
proton beam. (From Andreo, Phys Med Biol., 54(11), N205, 2009. With permission.)
417 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
positions and weights of each pencil beam or spot of a particular energy level
determine the lateral distribution for proton energy; weighting the pencil
beams or spots at each position within the feld determines the distribution
in-depth. In either method, the range of protons is changed either by insert-
ing absorbers into the beam path or by changing the beam energy upstream.
Typically, proton-beam energy uncertainty introduces a systematic range of
uncertainty of ±0.6–1.0 mm; however, because of the physical introduction of
beam-modifying devices in the beam line, the reproducibility of the range is
±1.0 mm for passively scattered proton beams.
13.2.3 Uncertainties in the Determination of Radiological
Thicknesses of Bolus/Compensator Materials and Accessories
Passively scattered proton beams utilize physical range compensators to
achieve distal conformance of the dose distribution to the target volume. The
thickness profle of the compensator is calculated based on the difference
between the distal ranges of the given ray to that of the global maximum
for the beam. Based on the stopping power of the compensator material
used, the water equivalent thicknesses necessary for the range pullbacks are
converted to physical thicknesses. The compensator is milled out of acrylic,
wax, or other low atomic number (Z) materials to minimize additional scat-
ter increased penumbra from the compensator. The nonuniformity of stock
compensator materials introduces small uncertainties in their relative stop-
ping power, which in turn affects the range of protons. Sharp gradients in
the compensator-thickness profle can also induce fuence perturbation as
protons are preferentially scattered away from the thicker part toward adja-
cent thinner areas. This scattering can result in hot and cold spots of 10%–
20% in dose near such gradients and minor range degradation. Furthermore,
nonuniformities in the thickness and/or composition of the accessories (e.g.,
immobilization devices, tabletops, and head holders) can also increase range
uncertainties. Range uncertainties introduced by both compensators and
accessories are generally systematic and ±1.0 mm.
13.3 RangeDegradationinPatients
Proton beams have a fnite and controllable penetration in-depth, which
is strongly affected by the stopping-power characteristics of the tissues
through which they pass. Therefore, patient-tissue heterogeneities and
their interfractional variability in the beam path during treatment add
to random uncertainties in range; thus, they contribute to range degrada-
tion. In clinical practice, two key parameters, the range and modulation,
are required to select the proton beam energy and spread-out Bragg peak
418 Proton Therapy Physics
(SOBP) width for adequate proximal and distal coverage of the target vol-
ume. Proton treatment–planning systems typically perform dose calcula-
tions based on a pencil beam grid with a resolution of the order of 1–3 mm.
The range and modulation width is then computed based on the most
proximal and distal points at which each pencil beam intercepts the target
volume. Afterwards, ray tracing is performed through the 3D image set to
calculate the total water equivalent thicknesses between these two points,
which in turn yields the proximal and distal ranges for each pencil beam.
The factors that contribute toward range degradation in clinical proton
beams include the following:
• Patient alignment and setup in the treatment beam
• Relative motion of internal structures with respect to the target
volume
• Misalignment of the apertures and compensator (if present) with the
target volume and critical organs
13.3.1 Patient Alignment and Setup in the Treatment Beam
If one wants the high-dose volume to cover the target up to its distal sur-
face over the entire feld, patient alignment and setup must be very precise.
Conformance of the dose distribution with the distal edge of the target vol-
ume, often referred to as “distal edge conformance,” depends on the location
of the distal target surface and on the presence or absence of intervening tis-
sue heterogeneities. Therefore, uncertainties in patient alignment and proton
beam setup directly translate into range degradation. The degree of range
degradation is highly variable and is dependent on tissue heterogeneities in
the treatment feld and the surface contour of the patient. Selecting “good”
beam directions is essential in proton beam therapy. One should avoid beam
directions that pass through complex or high-Z heterogeneities and large air
cavities that may change due to patient motion or misalignment or that are
tangential to the patient surface.
13.3.2 Relative Motion of Internal Structures with
Respect to the Target Volume
The fnite penetration of protons creates “distal edge conformance.” However,
the relative motion of internal structures with respect to the target volume
(e.g., due to bladder and rectal flling, tumor growth or shrinkage, and move-
ment of bony structures and/or air cavities along the beam path) results in
the degradation of high-dose conformation to the distal surface of the target
volume. The clinical consequences of this effect can be variable and poten-
tially severe. Hence, one should avoid beam directions that require protons
to stop directly in front of critical structures. Non-coplanar beam directions
419 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
that avoid critical structures directly, such as vertex or superior oblique felds
in treatments of the brain and the base of the skull, are common and often
advantageous in proton therapy.
13.3.3 Misalignment of the Apertures and Compensator
(If Present) with the Target Volume and Critical Organs
In passive beam scattering and uniform scanning, a brass or cerrobend
aperture controls lateral coverage, whereas a compensator that shifts the
SOBP upstream along each ray line achieves the distal range pullback.
Unfortunately, this approach has weaknesses. It does not allow for possi-
ble misalignment between the compensator and the patient because of to
patient-setup uncertainties and the motion of internal structures. It also
ignores multiple Coulomb scattering (MCS). One can mitigate the scatter-
ing problem by avoiding beam angles that result in sharp gradients in the
compensator, such as a tangential approach to bony ridges, large air cavi-
ties, or thick metal implants. Alternatively, one can smear the compensator
laterally so that its thickness at any point is the least thickness within its
neighborhood defned by the specifed smearing radius (see Chapter 10). The
consequence of the smearing process is that it assures target coverage, even
in the face of setup error and patient motion. This approach, however, has
two major drawbacks: (1) it exaggerates the vertical walls in the compensator
design, which can cause signifcant dose overshoot and undershoot, and (2)
it degrades distal dose conformance, limiting the ability to spare adjacent
critical structures distal to the target. Smoothing can be used to thin and
smooth out the compensator thickness profle in the feld-margin area. This
technique helps remove sharp gradients and allows for adequate penetration
even in the case of misalignment or patient motion but only at the expense
of less distal conformance. Because of misalignment of the apertures and
compensators, range degradation varies. One solution is to avoid proton
beam orientations that exacerbate the effect of aperture and compensator
misalignment. These approaches to compensation for distal conformance of
the target volume work reasonably well for most tissues in the human body;
however, they are not adequate when dense high-Z heterogeneities, such as
metallic implants, are in the beam’s path. Beam scanning can overcome some
of these issues. For example, intensity-modulated proton therapy, which
allows for conformal avoidance of such implants, is a possible alternative.
13.4 ImpactofTissue-DensityHeterogeneities
The infuence of and compensation for heterogeneities on dose distribu-
tion is far more critical for protons than photons. Heterogeneities alter the
420 Proton Therapy Physics
penetration and lateral scattering of protons in the patient. The dosimetric
impacts of these two effects in the presence of heterogeneities in proton
beams, relative to what occurs in a homogeneous medium, can potentially
be substantial because of the sharp dose falloff characteristics of protons.
When designing treatment beams, one must account for the presence of het-
erogeneities proximal to or within the target volume by not only calculating
their infuence on target volume coverage but also compensating for range
modifcations. The infuence of heterogeneities varies by clinical situation.
Three potential scenarios are possible: (1) the heterogeneity extends through
the entire proton beam; (2) the heterogeneity intercepts part of the proton
beam in the lateral direction; or (3) the heterogeneity is small and complexly
structured in the proton beam.
13.4.1 Bulk Heterogeneities Intersecting the Full Beam
A proton beam’s energy loss in a section of material of a particular areal
density (g/cm
2
) is similar for all materials with the exception of highly
hydrogenous substances (in which Z/A > 0.5) and high-Z elements (in
which Z/A < 0.5). Protons lose energy in a medium primarily through
electromagnetic interactions with atomic electrons. Because the mass of
protons is large compared with the mass of electrons, they lose only a
small fraction of their energy and are defected very little in each inter-
action. Although the probability of nuclear interactions increases with
energy of protons, its impact in the therapeutic energy range is small
except for the shape of the Bragg peak. Nuclear interactions essentially
decrease the intensity of protons in the beam by producing secondary
particles. These particles may be important from the biological point of
view because of their higher relative biological effectiveness (RBE) val-
ues but their impact on physical dose distribution is negligible. Therefore,
interposing a material composed of a substance other than that of the sur-
rounding medium primarily increases or decreases the beam’s range but
does not affect the shape of the depth dose in the region distal to the
heterogeneity. The change in a beam’s range (ΔR) in such a situation (mea-
sured in units of length and not medium-equivalent density) is altered by
an amount given by

R t
eq
medium
eq
slab
water
= −
( )
ρ ρ ρ / ,

(13.1)
where t is the physical thickness of the interposed slab, ρ
eq
medium

is the water
equivalent density of the interposed slab, and ρ
eq
slab
is the water equivalent
density of the surrounding medium. The water equivalent density is esti-
mated by comparing the mass stopping power of the material in ques-
tion with the mass stopping power of water at the energy of therapeutic
421 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
interest. Alternatively, it can be obtained by measuring the change in
residual range in water of protons passing through a water tank with and
without a physical thickness, t of the interposed slab. These relationships
hold equally when the interposed slab replaces the entire surrounding
medium. The interposed slab also affects the beam’s penumbra because
penumbras are largely caused by upstream multiple scattering, which is
dependent on the chemical composition of the interposed material; how-
ever, this phenomenon has little effect on tissue-equivalent materials and
can be ignored.
13.4.2 Bulk Heterogeneities Partially Intersecting the Beam
The infuence of bulk heterogeneity that partially intersects the pro-
ton beam is primarily limited to the interface between the two media.
The beam penetration is altered in the shadow of the heterogeneity and
decreases if the water equivalent density of the interposed heterogeneity
is greater than that of the medium. Equation 13.1 calculates the magnitude
of this decrease. The penetration is the same in the region not shadowed
by the heterogeneity. However, the differences in MCS of protons from
materials of various densities result in a perturbation of the dose at the
interface (i.e., a hot and cold spot at the interface). When any material of
density different from that of the surrounding medium is interposed in
the beam cross section, the beam penetration is altered in the shadow of
the material just as for the case of a fully intersecting heterogeneity and is
unchanged in the region not shadowed by the heterogeneity. However, at
the interface region, differences in MCS in the two adjacent materials cre-
ate a hot spot on the low-density side and a cold spot on the high-density
side. As a consequence of this effect, dose perturbation in air at the inter-
face can be as high as 50% in tissue:air interface (10). However, if one side
of the interface is not air, but rather the interface is between two mate-
rials of different scattering powers, then the dose perturbation is much
reduced; in the case of a bone:tissue interface, from ±50% to approximately
±9% (10). It is important to note that the magnitude of hot and cold spots
diminishes with depth in phantom due to increasing angular distribution
of the protons. Figure 13.3 illustrates the impact of introducing a com-
pensator with sharp edges in a 150-MeV proton beam. The difference in
MCS of tissue equivalent compensator material and air creates hot and
cold spots of the order of almost 10% at a mid-range depth in water. This
is probably the worst case scenario of dose perturbation at an interface in
clinical proton beams. The dose perturbation in the presence of bulk het-
erogeneity partially intersecting the beam within a patient is often much
smaller, especially if one side of the interface is not air, but rather the inter-
face is between two materials of different scattering powers. For example,
in the dose perturbation in the case of a bone, the tissue interface is much
smaller than for air:tissue interface.
422 Proton Therapy Physics
13.4.3 Small but Complexly Structured
Heterogeneities Intersecting the Beam
In most clinical situations, the patient presents a complex pattern of het-
erogeneities. The most extreme scenarios are found in the region at the
base of skull where protons may be directed along extended bone sur-
faces or in a complex bone–tissue–air structure such as the petrous ridge
or the paranasal sinuses. These complex heterogeneities create range per-
turbations and MCS-induced dose nonuniformities. Urie et al. (11) stud-
ied the infuence of these types of heterogeneities on proton beams and
concluded that MCS is the main cause of Bragg peak degradation. They
concluded that Bragg peak degradation cannot be predicted by simply
using the stopping powers of the materials composing the heterogene-
ities. They also suggested that Bragg peak degradation can be diminished
by increasing the angular divergence of the beam but only at the expense
of widening the lateral falloff. More recently, Sawakuchi et al. (12) car-
ried out systematic Monte Carlo simulation studies to understand this
phenomenon. Their Monte Carlo simulation data (Figure 13.4) confrmed
the fndings of Urie et al. and showed a trend of increasing distal falloff
width with increasing complexity of heterogeneities. They concluded that
MCS is the primary cause of Bragg peak degradation, nuclear scattering
contributes approximately 5% to the distal falloff of the Bragg peak, and
the energy spectra of the proton fuence downstream of various hetero-
geneity volumes are well correlated with Bragg peak distal falloff widths.
Most treatment planning algorithms that use analytical models cannot
–10
0
20
40
60
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
80
100
120
5 cm
2
4
6
8
10
12
14
D
e
p
t
h

[
c
m
.
H
2
O
]
20
40
60
80
100
120
–10 –5 0 5 10
Y [cm]
Measurement
6 cm.H
2
O 3 cm.H
2
O
Depth 8.7 cm
Eclipse (raw)
Eclipse (convolved)
Measurement (diode)
–5 0 5 10
Y [cm]
FIGURE 13.3
(Seecolorinsert.) Illustration of an edge-scattering effect. A 150-MeV proton beam traversing
through a tissue equivalent compensator with sharp edges introduces hot-and-cold spots of
the order of 10%. Note that the treatment-planning system can predict these hot-and-cold spots
within a few percent.
423 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
explicitly account for this effect; thus, there is a potential uncertainty in
distal edge degradation of ±1.0 mm.
13.5 CTConversionUncertainties
CT imaging remains the de facto standard in radiotherapy treatment plan-
ning. It provides a spatially accurate map of a patient’s anatomy together
with quantitative tissue measurements. CT Hounsfeld unit (HU) numbers
vary in value from −1000 for air to 0 for water and positive values for materi-
als with greater attenuation than water. These are derived directly from lin-
ear x-ray attenuation coeffcients. Although linear attenuation coeffcients are
functions of the x-ray energy spectrum, HU numbers can be experimentally
correlated to electron densities of known materials for a particular scanner
and radiographic technique with acceptable accuracy for megavoltage x-ray
treatment planning. Unfortunately, the theoretical relationship between
protons’ relative-linear stopping powers (RLSP) and linear x-ray attenu-
ation coeffcients is complicated and diffcult to evaluate analytically with
clinically acceptable accuracy. The RLSP values depend on physical density,
elemental composition, and mean excitation energy (I-value) of the material.
Yang et al. (13) show that physical density and elemental composition have
21.5
0.0
0.2
0.4
D

(
r
e
l
.

u
n
i
t
s
)
0.6
0.8
1.0
22.0
MCS/NS on
1 × 1
6 × 6
16 × 16
64 × 64
22.5
6 × 6 16 × 16 64 × 64
z (cm)
23.0 23.5 24.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
22.0
D

(
M
e
V

c
m
2

p
1
)

21.5 22.5
z (cm)
23.0 23.5 24.0
FIGURE 13.4
Degradation of a normalized Bragg peak distal falloff from a 230-MeV proton beam travers-
ing different density heterogeneities. The inset shows the absolute Bragg peak distal falloff.
For these simulations, both multiple Coulomb scatting and nuclear scattering were turned on.
Black areas shown in the inset represent compact bone (density = 1.85 g/cm
3
) in a mosaic-type
symmetrical geometries for equal total bone mass in each slab. (From Sawaguchi et al., Phys
Med Biol., 53(17), 4605, 2008. With permission.)
424 Proton Therapy Physics
a large effect on RLSP. For example, a 4% change in density results in a 4%
change in RLSP. Furthermore, data on human tissue densities and elemen-
tal compositions are sparse; therefore, for proton therapy, HU numbers, and
relative stopping power correlations are established either through the stoi-
chiometric method proposed by Schneider et al. (14) or the direct-ft method
proposed by Kanematsu et al. (15).
The stoichiometric method utilizes the chemical composition of test mate-
rials in conjunction with a simplifed version of the Bethe-Bloch formula to
compute RLSP. The HU numbers are then assumed to be represented by an
equation with three terms that correspond to photoelectric effect, coherent
scattering, and Compton scattering. Each term has a different Z-dependence
and includes a multiplicative constant. The goal of the calibration is to ft the
equation to the HU numbers for a given CT scanner for a large variety of tis-
sue equivalent test materials of known chemical composition and, from the
ft, deduce the values of the three constants. Given the constants, one can pre-
dict the HU number for any other material of known chemical composition.
In the direct-ft method, measurements of a wide variety of tissue equiva-
lent materials are made in both a CT scanner and a proton beam. These data
are then ft with a series of straight lines; typically, 3–4 straight lines cover the
whole range of HU numbers. Recent measurements at University of Florida
Proton Therapy Institute (UFPTI; Jacksonville, FL; S. Flampouri, personal com-
munication) showed that several parameters, including feld of view (FOV),
imaging kilovoltage peak (kVp), beam-hardening flters, reconstruction flters,
and patient size, infuence the accuracy of HU numbers and RLSP correla-
tion. The phantom size has the most impact on the HU numbers and RLSP
correlation. This is primarily attributed to how image reconstruction algo-
rithms handle beam hardening through patients in CT scanners. Figure 13.5
–1000
R
e
l
a
t
i
v
e

s
t
o
p
p
i
n
g

p
o
w
e
r
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
–500 0 500
HU
1000 1500
Large phantom
Plot area
Small phantom
Medium phantom
2000
FIGURE 13.5
Conversion of CT number to relative linear stopping power based on the stoichiometric
method (14). Data sets are obtained on a small, medium, and large phantoms containing ICRU
tissues. (Based on ICRU, Report 49, 1993.)
425 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
illustrates that the HU number can vary by as much as 150 HU for different
size phantoms, especially for higher-density materials. This variance implies
that a single direct-ft method can result in large uncertainties in RLSP. ICRU
Report 78 (10) notes that the overall accuracy of the conversion from HU num-
ber to water equivalent density is of the order of 2%–4% (1 standard deviation);
Moyers et al. reported similar numbers (16). However, Figure 13.6 indicates
that the overall accuracy can be improved to 1%–2% by using the direct-ft
method for each CT imaging protocol.
13.6 PlanningandDeliveryUncertainties
Although protons allow for control of dose deposition along and laterally
across the beam, the potential of dose uncertainties in proton therapy can be
quite large if adequate attention is not paid to the treatment planning and
delivery processes. In particular, one must consider patient selection; beam
delivery techniques; positioning, immobilization, and localization; imaging
for treatment planning; proton treatment planning; and uncertainty in plan-
ning and delivery.
13.6.1 Patient Selection
Proton therapy is an ideal option for patients for whom dose to normal-
tissue and/or organs at risk that surround the target volume pose a
0
20
40
#

B
e
a
m
l
e
t
s
60
80
100
120
0.25 0.2 0.3 0.35
Range difference (% range)
0.4
0
50
100
#

B
e
a
m
l
e
t
s
150
200
250
350
300
0.4 0.6 0.2 0.8 1.2 1
Range difference (% range)
1.4
FIGURE 13.6
Range uncertainties computed for a small pediatric and a large prostate patient. The discrep-
ancies in the proton range varied 0.4–0.7% and 0.6–1.2% for the prostate and pediatric patient,
respectively. Please note that these uncertainties are only due to the phantom size. Other
uncertainties such as position within the phantom, FOV, fltration, tissue composition, etc. are
not included. However, those uncertainties are much smaller in magnitude compared to the
phantom size.
426 Proton Therapy Physics
problem. Examples include spinal cord irradiation in pediatric patients
and skull-based tumors that are close to sensitive normal tissues, such
as the brainstem and optical chiasm. On the other hand, proton ther-
apy is not optimal if there are large heterogeneities in the beam’s path,
great potential for uncertainties in patient positioning and intrafrac-
tional internal-organ motion, or significant possibility of physiological
changes throughout treatment. Therefore, all potential candidates for
proton therapy must be carefully screened and evaluated using relevant
imaging studies that establish the clinical appropriateness of this treat-
ment modality.
13.6.2 Beam Delivery Techniques
Proton beams are delivered by scattering, scanning, or wobbling (a special
case of beam scanning; see Chapters 5 and 6). Scattered beams produce
uniform- dose distributions within the target volume for each beam, whereas
scanned beams can either produce uniform-dose distributions or highly
non-uniform-dose distributions with variable intensity within the target vol-
ume. In both cases, dose distributions are sensitive to materials interposed
upstream in the beam. All available beam delivery techniques must be fully
characterized in a treatment-planning system, and their inherent uncertain-
ties must be adequately documented to develop appropriate margin defni-
tion strategies.
13.6.3 Positioning, Immobilization, and Localization
The accuracy of beam placement relative to the patient, that is, relative to the
target volume(s) and the organ(s)-at-risk, is far more important in proton ther-
apy than in photon therapy. The sharp dose falloff in proton beams is a
double-edged sword. A small positioning inaccuracy can result in no dose
or too much dose at the point of interest. On the other hand, a small beam-
placement inaccuracy in photon beam therapy has very little effect; it just
smears the dose distribution. Therefore, the full advantage of protons can
only be achieved if there is good registration between the real or virtual
compensator and any heterogeneity within the patient.
Placement accuracies of 1–2 mm or even less are essential in proton ther-
apy; indeed, the emphasis on the beam-placement accuracy has less to do
with target-volume conformation (the target-volume defnition by itself has
the largest uncertainty) than with the conformal avoidance of nearby critical
structures.
Achieving the desired placement accuracy of 1–2 mm requires excellent
immobilization of the patient and accurate localization of the patient rela-
tive to the treatment equipment. The latter is usually accomplished by the
localization of bony landmarks or implanted fducials as seen in diagnostic
quality orthogonal-planar radiographs. Selecting an appropriate surrogate
427 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
for the target volume on a planar radiograph is essential. Timmerman
and Xing document that in some disease sites bony landmarks may not
serve as a good surrogate for the target; thus, the only possible solution is
volumetric imaging (17). At the present time, proton therapy systems do
not include on-board volumetric imaging for more accurate localization.
Hence, strategies for quantifying residual uncertainties in target local-
ization for each disease site need to be developed and implemented in
each clinic.
13.6.4 Imaging for Treatment Planning
Multimodality volumetric imaging is essential in all advanced radio-
therapy techniques, especially in proton therapy. Developing a realistic
patient model is far more important in proton therapy than in conventional
radiation therapy. A quality volumetric CT image set without contrast is
required for treatment planning and accurate characterization of tissue
densities and heterogeneities. A volumetric cine magnetic resonance imag-
ing (MRI) set is needed for better defnition of soft-tissue anatomy and
to create a patient-specifc motion model. Some clinical situations such as
lung may require a positron emission tomography (PET) image for more
accurate delineation of clinical target volumes. Each imaging modality has
its own limitation (e.g., high-Z material artifacts in CT, image distortion in
MRI, and poor resolution in PET). As a result, multimodality registration
is bound to have residual uncertainties. The magnitude of these uncertain-
ties is reported to be 0.5–6 mm and is technique and disease-site depen-
dent (18); consequently, each clinic should independently quantify these
uncertainties.
13.6.5 Proton Treatment Planning
Proton therapy planning is inherently an inverse process (see Chapters 10
and 11). The proton range, around which proton scattering causes hot and
cold spots, is dramatically altered in the shadow of tissue heterogeneities.
Therefore, designing a real or virtual compensator to alter the proton beam
to account for these heterogeneities is essential. The effects of heterogene-
ities cannot always be accurately predicted. For example, misregistration of
the compensator relative to the patient introduces both random and system-
atic uncertainties; beam scattering makes perfect compensation impossible;
and location of the heterogeneity can change. Therefore, one must be aware
of and mitigate the effect of possible hot-and-cold spots due to lateral scat-
tering effects as well as account for uncertainties associated with possible
misalignment of the compensator with the patient or internal organs and
tissues. These effects cannot be completely avoided, but their clinical conse-
quence can be mitigated with the selection of appropriate margins around
the target and critical structures. As suggested by Goitein (19), angular and
428 Proton Therapy Physics
depth feathering with multiple beams is another way of minimizing the
effect of heterogeneities, but it makes the planning and delivery process
more complex. In addition, metallic prostheses and surgical clips can cause
problems in more than one way. First, they cause severe artifacts in the CT
scans, which can contribute to large dose computation errors. Second, the
calculations of these metallic devices’ water equivalent thicknesses in vivo
have large uncertainties. The best solution is to override the HU numbers of
the imaging artifacts on treatment planning CT datasets with that of water
equivalent tissue and avoid proton beams being directed through the metal-
lic implants.
13.6.6 Uncertainty in Planning and Delivery
As we have shown, inherent and patient-specifc planning and delivery
uncertainties have far more dire consequences in proton therapy than in
photon therapy. Consequently, one must seek to understand the sources
of uncertainty and reduce them whenever possible as well as understand
the magnitude and implications of the inevitable residual uncertainties.
The mere process of identifying the sources and magnitudes of uncertain-
ties can be quite instructive and useful in establishing safe clinical prac-
tices. In particular, one must recognize that overall uncertainty estimates
tend to be local. In other words, a local clinical environment that includes
patient immobilization, imaging protocol, delineation strategy and proto-
col, treatment planning strategy, treatment localization, plan evaluation,
and treatment delivery equipment and technique has far greater infuence
on the overall uncertainty in proton therapy planning and delivery than
inherent uncertainties in the physics of proton therapy. Thus, each pro-
ton therapy clinic should estimate the sources and magnitude of residual
uncertainties in each step of the proton therapy process and develop miti-
gation strategies. Table 13.1 illustrates an example of such an uncertainty
analysis for nonmoving clinical targets and summarizes the source and
magnitude of each uncertainty. These uncertainties can only be mitigated
with better physics data; otherwise, the only solution is to account for
them in the margin recipes. However, other systematic uncertainties in
the proton range that are attributed to the reproducibility of the deliv-
ery system, CT calibration uncertainties, compensators, and accessories,
among other elements, can be substantially minimized through rigorous
quality assurance (QA) (see Chapter 8). Finally, patient-specifc uncertain-
ties can only be minimized by enforcing rigorous patient selection criteria
and better clinical protocols. Patients who have poor clinical dispositions
and signifcant heterogeneities or implants in the treatment area should
not be considered for treatment with protons. If proton therapy is clini-
cally warranted for such a patient, then appropriate margins should be
selected based on anticipated uncertainties in the planning and deliver of
proton therapy.
429 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
TABLE 13.1
Summary of Estimated Uncertainties in Treatment Planning and Delivery of
Nonmoving Targets with Proton Therapy
SourceofUncertainty
Uncertainty
beforeMitigation MitigationStrategy
Uncertainty
afterMitigation
Inherent range uncertainty
(pristine Bragg peak)
a
±1.3 mm None ±1–3 mm
Inherent range uncertainty
(spread out Bragg peak)
a
±0.6–1.0 mm None ±0.6–1.0 mm
Range reproducibility ±1.0 mm Rigorous QA ±0.5 mm
Compensator ±1.0 mm Rigorous QA of
compensator material
±0.5 mm
Accessories (table top,
immobilization jig, etc.)
±1.0 mm Rigorous QA of all
accessories
±0.5 mm
CT ±3.5% of range Site-specifc imaging
protocols
±1–2.0% of
range
Patient setup ±1.5 mm Rigorous patient
selection criteria
±1.0 mm
Intrafraction patient
motion
Variable Rigorous patient
selection criteria
±1.0 mm
Compensator position
relative to patient
Variable Rigorous patient
selection criteria
±1.0 mm
Range uncertainty
(straggling) due to
complex heterogeneities
±1 mm Rigorous patient
selection criteria
±0.5 mm
CT artifacts Variable Rigorous patient
selection criteria
±1.0 mm
Range computation in
water in a TPS
Variable Rigorous patient
selection criteria and
image edits
±0.5 mm
Range computation in
tissue of known
composition and density
in a TPS
±0.5 mm None ±0.5 mm
Multimodality image
registration
±1 mm Better dose
computation
algorithms
±0.5 mm
Treatment delivery (target
coverage uncertainty)
±1–3 mm Site-specifc image
registration protocols
±1–2 mm
Treatment delivery
(dosimetric uncertainty)
±1–3 mm Rigorous site-specifc
delivery technique
selection
±1 mm
Treatment delivery
(dosimetric uncertainty)
±1–3.0% Rigorous QA ±1.0%
a
Inherent uncertainty in the particle range determination caused by uncertainty of stopping
powers and its basic components, notably the mean excitation energy or I-value of a
substance.
430 Proton Therapy Physics
13.7 ConsideringUncertaintiesinPlanningandDelivery
Understanding and managing uncertainties are of extreme importance in
proton therapy for controlling tumors and reducing complications. These
uncertainties are often a result of the complex interplay of a variety of
error sources. Historically, the estimation and reporting of uncertainties
has been at best implicit. Experienced physicians recognize that “what you
see in the treatment plan is not what you get in the patient.” Currently
available radiotherapy treatment planning systems cannot explicitly show
the consequences of uncertainties on displayed plans. As a result, physi-
cians make mental assessments of the magnitude of the known uncertain-
ties and their dosimetric consequences. Such an assessment is acceptable
if the physician is able to discern all potential uncertainties and their con-
sequences. Unfortunately, these assessments become exceedingly diffcult
when greater geometric accuracy in dose delivery is warranted. A novel
method to estimate the uncertainty limit associated with a particular treat-
ment was originally described almost 30 years ago (20, 21). Goitein (20)
proposed three separate dose calculations to set higher and lower doses
at any point using extreme values for a few parameters, whereas Leong
(21) introduced a convolution method for blurring the planned dose with
a normal distribution of spatial displacement to investigate the effects of
random geometrical treatment uncertainties. However, these techniques
were never implemented into treatment-planning systems. More recently,
attempts have been made to predict the standard deviation of a planned
dose distribution (3, 22). These authors have demonstrated that with a com-
prehensive knowledge of spatial and dosimetric uncertainties in planning
and delivery, one can compute and display confdence-weighted dose dis-
tribution (with a preset confdence interval), confdence-weighted dose-
volume histograms, and dose-uncertainty-volume histograms. Examples
of these plan evaluation tools are given in Figure 13.7. ICRU (10) has also
described several other approaches for presenting uncertainty in proton
therapy and provides specifc recommendations for reporting proton ther-
apy uncertainties.
13.8 Summary
The rationale for the use of proton beams in radiotherapy, which is based
on their ability to provide uniform dose to the target while sparing the sur-
rounding tissue, is very compelling. This rationale is simply a consequence
of the physical characteristics of energy loss by protons as they penetrate into
matter. Protons have a fnite depth of penetration in material; the magnitude
431 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
of this penetration depends on the protons’ energy and the density of the irra-
diated material. This distinct advantage can turn into a double-edged sword
if adequate consideration is not given to the potential sources of uncertainties
in proton therapy. One must recognize that uncertainties are an inevitable
part of the planning and delivery of radiotherapy. In this way, protons are no
different from radiotherapy delivered with photons; however, the impact of
these uncertainties is much more profound in proton therapy. For example,
patient-positioning error, patient motion, misalignment of beam modifers,
changes in tissue characteristics, and dosimetric errors in planning and
delivery can result in a dose that is very different from what is planned on
being delivered to a patient. Therefore, we recommend the following proce-
dures for each patient considered for treatment with proton therapy:
• Analyze potential sources of uncertainty for each patient by evaluat-
ing their 3D/4D imaging data and clinical disposition.
• Make an effort to minimize the sources of uncertainties to the extent
possible.
• Document the magnitude of the residual uncertainties.
100
0.0
0 1000 2000 3000
Dose (cGy)
4000 5000 6000
Lower
bound
95%
0.1
0.2 N
o
r
m
.

v
o
l
u
m
e
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
80
60
40
20
0
0 1 2 3 4
Case 1
Case 2
5 6 7
Dose uncertainty (%)
(a)
(b)
(c)
Dose volume histogram
Upper
bound
FIGURE 13.7
(See color insert.) Illustration of confdence-weighted dose distribution (CWDD), conf-
dence-weighted dose-volume histogram (CWDVH), and dose-uncertainty volume histogram
(DUVH). The CWDD (a) is comprised of isodose lines with thicknesses proportional to the
local dose uncertainty, whereas the dose-uncertainty distribution was applied to the calcu-
lated dose distribution to make the upper and lower bounds of CWDVH (b). Finally, the DUVH
(c) is an accumulated histogram of dose uncertainty as a function of volume. (After Jin et al., Int
J Radiat Oncol Biol Phys., 78(3), 920, 2010.)
432 Proton Therapy Physics
• Develop strategies for the analysis, quantifcation, and display of
residual uncertainties.
• Implement a QA program that ensures that treatment can be given
with a confdence level that is established for the patient. For exam-
ple, a 95% confdence level will give a 95% assurance that the patient
receives the prescribed dose distribution.
References
1. International Commission on Radiation Units. International Commission on
Radiation Units and Measurements: Stopping powers and ranges for protons
and alpha particles. Report 24. 1976.
2. Herring DF, Compton DMJ. The degree of precision required in the radiation
dose delivered in cancer radiotherapy. Computers in radiotherapy. Br J Radiol
Special Report. 1971; 5(10):51–58.
3. Jin H, Palta J, Suh TS, Kim S. A generalized a priori dose uncertainty model of
IMRT delivery. Med Phys. 2008; 35(3):982–96.
4. Yan D, Xu B, Lockman D, Kota K, Brabbins DS, Wong J, et al. The infuence of
interpatient and intrapatient rectum variation on external beam treatment of
prostate cancer. Int J Radiat Oncol Biol Phys. 2001; 51(4):1111–19.
5. Yan D, Lockman D. Organ/patient geometric variation in external beam radio-
therapy and its effects. Med Phys. 2001; 28(4):593–602.
6. Andreo P. On the clinical spatial resolution achievable with protons and heavier
charged particle radiotherapy beams. Phys Med Biol. 2009; 54(11):N205–15.
7. International Commission on Radiation Units. International Commission on
Radiation Units and Measurements: Stopping powers for electron and posi-
trons. Report 37. 1984.
8. International Commission on Radiation Units. International Commission on
Radiation Units and Measurements: Stopping powers and ranges for protons
and alpha particles. Report 49. 1993.
9. International Commission on Radiation Units. International Commission on
Radiation Units and Measurements: Stopping powers of ions heavier than
helium. Report 73. 2005.
10. International Commission on Radiation Units. International Commission on
Radiation Units and Measurements: Prescribing, recording, and reporting pro-
ton beam therapy. Report 78. 2007.
11. Urie M, Goitein M, Holley WR, Chen GT. Degradation of the Bragg peak due to
inhomogeneities. Phys Med Biol. 1986; 31(1):1–15.
12. Sawakuchi GO, Titt U, Mirkovic D, Mohan R. Density heterogeneities and the
infuence of multiple Coulomb and nuclear scatterings on the Bragg peak distal
edge of proton therapy beams. Phys Med Biol. 2008; 53(17):4605–19.
13. Yang M, Virshup G, Clayton J, Zhu XR, Mohan R, Dong L. Theoretical variance
analysis of single- and dual-energy computed tomography methods for calcu-
lating proton stopping power ratios of biological tissues. Phys Med Biol. 2010;
55:1343–62.
433 Precision and Uncertainties in Proton Therapy for Nonmoving Targets
14. Schneider U, Pedroni E, Lomax A. The calibration of CT Hounsfeld units for
radiotherapy treatment planning. Phys Med Biol. 1996; 41(1):111–14.
15. Kanematsu N, Matsufuji N, Kohno R, Minohara S, Kanai T. A CT calibration
method based on the polybinary tissue model for radiotherapy treatment plan-
ning. Phys Med Biol. 2003; 48(8):1053–64.
16. Moyers MF, Miller DW, Bush DA, Slater JD. Methodologies and tools for proton
beam design for lung tumors. Int J Radiat Oncol Biol Phys. 2001; 49(5):1429–38.
17. Timmerman RD, Xing L. Image-Guided And Adaptive Radiation Therapy.
Philadelphia, PA: Lippincott Williams & Wilkins, 2009.
18. Brock KK. Results of a multi-institution deformable registration accuracy study
(MIDRAS). Int J Radiat Oncol Biol Phys. 2010; 76(2):583–96.
19. Goitein M. Radiation Oncology: A Physicist’s-Eye View (Biological and Medical
Physics, Biomedical Engineering). New York: Springer Press, 2008.
20. Goitein M. Calculation of the uncertainty in the dose delivered during radiation
therapy. Med Phys. 1985; 12(5):608–12.
21. Leong J. Implementation of random positioning error in computerised radiation
treatment planning systems as a result of fractionation. Phys Med Biol. 1987;
32(3):327–34.
22. Jin H, Palta JR, Kim YH, Kim S. Application of a novel dose-uncertainty model
for dose-uncertainty analysis in prostate intensity-modulated radiotherapy. Int
J Radiat Oncol Biol Phys. 2010; 78(3):920–28.
435
14
Precision and Uncertainties in Proton
Therapy for Moving Targets
MartijnEngelsmanandChristophBert
14.1 Introduction
For static targets one can assume that range uncertainties in the patient
geometry, though not known exactly, are consistent over the treatment
course, and one can estimate this uncertainty. Setup errors vary from day
to day and can also be estimated. These varying setup errors have a dose-
blurring effect on the tumor. In the worst case they can lead to a geometric
CONTENTS
14.1 Introduction ................................................................................................ 435
14.2 Motion from a Clinical Perspective ......................................................... 437
14.2.1 Over the Course of Treatment ...................................................... 437
14.2.2 Interfractional Motion ................................................................... 438
14.2.3 Intrafractional Motion ................................................................... 438
14.3 Magnitude of the Dosimetric Effect of Target Motion ......................... 439
14.3.1 Density Variations ......................................................................... 440
14.3.2 Interplay Effect ............................................................................... 441
14.4 Dealing with Motion ................................................................................. 443
14.4.1 The Importance of Motion Monitoring ...................................... 443
14.4.2 General Treatment-Planning Considerations ............................444
14.4.3 Motion Reduction .......................................................................... 445
14.4.4 Rescanning ..................................................................................... 447
14.4.5 Tracking ........................................................................................... 449
14.4.6 Adaptive Radiotherapy ................................................................. 451
14.5 Quality Assurance for Moving Tumors .................................................. 452
14.5.1 Treatment-Planning Quality Assurance..................................... 453
14.5.2 Treatment Delivery Quality Assurance ...................................... 454
14.6 Future Perspective ..................................................................................... 455
References ............................................................................................................. 456
436 Proton Therapy Physics
miss if the tumor moves too close to, or even outside of, the beam por-
tal. Having an estimate of the magnitude of range and setup uncertainties
allows the design of treatment plans that ensure proper target coverage
and sparing of organs at risk (OAR) for these static targets. Because the
density geometry is possibly inaccurate but consistent, this allows the use
of only a single computed tomography (CT) scan for treatment planning.
Uncertainties can be taken into account by safety margins in the case of
single-feld uniform dose (SFUD) treatments (Chapter 10) or, less straight-
forward, by means of robust planning (Chapter 15) in case of intensity-
modulated proton therapy (IMPT). Dose delivery to a moving target is
infuenced by all the uncertainties of static targets (see Chapter 13) and
adds considerable complexity to both treatment planning and treatment
delivery because of two aspects:
1. Treatment planning is typically performed on a static CT image,
whereas the actual density distribution is variable. Even a four-
dimensional (4D) CT scan used for treatment planning, which is not
yet common in clinical practice, is only a snapshot in time and does
not necessarily represent the 4D patient geometry during a treat-
ment fraction.
2. Depending on the mode of treatment delivery, target motion may
result in so-called interplay effects when the time structure of treat-
ment delivery is similar to the time structure of intrafractional
tumor motion.
A third effect, blurring of the (lateral) dose distribution even in the absence
of density variations and interplay effects, is similar to that of multiple setup
errors over a large number of fractions. This specifc effect can be taken into
account by classical safety margins (i.e., target expansion) and will not be
discussed in this chapter.
As a consequence of density variations and interplay effects, the “clas-
sical” approach of treatment planning on a single static CT scan, using
safety margins to expand the target volume and evaluating the dose
to the target and normal tissues on this CT scan, is clearly insuffcient.
Following classical forward planning, the dose distribution as observed
during treatment planning is not a good representation of what will be
delivered to the patient in any treatment fraction (Figure 14.1). This fgure
also shows that motion affects not only the dose to the target but also the
dose to the OAR.
This chapter provides an overview of the dosimetric consequences of tar-
get motion in proton radiotherapy, discusses strategies to mitigate these con-
sequences, and highlights the prerequisites for safe and accurate treatment
of moving tumors.
437 Precision and Uncertainties in Proton Therapy for Moving Targets
14.2 MotionfromaClinicalPerspective
Time-dependent variation in the target location and the patient density dis-
tribution can occur on different time scales: over the entire treatment course,
between subsequent treatment fractions (interfractional motion), and within
a treatment fraction (intrafractional motion). Some examples of density vari-
ations are shown in Figure 14.2. All of these will be briefy discussed in this
section. In Section 14.4, we will subsequently discuss how to effectively deal
with each type of motion.
14.2.1 Over the Course of Treatment
The term “motion," in this case, describes gradual, but systematic, variations
in the density distribution of the patient that can occur either because of a
redistribution of densities within the patient or the addition or disappear-
ance of matter. Examples of such variations are tumor shrinkage and growth
(1),  weight gain or loss, increase or decrease in lung density, and system-
atic variation in bowel and rectal flling. Redistribution of densities includes
changes in the motion pattern such as breathing trajectory or changes in the
baseline (2). McDermott et al. reported on the use of portal imaging to detect
anatomy changes in head and neck, prostate, and lung cancer (3). Barker
et  al. reported on the use of an integrated CT/linear accelerator system to
track tumor shrinkage, edema, and overall weight loss (4).
a) b)
FIGURE 14.1
Phantom simulating a unit density tumor (gray circle) in low-density lung tissue (white).
The thin black circle indicates a 10-mm 3D geometric expansion of the tumor into the plan-
ning target volume (PTV; see Chapters 10 and 11 for the applicability of the PTV for proton
therapy). (a) The dashed lines are isodose lines (50%, 80%, 90%, 95%, 100%) for a single pas-
sively scattered proton feld, incident from the top and designed to cover the PTV. (b) Isodose
lines for a 10-mm displacement of the tumor with respect to the treatment beam. The tumor
remains within the PTV but is underdosed, whereas the dose to certain parts of the lung is
increased.
438 Proton Therapy Physics
14.2.2 Interfractional Motion
Interfractional density variations can be as large as the gradual variations
over the entire treatment course, but they have a more random character.
Examples are variations in the amplitude of breathing, in the average tumor
position over the breathing cycle, and daily variation in rectal, bowel, and
bladder flling. For prostate tumors, daily variation in the rotation of the fem-
oral heads and corresponding variation in the patient exterior surface may
affect the proton range within the patient. Langen et al. provide an extensive
overview of interfractional position variation (5).
14.2.3 Intrafractional Motion
Much data has been published on the extent of intrafractional motion. Langen
et al. provide an overview of many of these studies (5). Without attempting
to be complete, we will discuss motion parameters for a few tumor sites.
For lung tumors, motion is typically largest for those tumors close to the
diaphragm and typically largest in the superior-inferior direction. Although
peak-to-peak motion of 30 mm can be observed, the typical motion is less
than 10 mm (e.g., 65% of patients in the study of Sonke et al.) (2). Hysteresis
in the motion trajectory can be observed (6) as well as a baseline drift over
the duration of the treatment fraction (7). Intrafractional variations in proton
a) b) c)
FIGURE 14.2
(Seecolorinsert.) Motion and density variation as a function of time. (a) Two CT slices acquired
a few weeks apart as an example of density variation over the course of the treatment, as indi-
cated by the white arrow. (Courtesy of Francesca Albertini, Paul Scherrer Institute.) (b) Two
CT slices for a prostate cancer patient on different treatment days as an example of interfrac-
tional variation. The variation in femoral head rotation affects the dose delivered by the typi-
cally applied lateral beam directions. (Courtesy of Lei Dong, MD Anderson Cancer Treatment
Center, Dallas, TX.) (c) Two breathing phases for a lung cancer as an example of intrafractional
variation. The red contours indicate the target position when in the exhale phase.
439 Precision and Uncertainties in Proton Therapy for Moving Targets
beam penetration can be especially large for tumors near the diaphragm or
heart. As the liver is relatively close to the diaphragm, peak-to-peak motion
with an average of 17 mm has been observed for these tumors under nor-
mal breathing conditions (8). For cardiac sarcomas, the heartbeat causes
both tumor excursion and, depending on the choice of beam angles, a large
variation (up to several centimeters) in water equivalent depth of the tumor.
Intrafractional motion of the prostate is mainly a consequence of moving gas
and feces and is typically less than a few millimeter (1 standard deviation)
(9), but the effects on proton penetration can be quite severe.
14.3 MagnitudeoftheDosimetricEffectofTargetMotion
In photon radiotherapy great effort is made, by means of image-guided
adaptive radiotherapy (10), to ensure translational and rotational alignment
of the target with the treatment felds. Density variations are a lesser con-
cern. They have only a minor effect on the dose distribution in the patient,
as the photon depth–dose distribution is rather shallow and insensitive to
density variations. Figure 14.3 shows the effect of a density variation along
the beam path for both a photon and a proton beam. For a proton beam, such
(motion-induced) density variations have a large dosimetric effect because
it can mean the difference, for example, between 100% and 0% of the pre-
scribed dose for the distal target edge. For the photon beam the variation in
the dose behind the density variation is limited to only a few percent.
I
n
c
r
e
a
s
e
d

d
e
n
s
i
t
y
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30
D
o
s
e

(
%
)

Depth (cm)
Photon (10 MV)
Proton SOBP
FIGURE 14.3
Central axis percent depth–dose (PDD) curves for a 10-MV photon beam and a proton spread-
out Bragg peak (SOBP). For each modality, the thin dashed lines are the PDD for the situation
of an increased density being present at a depth from 5 to 7 cm.
440 Proton Therapy Physics
Interplay effects in intensity-modulated radiation therapy (IMRT) have
limited dosimetric consequences if a suffcient number of treatment frac-
tions are delivered (11). In photon therapy, one can therefore estimate the
additional safety margin needed for treating moving tumors by a rather
straightforward blurring of the dose distribution inside the patient (12–14).
In proton therapy the fnite range and steep dose gradients make it much
more complex to deliver an accurate treatment for moving tumors (15, 16).
Because of the fnite range, density variations over time as well as the inter-
play effect can have severe dosimetric consequences. The next two sections
describe these consequences and their magnitude.
14.3.1 Density Variations
In case of single-feld uniform dose (SFUD) proton therapy, density varia-
tions (without interplay effect) affect the dose near the proximal and distal
edge of the target. For IMPT these density variations may furthermore have
dosimetric consequences within the target volume because of mismatches of
the possibly very steep dose gradients of the individual felds.
Engelsman et al. used a simplifed phantom geometry and beam setup
to analyze the effect of setup errors and intrafractional lung tumor motion
(17). They found that the minimum dose in the target could drop from 95%
down to 40% and 65% for a 5-mm setup error and 10-mm breathing motion,
respectively, if density variations are not proactively taken into account in
the design of the treatment plan.
Kang et al. analyzed a variety of forward planning approaches for lung
tumors in real patient geometries under intrafractional motion (18). None of the
planning approaches accurately predicted the dose distribution in the target
(PTV), when comparing the dose as accumulated over all phases of the breath-
ing cycle to the dose distribution as predicted by the plan created on the single
treatment-planning CT scan. Although the dose to critical structures was only
marginally affected, dose reductions in the PTV of up to 5% were observed.
Mori et al. analyzed the variation in water equivalent path length over the
breathing cycle for a set of 11 lung cancer patients (15). As a function of beam
angle and breathing phase, the average range variation observed was a few
millimeters, but maximum local range variations between 10 and 35 mm
were observed. Obviously these range variations affect the dose distribution,
necessitating the use of larger safety margins to ensure target coverage at the
cost of more dose to the OAR. Figure 14.4 shows an example of range varia-
tion for a single-beam direction aimed at a lung tumor.
Hui et al. analyzed the effect of interfractional motion and anatomic
changes for lung cancer patients by means of weekly 4D CT scans and dose
recalculation at the end-inhale and end-exhale phases (19). Although the
typical patient showed only little variation in target coverage, they conclude
that adaptive replanning may be indicated in selected patients, mainly to
mitigate dose variation in the surrounding OAR.
441 Precision and Uncertainties in Proton Therapy for Moving Targets
In current clinical practice the changing density distribution is taken into
consideration at the time of treatment plan design, based on the experience
of the dosimetrist or medical physicist. This approach leads to acceptable
dose distributions, but several studies showed that 4D treatment plan assess-
ment and/or adaptive planning approaches could further improve dose cov-
erage of the target volume and reduce dose to OAR.
14.3.2 Interplay Effect
The interplay effect describes the detrimental effect on the dose distribu-
tion for moving targets if delivering a (dosimetric) fraction of the intended
dose distribution is not near-instantaneous, as for example in pencil beam
scanning (PBS). These interplay effects can occur due to any motion not miti-
gated by motion reduction (e.g., gating, breath-hold) and for any remaining
motion within a gating window. SFUD proton therapy, even if delivered by
means of fast-spinning range modulator wheels and not by stationary ridge
flters, does not suffer from interplay effects because the motion of the beam
is much faster (e.g., periods of 100 ms) than target motion. Interplay effects
can, however, be substantial in the case of layer stacking (20, 21) and, more
generally, in the case of PBS. This section will not discuss layer stacking but
will focus on interplay effects for PBS only. Figure 14.5 shows an example of
the possible severity of the interplay effect for a single-feld irradiation of a
moving lung tumor with a scanned carbon beam.
A PBS dose distribution is typically delivered (and treatment planned)
by grouping the necessary spot positions in range layers (iso-energy lay-
ers). Although dose delivery within a range layer can be near instantaneous,
T 0%
S
I
L R
T 10% T 20% T 30% T 40%
15
(mm-WEL)
7.5
0
T 50% T 60% T 70% T 80% T 90%
FIGURE 14.4
(See color insert.) Range fuctuation for a posterior to anterior beam direction aimed at a
tumor moving in lung. The range variation is expressed in water equivalent length (WEL) and
superimposed on 4D CT images. (From Mori et al., Int J Radiat Oncol Biol Phys., 70(1), 253, 2008.
With permission.)
442 Proton Therapy Physics
the time needed to switch between layers can give rise to interplay effects
because the target motion phase changes between individual layers.
Interplay effects for PBS have long been recognized to be a potential issue
for proton radiotherapy (16, 22–28) and are one of the reasons why PBS is
currently not, or almost not, used in a clinical setting to treat patients with
moving tumors. Interplay affects the dose at the tumor edge and within the
tumor (16). Exactly how interplay affects the dose distribution depends on
the target motion characteristics as well as the characteristics of the dose
delivery system, such as the choice of scan pattern and the scanning speed.
Lambert et al. showed that scanning in planes parallel to the beam direc-
tion (i.e., parallel to the slowest scan direction) is worse than scanning in
planes perpendicular to the beam direction (16). Their computer simulation
on a simple homogeneous phantom showed that interplay effects can result in
100% of the target volume receiving a dose outside the recommended limits.
Phillips et al. showed that dose inhomogeneity increases most for motion
in the direction of the slowest scanning speed (22). They found that dose
uniformity in the target varied between 1% in the case of no motion, to 11%
in the presence of breathing motion. If scanning a single layer takes 1–2 s,
characteristic patterns may occur in the dose distribution (25): diagonal
stripes for motion perpendicular to the (major) scanning direction and stripe
(a) (b)
Stationary, CTV Stationary, ITV
R
T = 4s, ϕ = 0°
T = 4s,
ϕ = 90°
T = 4s,
ϕ = 0°
T = 4s, ϕ = 90°,
90% extr.
T = 4s, ϕ = 90°
50%
95%
105%
T = 4s, ϕ = 90°, 90% extr.
75
100
80
60
40
20
V
o
l
u
m
e

[
%
]
0
80 85 90 95
Dose [%]
100 105 110 115
Stationary
(d) (e)
(f )
(c)
FIGURE 14.5
(Seecolorinsert.) Isodose distributions for a single PBS irradiation of a moving lung tumor
showing the interplay effect between dose delivery and tumor motion. The blue, red, and yel-
low lines indicate the 50%, 95%, and 105% isodose levels, respectively. (a and b) Stationary
dose distributions for treatment plans to the CTV and to an internal target volume accounting
for respiratory motion only (ITVr; ICRU Report 62, 1999.). (c) Dose distribution for a breathing
period of T = 4s with the beam starting at the inhale breathing phase (φ = 0°). The interplay
pattern is sensitive to changes in initial breathing phase, (c) versus (d), and to changes in the
scan speed, (d) versus (e), simulated in this case by changing the extraction rate from the syn-
chrotron to 90% of the initial value. (f) Corresponding DVHs of the target. (Reprinted from Bert
et al., Phys Med Biol., 53(9), 2253, 2008. With permission.)
443 Precision and Uncertainties in Proton Therapy for Moving Targets
patterns for motion parallel to the scanning direction. Modern scanning sys-
tems, however, are able to scan a single layer in less than one-tenth of a sec-
ond. Typically the slowest scanning direction is the depth direction, that is,
from range layer to range layer, with current commercially available systems
having range layer alteration times of a single to a few seconds.
For actual patient geometries the extent of the effect is shown by, for example,
Bert et al (25). They performed a treatment-planning study using a number of
4D patient geometries and a large set of individual motion parameter combi-
nations (e.g., motion amplitude, breathing period). The volume of the clinical
target volume (CTV) covered by 95% of the prescribed dose was 71.0 ± 14.2%
(mean ± standard deviation) for a single fraction for a single beam direction.
They conclude that especially for small fraction numbers (i.e., hypofraction-
ation) treatment of moving targets with scanned particle beams requires
motion mitigation strategies such as rescanning, gating, or tracking.
14.4 DealingwithMotion
There are a variety of strategies available to mitigate the effects of motion in
proton radiotherapy. The best approach to deal with motion may differ for
different tumor sites and is likely a combination of some of the strategies
described below. Although some of these strategies act only at the time of
treatment delivery, all of them already have to be taken into account at the
time of treatment plan design. Gating, for example, controls the patient and
target position inside the treatment room, but the treatment plan has to be
designed to the correct phase(s) of a 4D CT scan. Residual uncertainty in the
target position (e.g., within the gating window) also has to be addressed dur-
ing treatment planning.
14.4.1 The Importance of Motion Monitoring
Most of the strategies discussed in the following sections (e.g., beam gat-
ing and especially beam tracking) depend heavily on accurate assessment of
the time-dependent target position and patient geometry. Although motion
monitoring is not unique to proton therapy, it should be clear that the impor-
tance of precise motion monitoring, when compared to photon radiotherapy,
is much higher because of the strong dosimetric impact. In addition, some
motion-monitoring devices are not fully compatible with a proton beam. We
will therefore provide a brief overview of the various motion-monitoring
strategies.
Motion-monitoring can be as simple as observing if the patient indeed
holds his breath during beam-on, for example, in deep-inspiration breath-
hold (29). It can also be as technologically advanced as real-time image-guided
444 Proton Therapy Physics
radiotherapy (IGRT) by means of integrating a magnetic resonance imaging
(MRI) scanner into the treatment room (30), although this has not yet been
attempted for proton therapy. Other strategies include the 4D tracking of
implanted markers (31) and motion phase/amplitude monitoring by means
of external markers. The former strategy has questionable usability in proton
therapy due to the disturbance of the deposited dose distribution. The lat-
ter strategy relies on assuming or measuring a correlation between external
markers and internal target position (32). A hybrid solution that does not
require ionizing radiation for measuring the position of implanted fducials
as described by Shirato et al. (31), but that can provide comparable accuracy,
is model-based prediction of internal target motion. In these approaches a
model is trained by parallel observation of internal motion (e.g., based on
implanted fducials) and an external motion surrogate, such as the height of
the chest wall. During treatment delivery the model then predicts internal
target position based on frequent assessment of the external surrogate posi-
tion. In case of longer irradiations the model might be updated or checked
by additional measurements of the internal motion. Clinically such a model
approach is used in the Cyberknife Synchrony (Accuray, Sunnyvale, CA) (33).
Accurate motion monitoring is not limited to the treatment room only but
obviously should also take place during the treatment preparation phase
(e.g., motion assessment during 4D CT scanning). Ideally, the same motion-
monitoring system is used both at the treatment preparation phase and dur-
ing treatment delivery.
14.4.2 General Treatment-Planning Considerations
During treatment planning one can (try to) address uncertainties in the actu-
ally delivered dose distribution as a consequence of a time-varying geome-
try. A simple approach is to choose beam directions that minimize the effect
of motion. For example, one should choose not to use beam directions that
skim the heart or that treat through the diaphragm. The resulting variation
in local proton range affects the required distal safety margin as well as the
probability to spare OARs distal to the target. In choosing beam directions it
may also be valuable to increase the number of felds in the treatment plan/
treatment fraction because this averages out the dose uncertainties of single
beams. Knopf et al. investigated the importance of the number and direction
of felds in a treatment plan (34) and suggested two strategies: For treatment
plans having two felds or less the beam directions should be chosen care-
fully, and an increased number of rescans is indicated in order to reduce the
interplay effects. For multiple-feld plans rescanning may not be necessary
for small target motion if at least some of the felds have a favorable direction
with respect to target motion.
With beam directions chosen, it is still a challenge to design a plan that
ensures target coverage in the presence of (remaining) motion. Chapter  10
provides a few approaches for the case of SFUD delivered by means of
445 Precision and Uncertainties in Proton Therapy for Moving Targets
passive scattering. Typically, in passively scattered proton therapy (PSPT)
one performs forward (or manual) treatment planning and chooses beam
parameters (range, modulation width, and range compensator shape) that
either ensure target coverage in every separate breathing phase or that will
likely ensure target coverage when the dose is accumulated over the motion
cycle. SFUD using PBS is similar, but next to providing target coverage under
density variation, it furthermore requires analysis of the interplay effect (e.g.,
by multiple 4D dose calculations with varying motion parameters).
Bert et al. suggested, for PBS and limited target motion, optimizing the
spot size and the distance between spots laterally, and Bragg peak shape
and distance between energy layers longitudinally for a reduction of the
dosimetric effect on motion (27). They show that increasing the overlap
between pencil beams provides a sort of “intrinsic” rescanning. As more
pencil beams contribute to the dose at each position in the target, no addi-
tional rescanning may be needed. Within the range layer, decreasing the
distance between spots or increasing the spot size increases the pencil beam
overlap. In the latter case, the lateral beam penumbra may, however, be nega-
tively affected. In the direction parallel to the beam one can decrease the
distance between range layers and potentially also the shape of the Bragg
peak by, for example, incorporating a small ripple flter to broaden the peak.
The effectiveness of the strategy of increasing the overlap of spots is, how-
ever, reduced at very high dose gradients where some spots will deliver no
or very little dose.
IMPT, by defnition, adds the ability to optimize the dose distribution over
multiple beams all at once. In case of static tumors and no uncertainties the
automatic optimization of IMPT plans allows the use of pencil beams that
are most benefcial in geometrically sparing OAR. With range and setup
uncertainties and, more important for this section, a variable-density geome-
try, robust optimization (Chapter 15) will furthermore allow the use of those
pencil beams that suffer least from density variations.
Regardless the use of SFUD or IMPT, one should not expect the treatment
plan on the static CT scan to appear perfectly conformal to the target. Target
motion and other density variations add to the necessary distal overshoot
and proximal undershoot already needed to ensure target coverage for range
uncertainties and setup errors.
Choosing the number and direction of beams wisely, maybe in combina-
tion with robust optimization, can help mitigate the effects of both (remain-
ing) intrafractional motion (e.g., for lung cancer) and interfractional density
variations (e.g., for prostate cancer). Increasing pencil beam overlap reduces
the effect of intrafractional motion.
14.4.3 Motion Reduction
A logical method to prevent unwanted effects of motion is to reduce the
motion itself. Reduction of tumor motion is not unique to proton therapy,
446 Proton Therapy Physics
but the potential gain is larger than in photon radiotherapy because it may
improve reproducibility in both the target position and the patient density
distribution. What follows is a brief description of a number of motion-
mitigation strategies. When applied during CT scan acquisition they help
reduce CT artifacts. When applied during treatment delivery they may pre-
vent variation in the day-to-day delivered dose to the target and healthy
tissues.
Use of an abdominal press reduces residual tumor motion (35), but may
limit the possible incident beam directions. Two other approaches to reduce
residual tumor motion are beam gating (36, 37) and breath-hold (38). In both
cases, treatment planning should ideally be based on a 4D CT scan  (39),
choosing a specifc phase of the 4D CT scan for treatment planning. If 4D
CT acquisition is not available, gated CT or CT acquisition in breath-hold
can be used if the extend of motion is checked by other means (e.g., in a
fuoroscopy study). The quasi-stationary geometry represented by the CT
phase can then be reproduced at the moment of treatment delivery as part of
patient positioning. In case of gating, the patient breathes freely with radia-
tion delivery inhibited if the target is not within the defned parts of the
breathing cycle, the gating window. The treatment beam is triggered on and
off automatically by a motion-monitoring system. Residual motion within
the gating window requires mitigation for interplay effects in case of PBS
as described above (increased spot overlap) or by combination with other
mitigation schemes such as rescanning (24). In case of breath-hold it is the
patient who is triggered, by audio or visual feedback, to maintain the cor-
rect target position for a prolonged time period of up to 20 s or as long as the
patient can comfortably manage. Again, radiation is only delivered with the
target close enough to the intended location. Both gating and breath-hold
increase the overall time to deliver a treatment fraction, which may be a
challenge for a sick patient.
Perhaps the most advanced method of minimizing breathing motion is
the use of apnea during controlled short anesthesia (“General intubation
anesthesia under oxygen insuffations in apnea”) as utilized at the Rinecker
Proton Therapy Center (Munich, Germany) (40).
As a more general approach, prescribing a diet can reduce inter- and
intrafractional position and density variation (9). It can also help control the
patient’s weight over the treatment course. Furthermore, it may reduce the
passing of gas that otherwise could affect the accuracy of, for example, pro-
ton therapy for prostate cancer.
Abdominal press, gating, breath-hold, and apnea reduce (the effect of)
intrafractional motion. These techniques may, however, reduce intrafrac-
tional motion at the cost of increasing interfractional variations, that is,
variation in the daily “frozen” target position. Rietzel et al. stated that the
reproducibility of the target position between beam-on periods should be
in the order of 3–5 mm to allow accurate delivery of (intensity-modulated)
particle therapy (41).
447 Precision and Uncertainties in Proton Therapy for Moving Targets
14.4.4 Rescanning
Rescanning, also called repainting, is a strategy to mitigate interplay effects
by controlling the timing of beam delivery with respect to the motion cycle.
Rather than delivering all dose continuously in one pass, dose delivery to an
appropriately sized internal target volume is broken up into several cycles,
thereby smoothing the delivered dose distribution. This decreases the risk of
large localized dose discrepancies at the cost of accepting smaller dose dis-
crepancies to a larger volume. To frst order, multiple rescans within a treat-
ment fraction has the same dose averaging effect as described by Bortfeld
et al. (11) for interplay effects in multiple-fraction IMRT treatments (i.e., the
standard deviation in dose to a point in the target is expected to reduce by the
square root of the number of rescans). Figure 14.6, however, shows that more
rescans are not automatically better. The effectiveness of the chosen rescan-
ning strategy depends as much on the target motion characteristics as on the
timing and dosimetric characteristics of treatment delivery. The Paul Scherrer
Institute (PSI), for example, is developing a PBS gantry that can change the
energy in about 80 ms per 5-mm range step. They can treat a 10 × 10 × 10-cm
3

target within 8 s, which is fast enough to allow dose delivery within a single
breath-hold, thereby circumventing interplay effects completely.
There are many variables to be adjusted as part of a rescanning strategy
(see below), and the optimal rescanning solution is best determined at the
time of treatment planning (41).
The only parameter that is typically fxed is that the direction of slowest
rescanning is the depth direction. Anything else (e.g., the scan path or the
scanning speed within a layer) can be subject of optimization, and many of
these variables have not yet been extensively researched in clinically realistic
density geometries. Where possible, in this section we will follow the scan-
ning/rescanning nomenclature as used by Zenklusen et al. (28).
Within a range layer the dose can be delivered by means of discrete spot
scanning, continuous scanning or continuous line scanning (see Chapters 6
No motion 1 rescan 4 rescans 6 rescans 8 rescans
max: 103.2%
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
a) b) c) d) e)
FIGURE 14.6
(Seecolorinsert.) 4D treatment-planning study of a tumor moving in a unit-density phantom
(gray). The thin dashed line indicates the target outline. The solid white line indicates a proton-
range adjusted internal target volume. The fgures show the calculated dose distributions ver-
sus the number of rescans, assuming the dosimetric and dose delivery timing characteristics
of Gantry 2 of the Paul Scherrer Institute. (a–e) Dose distribution for no motion and one, four,
six, and eight rescans, respectively. (Courtesy of Dirk Boye, Paul Scherrer Institute.)
448 Proton Therapy Physics
and 11). The choice of which method to use affects the time structure of dose
delivery within a layer and thereby the interplay effect. For example, indi-
rectly, if the intention is to limit the total treatment time, this can also affect
the number of rescans that can be performed.
There are two approaches for rescanning within a range layer. In isolayered
rescanning there is a maximum to the dose delivered per spot that is small in
absolute dose (particle numbers). This means that spots with a higher weight
will be rescanned more often than lower-weighted spots and that the beam
path varies for each rescan because the number of remaining beam positions
within a layer changes. In scaled-rescanning each spot is rescanned equally
often. This can lead to arbitrarily low spot weights, the application of which
may be limited by technical constraints of the treatment delivery system.
There are also several possibilities for rescanning the dose distribution to
the entire target volume. In volumetric rescanning the three-dimensional
(3D) dose distribution for a single feld is delivered one after another, with
the absolute dose delivered per scan reduced proportionally to the number
of rescans. As in scaled rescanning, this may lead to too low spot weights.
In nonvolumetric rescanning (also known as slice-by-slice rescanning) all
dose is delivered within an energy layer by means of rescanning, before
switching to the next energy layer and repeating this process. It is also fea-
sible to only rescan the deepest layers, which typically have the highest spot
weights. Because of the proton depth–dose distribution this will result in
intrinsic rescanning of the more proximal layers as well (41).
The time structure of rescanning is the fnal parameter that can be varied.
Furukawa et al. suggest the use of phase-controlled rescanning (PCR) (24).
PCR aims at temporally adjusting the number of rescans to the periodical
breathing cycle. In their case, PCR is used in combination with gating, and
thus the extraction from the synchrotron is adjusted such that the number of
rescans in an energy layer is synchronized to the length of a gating window.
This approach reduces the standard deviation in the target dose by roughly
a factor of 2 compared to when PCR is not used. For a cutoff of 2% target
dose inhomogeneity it allows a reduction in number of rescans from 20 to 6.
Whether or not this translates into a decrease in treatment delivery time will,
however, depend on the gating effciency. A similar approach was proposed
by Seco et al. who investigated fve different rescanning strategies by means
of a simulation study on a homogeneous phantom aiming to deliver a homo-
geneous dose over 30 fractions (26). The most effective method was breath-
sampled rescanning in which the layer-scan start times of each rescan are
distributed evenly throughout the breathing cycle. When rescanning 6–10
times, dose delivery errors were below 5% at the cost of only a minimal
increase in treatment time.
Zenklusen et al. analyzed various rescanning strategies (28). Their exten-
sive simulations showed that rescanning needs to achieve a dose inhomo-
geneity of less than 1.5% (root mean square) in order to comply with the
International Commission on Radiation Units and Measurements (ICRU)
449 Precision and Uncertainties in Proton Therapy for Moving Targets
recommendations of a target dose between 95% and 107%. For motion up to
5-mm amplitude their simulations indicated that, when using spot scanning,
it is best to have the number of rescans of a spot be proportional with the
spot weight (i.e., “isolayered rescanning”). Large tumor sizes beneft from
continuous line scanning as it allows more rescans per time period, thereby
substantially reducing the overall treatment time. For full beneft of continu-
ous line scanning it has to be combined with fast energy switching. They
furthermore concluded that for motion amplitudes above 5-mm rescanning
has to be combined with a strategy to control the motion amplitude, such as
breath-hold or beam gating. This reduces both dose inhomogeneity in the
target and the required safety margins.
For limited motion, rescanning is an effective method to reduce interplay
effects in PBS. There are, however, a number of downsides. Rescanning inevi-
tably increases the treatment time of each treatment fraction, but this increase
may be inconsequential with the development of faster scanning and layer
switching. More research is needed to determine the optimal beam scanning
parameters for specifc tumor sites and motion characteristics. For rescanning
to be most effectively applied to patient treatments, commercial treatment-
planning systems need to be able to allow optimization of all parameters,
taking into account the limitations of the various treatment delivery systems
and the patient motion characteristics (i.e., 4D treatment planning).
It is important to realize that rescanning addresses the consequences of
the interplay effect only (i.e., only one of the effects of intrafractional motion).
The amplitude of target motion and the corresponding density variation,
either intra- or interfractional, still has to be addressed in the treatment-
planning phase, by using safety margins and any of the approaches men-
tioned in Section 14.4.2.
14.4.5 Tracking
Arguably at the moment the most sophisticated and technically challenging
approach is so-called beam tracking. In beam tracking the aim is to adjust
the position of the beam to the time-varying position of the target, in three
dimensions. Figure 14.7 shows a possible implementation of beam track-
ing for carbon beam scanning and some dosimetric results obtained with
this system (42). The idea was originally proposed for photon therapy (43)
and has been clinically applied in, for example, Cyberknife treatments (44).
Tracking in photon therapy is a two-dimensional (2D) problem; one needs to
adjust the beam (or segments thereof) to the time-varying lateral 2D position
of the target with respect to the central beam axis. In proton therapy, lateral
target alignment is only half a solution, and one also has to adjust for the
third dimension: the water-equivalent radiological depth of each point in
the target as a function of time. We stress that the essence of tracking differs
from that of rescanning in that it is not a mitigation technique but rather
addresses the problem, motion, directly.
450 Proton Therapy Physics
There are three prerequisites to successful application of beam tracking
in proton radiotherapy. The frst is a highly accurate treatment delivery sys-
tem that allows fast position and energy switching. Saito et al. estimate that
the scanning system should be able to adapt to an updated target position
within a time-scale comparable or even shorter than the irradiation time of
a single spot (45). Updating the spot position in the depth direction on such
a short time scale is a challenge. PSI Gantry 2 allows a 5-mm shift in proton
range in about 80 ms, whereas Saito et al. developed a custom wedge-system
that allows 5-mm depth correction within 16 ms (45). Even higher energy
modulation speeds should be possible with electromagnetic solutions rather
than using the mechanical modulation methods of both PSI and Saito et al.
Chaudhri et al. proposed an energy modulation system that facilitates a pair
of dipole magnets to pass the beam through a stationary wedge-shaped
absorber within the beam line (46). The initial tests in “slow-motion” focus-
ing on beam parameters were promising. Implementation at full speed will
require further research (e.g., with respect to updating the settings of the
beam line).
The second prerequisite is accurate real-time monitoring of the target posi-
tion. Van de Water et al. found that the positioning error (root mean square)
should be less than 1 mm to ensure a suffciently homogeneous target dose
Lateral position
Beam
energy
Sensor Motion
TCS
Film
Beam
Scanner
magnets
Wedge
system
Absorber
Stationary
a)
c)
b)
–20
0
20
–20 0
y

[
m
m
]
20 40 –40 –20 0
x [mm]
–40
x [mm]
20 40 –40 –20 0
x [mm]
20 40 –40
0
1
–20 0
x [mm]
N
o
r
m
.

r
e
s
p
o
n
s
e
20 40
Moving Compensated Profiles
Target
0
50
60
70
80
R
e
l
.

d
o
s
e

[
%
]
90
100
110
120
5
Left Right
147%
139%
399%
Compensated
Moving
Compensated
Stationary
Moving
Distal
10 15 20 25
IC number
30 35 40 45 50
∆z
∆x
∆y
FIGURE 14.7
(a) Experimental motion tracking system as designed at the GSI Helmholtzzentrum für
Schwerionen forschung (GSI) facility in Darmstadt, Germany. The scanner magnets allow fast
variation of the pencil beam in the direction perpendicular to the central beam axis (Δx, Δy).
Required range adaptation is performed by a fast wedge system (Δz). (b) Results of ionization
chamber measurements positioned in the target volume normalized to measurements with a
stationary target. (c) Radiographic flm responses and corresponding dose profles along the
line indicated by the arrow in the panel labeled “stationary.” (From Bert et al., Radiat Oncol., 5,
61, 2010 and Bert et al., Med Phys., 34(12), 4768, 2007. With permission.)
451 Precision and Uncertainties in Proton Therapy for Moving Targets
(D
5
–D
95
< 5%) (47). This is in agreement with the report of Rietzel and Bert
who expressed that the millimeter precision that is achievable with state-
of-the-art fuoroscopic motion-monitoring systems should be suffcient for
beam tracking (41).
The third prerequisite is near-instantaneous range correction estimates.
As this third dimension, the target depth, can not (yet) be measured on-line
in real time; the current approach to account for time-dependent range varia-
tions is precalculation of the range correction for each motion phase and
scan position (48). Currently this is performed during the treatment plan-
ning phase. Based on 4D CT data and nonrigid registration maps, look-up
tables of compensation parameters are created. The motion phase at the time
of delivery of every single spot determines what compensation parameters
are applied.
The technical feasibility of on-line motion compensation has been shown
by means of computer simulation studies (47–51) and by means of phantom
irradiations (45, 52). Tumor tracking may have to be combined with rescan-
ning (“retracking”). Li et al. suggested retracking as a measure to deal with
target rotations (49). Van de Water et al. suggested retracking as a means to
reduce the sensitivity to positional errors, that is, allowing target position
errors up to 3 mm (47). They also stressed that, on top of the 3D pencil beam
position, the weights of pencil beams may have to be adjusted because time-
varying density gradients can affect the dose deposition of a pencil beam.
Lüchtenborg et al. have achieved real-time change of the weight of individual
pencil beams based on a database provided as part of the treatment plan (53).
These changes are used to compensate for target rotations and deformations.
The third prerequisite, accurate range correction estimates, is arguably the
weakest link, limiting the clinical application of beam tracking. Unless adap-
tive schemes are used (see the next section), the accuracy of precalculated
range corrections is limited by the representativeness of the 4D CT scan used
for treatment planning with respect to the actual time-dependent density
geometry at the moment of treatment delivery. Beam tracking is presum-
ably most successful at controlling the effect of intrafractional motion if both
interfractional motion and gradual density changes over the entire treatment
course are controlled as well.
14.4.6 Adaptive Radiotherapy
Gradual density variations that occur over the course of a fractionated treat-
ment may not have a clinically relevant dosimetric effect on a timescale of
one treatment fraction to the next, but over the course of a few fractions they
can have just as devastating an effect on the dose to the tumor as, for exam-
ple, a sizable setup error. The practice of repeated imaging is at the moment
not routine in the proton therapy community, perhaps justifably so, because
good clinical results have been obtained with proton therapy without taking
this into account. On the other hand, proton therapy has historically mainly
452 Proton Therapy Physics
been applied for tumor locations that suffer minimally from density varia-
tions (e.g., eye and brain tumors), and long-term follow-up and data for other
tumor sites (e.g., pancreas, prostate, lung) may not yet be suffcient to show
an effect.
Simply tracking the patient weight, or the more sophisticated use of patient
localization images (either portal images or cone beam CT, [3]) can serve as
the basis for a decision protocol to indicate a need for replanning, or at least
to assess continued adequacy of the existing treatment by recalculating the
dose distribution on the new patient geometry.
Variation in patient geometry over the course of treatment is best addressed
by adaptive radiotherapy. With the current state of proton therapy technol-
ogy, however (i.e., with passive-scattering still the dominant mode of pro-
ton therapy), gradual density variations can not effciently be addressed by
replanning. Design and then fabrication of updated feld-specifc hardware
(aperture, range compensator) is a time consuming and expensive process.
PBS allows for adaptive radiotherapy or even on-line changes of the treat-
ment plan because no patient-specifc hardware has to be built. Adaptive
schemes that take into account patient-specifc changes of the target region
are thus applicable and have the potential to increase the precision of proton
beam therapy by minimizing margins.
Adaptive treatment schemes might also be the method of choice to over-
come the main limitation of tracking, which is the uncertainty associated
with the 4D CT scan that is used for range assessment. If this scan is repeated
over the duration of the fractionated treatment schedule, variations in the
moving geometry can be assessed and incorporated into the treatment plan’s
database that result in the compensation vectors at time of treatment delivery.
14.5 QualityAssuranceforMovingTumors
Proton therapy in general, and IMPT specifcally, provides benefts for many
patients, but the clinical staff (i.e., radiation oncologists and clinical physi-
cists) have to be intricately aware of the uncertainties mentioned in this and
the previous chapter. The tighter we try to control and conform the dose by
means of new and evolving technology and treatment modalities, the more
susceptible we may be to “misses” due to remaining uncertainties that have
not been properly taken into account in the treatment plan design.
It is diffcult to draw a single conclusion as to the best strategy to deal
with time- varying density variations. There are many treatment delivery
para meters that can be optimized (see the Section 14.4), and one can com-
bine approaches such as gating and rescanning. The best strategy may also
depend on beam-line performance, something that is gradually improving
over time. In any case, it is important not to simply apply proton therapy to
453 Precision and Uncertainties in Proton Therapy for Moving Targets
any tumor site without at least performing a rudimentary sensitivity analy-
sis to density variations, motion, and interplay effects.
14.5.1 Treatment-Planning Quality Assurance
The effectiveness of any proton therapy delivery technique in dealing with
target motion is, judging by the available literature, typically validated in
silico using homogeneous or highly stylized phantoms. This simplifcation
helps in assessing the merits of the various techniques but does not exclude
the possibility of severe unexpected dose variations for any actual patient
characteristics. It is impossible to overemphasize the need for a priori assess-
ment of the accuracy of a proton therapy treatment plan, especially for mov-
ing tumors, by means of using a 4D treatment-planning simulation platform
that incorporates 4D CT, the patient’s breathing trace, and the time-resolved
dose delivery characteristics of the beam line, and that takes any technique-
specifc parameters into account (41, 48, 54).
In general, an estimate of target dose and normal tissue dose can be
obtained by recalculating the 3D dose distribution for a variety of possible
treatment scenarios (12). In photon therapy, the shape of the dose distribu-
tion to frst order can be considered invariant under density variations and
setup errors. This makes a probabilistic approach towards the likelihood
of “a good treatment plan” as suggested by, e.g., van Herk et al. quite fea-
sible (12). Rather than recalculating the dose distribution for every possible
setup error and density variation, one only has to shift it. Interplay effects are
proven to be small given a suffcient number of treatment fractions and/or
beam portals (11). But even in photon radiotherapy, clinical use of such dose-
error simulation platforms is very limited. Typically the appropriateness of
a treatment plan (and of a treatment) is judged, by the radiation oncologist
and the clinical physicist, based on dose-volume histograms (DVHs) and
axial dose distributions for a single static patient geometry: the treatment-
planning CT scan.
The application of proton therapy to tumor sites with a variable density
geometry (e.g., lung and liver instead of intracranial treatments) in combina-
tion with the advance of IMPT is a recent development and warrants cau-
tion. Interestingly, the development and application of dose-error simulation
platforms in proton therapy has not kept up with these new developments.
A similar probabilistic approach as described above (12) may be feasible
for proton therapy. Many variables can, however, have a signifcant degrad-
ing effect on the cumulative dose, for example, Hounsfeld unit-to-proton
stopping power conversion, setup errors, intrafractional and interfractional
density variation, variation in the motion characteristics, and timing of treat-
ment delivery with respect to this motion. A probabilistic plan evaluation
approach may therefore require a nearly prohibitive number of recalcula-
tions of the dose distribution making a priori plan evaluation an immense
numerical challenge. Some of the variables mentioned may have only
454 Proton Therapy Physics
a limited effect on the cumulative dose to the tumor, but this needs to be
proven comprehensively. Chapter 15 provides a framework for taking (some
of these uncertainties) into account intrinsically in the treatment plan design
by means of robust optimization. Furthermore, Mori et al. describe a tool
that allows a priori selection of beam directions with reduced sensitivity to
range variations over the motion cycle, thereby increasing the confdence
that what is treatment planned will also be delivered to the patient (55).
14.5.2 Treatment Delivery Quality Assurance
Proton radiotherapy, like any other means of radiation therapy, requires a
quality management program that assesses and ensures the continued accu-
racy of treatment delivery. This means system-wide quality assurance (QA)
as well as patient-specifc QA.
Aside from the general dosimetric QA (see Chapter 8), system-wide QA for
moving tumors also has to validate the motion-effect mitigation technique
applied. General testing of the system under reference conditions provides a
great amount of confdence, and such tests can be quite elaborate. The mini-
mal solution typically involves dosimetric measurements in a (solid) water
phantom positioned on a motion platform using a known motion trajectory.
As discussed below, however, more elaborate motion phantoms should be
developed to mimic the clinical situation more closely. Validation of each
step in the radiation therapy chain individually may not be able to anticipate
all circumstances that may occur during clinical operation. For complete-
ness, an end-to-end test should be designed and executed, simulating an
actual treatment as closely as possible. Several authors have therefore recom-
mended the development and use of a dedicated 4D motion phantom (41, 54).
Ideally such a phantom closely mimics a realistic patient density geometry,
has programmable motion characteristics, and has the possibility to measure
the (4D) dose distribution in several points and/or planes. Such a phantom
allows end-to-end testing from 4D CT scanning, to deformable registration,
to (robust) plan optimization, to in-room patient positioning, and to dose
delivery.
True a priori patient-specifc verifcation is very diffcult (if not impossible)
because the time-varying density geometry cannot be mimicked exactly. The
next best approach is to limit the duration of undesired dose delivery. In vivo
dosimetry (see Chapter 16), for example, can provide an early warning as to
the inadequateness of a delivered treatment fraction and allows the clini-
cal team to take corrective action. Another approach, that also only allows
correction after delivery of at least some dose, may be to perform closed-
loop dose accumulation. Using the treatment fraction–specifc 3D/4D patient
information, the on-line measured motion characteristics, and a detailed log
of all machine parameters as a function of time, one may be able to recalcu-
late a best estimate of the actually delivered dose. Patient-specifc QA and
adaptive therapy are thus closely interrelated.
455 Precision and Uncertainties in Proton Therapy for Moving Targets
14.6 FuturePerspective
The fnite range of protons allows for substantial sparing of OAR, but also
requires great caution in mitigating the detrimental dosimetric effects of
time-varying position and density variations. Figure 14.8 attempts to visual-
ize the susceptibility of a number of proton and photon treatment modalities
to these variations. Photon radiotherapy dose distributions suffer relatively
little from these uncertainties, or they can often be taken into account ade-
quately by means of a straightforward margining approach. The term “den-
sity variations” in this graph denotes range and setup uncertainties, as well
as density variations over time (intrafractional, interfractional, and gradual
changes over the entire treatment course). For the proton modalities, PSPT
is the only modality that does not suffer from interplay effects. IMPT is the
most sensitive treatment modality as, by defnition, multiple inhomoge-
neous dose distributions have to be matched accurately (in 3D) to ensure the
intended, and typically homogeneous, target dose coverage.
At the moment, motion in proton radiotherapy is a problem that has not
yet been completely solved. For PSPT one may be able to choose a practical
solution, realizing that the approach used may not ensure target coverage for
all possible patients and motion characteristics (see Chapter 10), but, for now,
perhaps the best strategy is to play it safe, for example, by performing “selec-
tion at the gate.” This means assessing motion at patient intake and choos-
ing the treatment modality, in the range from photon beam therapy to beam
tracking with IMPT, dependent on the observed motion characteristics.
Density variations
I
n
t
e
r
p
l
a
y

e
ff
e
c
t

IMPT
SFUD-PSPT
SFUD-PBS
3D-CRT
IMRT
Tomotherapy
B
r
a
c
h
y
-

t
h
e
r
a
p
y

FIGURE 14.8
Sensitivity of the proton modalities, and some photon modalities, to density variations and
interplay effect. The bottom left corner indicates the least sensitivity and the top right corner
the most sensitivity. 3D CRT, three-dimensional conformal (photon) radiotherapy.
456 Proton Therapy Physics
Of the strategies defned in Section 14.4, general treatment planning con-
siderations, gating, and apnea have been clinically applied for actual patient
treatments, and mostly for PSPT only. The proton radiotherapy community is,
however, longing to transfer the promises of PBS for static tumors (increased
dose conformity and OAR sparing, biology-guided adaptive radiotherapy) to
moving tumors as well. In the next two to fve years, according to Rietzel &
Bert (41), gating and rescanning will be applied in a clinical treatment envi-
ronment for PBS. Beam tracking is currently technically feasible but needs
more development and validation. It will likely not be clinically applied
within the next fve years. In the long run, perhaps the feld of proton therapy
will (have to) evolve toward in-room 4D imaging and on-line reoptimization
of the dose distribution, in combination with beam tracking or near-instan-
taneous dose delivery because then the high accuracy that is provided by the
biophysical properties of the beam can be ideally applied to the patient.
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461
15
Treatment-Planning Optimization
AlexeiV.Trofmov,JanH.Unkelbach,andDavidCraft
CONTENTS
15.1 Optimization of SOBP Fields ................................................................... 462
15.1.1 Optimization of Field Flatness ..................................................... 462
15.1.2 Forward Planning with SOBP Fields .......................................... 464
15.2 IMPT as an Optimization Problem ......................................................... 465
15.2.1 Setup of the IMPT Optimization Problem ................................. 466
15.2.2 Solving the Optimization Problem ............................................. 469
15.3 Multicriteria Optimization ....................................................................... 470
15.3.1 Prioritized Optimization .............................................................. 471
15.3.2 PS Approach ................................................................................... 471
15.3.3 Navigation of the PS ...................................................................... 472
15.3.4 Comparing Prioritized Optimization and PS-Based MCO ..... 474
15.4 Robust Optimization Methods for IMPT ............................................... 475
15.4.1 IMPT Dose in the Presence of Uncertainties ............................. 475
15.4.2 Robust Optimization Strategies ................................................... 476
15.4.2.1 The Probabilistic Approach ........................................... 477
15.4.2.2 The Robust Approach ..................................................... 478
15.4.2.3 Optimization of the Worst-Case Dose Distribution .... 478
15.4.3 Examples of Robust Optimization .............................................. 478
15.5 Temporospatial (4D) Optimization ......................................................... 480
15.5.1 Plan Optimization Based on a Known Motion Probability
Density Function ............................................................................ 482
15.5.2 Plan Optimization for an Uncertain Motion PDF ..................... 483
15.5.3 Optimizing a Different Fluence Map for Every Phase ............. 483
15.6 Accounting for Biological Effects in IMPT Optimization .................... 483
15.7 Other Applications of Mathematical Optimization in Proton
Therapy ........................................................................................................ 484
15.7.1 Scan Path Optimization ................................................................ 484
15.7.2 Beam Current Optimization for Continuous Scanning ........... 484
References ............................................................................................................. 484
462 Proton Therapy Physics
This chapter describes various applications of mathematical optimization
techniques in treatment planning for proton therapy. The most prominent
example is the optimization of beam weights for intensity-modulated pro-
ton therapy (IMPT). The conceptual and practical aspects of IMPT have
been introduced in previous chapters (see primarily Chapter 11). Here, we
focus on the mathematical aspects of treatment planning. First, in Section
15.1, we briefy recapitulate the basics of three-dimensional (3D) confor-
mal therapy, including the design of spread-out Bragg peaks (SOBPs), and
forward planning. In Section 15.2, we illustrate how IMPT inverse planning
is formulated as a mathematical optimization problem and comment on
methods to solve this problem. Then, we discuss advanced optimization
techniques for proton therapy: multicriteria optimization (Section 15.3),
robust optimization methods for handling range and setup uncertainty
(Section 15.4), incorporation of intrafractional motion in treatment plan-
ning (Section 15.5), and consideration of radiobiological effects in IMPT
optimization (Section 15.6). Finally, in Section 15.7, we review other
applications of mathematical optimization in proton therapy, such as the
optimization of beam current modulation and scan path for continuous
scanning.
15.1 OptimizationofSOBPFields
An SOBP is the foundation of forward treatment planning for 3D-conformal
proton therapy. It is used to achieve a longitudinal conformality of the
required dose to the target. In his seminal paper on therapeutic use of pro-
tons, Dr. Robert Wilson recognized the need for optimization of proton dose
distribution for clinical treatments, by pointing out that Bragg peaks need
to spread out to uniformly cover large tumor volumes. In his assessment
this could be “easily accomplished by interposing a rotating wheel of vari-
ous thickness” in the beam path (1), the method of modulation that is now
widely used for proton therapy (see Chapter 5). By using the word “easily,”
Dr. Wilson, perhaps, anticipated the fact that the problem of optimization of
modulation of SOBP would be relatively easy compared to the optimization
problems yet to arise in proton therapy.
15.1.1 Optimization of Field Flatness
To create a clinically relevant SOBP of the desired fatness in a passive beam
scattering system, a variety of components must operate in conjunction to
produce the desired beam parameters. Koehler et al. (2) described one of
the earliest examples of design of fat SOBPs using computer-based opti-
mization. Based on the input values of range and modulation width, the
463 Treatment-Planning Optimization
code written in Fortran IV iteratively searched for the set of amplitudes of
shifted pristine peaks, and spacings between them (in other words, relative
width, and thickness of the wheel steps), which realized the desired SOBP
(see Figure 15.1A). Notably, because the shape of the Bragg peak curve varies
with the beam energy, the weights of individual peaks in the SOBP need to
be optimized separately for different ranges in tissue, to avoid sloping in the
SOBP, as shown in Figure 15.1B and C.
In the early days of proton therapy, the wide variety of clinically required
combinations of range and SOBP modulation required a large number of
premanufactured wheels, with separate wheels required for shallow and
deep tumors, one wheel for a close set of modulation width (the smallest
steps of the propeller could be added or removed to allow for some varia-
tion in the total modulation width). A more fexible modern solution uses
a beam current modulation system, with a limited number of wheel tracks
(see Chapter 5). The pulled-back Bragg peaks can be individually controlled
to produce uniform dose plateaus for a large range of treatment depths using
only a small number of modulator wheels (3–5).
150
A B
C D
100
50
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
0
0
Depth [cm] Depth [cm]
Proton SOBP
Pristine peaks
Proton SOBP
Pristine peaks
Proton SOBP
Pristine peaks
Proton SOBP
Pristine peaks
20 5 10 15 0 20 5 10 15
0
Depth [cm] Depth [cm]
20 5 10 15 0 20 5 10 15
150
100
50
150
100
50
0
150
100
50
FIGURE 15.1
Depth–dose profle of a spread-out Bragg peak (SOBP), and constituent pristine peaks: optimi-
zation of pristine peak weights leads to (A) uniform SOBP dose, while variation in the pristine
peak dose profle may introduce a (B) raising or (C) falling slope in SOBP. In principle, arbitrary
profles of the peak dose can be achieved by optimization, for example, (D) a profle with the
integrated dose boost of 10% to the middle part of the SOBP.
464 Proton Therapy Physics
In principle, by temporally optimizing the beam current during the modu-
lation cycle, one can create SOBPs with arbitrary depth–dose profles. This
includes “intensity-modulated” felds according to the common defnition,
namely, dose distributions, that are inhomogeneous by design. Notably, the
beam current modulation literally constitutes intensity modulation of the
beam, regardless of whether the resulting distribution is inhomogeneous or
not. An example of inhomogeneous dose achievable with range modulation
is the SOBP including a simultaneous integrated dose boost delivered to a
subsection of the target, as in Figure 15.1D. It should be noted though that
this technique allows for intensity modulation only in depth, whereas the
beam intensity is homogeneous laterally.
15.1.2 Forward Planning with SOBP Fields
Procedures of forward planning for 3D-conformal proton therapy have
been well described by Bussière and Adams (6), as well as in Chapter 10 of
this book. Figure 15.2 illustrates how a “manual optimization” of a treat-
ment plan might be undertaken. The search for a satisfactory solution does
A B C
D E F
G
20 30 40 50
Dose [%]
60 70 80 90 100
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
H
Dose [%]
Spinal
cord
Stomach
Target
Liver
V
o
l
u
m
e

[
%
]
Dose [%] Dose [%]
I
FIGURE 15.2
(See color insert.) Forward planning and manual optimization for a case of retroperitoneal
tumor. Dose distributions from three beam directions are shown in (A–C). These can be com-
bined with various weights leading to a variety of clinically acceptable dose distributions, for
example, with doses shown in (D–F), and the DVH in (G–I), respectively.
465 Treatment-Planning Optimization
involve iterative adjustment; however, it is rather subjective (e.g., depends on
the planner’s training, habit, and judgment) and is not systematic (e.g., itera-
tions do not always lead toward a more preferable solution). Thus the process
cannot be termed optimization in the strictly mathematical sense.
First, the irradiation directions are selected as well as the range and SOBP
modulation width necessary to cover the target. Range compensators are
designed to conform the dose to the distal aspect of the target, and accom-
modations are made to prevent underdosing of the target in case of misalign-
ment of treatment feld and tissue heterogeneities, for example, using the
technique of compensator expansion, or “smearing” (7) (also see Chapter 10).
Once these steps are completed, a forward calculation is performed to deter-
mine the dose from the given feld, based on the assumed beam fuence. The
task of the planner is then to iteratively adjust the fuences, or “weights,” of
multiple beams and to combine their doses so that the resulting distribution
suits a particular set of requirements. For example, in the case illustrated
in Figure 15.2, irradiating the spinal cord up to the tolerance (Figure 15.2, D
and G) may be considered acceptable in a certain situation, because this con-
fguration minimizes the integral dose and the main irradiation direction is
least affected by internal motion (e.g., of liver with respiration for the right-
anterior beam) or variations in the stomach and bowel flling (for the left
beam lateral). In other situations, such as repeat treatments, cord tolerance
may be reduced, and other directions have to be used. In those cases, the
clinically optimal balance, between irradiation of various structures, needs
to be selected (compare, e.g., Figure 15.2, H vs. I).
15.2 IMPTasanOptimizationProblem
Intensity-modulation methods allow one to achieve highest conformality of
proton dose distributions to the target volume and best sparing of healthy
tissue. Unlike 3D-conformal treatments, in which each SOBP feld delivers
a uniform (within a few percent) dose to the whole target volume, indi-
vidual IMPT felds typically deliver nonuniform dose distributions (e.g.,
see Figure 15.3). Similar to IMRT with photons, these nonuniform feld con-
tributions combine to produce the desired therapeutic dose distribution,
which may be shaped to conform to the clinical prescription. An important
difference from photon intensity-modulated radiation therapy (IMRT) is
that the Bragg peak of the proton depth dose distribution introduces an
additional degree of freedom in modulation of the dose in depth along the
beam axis, in addition to the modulation in the transverse plane, which is
available in both IMRT and IMPT. Despite this difference, IMRT and IMPT
are very similar regarding the mathematical formulation of the treatment-
planning problem.
466 Proton Therapy Physics
To take full advantage of the possibility to sculpt the dose in depth,
IMPT treatments use narrow proton pencil beams, which can be scanned
across the transverse plane while changing energy and intensity to control
the dose to a point. The most common and versatile IMPT technique is the
3D-modulation method, in which individually weighted Bragg peak “spots”
are placed throughout the target volume (8). The examples in this chapter
use 3D-modulation; however, most optimization methods described below
are equally applicable to other techniques, such as single-feld uniform dose
(SFUD) treatments or the distal edge tracking (DET). SFUD treatments also
use weighted pencil beams distributed in three dimensions, but aim at deliv-
ering a homogeneous dose to the target from every individual feld direc-
tion. In the DET method, Bragg peaks are placed only at the distal surface of
the tumor (9).
15.2.1 Setup of the IMPT Optimization Problem
To apply general optimization methods to radiation therapy planning, tech-
nical limitations and treatment goals need to be formulated mathematically
B
C D E
A
FIGURE 15.3
(See color insert.) IMPT plan for a paraspinal tumor. (A) CT scan showing outlines of the
tumor and the spinal cord, (B) dose distribution from a 3D IMPT treatment plan, using three
beam directions. Dose contributions from individual beams are shown for (C) right-posterior
oblique, (D) posterior, and (E) left-posterior oblique felds. (The conventional IMPT plan did
not include any consideration of delivery uncertainties.)
467 Treatment-Planning Optimization
as objectives and constraints. For that purpose, the patient image data are
partitioned into volumes of interest (VOI), which could include targets, criti-
cal organs at risk of undesired side effects (organs at risk [OAR]), and other
tissue volumes. VOI are further divided into basic geometric elements called
voxels.
The total dose distribution from an IMPT feld delivered with a scanned
beam can be calculated as the sum of contributions from “static” pencil
beams fxed at various positions along the scan path. The dose from indi-
vidual pencil beams to various voxels of interest can be represented in the
form of the dose infuence matrix D
ij
, where i is the voxel index, and j is the
beam index. The total dose to any voxel is then calculated as follows:

d = x D
i j ij
j
⋅
∑

(15.1)
where x
j
is the relative “weight” of the beam j, which is proportional to the
total number of protons delivered at the given spot, that is the position of
Bragg peak. The weights x
j
are the optimization variables that need to be
determined in treatment planning. Because of the large number (thousands
or tens of thousands) of such pencil beams involved, IMPT treatment plan-
ning requires mathematical optimization methods (10, 11). The output of the
plan optimization is a set of beam weight distributions, often called intensity
or fuence maps. Unlike in IMRT, where a single two-dimensional (2D) fu-
ence map characterizes a feld, in IMPT, many beam energies may be used
to irradiate the target from the same direction, and optimization will yield
separate maps for every energy setting.
Dosimetric or other planning objectives may be defned for volumes
or individual voxels. The planning objectives and their priorities can be
expressed in the objective function (OF). The term optimization, in the con-
text of treatment planning, typically signifes the search for a set of plan
parameters that minimize the value of the OF, subject to a set of constraints
that have to be fulflled.
A widely used objective function that aims at minimizing the volume,
within a given OAR n, that exceeds the maximum tolerance dose D
max
is
given by the quadratic penalty function:

O d H d D d D
n i i
i OAR
n
( ) = −
( )
−
( )
∈
∑
max max
2

(15.2)
where H(d) is the Heavyside step function. Similarly, one can defne a qua-
dratic function that aims to reduce volumes of the tumor, which receive less
than the minimum dose D
min
. Objective functions may also include the gen-
eralized equivalent uniform dose (12):

O d
N
d
n
n
i
p
i OAR
n
p
( ) = ( )








∈
∑
1
1/

(15.3)
468 Proton Therapy Physics
where N
n
is the number of voxels in the VOI n, and p is an organ-specifc
parameter.
In addition, there may be constraints on the dose in a VOI that have to
be fulflled in order to make the treatment plan acceptable. For example,
one can request that the dose in every voxel belonging to the tumor should
be between a minimum dose D
min
and a maximum dose D
max
. This would
result in the hard constraint

D d D i VOI
i
min max
. ≤ ≤ ∀ ∈

(15.4)
In clinical situations, treatment objectives often directly confict each other:
for example, a target may not be completely irradiated to the prescribed level
if a dose-sensitive critical structure is immediately adjacent to it. In this case,
hard dosimetric constraints have to be used with care, and it is often nec-
essary to reformulate a constraint as an objective. For example, it may be
necessary to minimize the dose to an OAR that exceeds the tolerance dose
through a quadratic objective, rather than enforcing the dose to be below
the maximum dose in every voxel through a constraint. Such an objective
is often referred to as a “soft constraint” in the medical physics literature.
Multicriteria optimization methods, discussed in Section 15.3, address such
inherent treatment-planning contradictions.
Thus, one can formulate the general IMPT optimization problem as follows:
minimize (with respect to the beam weights x):

α
n n
n
O d ⋅
∑
( )

subject to the constraints:

d = x D
i j ij
j
⋅
∑


l C d u
m m m
≤ ( ) ≤


x
j
≥ 0.

(15.5)
In the above formulation the different objectives O
n
are multiplied by respective
weighting factors α
n
and are added together to form a single composite objec-
tive. By selecting and adjusting the weighting factors, the treatment planner
can prioritize different objectives and control the trade-off between them. The
approach of a weighted sum of objectives is pursued in most current treatment-
planning systems. (An alternative to this standard approach is multicriteria
optimization.) The functions C
m
denote a general constraint function, and l
m

and u
m
are upper and lower bounds. An example of a simple constraint function
is the minimum or maximum dose constraint mentioned above. Alternatively,
constraints on equivalent uniform dose (EUD) can be imposed (12).
469 Treatment-Planning Optimization
A number of additional parameters often need to be specifed before opti-
mization of beam weights is performed. These include, for example, the
choice of the algorithm for placement of Bragg peaks (8), as well as the vol-
ume used for placement (which may be larger than the target), the spacing of
peaks and layers in depth (13), and the size of the pencil beam used for deliv-
ery of therapy (14). These additional treatment parameters, or hyperparam-
eters, affect the outcome of optimization; however, they are not determined
through an optimization algorithm in the mathematical sense. Instead they
are chosen based on experience, planning studies, and physical or theoreti-
cal considerations.
15.2.2 Solving the Optimization Problem
IMPT represents a textbook example of a large-scale optimization
problem, especially if convex objectives and constraints are used. The
variables, the beam weights x, are continuous, that is, can take any non-
negative value (although these are often discretized, when sequenced for
delivery). The objectives can typically be formulated in closed form as a
function of the optimization variables, and also the gradient of the objec-
tive can be calculated analytically. Therefore a large variety of algorithms
can be applied. Those can be categorized into constrained and uncon-
strained methods. In the case of unconstrained methods, no dosimetric
hard constraints are applied, that is, all treatment goals are formulated as
objectives. The only constraints that always need to be fulflled to yield
a physically meaningful plan are the variable bound constraints x
j
≥ 0.
However, those can be treated through relatively simple methods such as
gradient projection methods. Most current treatment-planning systems
use unconstrained optimization methods. In this case, improved gradi-
ent methods are used such as quasi-Newton methods or the diagonalized
Newton method.
Constrained optimization for IMPT is still challenging because of the large
number of variables (10
3
to 10
5
) and the large number of voxels (10
5
to 10
7
).
If only linear objectives and constraints are used, the linear programming
framework can be applied. In the nonlinear case, sequential quadratic pro-
gramming methods have been used (RayStation; Raysearch Laboratories,
Stockholm, Sweden) as well as barrier-penalty methods (Monaco; Elekta,
Stockholm, Sweden).
Optimization problems may further be classifed as convex or nonconvex.
In a convex optimization problem, all of the constraints as well as the min-
imized objective function are convex functions. For example, linear func-
tions, and therefore, linear programming problems are convex. The feasible
region (i.e., all sets of spot weights x that fulfll the constraints) is then also
convex, being the intersection of convex constraint functions. With convex
objectives and a convex feasible region a local optimal solution is also a
global optimal solution. Thus, optimization would either yield the globally
470 Proton Therapy Physics
optimal solution or demonstrate that there is no feasible solution. All the
objectives and constraints described above (e.g., quadratic function, EUD)
are convex.
Conversely, a nonconvex optimization problem is any problem where
the objective is nonconvex or nonconvex constraint functions give rise to a
nonconvex feasible region. In this setting, multiple local optimal solutions
are possible and, in practice, considering the large number of variables in
IMPT, it is typically not possible to guarantee that an algorithm used to
solve the optimization problem indeed converges to the globally optimal
solution.
Nonconvex constraints are becoming increasingly common in optimiza-
tion. Examples of nonconvex objectives include typical radiobiological mod-
els of tumor control and normal tissue complication probabilities. Another
example is the dose-volume constraints, which can be conveniently defned
to specify the desired shape of the dose-volume histogram (DVH) directly
(15); for example, “the fraction of the volume of a specifc OAR irradiated to
40 Gy is not to exceed 30%.”
15.3 MulticriteriaOptimization
Optimization theory is built up around the single criterion optimization
problem, where there is one objective and other problem considerations are
included as constraints. In radiotherapy, the main objective—to cover the
target with the prescription dose—is in direct confict with the other objec-
tives of keeping the dose to the healthy organs to a minimum. If biologi-
cal response models such as tumor control probability (TCP) and normal
tissue complication probability (NTCP) were reliable, one might be able
to solve radiotherapy optimization well in a single criterion mode: maxi-
mize TCP subject to the NTCPs of the relevant organs at risk being below
acceptable levels. However, even in this setting, depending on the patient-
specifc trade-off (for the treatment plan under consideration, how much
gain in TCP is there if you allow NTCP for some organ to increase by some
amount), were there a tool to easily explore other options, a physician might
choose a different plan than the plan returned from the single-criterion
optimization.
Presently, the standard commercial systems available for treatment opti-
mization still attempt to solve the radiotherapy optimization problem with a
single-criterion approach, and this leads to a lengthy optimization iteration
cycle, where treatment planners try to fnd the set of weights and function
parameters that give a plan that best matches the physician’s goals for treat-
ment. The problem is, it is very diffcult to guess those weights and func-
tion parameters to get a good plan, and as the number of organs to consider
471 Treatment-Planning Optimization
increases, this task becomes increasingly more diffcult. Several groups are
at work to bring multicriteria optimization (MCO) into routine clinical usage
(16–22).
There are two main approaches to MCO for radiotherapy treatment plan-
ning: prioritized optimization and the Pareto surface (PS) approach. Below,
we describe the two approaches, show how they are related, and discuss
their pros and cons.
15.3.1 Prioritized Optimization
Prioritized optimization, or lexicographic ordering, as it is sometimes called
in the literature, is a natural approach for dealing with multiple objectives
when the objectives can be ranked in terms of importance (23, 24). Letting O
1

denote the highest priority objective, O
2
the second highest, etc., prioritized
optimization solves the following sequent of optimization problems for k
priority levels:
(1) minimize O
1
(x) subject to x ∈ X ;
(2) minimize O
2
(x) subject to x ∈ X , and O
1
(x) ≤ O
1
*
· (1 + ε);
…
(k) minimize O
k
(x) subject to x ∈ X, and, for all i < k, O
i
(x) ≤ O
i
*
· (1 + ε), (15.6)
where x is a set of the decision variables, X is a constraint set that represents
constraints on the beamlet fuences (upper and lower bounds) and is also
used to denote hard dosimetric constraints, such as voxel dose, organ mean
dose, or EUD that must be met by every considered solution. O
1
*
is the opti-
mal objective value from the frst optimization (i.e., the fuence values in the
case of IMPT), and ε is a small positive slip factor. Multiplication by (1 + ε)
allows a small degradation in the value of the frst optimization, thus hope-
fully permitting the second priority objective to achieve a good value, and
so forth.
The result of the fnal optimization is the single result of the prioritized
optimization approach. The choice of ε (and whether it is the same for each
step) and the priority ordering of the objectives will infuence the fnal result.
15.3.2 PS Approach
The PS approach does not prioritize the objectives, but instead treats every
objective equally. Unlike prioritized optimization, the PS approach yields
not a single plan, but a set of optimal plans that trade off the objectives in a
variety of ways. Given a set of objectives and constraints, a plan is consid-
ered Pareto-optimal if it is feasible and if there does not exist another feasible
472 Proton Therapy Physics
plan that is strictly better with respect to one or more objectives and that is at
least as good for the rest. Assuming that the objectives are chosen correctly,
Pareto-optimal plans are the plans of interest to planners and doctors. The
set of all Pareto-optimal plans comprises the PS.
The PS-based MCO problem can be formulated as follows:
minimize [O
1
(x), O
2
(x), … , O
N
(x)] subject to x ∈ X (15.7)
where X is used, as before, to represent all beamlet and dose constraints,
and N is the number of objective functions. The algorithmic decisions to
be made for this approach are as follows: (1) how to compute a reasonable
set of diverse Pareto-optimal plans and (2) how to present the resulting
information to the decision makers. Radiotherapy seems to be one of the
frst felds, if not the frst, to fully address the question of populating PSs
for N ≥ 3. Two main types of strategies populating the PS have been put for-
ward for the radiotherapy problem: weighted sum methods and constraint
methods.
Weighted sum methods are based on combining all the objectives into a
weighted sum and solving the resulting scalar optimization problem. By
solving the problem for a variety of weights, a variety of different Pareto-
optimal plans are found. If the underlying objectives and constraint set
are convex, every Pareto-optimal point can be found by some weighted
sum. Several publications describe methods to choose the weights appro-
priately, to produce a small set of plans that covers the PS sufficiently
well (18, 21, 25). These methods intrinsically take into account convex
combinations of calculated PS points when evaluating the goodness of
a set of Pareto plans. All of these methods get bogged down when the
number of objectives is large (e.g., >8). Fortunately, on a practical level,
even as few as N + 1 PS plans are often sufficient to determine good treat-
ment plans (26, 27).
Constraint methods use the objective functions as constraints (as in
prioritized optimization), and by varying the constraint levels, different
Pareto-optimal solutions are found. The state-of-the-art of constraint-based
method is the improved normalized normal constraint (NNC) method (28).
The main defcit of constraint-based methods is that error measures, which
give the quality of the PS approximation, are not a natural part of the algo-
rithm or output, as they are in the methods of Craft et al. (18) and Rennen
et al. (25).
Weighted sum and constraint methods are graphically depicted for 2D PSs
in Figure 15.4.
15.3.3 Navigation of the PS
The fnal task in a PS-based approach to treatment planning is to allow the
user to select a plan from the PS. Because the PS is represented by a fnite set
473 Treatment-Planning Optimization
of Pareto-optimal treatment plans, there are two natural approaches to plan
selection. The easiest way is simply to allow the treatment planner to select
one of the computed Pareto-optimal treatment plans. In the case of IMPT,
where treatment plans can be weighted and combined to form other valid
treatment plans, it makes sense to allow users to smoothly transition between
the computed solutions. When navigating across convex combinations of the
database plans, either forcing Pareto optimality or not, the standard method
is to present N sliders, one for each objective, and the underlying algorithmic
task is to determine how to move in the objective space in response to a slider
movement (21, 29).
An alternative to presenting the users with N sliders is to allow them
to select two of the N objectives and then display a 2D trade-off for those
two objectives. For the other N – 2 objectives, the user can impose upper
bounds, infuencing the 2D tradeoff surface being evaluated. The beneft of
this method is that it allows the user to visualize a 2D slice of PS, which may
yield intuition into the problem at hand. Figure 15.5 shows what this might
look like for examining the trade-off between sparing the lung and control-
ling hot spots within a target.
A) B) Weighted sum method e-Constraint method
Normalized normal
constraint method C)
O
2
O
2
w = (.6,.4)
w = (.2,.8)
O
2
O
1
O
1
O
1
FIGURE 15.4
Methods to compute a database of Pareto surface points. (A) Weighted sum, (B) e-constraint,
and (C) normalized normal constraint method.
Target dose
homogeneity
OAR Sparing
FIGURE 15.5
(Seecolorinsert.) Illustration of two Pareto-optimal plans, showing trade-offs in OAR sparing
vs. target dose homogeneity.
474 Proton Therapy Physics
15.3.4 Comparing Prioritized Optimization and PS-Based MCO
Prioritized optimization and PS MCO are compared graphically in Figure
15.6. It is important to note that both methods rely on optimization with hard
constraints. In the prioritized approach, this is obvious because objectives
move into the constraint section. In the PS method, constraints are impor-
tant in the problem formulation, to restrict the domain of the PS to a useful
one. For example, it makes sense to put an absolute lower bound on target
doses normally, even if a user is interested in exploring some underdosing
of the tumor to improve OAR sparing (otherwise, anchor plans for OAR
will be “all 0” dose plans, which are not helpful for planning). Similarly, a
hard upper maximum dose on all voxels is useful. Therefore, MCO meth-
ods in general are best used when a constrained solver is at hand. Solvers
implemented in RayStation (RaySearch Laboratories), Pinnacle (Philips
Healthcare, Andover, MA), Monaco (Electa), UMPlan/UMOpt (University
of Michigan, Ann Arbor, MI), and Astroid (Massachusetts General Hospital,
Boston, MA) are examples of solvers that allow true hard constraints (as
opposed to those that handle constraints approximately by using a penalty
function with a high weight).
The advantage of the prioritized approach is that it is a programmable
procedure that results in a single Pareto-optimal plan, but the disadvantage
is there is only one plan presented to the user at the end of the process.
PS methods on the other hand present all optimal options to the user, but
might be considered overwhelming for routine planning because the user
has to decide on selecting a single plan manually from the large number
of options on PS. However, plan selection in standard cases may be fast,
even with many options, because sliding with navigation sliders is much
more effcient than the reoptimization iteration loop. Notably, because the
navigation process is user-driven, it is not as reproducible as the prioritized
approach.
1
O
2
ε
A) Prioritized optimization method Pareto surface method
Actual pareto surface
Approximated pareto
surface
B)
O
2
O
1
O
1
2
FIGURE 15.6
Illustration of approaches to multicriteria optimization. (A) Prioritized optimization, and
(B) Pareto surface method.
475 Treatment-Planning Optimization
15.4 RobustOptimizationMethodsforIMPT
Uncertainties in proton therapy have been addressed in detail in Chapters 13,
and 14, and, for example, in publications by Lomax (30, 31). From the delivery
point of view, an optimal plan needs also to be “robust,” that is, designed in
such a way that slight deviations from the plan due to various uncertainties
during treatment delivery will not affect the quality of treatment outcome.
In other words, a robust treatment plan will deliver a clinically acceptable
dose distribution as long as the deviations from the planned do not exceed
the assumed levels.
Heuristics to mitigate the effects of uncertainty in patient setup and proton
range have been developed for different treatment modalities. These meth-
ods include compensator smearing in passively scattered proton therapy or
selection of favorable beam angles (see Chapter 10). Here, we discuss robust
optimization strategies specifcally for intensity-modulated proton therapy
(IMPT).
15.4.1 IMPT Dose in the Presence of Uncertainties
Doses delivered from different directions in IMPT are typically inhomoge-
neous and require the use of a number of proton energies. For this reason,
variations in the target setup and penetration depth during delivery can lead
to misalignment and mismatch of doses from individual felds, and, conse-
quently, alter the combined dose distribution.
To satisfy the requirement of dose conformity to the target, steep dose gra-
dients are often delivered at the target border. Such steep dose gradients
in the dose contributions of individual beams make IMPT plans yet more
sensitive to both range and setup errors. In particular, dose gradients in the
beam direction make the treatment plan vulnerable to range errors, because
an error in the range of the proton beams corresponds to a relative shift of
these dose contributions longitudinally inside the patient. As a consequence,
the dose within the target may not add up to a homogeneous dose as desired.
Hot and cold spots may arise. Moreover, dose may be shifted into critical
organs. Generally, the more conformal the combined IMPT dose is, the more
complex the fuence maps per feld are and the more sensitive the plans are
to the delivery uncertainties.
As an illustration, consider a conventional IMPT plan for a case of para-
spinal tumor, shown in Figure 15.3. The target entirely surrounds the spinal
cord, which is to be spared. Total IMPT dose distribution was optimized
using a quadratic objective function, thus aiming at a homogeneous target
dose. As is characteristic of IMPT, the homogeneous dose distribution in the
target is achieved through a superposition of highly inhomogeneous contri-
butions delivered from three beam directions.
476 Proton Therapy Physics
The dose distribution that results from a range overshoot of all pencil
beams in this plan (i.e., protons penetrate further into the patient than antici-
pated during planning) would lead to a higher dose to the spinal cord, as
shown in Figure 15.7A. Sensitivity of the same plan to setup errors is illus-
trated in Figure 15.7B, which shows the dose distribution resulting from a
3.5-mm setup error posteriorly (upwards in the picture). This shift has no
impact on the dose contribution of the posterior beam. However, the oblique
beams hit the patient surface at a different point. For a posterior shift, the
dose contributions of the oblique beams are effectively shifted apart, which
results in the cold spots around the spinal cord.
From this illustration, it is evident that, unlike in conventional x-ray
therapy, plan degradation in the presence of range and setup uncertain-
ties in IMPT cannot be prevented, to a satisfying degree, with safety
margins. Expanding the irradiated area around the target with margins
could potentially reduce underdosage at the edge of the target in the pres-
ence of an error. However, the general problem of misaligning the dose
contributions of different felds, which leads to dose uncertainties in all
of the target volume, cannot be solved through margins. This problem
instead relates to steep dose gradient in the dose contributions of indi-
vidual felds.
15.4.2 Robust Optimization Strategies
The methods presented in this section have been described largely in three
publications (32–34) that deal specifcally with range and setup uncertainty
in IMPT. In addition, a number of earlier publications investigate the han-
dling of uncertainty and motion in IMRT with x-rays. Some of that work
could also be applied to IMPT. For a review of developments in handling of
motion and uncertainty in IMRT, see Orton et al. (35). Although this section
illustrates robust optimization techniques in the context of range and setup
errors, the methodology is also applicable to other types of uncertainty, for
example, irregular breathing motion or uncertainty in the biological effec-
tiveness of radiation (36).
A B
FIGURE 15.7
(Seecolorinsert.) Estimated dose distribution from the plan in Figure 16.3, assuming (A) a 5-mm
range overshoot of all pencil beams, and (B) a systematic 3.5-mm setup error (posterior shift).
477 Treatment-Planning Optimization
Several approaches that apply either the concepts of stochastic program-
ming or robust optimization have been suggested for incorporating uncer-
tainty into IMPT optimization. The common feature of these approaches is
that the delivered dose distribution depends on a set of uncertain param-
eters. In the case of a rigid setup error without rotation, the set of uncer-
tain parameters would be a 3D vector describing the patient shift in space.
A simple model of range uncertainty, where it is assumed that all pencil
beams simultaneously overshoot or undershoot, would have one uncertain
variable that describes the range error of all beams. A more complicated
model of range uncertainty could allow for different range errors for differ-
ent pencil beams.
Below, we denote the set of uncertain parameters by a vector λ. The dose
distribution d(x, λ) delivered to the patient depends on the beam spot weights
x to be optimized, and the values of the uncertain parameters λ. The objec-
tive function used for treatment planning O(d(x, λ)) is a function of the dose
distribution.
15.4.2.1 The Probabilistic Approach
In the probabilistic or stochastic programming approach (34), a probabil-
ity distribution P(λ), refecting the probability for a given error to occur, is
assigned to the set of uncertain parameters. Treatment plan optimization is
performed by optimizing the expected value of the objective function:

minimize E O = O d x, P d [ ]
∫
( ( )) ( ) λ λ λ.

(15.8)
This composite objective function can be interpreted in a multicriteria view:
The composite objective is a sum of objectives for every possible error sce-
nario weighted with the probability of that error to occur. The general goal is
to fnd a treatment plan that is good for all possible errors, but larger weights
are assigned to those scenarios that are likely to occur, and lower weights to
large errors that are less likely to happen.
For a pure quadratic objective function, O d D
i i i
p s
= −
( )
∑
re
2
, the expected
value of the objective function is

E O = E d D +E d E d
i i
pres
i i
i
[ ] [ ] −
( )
− [ ] ( )




( ) ∑
2 2

(15.9)
which is the sum of two terms: the frst term is the quadratic difference of
the expected dose E[d] and the prescribed dose, and the second term is the
variance of the dose. Hence, minimizing the expected value of the quadratic
objective function aims at bringing the expected dose close to the prescribed
dose in every voxel and simultaneously minimizes the variance of the dose
in every voxel such that the expected dose is approximately realized even if
an error occurs.
478 Proton Therapy Physics
15.4.2.2 The Robust Approach
In robust optimization (32), the values of uncertain parameters are assumed
to be within some interval called the uncertainty set. Treatment planning
is performed by solving the robust counterpart of the conventional IMPT
optimization problem. For an introduction to robust optimization, see
Ben-Tal and Nemirovski (37). Typically, this means that the constraints of
the optimization problem have to be satisfed for every realization of the
uncertain parameters. For example, if the original problem constrained that
the maximum dose to the spinal cord be less than 50 Gray (Gy), the robust
counterpart would demand that the maximum spinal cord dose is less than
50 Gy for every possible range and setup error within the uncertainty set. For
objectives, this formulation of the robust counterpart results in a worst-case
optimization problem: that is, if the objective was to minimize the maximum
dose to the spinal cord, then the robust counterpart would minimize the
maximum spinal cord dose that can happen for any possible range or setup
error. Hence, the aim is to fnd a treatment plan, which is as good as possible
for the worst case that can occur.
15.4.2.3 Optimization of the Worst-Case Dose Distribution
Yet another approach to robust IMPT planning utilizes the concept of a
worst-case dose distribution (33). This hypothetical dose distribution is
defned voxel by voxel as the worst dose value that can be realized for any
error anticipated in the uncertainty model. For every target voxel, the worst
dose value is the minimum dose, whereas for nontarget voxels it is the max-
imum dose. The worst-case dose distribution is unphysical because every
voxel is considered independently. Whereas in one voxel the worst case may
correspond to a patient shift anteriorly, the worst case in another voxel may
correspond to a patient shift posteriorly. Hence the worst-case dose distribu-
tion cannot be realized. However, it can be considered as a lower bound for
the quality of a treatment plan. The method optimizes the weighted sum of
the objective function evaluated for the nominal case d
nom
(no errors) and the
objective function evaluated for the worst-case dose distribution d
wc
. If O is
the primary objective function, then the composite objective to be optimized
is given by O O d wO d
comp nom wc
= + ( ) ( ).
15.4.3 Examples of Robust Optimization
Incorporating uncertainty in IMPT optimization yields increasingly robust
treatment plans. Consider two treatment plans: a conventional plan opti-
mized without accounting for uncertainty, and a plan optimized for range
and setup uncertainty using the probabilistic approach (i.e., the setup and
range uncertainties modeled with a Gaussian distribution). Figure 15.8
shows the DVHs corresponding to dose distributions calculated for range
479 Treatment-Planning Optimization
and setup errors randomly sampled from these Gaussian distributions. For
the conventional plan, target coverage is strongly degraded in many cases,
and the dose to the spinal cord can be very high for some scenarios. The
variation in the DVHs of the robust plan is greatly reduced, ensuring better
target coverage and lower spinal cord doses.
To gain some insight into how this robustness is achieved, let us consider
the dose contributions of individual beams. Figure 15.9 compares four treat-
ment plans: the conventional plan, a plan optimized for range uncertainty
only, a plan optimized for setup uncertainty only, and a plan incorporating
both types of errors. The conventional plan is characterized by steep dose
100
80
60
40
20
0
0 10 20 30 40
Conventional
Robust
50 60 70 80 90
FIGURE 15.8
DVH comparison between a conventional and a robust IMPT plan. DVHs for the CTV and the
spinal cord are shown for randomly sampled range and setup errors.
A B
C D
FIGURE 15.9
For the case illustrated in Figure 15.3, dose contributions from the posterior beam from four dif-
ferently optimized plans. (A) Conventional IMPT, robust IMPT incorporating (B) range uncer-
tainty only, (C) setup uncertainty only, and (D) considering both range and setup uncertainty.
480 Proton Therapy Physics
gradients both in beam direction and laterally, especially around the spinal
cord. The plan optimized for range uncertainty shows reduced dose gradi-
ents in beam direction and avoids placing a steep distal falloff of a Bragg peak
in front of the spinal cord. The lateral falloff is used instead of the distal fall-
off to shape the dose distribution around the spinal cord. The plan optimized
for setup errors only shows reduced dose gradients in the lateral direction,
but it does not avoid placing a distal Bragg peak falloff in front of the criti-
cal structure and therefore does not provide robustness against range errors
per se. The plan optimized for both range and setup errors shows reduced
dose gradients both longitudinally, in the beam direction, and laterally.
In summary, robustness is achieved through a redistribution of dose
contributions among the beam directions and through avoiding unfavor-
able dose gradients. For our sample paraspinal case, the price of robustness
is a higher dose to the spinal cord for the nominal case. In a conventional
plan, the steep distal Bragg peak falloff is utilized, which allows for optimal
sparing of the spinal cord. If range errors are to be accounted for, the shal-
lower lateral falloff is used, leading to a more shallow dose gradient between
tumor and spinal cord for the nominal case. Publications by Pfugfelder et al.
(33) and Unkelbach et al. (34) provide a more detailed analysis. In the experi-
ence of the authors, all of the methods to account for uncertainty, described
above, lead to similar treatment plans and may be equally suited to account
for systematic uncertainties.
15.5 Temporospatial(4D)Optimization
Precision of therapy delivery can be affected not only by the changes in
setup and patient anatomy between treatment fractions, but also by the
intrafractional motion of the target, which could be due to respiration, peri-
stalsis, or organ settling due to gravity (see Chapter 14 for more details). If
no action is taken, there is always a risk that parts of the target may move
outside of the treatment feld, resulting in a loss of dose coverage. Even in
cases where treatment-planning margins are generous enough to cover the
full amplitude of motion, intrafractional motion would degrade dose gradi-
ents and increase irradiation of surrounding healthy tissues. An important
difference from x-ray therapy is that, in particle therapy, because of the lim-
ited range, the use of margin expansions, such as internal target volumes,
requires explicit consideration of possible changes in radiological depth to
target, because these are often affected by organ motion (38).
Additionally, as with x-rays, in dynamically delivered intensity-modulated
therapy, certain patterns of superposition of motion of the target and the
scanned beam, or so-called “motion interplay,” can have a severe impact on
the delivered dose (e.g., 39).
481 Treatment-Planning Optimization
Numerous ideas have been put forward that aim to mitigate the impact
of intrafractional motion: these include recommendations for selection
of planning image set, compensator expansion, internal margins (40, 41),
delivery methods using beam gating (42), feld rescanning (43), and target
tracking (44). In this section, we review approaches to incorporate intrafrac-
tional motion into the optimization of beam weights in IMPT. Those meth-
ods have been investigated primarily in the context of IMRT with photons.
Although the methodology can be transferred to IMPT, those approaches
have not been validated in detail regarding the specifc challenges men-
tioned above, that is, interplay effects and sensitivity to changes in radio-
logical path length.
Methods to incorporate intrafractional motion in plan optimization require
a characterization of the geometrical variation of the patient’s anatomy. For
respiratory motion, this can be obtained from respiratory-correlated com-
puted tomography (CT) (often called 4D CT), which provides the geometry
of the patient in several phases of the breathing cycle (45). The task of evalu-
ating the actual dose distribution delivered to a moving target requires frst
calculating instantaneous dose to all phases of the 4D CT. Figure 15.10 illus-
trates variation in the proton dose distribution delivered to a changing anat-
omy, throughout the respiratory cycle. Such instantaneous doses can then
be mapped onto a reference anatomical set, by using the correspondence
established between the voxels of different CT sets, obtained through elastic
image registration. The mapped dose can be subsequently added along with
contributions from all instances of variable anatomy, to yield the dose accu-
mulated throughout the respiratory cycle (46, 47).
Instantaneous dose
on phase-specific CT
Full inhalation
Full
A
B C
D E
exhalation
Mid-ventilation
Instantaneous dose
mapped to exhalation CT
FIGURE 15.10
Dosimetric evaluation of a treatment plan for a tumor in the liver, using respiratory-correlated
CT. Estimated instantaneous dose delivered during (A) the full exhalation, (B) full inhalation,
and (C) mid-ventilation phases of the respiratory cycle. To estimate the total dose, contribu-
tions from various instances of the anatomy have to be mapped onto the reference CT set, for
example, for (D) full inhalation dose (dose “B” mapped onto the full exhalation CT “A”), and
(E) mid-ventilation (dose “C” mapped onto CT “A”). (CT images courtesy of Dr. S. Mori (NIRS).
With permission.)
482 Proton Therapy Physics
15.5.1 Plan Optimization Based on a Known Motion
Probability Density Function
In a simple approach to include motion, it is assumed that motion is suf-
fciently well described by the reconstructed phases of a 4D CT and that the
dose delivered to a voxel i is obtained by summation of the dose contribu-
tions from all phases:

d = p d = p x D
i
r
r
i
r r
r
j ij
r
j
( ) ( ) ( ) ( )
∑ ∑ ∑
⋅ .

(15.10)
Here, r is an index to the instance of geometry, and the voxel index i refers
to an anatomical voxel defned in the reference phase. D
ij
(r)
is the dose infu-
ence matrix for phase r. Its calculation requires elastic registration of the CT
of phase r with the reference phase. The parameters p
(r)
are probabilities that
the patient is in phase r and are referred to as the motion probability density
function (PDF), which can be estimated from a recorded breathing signal.
Treatment planning can be performed by optimizing the beam weights
x
j
based on objectives and constraints evaluated with the cumulative dose
from Equation 15.10 above (48).
The general idea is that, rather than passively letting the motion deterio-
rate the original plan, one should anticipate it, and, in fact, actively engage it
in shaping the desired dose distribution. The resulting treatment plan would
deliver an inhomogeneous dose distribution to a static geometry. However,
the inhomogeneities are designed such that, after accumulating dose over
the whole breathing cycle, the desired dose distribution is obtained. Because
one of the most manifest effects of motion on the dose is the smoothing or
washout of gradients both within the target and at its borders, the logical
way to counter this effect is dose boosting at the edges of the target, in what
is termed “edge-enhancement” (49).
The exact pattern of optimum inhomogeneity enhancement is determined
by the form of motion PDF. Generally, the effect of motion on the dose may
be approximated as convolution of the dose with the PDF; thus, the desired
motion-compensated plan can be roughly approximated with the inverse
process: deconvolution. However, this is constrained by the requirement that
the fuences delivered at all pencil beam spots are physical; thus, if negative
values arise from deconvolution or during optimization, those need to be
reset to zero (or the minimum should be allowed, if the beam cannot be com-
pletely turned off, e.g., in a continuous scan).
Because the PDF does not depend on time, the use of probabilistic plan-
ning does not require complex technical delivery modifcations to ensure
synchronization of the beam with the motion cycle, and thus delivery of such
felds can be relatively easily implemented in practice. However, PDF-based
optimization methods rely on the reproducibility of target motion patterns
during delivery, and suffcient sampling of the motion PDF. When motion
deviates from the expectation, a signifcant dosimetric deviation may occur.
483 Treatment-Planning Optimization
15.5.2 Plan Optimization for an Uncertain Motion PDF
Through the use of robust planning techniques, the dosimetric outcome of
a treatment plan based on a known motion PDF can be made less vulner-
able to variations in the breathing pattern. This approach thus aims at fnd-
ing a treatment plan that yields an acceptable cumulative dose distribution
even if the actual breathing pattern during treatment differs from the esti-
mated motion PDF assumed for treatment plan optimization. Chan et al.
(50, 51) investigated robust optimization for respiratory motion by modeling
the variability in the breathing motion via uncertainties in the motion PDF
parameters p
(r)
.
15.5.3 Optimizing a Different Fluence Map for Every Phase
Instead of optimizing a single fuence map that is delivered irrespective
of the breathing phase the patient is currently in, one can also optimize a
separate fuence map x
j
(r)
for every phase. The objectives and constraints for
treatment plan optimization are formulated in terms of the cumulative dose,
with the distinction that the fuence map is different in every phase (48). The
delivery of such treatment plans would however require a synchronization
of the dose delivery with the breathing motion.
15.6 AccountingforBiologicalEffectsinIMPTOptimization
Treatment planning for proton therapy usually uses a constant relative bio-
logical effectiveness (RBE) factor of 1.1 for the conversion of physical dose d
i

to “biological” dose (see Chapter 19). The biological effective dose is defned
as the photon dose from a
60
Co source that would produce the same cell-kill
in the tumor. Under the assumption of a constant RBE, treatment plan opti-
mization can be performed based on the physical dose alone as described
in the preceding sections of this chapter. In other words, the physical dose
is the only measure that is needed to characterize the radiation feld and to
assess the quality of the treatment plan. However, this may be an oversimpli-
fcation and a second quantity may be needed to characterize the radiation
feld and its radiobiological effectiveness. This second measure is the linear
energy transfer (LET) (see Chapters 2 and 19).
Radiobiological experiments suggest that the amount of radiation-induced
cell-kill increases with higher LET, and consequently at the end of range of
the proton beams. To directly incorporate effects of varying RBE in IMPT
planning, the objective function needs to be formulated in terms of physi-
cal dose and LET, instead of dose alone. One approach has been suggested
by Wilkens and Oelfke (52), who formulate their objective function based
on the linear-quadratic cell survival model, where the α-parameter depends
484 Proton Therapy Physics
linearly on LET. Recently, Grassberger et al. (53) have demonstrated that it is
feasible in IMPT optimization to infuence the distribution of LET without
signifcantly altering the physical dose distribution.
15.7 OtherApplicationsofMathematical Optimization
inProtonTherapy
15.7.1 Scan Path Optimization
In 3D spot scanning, beam spots are typically placed on a regular grid over
the tumor region. In practice though, a large number of beam spots will be
assigned zero weight in the optimization of the treatment plan. Nevertheless,
in a naïve implementation of spot scanning, the beam would be steered in
a zigzag pattern over the entire grid, including the spot positions that cor-
respond to zero weight. Kang et al. (54) investigated the optimization of
the scan path of the beam in order to avoid regions with zero weight spots.
The problem corresponds to a “traveling salesman” problem and simulated
annealing has been applied to solve the problem.
15.7.2 Beam Current Optimization for Continuous Scanning
There are different ways to perform pencil beam scanning. In spot scan-
ning, the proton beam is steered to one desired position on the grid, delivers
dose according to the optimized spot weight, is switched off, and is moved
to the next grid point. In continuous scanning, the beam is constantly mov-
ing according to a predefned pattern. The intensity-modulated feld is deliv-
ered by modulating the beam current in time while the beam is repeatedly
scanned over the tumor volume. In this case, an additional computational
step is needed that converts the optimized spot weights defned at discrete
positions to the beam-current modulation that approximately delivers the
same fuence. For this step, optimization methods have been applied (14);
however, this optimization can be performed in fuence space. It does not
require dose calculation in the patient and is therefore easier to solve than
the optimization of spot weights.
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489
16
In Vivo Dose Verifcation
KatiaParodi
16.1 Introduction
The favorable physical and radiobiological properties of light ion beams
(i.e., protons and heavier ions up to charge Z ≈ 10) offer the possibility of a
highly precise and biologically effcient radiation therapy, which promises
improved clinical outcome for various tumor sites in comparison to conven-
tional radiotherapy with photons and electrons. However, because of the
increased physical selectivity, ion beam therapy is also more sensitive than
conventional radiation modalities to changes of the actual treatment situation
with respect to the planned one. In particular, the fnite “beam range” in tis-
sue is strongly infuenced by the radiological path length, which determines
the position of the Bragg peak in the tumor and thus the precise localization
CONTENTS
16.1 Introduction ................................................................................................ 489
16.2 In Vivo Treatment Verifcation and DGRT in Photon and Proton
Therapy ........................................................................................................ 491
16.3 PET Imaging ............................................................................................... 493
16.3.1 The Production of Irradiation-Induced β
+
-Activity .................. 494
16.3.2 The Imaging Process ..................................................................... 497
16.3.3 The Clinical Implementation ....................................................... 500
16.3.4 Worldwide Installations and Clinical Experience .................... 506
16.3.5 On-Going Developments and Outlook....................................... 509
16.4 Prompt Gamma Imaging .......................................................................... 512
16.4.1 The Production of Irradiation-Induced Prompt Gamma ......... 512
16.4.2 The Imaging Process ..................................................................... 512
16.4.3 Worldwide Preclinical Investigations ......................................... 514
16.4.4 The Foreseen Clinical Implementation ....................................... 515
16.5 Magnetic Resonance Imaging .................................................................. 516
16.6 Conclusion and Outlook ........................................................................... 519
References ............................................................................................................. 520
490 Proton Therapy Physics
of the intended dose delivery. Therefore, uncertainties in the knowledge of
the in vivo beam range in the patient is one of the major concerns in ion
therapy, hampering full clinical exploitation of the dosimetric advantages of
ion beams in clinical practice.
Major sources of random range (and thus dose delivery) errors during the
fractionated course of radiation therapy include patient positioning, anatom-
ical and physiological changes (Chapter 13), and, for certain tumor locations,
organ motion (Chapter 14). Additional sources of systematic range uncer-
tainties in the treatment-planning process may include the usage of semi-
empirical calibration of the planning x-ray computed tomography (CT) into
ion range, the presence of CT artifacts and the particle scattering in complex
anatomy or in the presence of metallic implants.
To account for all the possible sources of random and systematic errors
in clinical practice, cautious safety margins are added to the tumor volume
when designing the treatment plan. Moreover, treatment strategies tend to
rely on the more controllable but less conformal lateral penumbra of the
beam, rather than placing the sharper distal dose falloff in front of radiosen-
sitive structures (Chapters 10 and 11).
However, reduction of margins and safe application of doses tightly
sculpted to the tumor target is a major goal of modern radiotherapy to
avoid excess toxicity and promote dose escalation for increased tumor con-
trol. Therefore, the advances in the achievable selectivity of the dose deliv-
ery with external beam treatment modalities have been accompanied by an
increasing role of imaging in the whole radiotherapy process (1). The various
efforts span from precise identifcation of the target volume at the planning
stage to the evaluation of the patient geometry directly at the treatment site
and, eventually, quantifcation of the actual dose delivery in comparison
to the planned one as well as treatment response assessment for adaptive
strategies.
Nowadays, conventional and novel methods of image-guided radiother-
apy (IGRT) are increasingly well established in photon therapy for evalua-
tion of the patient geometry and tumor position directly at the treatment site.
Typical implementations include the usage of in-room radiographic (two-
dimensional, 2D) and volumetric (three-dimensional, 3D) x-ray kilovoltage
or megavoltage imaging for assessment of internal anatomy, as well as non-
ionizing monitoring sensors of external motion surrogates. Corresponding
IGRT solutions of 2D and/or 3D x-ray kilovoltage imaging also have been
adopted at most ion beam therapy centers. Even dedicated solutions tailored
to ion beam therapy have been developed, such as vertical CT systems for
volumetric in-room imaging of patients treated in the seated position (2) or
x-rays shining through a hole in the last bending magnet of a novel beam
gantry for beam’s eye view (BEV) portal imaging simultaneous with the
proton beam (3). In some implementations, time-resolved operation is sup-
ported for 4D capabilities (e.g. for fuoroscopic imaging of internal motion to
complement external surrogates during irradiation).
491 In Vivo Dose Verifcation
Indeed, IGRT techniques offer essential information not only for helping
reducing positional errors at the treatment site for the individual patients,
but also for obtaining population-based estimation of geometrical uncertain-
ties to optimize the choice of clinical safety margins in treatment planning
(1). However, they cannot provide the ultimate solution to the more stringent
issue of reduction of range uncertainties and in vivo treatment verifcation
in ion beam therapy, because they do not bear information on the interaction
of the ions with the penetrated tissue. Therefore, availability of additional
imaging techniques capable of assessing the beam range and the delivered
dose in vivo and noninvasively would be highly benefcial.
For optimal quality of patient care, the in vivo treatment verifcation meth-
ods should enable an independent validation of the complete therapy chain
from treatment planning to beam delivery. On the one hand, these methods
should provide in vivo confrmation of the successful tumor-conformal
dose delivery, in order to improve treatment confdence and thus promote
safe dose escalation studies for full clinical exploitation of the dosimetric
advantages of ion beams. This also promises to play an important role in the
increasingly considered high-dose hypofractionated therapy, where less or
even no subsequent fractions are available for compensation of errors. On
the other hand, in vivo treatment verifcation methods should also enable
prompt identifcation and quantifcation of unexpected deviations between
planned and actual dose delivery for promoting adaptive treatment strate-
gies toward dose-guided radiation therapy (DGRT) and, ideally, for inhibit-
ing improper dose delivery during treatment (“real-time” monitoring). This
chapter will address the specifc demands and challenges of in vivo treat-
ment verifcation and DGRT of proton therapy in comparison to photon therapy,
reviewing techniques already being investigated clinically or still at the stage
of research and development.
16.2 InVivoTreatmentVerificationandDGRT
inPhotonandProtonTherapy
The physical properties of the penetrating megavoltage photon beams enable
detection of the radiation traversing the patient simultaneously to the thera-
peutic treatment. This is typically achieved by using planar detectors such as
electronic portal imaging devices (EPIDs) (4) integrated into the linear accel-
erator treatment head, opposite to the radiation source beyond the patient.
Historically, EPIDs were initially developed and used for pretreatment
confrmation of the lateral feld position via analysis of 2D projections of the
transmitted irradiation with respect to visible landmarks such as implanted
markers or bony structures. However, latest research has shown that the por-
tal images can also be converted into portal dose measurements; compare, for
492 Proton Therapy Physics
example, Nijsten et al. (5). Therefore, EPID data are now being acquired dur-
ing irradiation for a quantitative dosimetric comparison with the correspond-
ing expectation based on the planned treatment. This can be done not only at
the detector level (2D transit dosimetry) but also within the patient (in vivo
3D dosimetry) by a proper backprojection approach (6). An implementation
independent from the therapy chain can be obtained when combining a dose
calculation engine different from the treatment-planning system (e.g., Monte
Carlo) with anatomical information of the patient in the treatment position as
acquired by a megavoltage cone beam CT shortly before irradiation (7).
The promising clinical results reported so far clearly indicate that the
advances in portal imaging and EPID dosimetry have opened new avenues
in the quality of adaptive radiation therapy (ART) based not only on detec-
tion of anatomical changes (IGRT), but also of dose delivery differences
(DGRT) in modern photon therapy. Unfortunately, the different properties
of charged particles with respect to neutral photon radiation prohibit the
usage of EPID dosimetry for in vivo quality assurance and DGRT of ion
beam therapy. In fact, the primary therapeutic ions are completely stopped
in the patient in order to place the Bragg peak in the tumor. Therefore, in
vivo noninvasive verifcation of the actually delivered treatment and, in par-
ticular, of the primary ion beam range has to rely on some kind of surrogate
signal induced by the therapeutic irradiation.
The more straightforward approach for verifcation of the treatment simul-
taneously to or shortly after ion beam delivery is based on the detection of
irradiation-induced secondary radiation emerging from the patient. This
radiation is produced as the result of nuclear fragmentation reactions between
the incoming ions and the target nuclei of the penetrated tissue. Because of
the intrinsic physical differences between the nuclear and electromagnetic
interactions underlying nuclear fragmentation and dose deposition, the sur-
rogate emission signal can only be correlated but not directly matched to
the delivered dose. Nevertheless, valuable information can be inferred from
the comparison of the measured signal with a corresponding expectation
(e.g., based on the planned treatment, the time course of the beam delivery
and the chosen imaging strategy). Section 16.3 will address the already clini-
cally investigated unconventional usage of positron emission tomography
(PET), aiming to exploit the transient pattern of β
+
-activation generated as
a byproduct of the therapeutic irradiation. Section 16.4 will present the very
encouraging investigations on prompt-gamma imaging, which promises
several advantages over PET imaging but is still hampered by the main chal-
lenge of the realization of an effcient detector solution.
In addition to irradiation-induced secondary radiation emitted as the result
of nuclear reaction processes, other imaging possibilities are being explored
that may enable in vivo range verifcation on a different time scale before
treatment or even days up to weeks after completed fractionated therapy.
The latest novel method being clinically evaluated is magnetic resonance
imaging (MRI). This intriguing technique addressed in Section 16.5 aims to
493 In Vivo Dose Verifcation
exploit irradiation-induced physiological processes such as bone marrow
replacement, which is found to become manifest in follow-up MRI scans
after completion of the entire fractionated therapy course.
Finally, when available, ion beams at higher energies than for therapy
could be used for transmission imaging of the residual ion range beyond
the patient before or even in-between treatments (e.g., when range variation
due to organ motion is of concern). Radiographic and tomographic imple-
mentations could enable indirect validation and even substitution of the
semi-empirical x-ray CT-range calibration curve, besides low-dose image
guidance of the patient position at the treatment site (8, 9). However, this
method cannot provide in vivo treatment verifcation and DGRT because it
does not rely on a signal induced by the interaction of the therapeutic beam
with the patient. Hence, it will not be addressed further.
A schematic representation of the different time scales of the available
techniques, with emphasis on those reviewed in this chapter, is summarized
in Figure 16.1.
16.3 PETImaging
PET currently offers the only technically feasible method for a volumetric,
in vivo, and noninvasive verifcation of the actual treatment delivery and, in
Long after therapy (T days - weeks)
Magnetic Resonance Imaging (MRI)
Long after treatment (T ~ 10 – 20 min)
Offline PET (/CT)
T
Post treatment (T ~ 0 – 10 min)
In-room or nearby PET(/CT)
In-beam “delayed” (T ms – min)
PET
In-beam “real-time” (T < ms)
Prompt gamma, emitted particles
Pre-treatmnt (-T ~ min)
Radioactive ion (RI) beams
Ion radiography / tomography
Irradiation
Time
Sum
of Fxs
Selected Fx
Each or
selected Fx
Each Fx
Each Fx
First or each fraction (Fx)
FIGURE 16.1
Schematic representation of the different imaging approaches for in vivo dose or range veri-
fcation on different time scales and delays ΔT with respect to the time of irradiation (upper
axis). White characters refer to methods only mentioned but not further addressed in the text
because either limited to heavy ion applications (RI imaging, emitted particles) or not induced
by the therapeutic irradiation (ion radiography/tomography). The right arrow suggests pos-
sible clinical implementations for monitoring frst, individual, or selected fractions (FXs), up to
the integral fractionated treatment course (cf. text).
494 Proton Therapy Physics
particular, of the ion beam range in the patient during or shortly after irra-
diation. This unconventional application of a well-established nuclear medi-
cine technique exploits the coincident detection of the annihilation photon
pairs resulting from the β
+
-decay of positron-emitting isotopes formed as
a byproduct of the therapeutic irradiation. The mechanism of activity pro-
duction, the image formation process, the data acquisition strategies, the
clinical implementation, and the worldwide installation and experiences are
reviewed in the following sections.
16.3.1 The Production of Irradiation-Induced β
+
-Activity
Nuclear interactions between the impinging ion beam and the target nuclei
of the traversed tissue are typically regarded as a major drawback for thera-
peutical applications. In fact, they are responsible for modifying the compo-
sition and energy spectrum of the radiation feld, preventing primary ions to
reach the Bragg peak for localized dose deposition in the tumor via inelastic
Coulomb collisions. However, this drawback is somewhat compensated by
the fact that fragmentation reactions may yield with a considerable probabil-
ity positron-emitting nuclei (cf. typical cross sections of relevance for proton
therapy in Figure 16.2), thus opening the possibility of PET-based in vivo
treatment verifcation.
Nuclear fragmentation is a complex two-stage process resulting in the
fast (within ca. 10
−22
s) production of excited prefragments, which eventu-
ally approach the fnal state via nucleon evaporation and photon emission
in about 10
−21
to 10
−16
s (11). A schematic illustration is given in Figure 16.3.
Among the possible reaction yields, neutron-defcient nuclei are produced
that are likely to undergo β
+
-decay. Depending on the primary ion beam
species, the mechanism of β
+
-activation includes either target fragmentation
only or the formation of both target and projectile positron-emitting frag-
ments. Although the focus of this contribution is on proton therapy only,
0
0
20
40
60
80
C
r
o
s
s

s
e
c
t
i
o
n
/
m
b
100
120
100 200
Energy/MeV
12
C(p,p+n)
11
C
16
O(p,p+n)
15
O
300 400
FIGURE 16.2
Compilation of available experimental cross sections for the main (p, pn) [including (p, d)] reac-
tion channels on carbon and oxygen yielding positron emitting
11
C and
15
O, respectively. (After
Parodi, PhD thesis, Dresden University of Technology, 2004.)
495 In Vivo Dose Verifcation
all the possible mechanisms of irradiation-induced β
+
-activity will be briefy
reviewed. This is because of their relevance in the historical developments of
PET monitoring (cf. subsections 16.3.3 and 16.3.4).
Protons and light ions up to beryllium can only contribute to the β
+
-activation
of the target nuclei of the irradiated medium. This is because they either do
not fragment at all (protons Z = 1), or they cannot produce positron-emitting
projectile fragments (Z ≤ 4). Typical reaction products in living tissue include
light isotopes such as
11
C,
15
O, and
13
N, with half-lives T
1/2
of about 20, 2, and
10 min, respectively. These β
+
-active target fragments are formed all along
the ion beam path as long as the energy is above the threshold for nuclear
interaction. The latter is mostly located at 10–20 MeV/u, corresponding to
about 1–4 mm residual ion range in tissue. Because of the interaction kine-
matics, the activated target recoils remain approximately at the place of pro-
duction. Therefore, according to the typically weak energy dependence of
the reaction cross sections for most of the therapeutically relevant ion beam
energies in the most abundant tissue constituents (cf. Figure 16.2), the charac-
teristic track of activation in homogeneous media exhibits a rather constant
Target
Target fragment
12
C ion
Proton
Projectile fragment
ν
f
≈ 0
ν
f
≈ ν
p ν
p
Projectile
Projectile Projectile
Abrasion Ablation
Target
Target fragment
Abrasion Ablation
n
p,d,t
n
p,d,t
evap.
-emission
-emission


FIGURE 16.3
Schematic representation of peripheral nuclear collisions with special emphasis on the dif-
ferent fragmentation mechanisms undergone by carbon ions (projectile and target fragments
with related velocities v) and protons (target fragments only). Different reaction products are
also illustrated, including evaporation of nucleons and light fragments as well as γ-emission.
(Adapted from Schardt et al., Rev Mod Phys, 82, 383, 2010.)
496 Proton Therapy Physics
or slowly rising slope, dropping to zero few millimetres in front of the Bragg
peak (Figure 16.4). For primary proton beams, the contribution of secondary
radiation other than protons (e.g., neutrons) to the activation of the traversed
tissue can be assumed to be negligible (13). Differently, for heavier primary
ions (1 < Z ≤ 4), the longer ranging non-positron-emitting projectile frag-
ments yield an additional tail of β
+
-emitting target fragments beyond the
Bragg peak, as experimentally observed for
3
He and
7
Li ions in Fiedler et al.
(14) and Priegnitz et al. (15).
In addition to the formation of β
+
-active target fragments, heavier ions
(Z  ≥  5) can also yield positron-emitting projectile fragments. This is also
called “auto-activation” of the beam (17, 18), for distinction to the direct exter-
nal implantation of primary β
+
-radioactive ions (19). Because the stopping in
matter is a faster process than the radioactive decay, the activity contribution
from β
+
-emitting projectile fragments is formed at their end of range. This
can be particularly advantageous for beam range verifcation, as β
+
-active
isotopes of the primary ion beam are typically formed in abundance and
tend to accumulate shortly before the range of the primary stable ions due
to the kinematics of the nuclear reaction (20). Therefore, the auto-activation
(e.g., of a
12
C ion beam) results in a marked activity maximum shortly before
the Bragg peak due to the major contribution of the long-lived
11
C and, to a
lesser extent, of the short-lived
10
C (T
1/2
≈ 20 s), superimposed onto the pedes-
tal of β
+
-active target fragments (Figure 16.4).
Nevertheless, the weaker spatial correlation between the depth distribu-
tions of dose and positron emitters for proton in comparison to carbon ion
irradiation (cf. Figure 16.4) is somewhat outweighted by the approximately
three times higher activity yield at the same range and delivered dose, as
experimentally shown by Parodi, Enghardt, and Haberer (21). This is mainly
0.0
A
r
b
i
t
r
a
r
y

u
n
i
t
s
0.2
0.4
0.6
0.8
1.0
1.2
0 20 –20
Activity
Dose
1
H
40 60 80 100 120 0 20 –20
Activity
Dose
3
He
40 60 80 100 120 0 20 –20
Activity
Dose
12
C
40 60 80 100 120
Penetration depth (mm)
FIGURE 16.4
Depth distributions of calculated dose (dashed line) and measured β
+
-activity (solid line)
for 
1
H (left),
3
He (middle), and
12
C (right) ions impinging in homogeneous targets of polymethyl
methacrylate (PMMA, C
5
H
8
O
2
). As a consequence of the different fragmentation mechanisms
(cf. Figure 16.3 and text), projectile fragments of
12
C ions yield a pronounced activity maximum
shortly before the Bragg peak (right panel). For the lighter ion beams (left and middle), activa-
tion is only due to the target fragments produced along the beam penetration depth, including
a tail beyond the Bragg peak from lower charge projectile fragments of the primary
3
He beam
(middle). (Adapted from Parodi, PhD thesis, Dresden University of Technology, 2004; Fiedler
et al., IEEE Trans Med Sci, 53, 2252, 2006; and Pawelke et al., Proc. IBIBAM meeting, 2007.)
497 In Vivo Dose Verifcation
due to the higher fuence of protons required to compensate their lower
energy loss rate in the delivery of the same dose.
16.3.2 The Imaging Process
Regardless of the formation mechanism, the transient pattern of β
+
-activation
induced as a byproduct of the irradiation can be imaged via PET techniques.
The frst step in the image formation process is the β
+
-decay of the irradi-
ation-induced positron emitter A(Z, N), with mass number A and neutron
number N at a random time, depending on the isotope half-life:
A(Z, N) → A(Z – 1, N + 1) + e
+
+ ν
e
. (16.1)
In this radioactive transformation, one proton is transformed into one neu-
tron, and a positron and a neutrino are emitted with a continuous energy
spectrum. While the neutrino escapes without interaction, the positron is
slowed down typically within a few millimeters path in the medium, los-
ing its energy in Coulomb inelastic collisions with the atomic electrons and
suffering several angular defections. Once almost at rest, the positron either
annihilates as a free particle with an electron of the medium into two pho-
tons, or it captures an electron to form an unstable bound state e
−
e
+
, so called
positronium. Although the two different atomic states of the positronium can
lead to different annihilation processes into two (para-positronium) or three
(ortho-positronium) photons, the three γ-emission is in practice negligible.
Thus, all the detectable radiation can be attributed to the two annihilation
γ-quanta that, according to the momentum and energy conservation law, are
emitted in opposite directions and carry an energy of 511 keV each, equal to
the positron and electron rest mass. Deviations from perfect co-linearity can
occur because of the residual energy of the electron-positron system, result-
ing in emission angles that approximately follow a Gaussian distribution
centred at 180° with ca. 0.3° full-width at half-maximum (FWHM) for typical
residual energy values of about 10 eV.
The 511-keV photon pairs are energetic enough to penetrate the tissue sur-
rounding the place of annihilation and eventually escape from the patient.
Therefore, the PET signal can be acquired by opposite detector pairs sur-
rounding the patient and operated in coincidence (Figure 16.5). Because of
the relatively high photon energy, dense high-Z inorganic scintillators are
usually used for stopping the penetrating photon radiation and, at the same
time, for enabling fast timing performances of coincident detection typically
within a few nanoseconds time window. Commonly used PET detectors
are based on bismuth germanate (BGO), gadolinium orthosilicate (GSO), or
lutetium oxyorthosilicate (LSO) scintillator crystals, though other promising
materials such as lanthanum bromide (LaBr
3
) now are being investigated (22).
The detected coincidences can be attributed to radiation either emerg-
ing from a single annihilation event (“true” or “scattered”), or belonging
498 Proton Therapy Physics
to independent emissions accidentally occurring close in time (“random”).
Under the assumption of perfect co-linearity of the annihilation photon
pairs, true coincidences refer to emission events originating along the line
of response (LOR) connecting the two opposed crystals fred in coincidence.
Differently, scattered coincidences are generated by events where at least one
photon has experienced a scattering process and thus a change with respect
to the initial direction. This results in a mismatch between the detected LOR
and the original annihilation place. A similar mismatch obviously applies to
random coincidences due to the different origins of the independent anni-
hilation events accidentally detected in the same coincidence window (see
Figure 16.6).
For a reliable reconstruction of the β
+
-activity distribution underlying the
measured signal, the amount of true coincidences has to be recovered from
the whole collected data. This can be achieved via proper corrections for ran-
dom (23) and scattered (24) coincidences. In this process, the properties of the
used detector system can be critical. In particular, energy resolution is help-
ful for discrimination of scattered events, whereas short decay constants are
essential for good coincidence timing and related random suppression. The
latter has also been the main argument for the rapid establishment of latest
Coincidence
processor
Image reconstruction
Detector hit 2
Detector hit 1
180°
γ
γ
β
+
-emitter
e
-
E
γ
= 511 keV
e
+
FIGURE 16.5
Schematic representation of the PET imaging process in the case of a full-ring detector sur-
rounding the activity source. All the depicted steps of β
+
-decay, positron emission and mod-
eration in the medium, annihilation and concident detection of the resulting γ-pairs for
subsequent image reconstruction are explained in the text.
True coincidence Random coincidence Scattered coincidence
FIGURE 16.6
Schematic illustration of true (left), random (middle), and scattered (right) coincidence events
in PET acquisitions. The solid lines indicate the real photon paths, whereas the dashed lines
depict the assigned lines of response to the detected coincident γ-ray pairs. Obviously, solid
and dashed lines coincide only in the case of true coincidence (left). (After Parodi, PhD thesis,
Dresden University of Technology, 2004.)
499 In Vivo Dose Verifcation
generation lutetium-based scintillators like LSO, whose timing properties
(and light output) outperform the more traditional detector systems based
on BGO. This is at the expense of a minor amount of intrinsic radioactiv-
ity that is responsible for a small background (especially of random coinci-
dences) in the measurable signal. This detector radioactivity is of no concern
in standard nuclear medicine imaging, but it may become more relevant at
the typical low activity levels of ion therapy monitoring, as discussed below.
The quantitative amount of decays from the activity source can be then
recovered from the estimated number of true coincidences by taking into
account the total photon attenuation along each LOR as well as the quan-
tum detection effciency of the hit crystal pairs. The 3D distribution of the
β
+
-activity map can be fnally recovered from the measured projections
using tomographic reconstruction algorithms, typically approximating the
position of the β
+
-decay with the annihilation emission place and including
a normalization for the space-dependent geometrical probability of detec-
tion from each emission position. The most reliable solutions are in general
provided by iterative methods using the maximum-likelihood expectation
maximization (MLEM, 25) or the ordered subsets expectation maximiza-
tion (OSEM, 26) algorithms. Because of the typical detector granularity of
4–6 mm as well as the intrinsic limitations coming from the nonperfect co-
linearity of the annihilation photons and the fnite positron range, spatial
resolutions of approximately 4–5 mm FWHM are generally attainable in
the center of the scanner feld-of-view. It should be noticed that this coarse
resolution introduces a blurring of the imaged map of activation, but it does
not alter the center of gravity of the distributions. Thus, it does not prevent
millimeter accuracy for localization of the distal activation falloff, which is
correlated with the primary proton beam range (cf. Section 16.3.1 and Figure
16.4), as experimentally demonstrated in phantom studies (Figure 16.7) as
long as suffcient counting statistics are detected (27). When available, addi-
tional information on the arrival time difference (time-of-fight, TOF) of the
photons on the crystals fred in coincidence can be used to reduce the uncer-
tainty of the reconstructed spatial position of the emission along the LOR.
According to the 3 · 10
10
cm/s speed of light and the time resolutions of 500
ps achievable with the latest generation PET scanners, the uncertainty in
the localization of the emission event can be reduced to ±7.5 cm. Thus, TOF
information cannot dramatically improve spatial resolution, but it can offer
increased signal-to-noise ratio in the reconstructed images.
In comparison to conventional tracer imaging in diagnostic nuclear medi-
cine, a major challenge for the unconventional application of PET imaging
to the verifcation of ion treatment is the extremely low counting statis-
tics. The irradiation-induced activity signal amounts to approximately 0.2–
10  kBq/Gy/cm
3
depending on the ion type, the time course of irradiation,
and the involved anatomical site (15, 28–30). For typical fraction doses of
0.5–2 Gy this corresponds to activity densities that can be far below those of
≈10–100 kBq/cm
3
reached in standard PET imaging. Moreover, once positron
500 Proton Therapy Physics
emitters are formed in living body by external irradiation, they undergo a
complex hot chemistry and can be partly spread out by diffusion or even car-
ried away (washed out) from the location of activity production by different
physiological processes (e.g., perfusion) occurring at different time scales. As
a result, the irradiation-induced activity tends to disappear more quickly in
living tissues than in inorganic matter, thus following not only a physical but
also a so-called biological decay with varying half-lives from 2 up to 10,000 s,
according to pioneering investigations in dead and living animals (31, 32).
16.3.3 The Clinical Implementation
Different imaging strategies can be implemented clinically for acquisition
of the irradiation-induced activity signal, exploiting different portions of
the characteristic time curve of the activity build-up and decay during and
after therapeutic beam application (Figure 16.8). In situ detection of the tran-
sient activation of the patient directly in the treatment position can be per-
formed during (“in-beam”) or immediately after (“in-room on-board”) end
of irradiation by means of customized systems fully integrated in the dose
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 50
Activity
A
r
b
i
t
a
r
y

u
n
i
t
s
Dose
100
Penetration depth/mm
150 200
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 50
A
r
b
i
t
a
r
y

u
n
i
t
s
156.06 - 171.62 MeV
156.60 - 171.13 MeV
157.13 - 172.63 MeV
157.66 - 173.13 MeV
100
Penetration depth/mm
150 200
FIGURE 16.7
Experimental validation of the range resolving power of in-beam PET for proton irradiation
of thick PMMA targets. Top: the planned spread-out-Bragg peak dose (dashed line, built by 11
mono-energetic beams in the 156.06–171.62-MeV interval) and the corresponding measured
activity (solid line) depth profles. Bottom: the panel additionally depicts the activity depth
distributions measured when changing the nominal SOBP plan in energy steps correspond-
ing to incremental variations of less than 1 mm in depth. (After Parodi, PhD thesis, Dresden
University of Technology, 2004.)
501 In Vivo Dose Verifcation
delivery environment (28, 33). Alternatively, the patient can be moved to a
remote installation for imaging starting from 2 up to 20 min after therapeutic
beam application using conventional nuclear medicine PET scanners located
inside (“in-room”) or outside (“off-line”) the treatment room (30).
Indeed, the on-line implementations (in-beam and in-room on-board) are
the most appealing solutions, which better preserve the correlation between
the measurable signal and the delivered dose by detecting the major activi-
ity contribution from short-lived emitters such as
15
O and by minimizing the
signal degradation from positioning uncertainties and biological washout.
However, they are also the most demanding approaches, which require the
development of dedicated detector instrumentation with typical dual-head
geometrical confguration in order to avoid interference with the beam as
well as to enable fexible patient positioning. In-beam implementations addi-
tionally offer the possibility to measure the time-resolved formation of the
activity during irradiation. However, they also require customization of the
data acquisition system for synchronization with the beam delivery and for
rejection of the undesired background, for example, due to prompt-gamma
emission, during the “beam-on” time (34). In fact, unless novel dedicated
0
0 500 1000 1500
Time / s
0 500 1000 1500
Time/s
a)
C
o
u
n
t

r
a
t
e
/
c
p
s
b) c) d)
a) b) c) d) 15
O
11
C
10
C
2000
4000
6000
8000
0
C
o
u
n
t

r
a
t
e
/
c
p
s
1000
2000
3000
4000
5000
FIGURE 16.8
Illustration of the different time windows for detection of the β
+
-activity build-up and decay
during and after irradiation. Top: (a–d) The measured (solid line) coincidence rate detected for
an approximately 10-min proton irradiation of a PMMA target. The dashed line refers to the
calculation using the estimated contributions of the different isotopes separately shown in the
bottom panel (a–d). The corresponding different strategies of in-beam (a), in-room on-board
(b), in-room (c), and off-line (d) PET imaging are discussed in the text. (Adapted from Parodi,
PhD thesis, Dresden University of Technology, 2004; and Parodi et al., Trans Nucl Sci, 52, 778,
2005.)
502 Proton Therapy Physics
solutions are implemented (35), the prompt radiation background during
beam extraction currently limits meaningful in-beam PET detection only to
the pauses of pulsed beam delivery, thus reducing the amount of measur-
able decays from the produced isotopes in dependence of the accelerator
duty cycle and dose rate. This is especially crucial for conventional in-beam
PET data acquisition at effcient accelerator systems such as continuous-wave
cyclotrons and dedicated clinical synchrotrons (36). Therefore, although in-
beam solutions ideally offer the optimal workfow for exploitation of the
activity signal already during beam delivery, they may still require prolon-
gation of the measurement for a few minutes after the end of the irradiation
for suffcient counting statistics, similar to the in-room on-board solutions.
This is obviously at the expenses of patient throughput in the treatment
room. In terms of imaging performances, for both on-line implementations
the space-variant detector response of dual-head confgurations in com-
bination with the generally low counting statistics of irradiation-induced
activation pose challenging issues for trustful image reconstruction, thus
requiring careful design of the detector geometry (37) and cautious inter-
pretation of the reconstructed activity distributions. In particular, existent
limited angle installations are either restricted to central planar imaging
(33) or suffer from severe degradation of the imaging performances far from
the central plans of the feld-of-view in the tomographic reconstruction (28,
37). In this respect, theoretical investigations have indicated the promise of
future ultra-fast TOF techniques with timing resolution less than 200 ps,
which would enable almost artefact-free, real-time images for the next-gen-
eration in-beam installations currently being under investigation (38), as
addressed in Section 16.3.5.
Postradiation in-room and off-line imaging can rely on commercially
available full-ring tomographs, but requires accurate replication and fxation
of the treatment position. Especially for in-room instrumentation, this can be
achieved using modern robotic positioning systems with minimal perturba-
tion of the patient fxation. Availability of CT imaging in combined PET/CT
scanners can considerably help coregistration at the expenses of additional
radiation exposure of the patient, which can be however justifed in the con-
text of IGRT. For in-room instrumentation, moderate efforts are required for
integration of the scanner in the treatment environment and for optimiza-
tion of the workfow in order to minimize the occupation of the treatment
room after irradiation. Off-line imaging outside of the treatment room is less
demanding in terms of integration efforts, but requires longer measuring
times for accumulation of suffcient counting statistics as in the in-beam
or in-room acquisition during or shortly after treatment (cf. Figure 16.8).
Moreover, off-line imaging can only enable detection of the integral fraction
dose delivery, without the capability to resolve the contribution of the frst
applied treatment feld. This restricts verifcation of the in vivo beam range
to non-opposing-beam portals for multifeld irradiation. Individual moni-
toring of the frst-delivered treatment feld is instead possible with in-room
503 In Vivo Dose Verifcation
instrumentation, provided that modifcation of the patient position for trans-
portation into the scanner is accepted by the clinical staff when additional
felds are to be delivered after the PET imaging. Obviously, minimization of
the time elapsed between irradiation and in-room or off-line imaging is cru-
cial to keep the degradation of the measurable signal at an acceptable level,
taking into account the typical half-lives of 2 and 20 min for the main 
15
O
and 
11
C products, respectively, as well as the typical time scale of 2 up to
10,000 s for the different components of biological washout (32). This would
ideally require delays of a couple of minutes at most, which seem to be fea-
sible for in-room installations. Larger delays may be unavoidable for off-line
implementations, depending on the vicinity of the installation and the auto-
mation of the workfow. The loss of activity in the time elapsed between
irradiation and imaging consequently affects the choice of the acquisition
time window, which has to be selected as a reasonable compromise between
counting statics, patient throughput in the treatment room (in-room imag-
ing), and patient comfort in prolonged acquisitions (off-line imaging). This
typically translates into measuring times of approximately 5 min for in-room
imaging and maximum 30 min for off-line imaging. In terms of tomographic
imaging, full-ring scanners typically provide improved performances
compared with limited angle in situ installations, but may suffer from the
shortcomings of the postradiation application in terms of reduced counting
statistics and increased washout in dependence of the imaging delay and the
acquisition time window. Furthermore, reconstruction algorithms of com-
mercial scanners are typically optimized for imaging high level, localized
activity concentrations as typically administered in standard tracer imaging
and may thus suffer limitations in the imaging of low level, extended activity
distributions as induced by therapeutic irradiation. Additional issues can be
due to the minor amount of intrinsic radioactivity of the PET detector com-
ponents (e.g., LSO-based) that may generate a background noise comparable
with the signal to be imaged (29).
Regardless of the chosen imaging strategy, the irradiation-induced activity
within the patient represents only a “surrogate” signal that is correlated but
not directly matching the delivered dose (cf. Figure 16.4). The distinction is
clearly due to the different nuclear and electromagnetic processes underly-
ing the mechanisms of β
+
-activation and energy deposition, respectively. The
ideal clinical exploitation of PET imaging would require a solution to the
challenging ill-posed inverse problem directly relating the measured activ-
ity to the actual dose delivery. Despite promising attempts to establish this
relationship for phantom studies (39, 40), a straightforward solution is not yet
available for application to low statistics and washout-affected patient data.
Nevertheless, useful clinical information on the correct delivery of the
intended treatment feld and beam range can be obtained from the compari-
son of the measured PET images with an expected pattern of β
+
-activation.
This can be either the reference activity measured at the frst day of treat-
ment (41) or a detailed calculation taking into account the patient-specifc
504 Proton Therapy Physics
treatment plan and the fraction-specifc time course of irradiation and PET
acquisition, as well as the detector-dependent imaging performances (28).
The former approach only enables a consistency check over the course of
fractionated therapy, whereas the latter may allow a direct in vivo valida-
tion of the planned beam range in the patient when the PET calculation
shares similar physical beam models as the treatment-planning system and,
in particular, the same CT-range calibration curve (42). Indeed, the pos-
sibility of in vivo validation of the beam range in the patient is of utmost
importance when starting the operation of a new ion beam therapy facility
or when introducing new ion species into clinical practice, as demonstrated
by the clinical experience of in-beam PET monitoring of
12
C ion treatments
at Gesellschaft für Schwerionenforschung (GSI), Darmstadt, Germany (28).
However, the computational approach implemented in Pönisch et al. (42),
tailored to application at the GSI pilot therapy project, could exploit the
reduced sensitivity of carbon ion–induced activation to the patient tissue
stoichiometry because of the relevance of projectile-fragmentation processes
(cf. Section 16.3.1 and Figure 16.4). For proton therapy, the computational
model must carefully take into account both the elemental composition of
the medium and the different reaction channels leading to the production of
the positron emitters whose decay can be measured in the considered acqui-
sition time window. Preclinical studies in homogeneous materials of known
compositions highlighted the beneft of directly using available experimen-
tal cross sections folded with the energy-dependent proton fuence rather
than relying on the predictions of general-purpose nuclear models (21, 27).
Moreover, they highlighted changes of the distal activity falloff up to a cou-
ple of millimeters, depending on the acquisition time window, due to the
signal contribution from different isotopes such as
11
C,
10
C, and 
15
O, as well
as the different energy dependence and threshold of the reaction cross sec-
tions (27). First computations of proton-induced activation in clinical cases
were implemented using either full-blown Monte Carlo simulation meth-
ods (13, 43) or analytical convolution of the planned dose distribution with
proper reaction-dependent flter functions (43, 44). Clearly, the accuracy of
the computational methods strongly depends on the used cross sections
for the involved activation channels, as well as on the extraction of informa-
tion on the tissue elemental composition from the available CT images. In
this respect, a recent Monte Carlo study quantifed the uncertainties of the
CT conversion scheme already to account for a 1-mm limitation in the accu-
racy of range verifcation from PET images (45). Moreover, the computational
modeling cannot be limited to the description of the physical production
and decay of positron emitters, but must also include the complex effect of
biological washout, which can considerably affect the magnitude and spatial
pattern of the measurable activity especially in postradiation imaging. For
this purpose, a frst solution has been proposed in Parodi et al. (43) on the
basis of literature data for implanted radioactive ions in animal tissue (32),
as well as time-decay analysis of activity curves in regions of interest set in
505 In Vivo Dose Verifcation
different tissue for clinical PET acquisitions after proton therapy. The basic
idea is the model suggested in Mizuno et al. (32), which decomposes the
biological processes (C
bio
) into fast (f), medium (m), and slow (s) components
affecting the physical activity (A
phys
) decay in the fnal measurement (A
meas
)
as follows:
A
meas
(t) = C
bio
(t) A
phys
(t)
C
bio
(t) = [M
f
exp(–λ
bio f
t) + M
m
exp(–λ
bio m
t) + M
s
exp(–λ
bio s
t)]; ∑M = 1. (16.2)
A patient-independent segmentation of the patient CT was then proposed to
identify different tissues (e.g., brain, muscle, fat) for assignment of the bio-
logical M and λ coeffcients selected on the basis of the above-mentioned
literature (32) and clinical data (36, 43). This modeling already provided
very encouraging results with quantitative agreement between calculation
and predictions from 5% to 30%, especially for head-and-neck tumor loca-
tions  (43). However, other investigations reported more severe deviations
in extracranial anatomical sites, especially in the pelvic region (46), thus
demanding further model refnements.
In addition to range verifcation, PET imaging can also confrm the lateral
position of the irradiation feld as well as detect unpredictable deviations
between planned and actual treatment caused by minor misalignments or
local anatomical and/or physiological changes of the patient, which introduce
density modifcations in the beam path (10, 41). Although the latter modifca-
tions of the patient position and/or morphology can also be deduced from
in-room radiographic or tomographic kilovoltage x-ray imaging, the PET
method has the advantage of not delivering any additional radiation expo-
sure to the patient (when using the planning CT for attenuation correction
and anatomical coregistration). Furthermore, the in-beam implementation
may detect transient modifcations occurring during treatment, which could
be missed by pre- or posttreatment imaging.
When discrepancies between measurement and expectation are detected,
a PET-guided quantifcation of the most likely applied dose corresponding
to the experimental observation can be performed. This requires careful
inspection of the PET images possibly supported by computer-aided tools
for interactive or ideally automatized assessment of the underlying reason of
mismatch (e.g., mispositioning or anatomical change), in combination with
the access to the treatment-planning system for the recalculation of the dose
delivery. This indirect approach of PET-based dose reconstruction was pro-
posed and clinically implemented for carbon ion therapy (10). Eventually,
improvement of the PET imaging performances and better understanding
of the current uncertainties in the knowledge of the tissue stoichiometry,
reaction cross sections, and washout parameters might enable direct dose
reconstruction based on the promising preclinical approaches proposed in
Parodi and Bortfeld (39) and Fourkal, Fan, and Veltchev (40).
506 Proton Therapy Physics
16.3.4 Worldwide Installations and Clinical Experience
The original proposition of using the (at that time newly developed) PET
technology for the monitoring of ion irradiation dates back to the 1970s in
connection with the pioneering heavy ion therapy program at the Lawrence
Berkeley National Laboratory (LBL), Berkeley, CA. Here, a dedicated in-beam
planar positron camera was installed directly at the treatment site in order to
verify the range of low-dose β
+
-radioactive beams (e.g.,
19
Ne) injected into the
patient prior to the therapeutic treatment with the stable isotope (e.g.,
20
Ne)
(17, 19). Unfortunately, the prototype system never reached clinical routine
use, mostly because of activation of the BGO detector itself and the prema-
ture end of the therapy project due to the BEVALAC accelerator shutdown in
1993. Nevertheless, after the encouraging frst results demonstrated at LBL,
the PET method was further pursued for heavy ions at the new carbon ion
therapy facilities established at the Heavy Ion Medical Accelerator at Chiba
(HIMAC), Japan (18), and GSI (28).
In particular, at the experimental carbon ion therapy facility at GSI the frst
in-beam tomographic PET installation has been realized by the Research
Centre of Dresden-Rossendorf, in order to measure the autoactivation of the
primary stable
12
C ion beam during irradiation (28). The dedicated tomograph
was assembled from commercial BGO-detector components and optimized
with respect to geometrical confguration and data acquisition for complete
integration into the treatment environment (47). In the recently concluded 11
years of clinical operation, each individual therapeutic fraction of more than
400 patients mainly treated for head-and-neck and pelvic tumors has been
monitored with the system, demonstrating clinical feasibility as well as valu-
able clinical feedback (48). PET played an essential role at the beginning of
the clinical pilot project back in 1997 to spot inaccuracies of the initially used
CT-range calibration curve, especially in the soft tissue region, triggering
its improvement (49). Over the several years of operation, PET also proved
to be a very useful tool for detecting and quantifying deviations between
planned and delivered treatment due to small positioning inaccuracies or
anatomical modifcations in the time course of fractionated therapy (10, 48).
Moreover, a recent in silico study based on the collected clinical data indi-
cated the capability of achieving a sensitivity of ca. 92% and a specifcity of
ca. 96% for detection of ±6-mm range modifcations for the considered ana-
tomical indications (50). Finally, the installation has been used for the frst
promising phantom experiments addressing the feasibility of time-resolved
4D PET imaging for confrmation of motion-compensated carbon ion beam
tracking delivery to moving targets (51).
For protons, detectability and usability of the irradiation-induced β
+
-target
activation was frst investigated at the Brookhaven National Laboratory
(BNL), Upton, NY, in the late 1970s, using an in-beam pair of position-
sensitive BGO detectors for irradiation of tissue-equivalent plastics and fro-
zen animal samples (31). Later on in the 1990s, feasibility phantom studies
507 In Vivo Dose Verifcation
were carried out using commercial off-line PET scanners by different groups
in the Netherlands and Canada (52, 53). Thorough investigations of the activ-
ity detection during and after proton irradiation of homogeneous and inho-
mogeneous targets have been performed with an in-beam limited-resolution
BGO-based prototype at the Michigan State University, East Lansing, MI (54),
and with the dedicated in-beam PET installation at GSI Darmstadt (21, 27). In
particular, the latter phantom experiments indicated that the proton-induced
activation is about three times larger than that produced by
12
C ion beams of
the same range at the same physical dose delivery, hence further renewing
the interest in PET monitoring for the more widely used proton therapy.
For clinical application with passively scattered proton beams, the frst tri-
als have been performed with commercial full-ring PET scanners a few min-
utes after treatment, thus suffering from major coregistration issues between
the treatment and imaging positions and lacking a calculation modeling for
comparison with the measured images (30, 55). Confrmation of the irradi-
ated area from measured off-line PET scans has been performed on a regu-
lar basis at the combined proton and carbon ion therapy facility of Hyogo,
Japan, since 2002 (56). However, this implementation is limited to a qualita-
tive comparison between the measured PET images and the planned dose
distribution or available PET scans from previous treatment fractions.
The frst attempt to overcome the coregistration issues of off-line imaging
via the usage of a combined PET/CT scanner together with the establish-
ment of a detailed modeling of the expected pattern of activation, includ-
ing biological washout, has been realized at Massachusetts General Hospital
(MGH), Boston, MA. The pilot clinical study reported in Parodi et al. (43)
included nine patients with tumors in the cranial base, spine, orbit, and eye.
Postradiation imaging was done for a duration of 30 min starting up to 20
min after a single treatment fraction was delivered in one or two felds for
a total dose of 1.8–3 GyE up to 10 GyE (ocular melanoma). This study high-
lighted the importance of using the same treatment immobilization device at
the imaging site despite the availability of the additional CT used for coreg-
istration to the planning CT. Moreover, it indicated the possibility to achieve
good spatial correlation and quantitative agreement between the measured
and calculated activity distributions when taking metabolic processes into
account according to Equation 16.2. In particular, for head-and-neck patients
the beam range could be verifed within 1–2 mm in favorable locations of
well-coregistered, low-perfused bony structures. However, low spine and
eye sites indicated the need for better fxation and coregistration methods,
thus calling for further technological and methodological improvements.
Following these promising results, a successive study extended the popu-
lation of patients to a total (including the pilot trial) of 23 subjects receiv-
ing at least one postradiation PET/CT acquisition after proton treatment
(57). For quantitative data analysis different strategies were implemented
and compared to address the agreement between measured and calculated
depth activity distributions in terms of range verifcation. This work helped
508 Proton Therapy Physics
identifying and characterizing the limitations and promises of the PET veri-
fcation method for different tumor entities in different anatomical locations
(cranial base, spine, orbit, eye, sacrum, and prostate), overall supporting the
initial fndings of the pilot investigation. In fact, both the clinical studies
confrmed the potential of the technique for millimeter range verifcation in
favorable locations such as well coregistered and low-perfused bony struc-
tures for lesions in the head and cervical spine. However, they also identifed
challenges especially for extracranial tumor sites, due to major limitations
from biological washout, breathing motion, coregistration issues, and lack of
Hounsfeld unit tissue correlativity for reliable extraction of elemental com-
position to be used in the activation modelling (43, 46). Most of these draw-
backs were however ascribed to the suboptimal implementation relying on
a remote PET/CT installation within ca. 10-min walking distance from the
proton therapy center, resulting in up to 20 min of time elapsed between
irradiation and imaging. Moreover, off-line acquisition could only measure
the global activation produced by the fraction dose, without the possibility to
resolve the activity contribution of the individual treatment felds applied to
the patient. This made the method of range verifcation only feasible for the
considered cases of single- or multiple-angulated treatment felds, while pre-
senting major shortcomings in the case of opposed beams.
After the MGH experience, other proton therapy facilities have started
addressing the capability of off-line PET/CT not only for in vivo verifcation of
the beam range and confrmation of the treated volume (58), but also for assess-
ment of patient-specifc information on prostate motion and patient position
variability during daily proton beam delivery to help establish patient-specifc
planning target volume margins (59). In these clinical studies approximately 30
patients with tumors of the brain, head and neck, liver, lung, sacrum (58), and
prostate (59) have been imaged at commercial off-line PET/CT installations for 5
or 30 min starting 7 or 15 min after the end of irradiation, respectively.
Nowadays, on-going efforts in the clinical environment are mainly
devoted to optimal implementation and evaluation of imaging strategies
relying either on conventional commercial instrumentation installed nearby
the treatment site (off-line) or on new industrial prototypes tailored to in-
room PET imaging.
In particular, a novel dedicated BGO-based dual-head planar camera has
been integrated into the proton beam gantry at the National Cancer Center
of Kashiwa, Japan (41), for routine verifcation of the delivered treatment
with respect to the reference activation at the frst day of irradiation. In
this in-room on-board implementation, the 200-s-long measurement can be
started immediately after the end of irradiation without changing the patient
position. Despite the limitations to central planar imaging, the frst relevant
clinical results from the investigation of 48 patients with tumors of the head
and neck, liver, lungs, prostate, and brain included early detection of beam
range variations due to anatomical modifcations with respect to the plan-
ning CT, similar to the fndings reported in (10, 48) for tomographic in-beam
509 In Vivo Dose Verifcation
PET monitoring of
12
C ion therapy. A very recent study also suggested the
applicability of the on-board PET installation to verify patient positioning
via radioactive markers (called molecular image-guided radiation therapy
[m-IGRT]), alternatively to x-ray radiographic IGRT (60).
At MGH, a prototype of a mobile full-ring neuro-PET scanner based on
cesium iodide (CsI)-scintillators is being characterized and clinically investi-
gated for in-room detection of the β
+
-activation shortly after the end of irra-
diation (61). In this concept, the PET scanner can be rolled into the treatment
room where it is needed, and the robotic table is then used for positioning
the immobilized patient in the feld-of-view of the detector a few minutes
after the therapeutic beam delivery is completed. The considerable reduc-
tion of the time elapsed between irradiation and imaging enables only a few
minutes of acquisition time, promising to overcome the major drawbacks of
the off-line implementation at a remote PET/CT scanner. This is however at
the expense of the missing additional CT imaging for attenuation correction,
for coregistration to the planning CT, and/or for assessment of anatomical
modifcations. Moreover, the applicability of this instrumentation is limited
to cranial or pediatric indications because of the small-bore opening.
Finally, at the newly operational Heidelberg Ion-Beam Therapy Center in
Germany, a commercial, latest generation PET/CT scanner has been recently
installed outside of the treatment rooms and is currently being characterized
in view of forthcoming clinical application after scanned proton and carbon
ion therapy. Before this dedicated installation, a proof-of-principle frst-time
measurement after actively shaped proton treatment has been realized at a
remote PET/CT scanner in the nearby Heidelberg University Hospital start-
ing more than 20 min after the irradiation (62).
Examples of installations and results for different implementations are
shown in Figures 16.9 and 16.10.
16.3.5 On-Going Developments and Outlook
In addition to the on-going clinical studies using conventional or proto-
type instrumentation tailored to off-line and in-room PET imaging, several
research institutions are working on technological advances toward the
development of next-generation, dedicated in-beam PET detectors. In par-
ticular, major efforts are being invested to advance the performances of fast
scintillators such as LSO, LYSO (cerium-doped lutetium yttrium orthosili-
cate), and LaBr
3
or to investigate alternative detection concepts such as resis-
tive plate channels (RPC, 64) for realization of dedicated dual-head TOF-PET
scanners. The fnal goal is to enable direct, event-by-event reconstruction of
the activity measured during patient irradiation, with minimal degradation
of the image quality despite the limited-angle geometry (38). However, the
applicability of PET techniques to detection during proton beam delivery
strongly depends on the accelerator and, in particular, the time structure of
the extracted beam. In fact, the time structure of a synchrotron easily enables
510 Proton Therapy Physics
detection in the pauses of the pulsed irradiation. Differently, a continuous
wave cyclotron poses issues related to the considerable background radia-
tion, making true in-beam detection impossible unless novel data acquisition
strategies are implemented as proposed in Enghardt et al. (35). Thus, careful
workfow considerations are required for those facilities where a prolonga-
tion of the in-beam PET detection after the end of irradiation is needed for
counting statistics, in order to maintain an acceptable compromise between
imaging performances and patient throughput.
Overall, despite the already demonstrated clinical value in selected ana-
tomical locations (e.g., head and neck) as well as the promise of the on-going
Rotating
Rotating
Moving
Moving
Detector
head
Detector head
Proton
Gamma ray
FIGURE 16.9
Example of installations being investigated for clinical in vivo PET verifcation of proton ther-
apy. (Adapted from Nishio et al., Int J Radiat Oncol Biol Phys, 76(1), 277, 2005; and Parodi et al.,
Nucl Instrum Methods A, 591, 282, 2008.) Top left and bottom: off-line PET/CT and movable in-
room PET scanner, respectively, at Massachusetts General Hospital in Boston, MA. (Adapted
from Parodi et al., Int J Radiat Oncol Biol Phys 68, 920, 2007; Knopf et al., Phys Med Biol, 54, 4477,
2009; and España et al., Med Phys, 37, 3180, 2010.) Top right: dual-head in-room on-board cam-
era integrated into the beam gantry at the National Cancer Center of Kashiwa, Japan. (Adapted
from Nishio et al., Int J Radiat Oncol Biol Phys, 76(1), 277, 2005.)
511 In Vivo Dose Verifcation
methodological and technological developments, the PET method intrinsi-
cally suffers from the major drawbacks of low counting statistics and biologi-
cal washout. Indeed, both issues could be mitigated in the near future by the
likely changes of current fractionation schemes toward hypofractionation
treatments with higher dose delivery, as well as by improved imaging detec-
tion during or shortly after ion irradiation. In particular, the planned future
generation of ultra-fast, in-beam TOF scanners promises quantitative and
artifact-free imaging to be achieved almost simultaneously to the data acqui-
sition. Nevertheless, the PET signal is intrinsically “delayed” with respect to
the time of beam interaction with the tissue according to the 2–20-min half-
life time of the most abundant β
+
-emitter products. This makes IGRT and
Planned dose
mGy
Port-1
Dose Activity (2.5 GyE) Activity (32.5 GyE)
Bq/ml Bq/ml Bq/ml
–1500 –200 –150 –100 –50 200 –1000–500 0 0 0 50 100 150
–150 –100 –50 0 50 100 150
Day 1
Day 4
Day 7
Day 13
–100
R
e
l
a
t
i
v
e

a
c
t
i
v
i
t
y

n
o
r
m
a
l
i
z
e
d

a
t

I
.
C
.

[
%
/
1
0
0
]
–50 50 100
Depth [mm]
0
500 1000 1500
Physical MC PET MC PET + washout PET/CT Meas.
FIGURE 16.10
(Seecolorinsert.) Examples of different clinical implementations of in vivo PET-based verifca-
tion of proton therapy. The top row refers to off-line PET/CT imaging long after irradiation at
MGH, Boston (cf. Figure 16.9). In particular, the mismatch of the PET/CT measurement (PET/CT
Meas) with the planned dose is evident. Instead, a good agreement is obtained for the PET MC
modeling when taking biological washout into account (MC PET + washout), in contrast to the
physical activation alone (Physical MC PET). The rainbow colorbars give absolute dose or activ-
ity values, and the gray scale refers to arbitrary rescaled CT values. The bottom row refers to in-
room on-board imaging immediately after irradiation at the National Cancer Center, Kashiwa,
Japan (cf. Figure 16.9). For this patient, the planar activity measurements taken at different days
(cf. quoted accumulated dose on top) revealed inconsistency, with a clear trend to activation at
larger penetration depth (cf. activity profles in right inset). This fnding prompted the detection
of a serious anatomical modifcation of the patient (more than 100-cm
3
tumor shrinkage on a
new CT image), thus calling for plan adaptation. (Adapted from Nishio et al., Int J Radiat Oncol
Biol Phys, 76(1), 277, 2005; and Parodi et al., Int J Radiat Oncol Biol Phys 68, 920, 2007.)
512 Proton Therapy Physics
DGRT diffcult to achieve in real-time, thus stimulating research on other
viable approaches of in vivo imaging.
16.4 PromptGammaImaging
To overcome the intrinsic limitations of PET imaging, different research
groups have recently started investigating complementary or maybe even
alternative imaging techniques still based on the detection of the emerging
secondary radiation induced by nuclear interactions. The proposed most
promising approach exploits the challenging detection of prompt gammas.
16.4.1 The Production of Irradiation-Induced Prompt Gamma
Gamma emission from excited nuclear states is a typical process occurring in
the fnal de-excitation phase of prefragments formed in nuclear interactions
between the therapeutic ion beam and the irradiated tissue (Figure 16.2).
Indeed, this is also the process responsible for the major component of the
undesired radiation background, which complicates in-beam PET detection
during real beam-on time, as experimentally addressed in Parodi et al. (34).
According to the typical energy dependence of the reaction cross sections,
the prompt-gamma yield increases toward the end of the beam path until the
energy of the primary ions and of the secondary hadronic radiation drops
below the reaction threshold, resulting in a distal falloff correlated with the
primary beam range (Figure 16.11). After the nuclear fragmentation reaction
has occurred, the de-excitation prompt gammas are typically emitted in a
very short time (<1 ns) and isotropically in space. The energy spectrum can
be very broad, extending up to several, or even tens, of megaelectronvolts.
The shape exhibits an almost exponentially decreasing continuum superim-
posed onto several emission lines corresponding to the transitions between
the discrete energy levels of the excited nuclei. Because de-excitation emis-
sion can also occur in-fight, the width of the spectral lines can be affected by
Doppler broadening.
16.4.2 The Imaging Process
The energetic prompt gammas are able to escape from the patient after
production, with a reduced attenuation in comparison to the 511-keV anni-
hilation photon pairs. Therefore, detection of this penetrating radiation
preserving spatial information on the place of emission may be exploited
for a real-time verifcation of the treated area and, in particular of the beam
range (66). In addition, spectroscopic identifcation of the characteristic emis-
sion lines can be used as a means to determine tissue composition (65, 67).
513 In Vivo Dose Verifcation
The main principle of the imaging process is similar to standard single-
photon emission imaging. This requires a photon detector and a collima-
tion system for selecting a particular angular direction from the isotropic
gamma emission, differently from the intrinsic collimation of the PET sig-
nal. However, the following considerations rule out the applicability of con-
ventional photon detection systems that are well established in diagnostic
nuclear medicine imaging.
First, the emission energy of the radiation to be detected is not known a
priori, in opposition to the known emission energy of radioactive tracers in
nuclear medicine. Moreover, the high spectral energies in the megaelectron-
volts regions make the collimation process quite challenging. Mechanical
approaches similar to the gamma (or Anger) camera solutions indeed
require much more bulky material for effcient collimation of the penetrating
radiation. Alternative solutions under investigation aim to achieve electronic
collimation via exploitation of the known kinematics of Compton scatter-
ing. However, the applicability of conventional Compton camera setups is
complicated by the fact that the scattered photon is typically not completely
stopped in the subsequent absorber. Therefore, alternative designs are being
explored that exploit multiple scattering processes until the fnal interaction
(ideally complete absorption) of the energy-degraded prompt gamma occurs
in the last component of the multistage detector assembly (68). Directional
information can be recovered from the intersection of the characteristic
Compton cones (in which scattering at a certain angle take place) with the
plane of emission. This is particularly appealing in the case of scanned ion-
beam irradiation, where the prompt-gamma signal can be resolved along the
impinging direction of each individual pencil beam. Finally, the signal of
0.0
0.2
0.4
0.6
0.8
1.0
50 0 100 150 200 250
Ca
O
C
N
Proton energy (MeV)
N
o
r
m
a
l
i
z
e
d

g
a
m
m
a
-
r
a
y

p
r
o
d
u
c
t
i
o
n
0.0
0.2
0.4
0.6
0.8
1.0
50 0 100 150 200 250
Depth (mm)
: IC
: PGS
R
e
l
a
t
i
v
e

d
o
s
e

(
n
o
r
m
a
l
i
z
e
d
)
FIGURE 16.11
Left: relative gamma-ray production as a function of energy for proton interaction on carbon
( ), nitrogen ( ), oxygen ( ), and calcium ( ). (Adapted from Polf et al., Phys Med Biol, 54, 731,
2009.) Right: promising correlation between the depth–dose profles measured with an ioniza-
tion chamber (IC) and the corresponding prompt-gamma scans (PGS) along the proton beam
penetration in water. (From Min et al., Appl Phys Lett, 89, 1063, 2011. With permission.) The pio-
neering detection of right-angled prompt gammas was achieved with a collimated and neutron-
shielded CsI scintillator at the National Cancer Center, Seoul, Korea, as described in the text.
514 Proton Therapy Physics
interest is typically embedded in a large radiation background due to neu-
trons, in addition to scattered photons. This requires either dedicated shield-
ing techniques for neutron absorption or data acquisition strategies such as
pulse-shape-discrimination or time-of-fight (69), capable of separating the
signal induced by the different radiation components.
Therefore, although several proof-of-principle measurements have been
recently accomplished by different investigators with nonoptimal detector
setups in order to address the promise of this technique, a viable imaging
solution is not yet existent and is still the subject of on-going research.
16.4.3 Worldwide Preclinical Investigations
The initial experimental investigations have been limited to the detection of
collimated (mostly right-angled) prompt gammas, scanned along the proton
beam penetration depth in homogeneous targets for 1D assessment of spatial
correlation with the dose delivery and the ion beam range. The frst pioneer-
ing study has been performed with a CsI(Tl) scintillator and a collimator
system consisting of lead, paraffn, and B
4
C powder to suppress the consid-
erable background from scattered photons and neutrons, respectively  (66).
The prompt-gamma scans (PGSs) along the beam penetration in water were
successfully compared to ionization chamber (IC) measurements of depth
dose to illustrate the promising correlation with the Bragg peak location
(Figure 16.11).
In addition to further efforts of the research team at the Korean National
Cancer Center, Seoul, for testing alternative detector concepts such as pinhole
or Compton cameras (70), recent Monte Carlo and experimental investigations
were reported by Polf et al. (65, 67) with the innovative goal to provide spec-
troscopic insight on the tissue composition from the acquired prompt-gamma
energy spectra. For this challenging purpose, promising results could be dem-
onstrated at the Cyclotron Institute at Texas A&M University in Houston, Texas,
with a dedicated experimental setup consisting of a high-purity germanium
(HPGe) detector shielded either with lead or a Compton suppression system.
In addition to the results for proton beams, a similar correlation between
prompt-gamma profles and ion range could be experimentally demon-
strated also for carbon ions (71). Therefore, several groups are currently con-
centrating their research on the optimization of the detector layouts aiming
to develop novel prototype solutions for an effcient, at least 1D detection of
prompt gammas emitted during proton or carbon ion irradiation. Although
currently proposed concepts are limited to estimated detection effciencies
ranging in the order of 10
−6
to 10
−5
for gamma energies in the few megaelec-
tronvolt range, on-going developments hold the promise to eventually make
prompt-gamma detection a viable method for real-time in vivo verifcation
of ion beam delivery.
A very recent Monte Carlo study has also addressed the frst-time com-
parison of in-room PET imaging versus prompt-gamma emission for real
515 In Vivo Dose Verifcation
clinical indications of passively scattered and pencil beam proton beam
delivery (72). Although this theoretical approach was limited to account only
for the prompt-gamma production without calculation of detector response,
the detailed analysis could anticipate a clear advantage of prompt-gamma
imaging, especially for pencil beam scanning. This was mainly attributed
to the typically lower energy thresholds resulting in an improved spatial
correlation between prompt-gamma and dose–depth profles, as well as the
reduction of intrinsic PET uncertainties, such as physiological washout and
delayed detection (Figure 16.12). However, despite the estimated superior (up
to a factor of 80) prompt-gamma yield and the reduced (factor of about  5)
signal attenuation in the patient with respect to the considered in-room PET
implementation (5-min acquisition starting 2 min after a 30-s-long irradia-
tion), the signal-to-noise realistically available in prompt-gamma measure-
ments will ultimately depend on the achievable detection effciency for
clinical applicability.
16.4.4 The Foreseen Clinical Implementation
Similar to the β
+
-activation, the irradiation-induced prompt-gamma produc-
tion only represents a “surrogate” signal correlated but not directly matching
the delivered dose (cf. Figure 16.12). Therefore, unless a straightforward rela-
tionship between prompt-gamma emission yield and dose deposition can be
established, this promising technique will have to rely on the comparison
of the measured signal with an expectation (e.g., deduced from detailed MC
calculations). Because of the manifold reaction channels leading to nuclear
excitation and subsequent gamma emission, direct usage of experimental
cross sections folded with proton fuence does not seem to be a viable solu-
tion. This is a major restriction having to entirely rely on the accuracy of
Dose
100
0
5961.3
0
PG
(
%
)
(
C
o
u
n
t
s
/
c
G
y
)
268.3
0
(
C
o
u
n
t
s
/
c
G
y
)
PET
with washout
FIGURE 16.12
(Seecolorinsert.) Theoretical MC comparison between total prompt gamma emissions (PG,
middle) and measurable PET coincidences (PET with washout, right) when taking biological
washout into account and assuming a 5-min acquisition starting 2 min after a 30-s delivery of
a proton pencil-like beam (Dose, left) impinging from the left (cf. arrow) on an head-and-neck
patient. (Adapted from Moteabbed et al., Phys Med Biol, 56, 1063, 2011.)
516 Proton Therapy Physics
the available nuclear models, differently from the fexible computational
approach using experimental cross sections for calculation of proton-induced
β
+
-activity in PET (cf. Section 16.3.4). Hence, clinical applicability will require
extensive experimental validation of prompt-gamma yields independent of
the proton beam properties and the irradiated tissue type.
The fnal choice of feasible detection solution as well as the strategy for
clinical implementation will also considerably depend on the specifc beam
delivery and time structure at the selected proton therapy facility. Passively
shaped scattered broad beams spread typical therapeutic proton beam
intensities over large (several cm
3
) volumes, hence most likely requiring
time-integrated 3D reconstruction of prompt-gamma emissions for draw-
ing conclusions on the correctness of the entire dose delivery. Differently,
if effcient detection per incident pencil beam might be guaranteed dur-
ing dynamic beam scanning irradiation, even 1D prompt-gamma imag-
ing might be envisioned as a tool for real-time monitoring of the delivered
beam range, with the possibility of prompt interruption of the irradiation if
deviations from the expectation are detected. Alternatively, prompt-gamma
imaging of a subset of pencil beams could be evaluated as a range probe
before the application of the entire treatment (72), similar to the original PET
proposition of using low-dose implanted radioactive beams for pretreatment
range assessment (cf. Section 16.3.4). Spatial information on the impinging
pencil beam direction could be obtained by placing a fast position-sensitive
detector (e.g., an hodoscope) in front of the patient and by complementing
this entrance information with the most-likely path suffered by protons trav-
eling in the human body, similar to computational approaches developed
for image reconstruction in proton radiography or tomography (73). Artistic
views of possible clinical implementations originally depicted for applica-
tion to the less scattering (straight-line approximation) carbon ion beams is
reported in Figure 16.13a and b, for the two promising detector solutions of
gamma and Compton cameras, respectively.
Unfortunately, optimal large-scale instrumentation fulflling the con-
ficting requirements of high detection effciency, good spatial and time
resolution, and effective suppression of the considerable background from
secondary neutrons as well as scattered photons and, possibly, enabling
recovery of 3D spatial information on the treated volume is still at the
research and development phase. Therefore, the promising prompt-gamma
imaging technique cannot be considered yet mature for clinical application,
differently from the PET methodology described in Section 16.3.
16.5 MagneticResonanceImaging
The last methodology having being proposed for in vivo range verifcation
of proton therapy relies on the unconventional interpretation of standard
517 In Vivo Dose Verifcation
x position
y position
a)
b)
Collimators
1
st
scatterer (E,x,y)
2
nd
scatterer (E,x,y)
Absorber (E,x,y,t)
Gamma ray
Gamma ray
Photon
detectors (z)
Start
Start
Stop (delayed)
Stop
(delayed)
Hodoscope (x,y)
Hodoscope (x,y,t)
Patient
Patient
Carbon
beam
Carbon
beam
FIGURE 16.13
Artistic views of possible clinical implementations of real-time prompt gamma imaging
of scanned pencil-like ion beams (in this example, carbon) by using either a multicolli-
mated multidetector prompt-gamma camera (a) or a multistage Compton camera (b). The
upstream hodoscope detector serves to tag the ions in time and space prior to the entrance
in the patient, whereas the TOF technique is used to separate the gamma signal from the
neutron background (cf. text). (Adapted from Testa, PhD thesis, University Claude Bernard,
2010.)
518 Proton Therapy Physics
T1-weighted diagnostic magnetic resonance (MR) images. In fact, routine
follow-up investigations of patients receiving craniospinal proton irradia-
tion at MGH surprisingly revealed a sharp demarcation of a hyperintense
T1-weighted signal in the posterior part of the vertebral bodies (74). This sig-
nal, visible on MR images acquired after completion of proton therapy, was
attributed to radiation-induced fatty replacement of bone marrow, which can
be detected as early as 10 days after radiotherapy and is observed to per-
sist up to 21 months after treatment. Visual comparison with the treatment
plans indicated a clear correlation between the sharply delineated bone mar-
row changes and the distal dose falloff for the considered posterior-anterior
felds, directly placing the characteristic proton Bragg peaks only in the pos-
terior part of the vertebral body (thecal sac).
Whereas the enthusiasm for this intriguing fnding was initially addressed
to the “visual” demonstration of the improved sparing of normal tissues in
proton radiotherapy, the authors soon recognized the potential of the method
to address in vivo verifcation of the beam range. Although such posttreat-
ment information cannot enable patient-specifc IGRT or DGRT for correction
of the already entirely delivered therapeutic dose, it can still provide essential
clinical information for improvement of population-based treatment margins
in specifc indications. Therefore, in a second study (75) the same research
team attempted a challenging quantifcation of the relationship between
radiation dose and MRI signal intensity (SI). This was done on a population-
based approach by analyzing the correlation of the MR signal with the more
controllable lateral penumbra of the proton dose in the irradiated sacrum.
Using the so-established general dose-SI relationship, the distal falloff of the
“actually delivered” dose was deduced from the MRI images and compared
to the planning one in order to estimate proton range delivery errors in the
lumbar spine (Figure 16.14). The initial fndings indicated a tendency to over-
shoot about 1.9 mm (95% confdence interval, 0.8–3.1 mm), which is, however,
well within the already used clinical margins (75). Moreover, the magnitude
of the observed overshoot was judged to be in the same order of magnitude
of the inherent uncertainties of the method. The latter are mainly attributed
due to the patient-specifc validity of a general dose-SI relationship deduced
in a different anatomical region than the lumbar spine, to the usage of heu-
ristic rules for determination of the data to be reliably used in the analysis,
and to the coregistration between MRI and planning CT data (though the
quality of coregistration was claimed to be very good in the presented study).
Nevertheless, this work indeed represented the frst worldwide demonstration
of in vivo proton range verifcation using posttreatment spine MRI changes.
Therefore, further investigations are on-going to improve the methodology
and to extend the technique to MRI sequences, which may enable earlier
detection of bone marrow changes in the lumbar spine or of other physiologi-
cal processes in different anatomical sites (e.g., the liver). The ultimate goal is
to allow for treatment adaptation already during the course of fractionated
therapy by using relatively inexpensive and nonionizing MRI (75).
519 In Vivo Dose Verifcation
16.6 ConclusionandOutlook
This chapter has reviewed the main methods currently under experimen-
tal or clinical investigation for in vivo range and dose verifcation in pro-
ton therapy. Although none of the reported techniques can yet achieve the
level of accuracy currently obtained for EPID-based dose reconstruction in
photon therapy (7), all the methods hold great promise to complement each
other and enable proton treatment verifcation at different time scales (cf.
Figure 16.1) and in different anatomical locations. Indeed, despite the dis-
cussed shortcomings of delayed emission and biological washout, PET imag-
ing still represents the most mature technique readily available for clinical
implementation with relatively moderate efforts. Initial promising clinical
results could be already demonstrated at least for favorable anatomical loca-
tions such as the head-and-neck (41, 43, 57). Therefore, it can be expected
that the on-going developments toward new generation detectors of in-
beam TOF-PET and prompt-gamma imaging will eventually enable real-
time monitoring of the beam range and DGRT for state-of-the-art proton
pencil beam scanning in the near future. For certain indications, fraction-
specifc information from emission imaging could be complemented by MR
imaging at regular time intervals during the treatment course in order to
optimize treatment margins for reduction of toxicity and safe dose escala-
tion studies. Finally, extension to time-resolved 4D monitoring of motion-
compensated beam delivery could play an important role in promoting safe
treatment of moving targets. Therefore, it can be foreseen that the synergetic
a) b)
Beam direction
10
20
30
40
50 GyRBE
0
0
–0.1
–0.05
0
0.05
0.1
0.15
0.2
0.25
5 10 15 20 25
Radiation dose (GyRBE)
N
o
r
m
a
l
i
z
e
d

s
i
g
n
a
l

i
n
t
e
n
s
i
t
y
30 35 40 45 50
123 cm
36 GyRBE
c)
FIGURE 16.14
(Seecolorinsert.) Illustration of the clinical workfow and results of MRI-based in vivo range
verifcation. The less-controllable lateral penumbra of the beam in the sacrum (a) is used to
determine a dose-signal intensity curve (b). From the analysis of more patient data a general
dose-SI curve is obtained and used to calculate the 50% distal isodose deduced from the MRI
scan (red lines, c) for comparison with the planned one (blue lines), showing in this example a
generalized beam overpenetration in the lumbar spine. (Adapted from Gensheimer et al., Int J
Radiat Oncol Biol Phys, 78(1), 268, 2010.)
520 Proton Therapy Physics
unconventional usage of different imaging modalities within and outside
the treatment room will play a fundamental role in promoting full-clinical
exploitation of the dosimetric advantages of proton beam therapy.
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525
17
Basic Aspects of Shielding
NisyElizabethIpe
CONTENTS
17.1 Introduction ................................................................................................ 526
17.2 Secondary Radiation ................................................................................. 526
17.2.1 Physics of Secondary Radiation Production .............................. 527
17.2.1.1 Intranuclear Cascade ...................................................... 527
17.2.1.2 Production of Muons and Electromagnetic Cascade .... 529
17.2.1.3 Evaporation Nucleons and Activation ......................... 529
17.3 Neutron Energy Classifcation and Interactions ................................... 530
17.4 Neutron Yield, Average Energy, and Angular Distribution ................ 532
17.5 Unshielded Neutron Spectra .................................................................... 535
17.6 Characteristics of Shielded Neutron Field ............................................. 536
17.7 Neutron Monitoring .................................................................................. 537
17.8 Calculational Methods .............................................................................. 537
17.8.1 Conversion Coeffcients ................................................................ 537
17.8.2 Analytical Methods ....................................................................... 538
17.8.2.1 Point Source ..................................................................... 538
17.8.2.2 Removal Cross Section ................................................... 539
17.8.2.3 Attenuation Length ......................................................... 540
17.8.2.4 Moyer Model .................................................................... 541
17.8.3 Monte Carlo Calculations ............................................................. 541
17.8.4 Computational Models .................................................................. 542
17.9 Shielding Design Considerations ............................................................544
17.9.1 Beam Losses .................................................................................... 544
17.9.1.1 Synchrotron- and Cyclotron-Based Systems ............... 544
17.9.1.2 Treatment Rooms ............................................................ 545
17.9.1.3 Fixed Beam and Gantry Rooms .................................... 546
17.9.1.4 Beam-Shaping Techniques............................................. 546
17.9.2 Workload ......................................................................................... 546
17.9.3 Regulatory Dose Limits ................................................................ 547
17.9.3.1 Occupancy Factor ............................................................ 548
17.9.4 Shielding Materials ........................................................................ 548
17.9.4.1 Earth .................................................................................. 548
17.9.4.2 Concrete and Heavy Concretes ..................................... 548
17.9.4.3 Steel and Iron ................................................................... 549
526 Proton Therapy Physics
17.1 Introduction
Shielding considerations for particle accelerators came into play in the 1930s,
when construction and operation of particle accelerators at Cambridge by
Cockroft and Walton and at Berkeley by Lawrence and Livingstone (1, 2) frst
occurred. These accelerators were of low energy and intensity, and many of the
early cyclotrons were constructed underground to avoid unexpected radio-
logical problems. However, with the advent of larger accelerators producing
particles with much higher energies (e.g., the Cosmotron at Brookhaven and
the Bevatron at Berkeley), knowledge of the prompt radiation felds and the
requirements for effective shielding design became important.
The prompt radiation feld produced by protons in the therapeutic energy
range of interest, 67–330 MeV, is comprised of a mixture of charged and neu-
tral particles as well as photons, with neutrons being the dominant compo-
nent. The neutrons have energies as high as the incident proton energy. In
contrast, the average energy of neutrons from photon therapy linear accel-
erators (linacs) is only a few megaelectronvolts (MeV). Therefore, physicists
who perform shielding calculations for photon therapy linacs seldom have
the expertise to shield proton therapy facilities. The requirements for the
physicist performing shielding design for proton therapy facilities include a
strong foundation in the basic aspects of shielding as well adequate experi-
ence in the shielding of neutrons of all energy ranges, especially high-energy
neutrons, that is neutrons with energies > 100 MeV. An extensive coverage of
shielding design and radiation safety for charged particle therapy facilities
can be found in the Particle Therapy Cooperative Group (PTCOG) Report
1 (3). Basic aspects of shielding such as the production of secondary radia-
tion, characteristics of the prompt radiation feld, neutron interactions, and
shielding design considerations will be covered in this chapter.
17.2 SecondaryRadiation
Secondary radiation consists of prompt and residual radiation. Prompt radi-
ation is produced while the machine is on. Residual radiation is produced by
activated materials, that is, materials that have become radioactive during
beam operation. Thus, residual radiation remains even after the machine is
17.9.4.4 Polyethylene ..................................................................... 550
17.9.4.5 Lead ................................................................................... 550
17.9.5 Transmission................................................................................... 550
References ............................................................................................................. 551
527 Basic Aspects of Shielding
turned off, for a time period that is determined by the half-life of the activated
material. Secondary radiation is produced by the interaction of protons with
beam line components. It is produced at locations where beam losses occur:
in the synchrotron and cyclotron during injection, during energy degrada-
tion in the cyclotron, during beam transport to the treatment room, and in
beam-shaping devices in the treatment nozzle. Thus, the accelerators, beam
transport line, and treatment room require shielding. It is also produced in
the patient, dosimetric phantom, and beam stop. It is produced at locations
where beam losses occur. The large shielding thicknesses for the rooms are
determined by the prompt radiation, whereas the residual radiation requires
considerably less localized shielding.
17.2.1 Physics of Secondary Radiation Production
Proton interactions are described in Chapter 1. Nuclear evaporation and the
intranuclear cascade are the two nuclear processes that are important in the
determination of particle yields from proton-nuclear interactions (1–3).
The interaction of low-energy protons (E
P
< 10 MeV, where E
P
is the energy of
the incident proton) with a nucleus can be described by the compound nucleus
model. The incident particle is absorbed by the target nucleus, resulting in the
formation of a compound nucleus. The compound nucleus is in an excited
state with a number of allowed decay channels. The preferred decay chan-
nel is the entrance channel. As the energy of the incident particle increases,
the number of levels available to the incident channel increases consider-
ably. Instead of discrete levels in the quasi-stationary states of the compound
nucleus, there is a complete overlapping of levels inside the nucleus. Under
these conditions, the emission of particles can be described by an evaporation
process similar to the evaporation of a molecule from the surface of a liquid.
The interaction of protons in the energy range of 50 to 1000 MeV with matter
results in the production of an intranuclear cascade (spray of particles), in which
neutrons have energies as high as the incident proton. Thus, the intranuclear
cascade is an important consideration for therapeutic protons. There are fve
distinct and independent stages to be considered, as shown in Figure 17.1 (1):
Intranuclear cascade
Production of muons
Electromagnetic cascade
Evaporation of nucleons
Activation
17.2.1.1 Intranuclear Cascade
An intranuclear cascade is produced when an incoming hadron (proton,
neutron, etc.) with energy less than a few hundred MeV, interacts with
528 Proton Therapy Physics
individual nucleons in a nucleus, producing a spray of particles, such as pro-
tons, neutrons, and π mesons (pions). Pions can be charged (π
±
) or neutral.
Charged pions have a rest mass of 139.6 MeV/c
2
(where c is the velocity of
light) and neutral pions have a mass of about 135 MeV/c
2
. Therefore, neu-
tral and charged pions are produced at energies above 135 and 139.6 MeV,
respectively. The scattered and recoiling nucleons from the interaction pro-
ceed through the nucleus. Each of these nucleons may in turn interact with
other nucleons in the nucleus, leading to the development of a cascade. Some
of the cascade particles that have suffciently high energy escape from the
nucleus, whereas others do not. The residual nucleus evaporates particles
such as alpha particles and other nucleons. In the third stage, after particle
emission is no longer energetically possible, the remaining excitation energy
is emitted in the form of gamma rays.
A large fraction of the energy in the cascade is transferred to a single
nucleon. This nucleon, with energy greater than 150 MeV, propagates the
cascade. The cascade neutrons that arise from individual nuclear interac-
tions are forward-peaked and have longer attenuation lengths than evapora-
tion neutrons. However, it is important to note that although the high-energy
neutrons transport the cascade, the lower-energy neutrons deposit a major
fraction of the absorbed dose, even outside thick shields.
Nucleons with energies between 20- and 150-MeV transfer energy to sev-
eral nucleons. Therefore, on an average each nucleon receives energy of
Incoming hadron
p
n
π
0
Activation


n
n




Evaporation of nucleons and fragments
Intranuclear cascade
e
+
e
–
Electromagnetic cascade
Muon production
n


π
0
π

π

p
FIGURE 17.1
Schematic representation of various stages of intranuclear cascade. (From National Council
on Radiation Protection and Measurements, Radiation Protection for Particle Accelerator
Facilities, Report 144, 2003. With permission.)
529 Basic Aspects of Shielding
about 10 MeV. Charged particles at these energies are quickly stopped by
ionization. Thus, neutrons predominate at low energies.
17.2.1.2 Production of Muons and Electromagnetic Cascade
Charged pions decay into muons and neutrinos. Muons have a mass of
105.7 MeV/ c
2
and are very penetrating particles. They deposit energy by ioniza-
tion. Photonuclear reactions are also possible. Protons and pions with energy
less than 450 MeV have a high rate of energy loss. Thus, neutrons are the princi-
pal propagators of the cascade with increasing depth in the shielding.
Neutral pions decay into two energetic gamma rays that initiate electro-
magnetic cascades. The photons that are produced interact through pair
production or Compton collisions, resulting in the production of electrons.
These electrons radiate high-energy photons (bremsstrahlung), which in
turn interact to produce more electrons. At each step in the cascade, the
number of particles increases, and the average energy decreases. This pro-
cess continues until the electrons fall into the energy range where collision
losses dominate over radiative losses and the energy of the primary electron
is completely dissipated in excitation and ionization of the atoms, resulting
in heat production. This entire process resulting in a cascade of photons,
electrons, and positrons is called an electromagnetic cascade. A very small
fraction of the bremsstrahlung energy in the cascade goes into the produc-
tion of hadrons such as neutrons, protons, and pions. The energy that is
transferred is mostly deposited by ionization within a few radiation lengths.
The attenuation length is the distance traveled through which the intensity
of the radiation is reduced to 37% of its original value. However, the attenu-
ation length of these cascades is much shorter than the absorption length,
which is the reciprocal of the inelastic cross section and therefore does not
include elastic scattering of neutrons. Thus, the electromagnetic cascade
does not contribute signifcantly to the energy transport. It is important to
note that the intranuclear cascade dominates for protons in the therapeutic
energy range of interest.
17.2.1.3 Evaporation Nucleons and Activation
The energy of those particles that do not escape is assumed to be distributed
among the remaining nucleons in the nucleus, leaving it in an excited state.
It then de-excites by emitting particles, mainly neutrons and protons that
are referred to as evaporation nucleons, alpha particles, and some fragments.
The evaporation nucleons are so called because they can be considered as
boiling off a nucleus that is heated by the absorption of energy from the inci-
dent particle. The energy distribution of emitted neutrons can be described
by the following equation:
n(E)dE = aEe
–E/τ
, (17.1)
530 Proton Therapy Physics
where a is a constant, E is the energy of the neutron, and τ is the nuclear tem-
perature that has the dimensions of energy with a value that lies between 0.5
and 5 MeV. The evaporated particles are emitted isotropically in the laboratory
system, and the energy of the evaporation neutrons extends to 8 MeV (1, 2).
Similar equations may be used to describe the emission of charged par-
ticles, but the emission of low-energy charged particles is suppressed by
the Coulomb barrier. If low-energy particles are emitted, they are stopped
near their point of emission. These particles do not contribute to the cas-
cade, but they contribute to local energy deposition. Therefore, charged par-
ticles produced by evaporation do not impact the determination of shielding
thickness. The evaporation neutrons travel long distances, continuously
depositing energy. Evaporation neutrons produced by interactions near
the source contribute to dose inside the shield and to leakage dose through
doors and openings. However, because they are strongly attenuated in the
shield, they do not contribute to dose outside the shield. The dose outside
the shield is dominated by evaporation neutrons produced near the outer
surface of the shield.
The remaining excitation energy may be emitted in the form of gammas.
The de-excited nucleus may be radioactive, thus leading to residual radiation.
17.3 NeutronEnergyClassificationandInteractions
The secondary radiation feld produced by protons is quite complex; how-
ever, neutrons dominate the radiation feld. Therefore, it is important to
understand how neutrons interact. Neutrons are classifed according to their
energy as follows:
Thermal: E
-
n
= 0.025 eV at 20º C. Typically E
n
≤ 0.5 eV
Intermediate: 0.5 eV < E
n
≤ 10 keV
Fast: 10 keV < E
n
≤ 20 MeV
Relativistic: E
n
> 20 MeV
High-energy neutrons: E
n
> 100 MeV
where E
n
is the energy of the neutron and E
-
n
is the average energy of the
neutron.
Because neutrons are uncharged, they can travel appreciable distances in
matter without undergoing interactions. A neutron can undergo an elastic or
an inelastic reaction on collision with an atom (4). An elastic reaction is one
in which the total kinetic energy of the incoming particle is conserved. In an
inelastic reaction, the nucleus absorbs some energy and is left in an excited
state. Inelastic scattering can occur only at energies above the lowest excited
state (or inelastic scattering threshold) of the material. The lowest excited states
531 Basic Aspects of Shielding
in lead and iron are 0.57 and 0.847 MeV, respectively. The neutron can also be
captured or absorbed by a nucleus in reactions such as (n, 2n), (n, p), (n, α), or
(n,  γ). The sum of the inelastic and (n, 2n) cross sections in the energy range
< 20 MeV is called the nonelastic cross section (5). The inelastic scattering domi-
nates at lower energies, whereas the (n, 2n) reactions dominate at higher ener-
gies. The energy loss in any inelastic collision cannot be determined exactly,
but there is a minimum energy loss that equals the energy of the lowest excited
state. Usually there is a large energy loss in a single collision, which results in
the excitation of energy states above the ground state, followed by the emission
of gamma rays. In the (n, 2n) reaction, the minimum energy loss is equal to the
binding energy of the neutron. This reaction produces a large number of lower-
energy neutrons because the energies of the two neutrons that are produced
are similar. A large amount of elastic scattering takes place in high-Z materi-
als, but results in negligible energy loss. However, elastic scattering increases
the path length of the neutrons in the shielding material, thus providing more
opportunities for inelastic and (n, 2n) reactions to occur. The mean free path
is the average distance traveled by the particle in the material between two
interactions.
Thermal neutrons (n
th
) are in approximate thermal equilibrium with their
surroundings. They gain and lose only small amounts of energy through
elastic scattering, but they diffuse about until captured by atomic nuclei.
Thermal neutrons undergo radiative capture, that is, neutron absorption
leads to the emission of a gamma ray, such as in the
1
H(n
th
, γ)
2
H reaction. The
capture cross section for this reaction is 0.33 × 10
−24
cm
2
, and the gamma ray
energy is 2.22 MeV. This reaction occurs in hydrogenous shielding materi-
als such as polyethylene and concrete. Borated polyethylene is used instead
of polyethylene, because the cross section for capture in boron is much
higher (3480 × 10
−24
cm
2
) and the subsequent capture gamma ray from the
10
B
(n
th
, α)
7
Li has a much lower energy of 0.48 MeV. The capture cross sections
for low-energy neutrons (<1 keV) decrease as the reciprocal of the velocity or
as the neutron energy increases. Intermediate energy neutrons lose energy
by scattering and are absorbed.
Fast neutrons include evaporation neutrons. They interact with matter
mainly through a series of elastic and inelastic scattering and are fnally
absorbed after giving up their energy (6). Approximately 7 MeV is given
up to gamma rays, on an average, during the slowing down and capture
process. Inelastic scattering is the dominant process in all materials at neu-
tron energies above 10 MeV. Elastic scattering dominates at lower energies.
Below 1 MeV, elastic scattering is the principle process by which neutrons
interact in hydrogenous materials. When high-Z material is used for shield-
ing, it must always be followed by hydrogenous material. A useful rule of
thumb is that the hydrogenous material should have a thickness of at least
one high-energy inelastic interaction mean free path (6). The reason for the
latter requirement is because the energy of the neutrons may be reduced by
inelastic scattering to a lower energy where they may be transparent to the
532 Proton Therapy Physics
nonhydrogenous material. For example, lead is virtually transparent to neu-
trons with energy below 0.57 MeV (5).
Relativistic or “cascade” neutrons arise from cascade processes in pro-
ton accelerators. They are important in propagating the radiation feld. The
high-energy component of the cascade with neutron energies above 100 MeV
propagates the neutrons through the shielding and continuously regenerates
lower-energy neutrons and charged particles at all depths in the shield via
inelastic reactions with the shielding material (7).
The reactions occur in three stages for neutrons with energies between 50
and 100 MeV (8). In the frst stage, an intranuclear cascade develops, where
the incident high-energy neutron interacts with an individual nucleon in the
nucleus. In the second stage the residual nucleus is left in an excited state and
evaporates particles such as alpha particles and other nucleons. In the third
stage, after particle emission is no longer energetically possible, the remain-
ing excitation energy is emitted in the form of gamma rays. The de-excited
nucleus may be radioactive. For neutrons with energy below 50 MeV, only
the second and third stages are assumed to be operative.
17.4 NeutronYield,AverageEnergy,andAngularDistribution
The prompt radiation feld produced by protons of energies up to 330 MeV
encountered in proton therapy is quite complex, consisting of a mixture of
charged and neutral particles as well as photons. However, neutrons are
the dominant component. As the proton energy increases, the threshold for
nuclear reactions is exceeded, and more nuclear interactions can occur. At
energies above 50 MeV, the intranuclear cascade process becomes important.
The neutron yield of a target is defned as the number of neutrons emit-
ted per incident primary particle. Between proton energies of 50 and 500
MeV the neutron yields increase as approximately E
P
2
, for all target materi-
als, where E
P
is the energy of the incident proton (2). The neutron yield from
a target depends on the target material and dimensions.
Thick targets are targets in which the protons are completely stopped, that
is, the thickness is greater than or equal to the particle range. By contrast,
thin targets are targets with thicknesses that are signifcantly less than the
particle range. Thus, for example, the protons lose an insignifcant amount of
energy in the target, and the kinetic energy available for neutron production
in the target is the full incident proton energy (2).
Calculations and measurements of neutron yields, energy spectra, and
angular distributions for protons of various energies incident on different
types of materials have been reported in the literature (2, 9–15). Comparisons
between calculations and measurements have also been made (12–14).
Table 17.1 shows the neutron yield (integrated over all angles) for protons
with energies ranging from 100 to 250 MeV, incident on thick iron targets.
533 Basic Aspects of Shielding
The data is based on calculations with the Monte Carlo code, FLUKA (11, 16).
The total yield (n
tot
), and yields for neutron energy (E
n
) less than and greater
than 19.6 MeV are shown. FLUKA uses cross section tables below 19.6 MeV
and models above 19.6 MeV. As expected, the neutron yield increases with
increasing proton energy.
The average neutron energies (E
-
n
) for various emission angles are
shown in Table 17.2 for the targets described in Table 17.1 (11). As the pro-
ton energy increases, the average neutron energy in the forward direc-
tion (0°  to 10°) increases, thus resulting in the hardening of the spectra.
However, at very large angles (130° to 140°) the average energy does not
change signifcantly with increasing proton energies; therefore the spectra
does not change much.
Table 17.3 shows the neutron yield as a function of target dimensions for
250-MeV protons (11). Table 17.4 shows the average neutron energies at 250
MeV as a function of iron target dimensions. The total neutron yield and the
yield for E
n
<19.6 MeV increases with both target radius and target thickness,
but the yield for E
n
 >19.6 MeV decreases. The data indicate that the average
TABLE 17.1
Neutron Yields for 100- to 250-MeV Protons Incident on a Thick Iron Target
Proton
EnergyE
P
(MeV)
Range
(mm)
IronTarget
Radius
(mm)
IronTarget
Thickness
(mm)
NeutronYield(neutrons
perproton)
E
n
<19.6
MeV
E
n
>19.6
MeV n
tot
100 14.45 10 20 0.118 0.017 0.135
150 29.17 15 30 0.233 0.051 0.284
200 47.65 25 50 0.381 0.096 0.477
250 69.30 58 75 0.586 0.140 0.726
Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.
TABLE 17.2
Average Neutron Energies for Various Emission Angles as a Function of
Proton Energy
a
EmissionAngles
0°to10° 40°to50° 80°to90° 130°to140°
Proton energy (MeV)
100 22.58 12.06 4.96 3.56
150 40.41 17.26 6.29 3.93
200 57.73 22.03 7.38 3.98
250 67.72 22.90 8.09 3.62
a
Average neutron energy, E
-
n
, is expressed as megaelectron volts (MeV).
Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.
534 Proton Therapy Physics
neutron energy increases with increasing target thickness at the 0° to 10°
and 40° to 50° emission angles, but decreases for emission angles larger than
80° to 90°. As the target thickness increases, the proton interactions increase,
resulting in an increase in the secondary neutron yield. At frst, the yield
is dominated by the high-energy neutrons, but as the thickness is further
increased, the high-energy neutrons interact, producing more low-energy
neutrons. Therefore, the high-energy neutron yield decreases and the low-
energy neutron yield increases, whereas the overall neutron yield increases.
The low-energy neutrons get attenuated in the target as the thickness is
further increased. The net result is an increase in total neutron yield with
increasing target thickness until it reaches a maximum and then a decrease
due to the attenuation of low-energy neutrons in the target material.
According to data provided by Tesch (15), the ratios of neutron yields from
different target materials for thick targets are independent of E
P
in the energy
range of 20 MeV to 1 GeV, (which covers the therapeutic energy range of
interest). The data are given relative to medium mass number (A) by C:Al:Cu-
Fe:Sn:Ta-Pb = (0.3 ± 0.1):(0.6 ± 0.2):(1.0):(1.5 ± 0.4):(1.7 ± 0.2). This indicates that
as the mass number increases the neutron yield increases.
TABLE 17.3
Neutron Yield for 250-MeV Protons as a Function of Iron Target
Dimensions
IronTarget
Radius(mm)
IronTarget
Thickness(mm)
NeutronYield(neutronsperproton)
E
n
<19.6MeV E
n
>19.6MeV n
tot
37.5 75.0 0.567 0.148 0.715
58.0 75.0 0.586 0.140 0.726
75.0 75.0 0.596 0.136 0.732
75.0 150.0 0.671 0.111 0.782
Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.
TABLE 17.4
Average Neutron Energies at 250 MeV for Various Emission Angles as a Function of
Iron Target Dimensions
EmissionAngles
IronTarget
Radius(mm)
IronTarget
Thickness(mm) 0°to10°
40°to
50°
80°to
90° 130°to140°
37.5 75.0 73.6 25.9 8.1 3.9
58.0 75.0 67.7 22.9 8.1 3.6
75.0 75.0 64.7 21.3 8.1 3.5
75.0 150.0 70.3 23.5 6.9 3.2
Average neutron energy, E
-
n
, is expressed as megaelectron volts (MeV).
Source: Particle Therapy Cooperative Group, Report 1, 2010. With permission.
535 Basic Aspects of Shielding
17.5 UnshieldedNeutronSpectra
Figure 17.2 shows the unshielded neutron spectra for neutrons at various
emission angles, produced by 250-MeV protons incident on a thick iron tar-
get (without any concrete shielding) described in Table 17.1 (11). The double
differential neutron spectra shown as lethargy plots were calculated with
FLUKA. Neutron lethargy, or logarithmic energy decrement, u, is a dimen-
sionless logarithm of the ratio of the energy of source neutrons (E
0
) to the
energy of neutrons (E) after a collision:

u In
E
E
=
0
(17.2)

E E u = −
0
exp( ).
(17.3)
A plot of E versus u will show an exponential decay of energy per unit
collision,  indicating that the greatest changes of energy (∆E) result from
the early collisions. The energy distributions in these fgures are typi-
cally characterized by two peaks: a high-energy peak (produced by the
scattered primary beam particle) and an evaporation peak at ~2 MeV. The
high-energy peaks shift to higher energies with increasing proton ener-
gies, which are particularly evident in the forward direction (0° to 10°). The
high-energy peak for the unshielded target is not the usual 100-MeV peak
that is observed outside thick concrete shielding, which will be discussed
in the next section.
0.1 1 10 100
Neutron energy [MeV]
Φ
(
E
)
·
E

[
c
m
–
2

s
r
–
1

p
e
r

p
r
o
t
o
n
]
1.0 × 10
–10
0.0
2.0 × 10
–10
3.0 × 10
–10
4.0 × 10
–10
5.0 × 10
–10
6.0 × 10
–10
7.0 × 10
–10
8.0 × 10
–10
9.0 × 10
–10
0° - 10°
40° - 50°
80° - 90°
130° - 140°
FIGURE 17.2
Unshielded neutron spectra for neutrons at various emission angles, produced by 250-MeV
protons incident on a thick iron target (without any concrete shielding). (From Agosteo,
Magistris, Mereghetti, Silari, Zajacova. Nucl Instrum Methods Phys Res B 2007; 265:581–89.
With permission.)
536 Proton Therapy Physics
17.6 CharacteristicsofShieldedNeutronField
The high-energy component of the cascade with neutron energies (E
n
) above
100 MeV propagates the neutrons through the shielding and continuously
regenerates lower-energy neutrons and charged particles at all depths in
the shield via inelastic reactions with the shielding material (7). However,
the greater yield of low-energy neutrons is more than compensated for by
greater attenuation in the shield due to a higher cross section at low energy.
Shielding studies indicate that the radiation feld reaches an equilibrium con-
dition beyond a few mean-free paths within the shield. Neutrons with ener-
gies greater than 150 MeV regenerate the cascade even though they are present
in relatively small numbers. They are accompanied by numerous low-energy
neutrons produced in the interactions. The typical neutron spectrum observed
outside a thick concrete shield consists of peaks at a few MeV and at ~100 MeV.
Figure 17.3 shows normalized neutron spectra in the transverse direction
at the surface of the concrete and at various depths in the concrete, for 250-
MeV protons incident on a thick iron target (11). The low-energy neutron
component is attenuated up to about a depth of 100 cm with a short attenua-
tion length, thus, giving rise to a less intense but more penetrating spectrum
with a longer attenuation length. A fast attenuation region is observed at
small thicknesses. Beyond 100 cm, the spectrum reaches equilibrium.
Thus, the neutron energy distribution consists of two components: high-
energy neutrons produced by the cascade and evaporation neutrons with
energy peaked at ~2 MeV. As previously mentioned, the high-energy neutrons
0.1 1
0 cm
20 cm
40 cm
60 cm
100 cm
600 cm
10 100
Neutron energy [MeV]
N
o
r
m
a
l
i
z
e
d

Φ
(
E
)
·
E

[
a
.
u
.
]
0.1
0.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
FIGURE 17.3
Normalized neutron spectra in transverse direction at surface of a concrete shield, and at
various depths, produced by 250-MeV protons incident on a thick iron target. (From Agosteo,
Magistris, Mereghetti, Silari, Zajacova. Nucl Instrum Methods Phys Res B 2007; 265:581–89.
With permisson.)
537 Basic Aspects of Shielding
are anisotropic and forward peaked, but the evaporation neutrons are isotro-
pic. The highest-energy neutrons detected outside the shielding are those that
arrive without interaction or that have undergone only elastic scattering or
direct inelastic scattering with little loss of energy, and a small change in direc-
tion. Low-energy neutrons and charged particles detected outside the shield-
ing are those that have been generated at the outer surface of the shield. Thus,
the yield of high-energy neutrons (E
n
> 100 MeV) in the primary collision of the
protons with the target material determines the magnitude of the prompt radi-
ation feld outside the shield in the therapeutic proton energy range of interest.
The charged particles produced by the protons will be absorbed in shielding
that is suffciently thick to protect against neutrons. Thus, neutrons dominate
the radiation feld outside the shielding. Degraded neutrons might undergo
capture reactions in the shielding, giving rise to neutron-capture gamma rays.
17.7 NeutronMonitoring
Because the neutron energy spectra extend to the energy of the incident pro-
ton, it is important to use wide-energy range instruments for neutron moni-
toring. Rem-meters are typically used for neutron monitoring. A rem-meter
is comprised of a thermal neutron detector such as a BF
3
(boron trifuoride) or
3
He (helium) proportional counter or a
6
Li (lithium) glass scintillation coun-
ter that is surrounded by a polyethylene neutron moderator. The modera-
tor slows down fast and intermediate energy neutrons to thermal neutrons,
which are then detected by the thermal neutron detector. Most conventional
rem-meters are insensitive to neutrons of energies above 15 MeV, and many
of them have rapidly decreasing responses above about 7  MeV. Therefore,
they can underestimate the neutron dose equivalent by as much as a factor
of 3 when used outside the shielding of a particle therapy facility (1). Wide-
energy rem-meters consist of high-atomic number inserts such as lead or
tungsten in the polyethylene moderator (17, 18), which cause neutron multi-
plication and energy degrading reactions such as (n, 2n). Thus, the sensitivity
to high-energy neutrons is improved. An example of such a rem-meter is the
FHT 762 Wendi-2 (Thermo Fisher Scientifc, Waltham, MA), which has an
excellent energy response from thermal to 5 GeV.
17.8 CalculationalMethods
17.8.1 Conversion Coefficients
The concept of effective dose (E) is discussed in Chapter 18. The ambient
dose equivalent, H*(d), at a point in a radiation feld, is the dose equivalent
538 Proton Therapy Physics
that would be produced by the corresponding expanded and aligned feld,
in the International Commission on Radiation Units and Measurements
(ICRU) sphere (diameter = 30 cm, 76.2% O, 10.1% H, 11.1% C, and 2.6% N) at
a depth, d, on the radius opposing the direction of the aligned feld (19). The
ambient dose equivalent is measured in Sv. For strongly penetrating radia-
tion, a depth of 10 mm is recommended, and for weakly penetrating radia-
tion, a depth of 0.07 mm is recommended. In the expanded and aligned feld,
the fuence and its energy distribution have the same values throughout the
volume of interest as in the actual feld at the point of reference, but the fu-
ence is unidirectional.
Conversion coeffcients are used to relate the protection and operational
quantities to physical quantities characterizing the radiation feld (19).
Frequently radiation felds are characterized in terms of absorbed dose or
fuence. The fuence, Φ, is the quotient of dN by da, where dN is the number
of particles incident on a sphere of cross-sectional area da. The unit is m
−2
or
cm
−2
. Thus, for example, the effective dose, E, can be obtained by multiply-
ing the fuence with the fuence-to-effective dose conversion coeffcient. The
ambient dose equivalent, H*(d), can be obtained by multiplying the fuence
with the fuence-to-ambient dose equivalent conversion coeffcient.
Conversion coeffcients have been calculated by various authors using the
Monte Carlo transport codes (16, 19–21) for many types of radiation (pho-
tons, electrons, positrons, protons, neutrons, muons, charged pions, and
kaons) and incident energies (up to 10 TeV). Pelliccioni (20) has summarized
most of the data. Because the conversion coeffcient for H*(10) for neutrons
becomes smaller than that for E(AP) (where AP refers to anterior-posterior)
above 50 MeV, use of E(AP) may be considered more conservative for high-
energy neutrons. The conversion coeffcient for E(AP) becomes smaller than
that for posterior-anterior (PA) irradiation geometry, E(PA), at neutron ener-
gies above 50 MeV. However, the integrated dose from thermal neutrons to
high-energy neutrons is highest for AP geometry, and therefore the choice of
E(AP) is more conservative than the choice of E(PA). The term “dose” is used
in a generic sense for the dose equivalent or effective dose in this chapter.
17.8.2 Analytical Methods
Most analytical models consist of line-of-sight or “point kernel” models. They
are limited in their use because they are based on simplistic assumptions and
geometry. Many of the models are restricted to transverse shielding. Further,
they do not account for changes in energy, angle of production, target mate-
rial and dimensions, and concrete material composition and density.
17.8.2.1 Point Source
A radiation source can be considered a point source if the distance at which
the dose is determined is at least fve times the dimension of the radiation
539 Basic Aspects of Shielding
source. For a point source, the dose decreases as the square of the distance.
Because protons have a defned range in the target material, the dimension of
the source can be considered to be the range of the proton in the target mate-
rial. For example, the range of a 230-MeV proton in tissue is 32 cm, whereas
the distance from the target to the point of interest outside the shielding
walls is typically greater than 1.6 m (5 × 32 cm).
17.8.2.2 Removal Cross Section
For fast neutrons (E
n
< 20 MeV), the most common approach to calculate
shielding thicknesses is that of the removal cross-section theory (8). To use
this approach, the following principles must hold:
1. The shield must have adequate thickness, and the neutron energy
distribution must be such so that only a narrow band of the most
penetrating neutrons contribute to the dose outside the shield.
2. There must be suffcient hydrogen distributed homogeneously in
the shield or in the outer portion of the shield, to ensure that there is
a very short characteristic transport length for neutrons with ener-
gies lying in the range of thermal to 1 MeV.
3. The source energy distribution and the shield material (nonhydrog-
enous) properties must be such that they ensure a short transport
length for slowing down neutrons from the highest energy to 1 MeV.
The dose equivalent, H(d), as a function of shield thickness, is approxi-
mately given by the line of-sight equation:

H d
H e
r
d
( )
r
=
∑
0
2


(17.4)
where H
0
is the unshielded dose at a distance of 1 m from the source, r is the
distance from the source to the point of interest outside the shield, and d is
the thickness of the shield in centimeters, and ∑
r
is the macroscopic removal
cross section in cm
−1
:

Σ
r
r
=
N
A
0
σ ρ

(17.5)
where σ
r
is the microscopic removal cross section in cm, N
0
is Avogadro’s
number, ρ is the density (g cm
−3
), and A is the mass number. The attenuation
data for fast neutrons can be adequately described by removal cross sections
even though neutrons of energy lower than a few MeV dominate at greater
depths in the shielding.
540 Proton Therapy Physics
17.8.2.3 Attenuation Length
Radiation transmission can be approximated by an exponential function
over a limited range of thickness (2). The attenuation length, λ, is usually
expressed in centimeters (or meters) and in g cm
−2
(or kg m
−2
) when multi-
plied by the density (ρ). The value of λ changes with increasing depth in the
shield for thicknesses (ρd) that are less than ~100 g cm
−2
, because the “softer”
radiations are more easily attenuated, and the neutron spectrum “hardens.”
Figure 17.4 shows the attenuation length (ρλ) for mono-energetic neutrons
in concrete as a function of energy. The attenuation length increases with
increasing neutron energy at energies greater than ~20 MeV. The increase
in attenuation length is indicative of the change from the energy region in
which neutrons interact mainly by elastic scattering with the target nuclei as
a whole, to the region where interaction occurs more likely with individual
nucleons in a target, thus, leading to an intranuclear cascade. In the past,
it has typically been assumed that the attenuation length reaches a high-
energy limiting value of about 120 g cm
−2.
, even though the data in Figure 17.4
show a slightly increasing trend above 200 MeV.
Comparison of neutron dose attenuation lengths measured at various facil-
ities, for concrete and iron, respectively, as a function of the effective maxi-
mum energy (E
max
) of the source neutrons, for neutrons with energies from
thermal to maximum has been made by Nakamura (22) and include measure-
ments for E
max
ranging from 22 to 700 MeV and various production angles
for a variety of neutron sources. According to Nakamura, the measured
neutron dose attenuation length (thermal to maximum energy) for concrete
at 22 MeV is about 30 g cm
−2
, in the forward direction, and then gradually
increases above 100 MeV to a maximum value of about 130 g cm
−2
, which may
be considered the high-energy limit. It is important to note that, in addition
1
0
500
1000
1500
10 100 1000
Neutron energy [MeV]
High energy limit
Concrete ρ = 2.4 g cm
–3
A
t
t
e
n
u
a
t
i
o
n

l
e
n
g
t
h

[
ρ
λ
(
k
g

m
–
2
)
]
FIGURE 17.4
Attenuation length (ρλ) for monoenergetic neutrons in concrete as a function of energy. (From
National Council on Radiation Protection and Measurements, Radiation Protection for Particle
Accelerator Facilities, Report 144, 2003. With permission.)
541 Basic Aspects of Shielding
to particle type and energy, λ also depends on the production angle (θ), mate-
rial composition and density. Monte Carlo calculations by the author indicate
that, for concrete, shielding for 250-MeV protons in the forward direction can
differ by about 30 cm for shielding thicknesses of the order of 2 to 3 m when
two concretes with the same density but differing compositions are used.
Therefore, all concretes will not have the same λ at a given angle and energy,
and the differences can be fairly signifcant, especially in the forward direc-
tion for concretes with different compositions and densities.
17.8.2.4 Moyer Model
Burton Moyer developed a semi-empirical method for the shield design of
the 6-GeV proton Bevatron (1) in 1961. This model is only applicable to angles
close to 90°, and the transverse shielding for a high-energy proton accelera-
tor is determined using the following simple form of the Moyer model (23):

H=

H
r
E
E
d
0
2
P
0






−






α
λ
exp

(17.6)
where H is maximum dose equivalent rate at a given radial distance (r) from
the target, d is shield thickness, E
P
is proton energy, E
0
is 1 GeV, H
0
= 2.6 ×
10
−14
Sv m
2
, and α is about 0.8.
The Moyer model is effective in the gigaelectronvolt (GeV) region because
the neutron dose attenuation length (λ) is nearly constant regardless of
energy. However, the model is restricted to the determination of neutron
dose equivalent produced at an angle between 60° and 120°. At proton ener-
gies in the therapeutic range of interest, the neutron attenuation length
increases considerably with energy. Therefore, the Moyer model is ineffec-
tive and inappropriate for use in proton therapy shielding.
Kato and Nakamura have developed a modifed version of the Moyer
model that includes changes in attenuation length with shield thickness and
also includes a correction for oblique penetration through the shield (24).
In the past, high-energy accelerators were shielded using analytical meth-
ods. However, with the advent of powerful computers, sophisticated Monte
Carlo codes have superseded analytical methods.
17.8.3 Monte Carlo Calculations
Monte Carlo codes such as FLUKA, MCNPX, and MCNP are used extensively
for shielding calculations. These codes can be used to do a full simulation,
modeling the accelerator or beam line and the room geometry in its entirety.
They can also be used to derive computational models as discussed in the
next section. Monte Carlo codes have been used in the shielding design of
several particle therapy facilities (25–30). One unique feature of these codes
542 Proton Therapy Physics
is their ability to generate isodose curves (dose contours), which provide a
visualization of the secondary radiation feld, thus, facilitating the identif-
cation of weak spots in the shielding design (26). For comparison of Monte
Carlo calculations to experimental data, the actual experimental confgura-
tion should be modeled, including the instrument response and the concrete
composition. Further, the experiment should have been performed using
the appropriate instrumentation such as wide-energy neutron rem-meters.
Any deviations from the above conditions will result in large discrepancies
between measurements and simulations. Unfortunately, there is a paucity
of published data for charged particle therapy facilities that meet all these
conditions.
The use of Monte Carlo codes is time consuming. In the early stages of
design, the facility undergoes several iterations of changes in layout, and
therefore, a full Monte Carlo simulation is not practical or cost effective. Full
simulations should be performed only after the layout has been fnalized.
Monte Carlo simulations are especially effective for special issues such as
maze design, penetration shielding, skyshine, and groundshine. Skyshine
is the radiation refected back to earth by the atmosphere above a radiation-
producing facility. Therefore, even if there is no occupancy above the roof
of a radiation-producing facility, a minimal thickness of roof shielding is
required to minimize skyshine. Groundshine is the radiation refected back
to the point of interest by the earth below the foor slab to the point of inter-
est. For the same reasons mentioned above, the foor slab will also require a
minimal shielding thickness to minimize groundshine.
17.8.4 Computational Models
Computational models (derived using Monte Carlo codes) that are indepen-
dent of geometry typically consist of a source term and an exponential term
that describes the attenuation of the radiation. Both the source term and the
attenuation length are dependent on particle type, incident proton energy,
and angle. Such models were frst determined by Agosteo et al. (10) using
experimental double differential neutron spectra, but the early data are now
obsolete (11). Computational models have also been published by Ipe (30).
Shielding can be estimated over a wide range of thicknesses by the fol-
lowing equation for a point source, which combines the inverse square law
and an exponential attenuation through the shield and is independent of
geometry (10):
H(E
p
, θ, d/λ(θ))=
H E
r
d
g
0 p
2
( , )
exp
( ) ( )
θ
λ θ θ
−






(17.7)
where H is the dose equivalent outside the shielding; H
0
is source term at
a production angle θ with respect to the incident beam and is assumed to
543 Basic Aspects of Shielding
be geometry independent; E
p
is the energy of the incident particle; r is the
distance between the target and the point at which the dose equivalent is
scored; d is the thickness of the shield; d/g(θ) is the slant thickness of the
shield at an angle θ; λ(θ) is

the attenuation

length for dose equivalent at an
angle θ and is defned as the penetration distance in which the intensity of
the radiation is attenuated by a factor of e; and g(θ) = cosθ for forward shield-
ing; g(θ) = sinθ for lateral shielding; g(θ) = 1 for spherical geometry.
Computational models are useful especially during the schematic phase
of the facility design, when the design undergoes several changes, to deter-
mine the barrier shielding (31). The entire room geometry is not modeled, but
usually spherical shells of shielding material are placed around the target,
and Monte Carlo codes are used to score dose at given angular intervals and
in each shell of shielding material. Plots of dose versus shielding thickness
can be ftted to obtain source terms and attenuation lengths as a function of
angle, and at the energies of interest, with the appropriate target. In some
cases the data may require a double exponential ft. For example, Agosteo
(11) notes that the source term and attenuation length in the forward direc-
tion (0°–10°) for total ambient dose equivalent, H(10), in ordinary concrete,
produced by 250-MeV protons incident on a thick iron target are given by
H
0
 = (9.8 ± 1.0) × 10
−15
Sv m
2
per proton and λ = 105.4 ± 1.4 g cm
−2
, respectively.
In contrast, the data in the 80°–90° direction can be ftted with a double expo-
nential. The frst source term and attenuation length are given by H
01
= (1.4 ±
0.4) × 10
−15
Sv m
2
per proton and λ
1
= 49.7 ± 5.7 g cm
−2
, respectively; and the
second source term and attenuation length are given by H
02
= (1.4 ± 0.4) ×
10
−15
Sv m
2
per proton and λ
2
 = 83.7 ± 2.0 g cm
−2
. Plots of dose equivalent ver-
sus shielding indicate that there is a dose build-up in the forward direction,
at small depths. However, at large angles, the low energy component of the
radiation is attenuated quickly in small thicknesses. This is because the neu-
tron spectrum changes with depth in the shield. The spectrum hardens with
depth and reaches equilibrium after a depth of about 100 cm. Thus, there are
two attenuation lengths. The second attenuation length is also referred to
as the effective attenuation length and is valid for thicknesses greater than
100 cm of concrete.
The source terms and attenuation lengths will depend on the composi-
tion and density of the shielding material. A thick target can be used to
determine dose rates from the beam incident on the patient. However, it is
important to note that the use of a thick target is not necessarily conserva-
tive in all cases, because for a thin target, the intranuclear cascade may
propagate in the downstream shielding. Ray traces can be performed at
various angles and the source terms and attenuation lengths can be used
for dose calculations. These models are also useful in identifying thin
shielding and facilitate improved shield design. Published computational
models should not be used for calculations, but computational models for
energies, targets, and concrete composition that are facility specifc should
be derived.
544 Proton Therapy Physics
17.9 ShieldingDesignConsiderations
In radiation protection, the primary goal of shielding is to attenuate second-
ary radiation to levels that are within regulatory or design limits for indi-
vidual exposure. This requires knowledge of the various parameters such as
beam losses (including location, target material, and dimensions), treatment
parameters, facility layout, adjacent occupancies, shielding material compo-
sition, and density and regulatory dose limits (1, 31).
17.9.1 Beam Losses
The shielding thicknesses for various parts of the facility may range from
about 60 cm to about 7 m of concrete. Beam losses result in the production
of secondary radiation. Therefore, to design effective shielding, the beam
losses and sources of radiation for proton therapy facilities must be well
understood. This requires knowledge of how the accelerators operate and
deliver beam to the treatment rooms. The equipment vendor should provide
specifc details of beam losses, duration, frequency, targets (material and
dimensions), and locations. Higher beam losses will occur during start-up
and commissioning as the beam is tuned and delivered to the fnal destina-
tion and should be planned for.
17.9.1.1 Synchrotron- and Cyclotron-Based Systems
Synchrotrons are designed to accelerate protons to the exact energy required
for therapy, thus eliminating the need for energy degraders (see Chapter 3).
This results in less local shielding and less activation of beam-line compo-
nents. Sources of radiation for the synchrotron injector include x-rays from
the ion source, x-rays produced by back-streaming electrons striking the
linac (linear accelerator) structure, and neutrons produced by the interac-
tion of the ions with the linac structure toward the end of the linac. The
target material is typically copper or iron. The production of x-rays from
back-streaming electrons will depend on the vacuum conditions and the
design of the accelerator (32). The use of a Faraday cup to intercept the beam
downstream of the linac must also be considered. Typically for synchro-
trons, beam losses can occur during the injection process, radiofrequency
(RF) capture and acceleration, and during extraction. Some of these losses
may be distributed in the synchrotron, whereas others may occur locally.
Losses will be machine-specifc, and therefore the equipment vendor
should provide this information. Particles that are not used in a spill may
be defected on to a beam dump or stopper and will need to be considered
in the shielding design and activation analysis. If the particles are deceler-
ated before being dumped, they are not of concern in the shielding design or
activation analysis. X-rays may be produced at the injection and extraction
545 Basic Aspects of Shielding
septa due to the voltage applied across electrostatic defectors and may need
to be considered in special cases.
About 20% to 50% of the accelerated beam particles can be lost continu-
ously in the cyclotron. Signifcant self-shielding is provided by the steel
in the magnet yoke, except in regions where there are holes through the
yoke. These holes need to be considered in the shielding design. Losses at
very low proton energies are not of concern for prompt radiation shield-
ing, but can contribute to activation of the cyclotron. The shielding is
determined by beam losses that occur at higher energies and those due
to protons that are close to their extraction energy (230–250 MeV depend-
ing on the cyclotron type), striking the dees and the extraction septum,
which are made of copper. These beam losses also result in activation of
the cyclotron.
The energy selection system (ESS) consists of an energy degrader, collima-
tors, spectrometer, energy slits, and a beam stop. The ESS allows the pro-
ton energy to be lowered after extraction. The intensity from the cyclotron
is increased as the degraded energy is decreased in order to maintain the
same dose rate at the patient. Thus, copious amounts of neutrons are pro-
duced in the degrader, especially at the lower energies, resulting in thicker
local shielding requirements in this area. The degrader scatters the protons
and increases the energy spread. A collimator is used to reduce the beam
emittance. A magnetic spectrometer and energy slits are used to reduce the
energy spread. Beam stops are used to tune the beam. Neutrons are also
produced in the collimator, slits, and beam stop. Losses in the ESS are large
and also result in activation.
Losses occur in the beam transport line for synchrotron- and cyclotron-
based systems. Although these losses are usually very low (~1 %) and are
distributed along the beam line, they need to be considered for shielding
design. The target material is typically copper or iron. During operation, the
beam is steered onto Faraday cups, beam stoppers. Beam incident on these
components also needs to be considered in the shielding design.
17.9.1.2 Treatment Rooms
The radiation produced from the beam impinging on the patient (or phan-
tom) is a dominant source for the treatment rooms. Thus, a thick-tissue tar-
get should be assumed in computer simulations for shielding calculations.
In addition, losses in the nozzle, beam-shaping, and range-shifting devices
must also be considered in the shielding design. The contributions from adja-
cent areas, such as the beam transport and other treatment rooms, should
also be taken into account. Typically, the large facility treatment rooms do
not have shielded doors, and therefore the effectiveness of the maze design is
critical. The smaller single-room facilities have shielded doors. In such cases,
a full computer simulation for the maze is recommended. Treatment rooms
either have fxed beam rooms or gantries.
546 Proton Therapy Physics
17.9.1.3 Fixed Beam and Gantry Rooms
Either a single horizontal fxed beam or dual (horizontal and vertical or
oblique) beams are used in fxed beam rooms. Shielding walls in the for-
ward direction are much thicker than the lateral walls and the walls in the
backward direction. The Use Factor (U) is defned as the fraction of time that
the primary proton beam is directed toward the barrier. For rooms with dual
beams the Use Factor for the wall in the forward (0°) direction for each beam
should be considered. This may be either one-half for both beams and two-
thirds for one beam and one-third for the other. For a single beam, the use
factor is one for the wall in the forward direction.
The beam is rotated about the patient in gantry rooms. In some cases, the
gantries may rotate completely (360°), but in other cases only partial rotation
is possible (~180°). For full rotation, on average, it can be assumed that the
use factor for each of the four barriers (two walls, foor, and ceiling) is 0.25. In
some designs, the gantry counterweight (made of large thicknesses of steel)
acts as a stopper in the forward direction. However, it usually covers a small
angle and is asymmetric. The ceiling, lateral walls, and foor are exposed to
the forward-directed radiation. The walls in the forward direction can be
thinner than for fxed beams, because of the lower use factor.
17.9.1.4 Beam-Shaping Techniques
The various techniques used to shape and deliver the beam to the patient can
be divided into two categories: passive scattering and pencil beam scanning.
In passive scattering, a spread-out Bragg peak (SOBP) is produced by a
range modulation wheel or a ridge flter located in the nozzle (33). Lateral
spread of the beam is achieved by scatterers located downstream. Typically,
for small felds, a single scatterer is used, whereas for large felds, a dou-
ble scatterer is used. A collimator (specifc to the treatment feld) located
between the nozzle exit and the patient is used to shape the feld laterally.
A range compensator is used to correct for the shape of the patient surface,
inhomogeneities in the tissues traversed by the beam, and the shape of the
distal target volume. A much higher beam current is required at the nozzle
entrance when compared to the other delivery techniques, because there are
losses due to the incidence of the primary beam on the various delivery and
shaping devices. The typical maximum effciency of a passive scattering sys-
tem with a patient feld is about 45%. Thus, more shielding is required for
passive scattering when compared to pencil beam scanning.
17.9.2 Workload
The term workload is used in a generic sense to include for each treatment
room the following: each proton energy, the beam-shaping method, the
number of fractions per week and the time per fraction, the dose per frac-
tion, and the proton current required to deliver a specifc dose rate. Once the
547 Basic Aspects of Shielding
workload for the treatment room has been established, one must determine
the corresponding energies and currents from the cyclotron or the synchro-
tron. The workload for each facility will be facility specifc and equipment
specifc. Therefore, the workload will vary from facility to facility and from
one equipment vendor to the other. An example of a workload can be found
in PTCOG Report 1 (1).
17.9.3 Regulatory Dose Limits
The use of protons for therapy purposes is associated with the generation
of secondary radiation. Therefore, protection of the occupationally exposed
workers and members of the public must be considered. Most of the national
radiation protection regulations are based on international guidelines or
standards. In the United States, medical facilities are subject to state regula-
tions. These regulations are based on standards of protection issued by the
U.S. Nuclear Regulatory Commission (34).
Table 17.5 shows the radiological areas and the dose limits for the follow-
ing countries: United States (34), Japan (35), Italy (36), and Germany (37). The
dose limits for the countries of Italy and Germany are similar for controlled,
supervised, and public areas. In Germany, areas with dose rates > 3 mSv/h
are defned as restricted areas. In the United States, controlled areas have
dose limits that are much lower than the dose limits for other countries.
Thus, for example, although in the United States the control room adjacent to
the treatment room has a design dose limit of 5 mSv/yr, dose limits for con-
trolled areas in other countries are much higher. Therefore, a cookie-cutter
design originating in one country could potentially underestimate or over-
estimate the shielding in some areas for a proton therapy facility in another
country, assuming similar patient workload, usage, and beam parameters.
TABLE 17.5
Classifcation of Radiological Areas and Dose Limits in Various Countries
Area UnitedStates Japan Italy Germany
Restricted — — No general regulation
(RSO
a
judgement)
Controlled ≤5 mSv/y <1 mSv/week <3 mSv/h
Supervised (area
near controlled
area)
<1.3 mSv/3 months
at boundary of
controlled area
<6 mSv/y <6 mSv/y
Public ≤1 mSv/y,
20 µSv in 1 h
with T = 1
<250 µSv/3 months
(outside of site
boundary)
<1 mSv/y,
recommended
operational limit = 0.25
mSv/y
<1 mSv/y
a
RSO, radiation safety offcer
Source: Modifed from Particle Therapy Cooperative Group, Report 1, 2010. With permission.
548 Proton Therapy Physics
17.9.3.1 Occupancy Factor
The occupancy factor (T) for an area is the average fraction of the time that
the maximally exposed individual is present in the area while the beam is
on (38). If the use of the machine is spread out uniformly during the week,
the occupancy factor is the fraction of the working hours in the week dur-
ing which the individual occupies the area. For instance, corridors, stair-
ways, bathrooms, or outside areas have lower occupancy factors than offces,
nurses’ stations, wards, staff, or control rooms. The occupancy factor for con-
trolled areas is typically assumed to be 1 and is based on the premise that a
radiation worker works 100% of the time in one controlled area or another. In
the United States, the regulatory agencies allow the use of occupancy factors.
17.9.4 Shielding Materials
Earth, concrete, and steel are typically used for particle accelerator shield-
ing (2). Other materials such as polyethylene and lead are used to a limited
extent. For particle therapy facilities, neutrons are the dominant secondary
radiation, and when steel is used, a layer of hydrogenous material must be
used in conjunction with the steel.
17.9.4.1 Earth
Earth is often used as shielding material at underground accelerator facili-
ties. However, it must be compacted to minimize cracks and voids, and attain
a consistent density. Because earth is primarily composed of silicon dioxide
(SiO
2
), it is suitable for shielding of both gamma radiation and neutrons (2).
Its water content improves the shielding of neutrons. However, the water
content can vary from 0% to 30%. The density of earth typically ranges from
1.7 to 2.2 g/cm
3
and depends on the soil type, water content, and degree of
compaction. The activation of the ground water must also be considered for
underground facilities.
17.9.4.2 Concrete and Heavy Concretes
Concrete is a mixture of cement, coarse and fne aggregates, water, and some-
times supplementary cementing materials and/or chemical admixtures.The
density of concrete depends on the amount and density of the aggregate,
the amount of air that is entrapped or purposely entrained, and the water
and cement contents. Typically, ordinary concrete has a density that varies
between 2.2 and 2.4 g cm
−3
. Concrete has many advantages compared to other
shielding materials (2). For example, it can be poured in almost any confgu-
ration, provides shielding for both photons and neutrons, and is relatively
inexpensive. Poured-in-place concrete has suffcient structural strength that
it can be used to support the building and any additional shielding. It is
important to ensure that there are no hollow structural support columns in
549 Basic Aspects of Shielding
the concrete shielding walls. Concrete is also available in the form of blocks.
If blocks are used, they should be interlocked or staggered both horizontally
and vertically to minimize gaps. Water exists in concrete in both the free and
bound form. As previously mentioned, the water content of concrete plays a
signifcant role in the shielding of neutrons. With time, the free water evapo-
rates, but the concrete also hydrates, that is, it absorbs moisture from the sur-
rounding environment until it reaches some equilibrium. About 3% of the
water may evaporate in the frst 30 days or so. Therefore, all shielding calcu-
lations should be performed using the equilibrium density and not the wet
density. For neutron shielding, a minimum water content of about 5.5% is
recommended. In the United States, ordinary concrete is usually considered
to have a density of 2.35 g cm
−3
(147 lb feet
−3
). Concrete used for foor slabs
in buildings is typically lightweight with a density that varies between 1.6
and 1.7 g cm
−3
. The poured-in-place concrete is usually reinforced with steel
rebar, which makes it more effective for neutrons. Measured radiation doses
with heavily reinforced concrete may be lower than calculated doses because
the steel rebar is not included in the concrete composition. The disadvantage
of concrete is that takes months to pour. Continuous pours are preferred for
the concrete walls and ceiling. For noncontinuous concrete pours, appropri-
ate measures (e.g., such as sandblasting of poured surface before pouring the
next portion, use of keyways, and staggered joints) should be used to ensure
that there are no thin spots at the cold joint. Also, for noncontinuous pours,
the ceiling should be notched into lateral walls.
Heavy concretes contain high-Z aggregates or small pieces of scrap steel
or iron that increase their density and effective Z. Densities as high as 4.8 g
cm
−3
can be achieved. The pouring of such high-Z aggregate-enhanced con-
crete is a special skill and should not be undertaken by an ordinary concrete
contractor because of settling, handling, and structural issues (38). Ordinary
concrete pumps are not capable of handling such dense concrete. The high-Z
aggregates could sink to the bottom, resulting in a nonuniform composi-
tion and density. The high-Z aggregate–enhanced concrete is also sold in the
form of prefabricated interlocking or noninterlocking modular blocks. It is
preferable to use the interlocking blocks to avoid the streaming of radiation.
Concrete enhanced with iron ore is particularly effective for the shielding of
relativistic neutrons. One important consideration in the choice of shielding
materials is their susceptibility to radioactivation by neutrons, which can last
for decades. Activation of concrete is discussed in PTCOG Report 1 (1).
17.9.4.3 Steel and Iron
Steel is an alloy of iron and is used for shielding photons and high-energy
neutrons. The high density of steel (~7.4 g/cm
3
) together with its physical
properties leads to tenth-value thickness for high-energy neutrons of about
41 cm (39). Therefore, steel is often used when space is at a premium. Steel
or iron are usually available in the form of blocks (2). Iron has an important
550 Proton Therapy Physics
defciency in shielding neutrons because it contains no hydrogen. Natural
iron is composed of 91.7%
56
Fe, 2.2%
57
Fe, and 0.3%
58
Fe. The lowest inelastic
energy level of
56
Fe is 0.847 MeV (2). Neutrons with energy above 0.847 MeV
will lose energy by inelastic scattering in
56
Fe, but below this energy, neutrons
can only lose energy by elastic scattering, which is a very ineffcient process.
Therefore, there is a build-up of neutrons below this energy. Furthermore,
the neutron quality factor is at a maximum near 0.7 MeV. In addition, natu-
ral iron has two regions where the total cross section is very low because of
resonances in
56
Fe. There is one resonance at 27.7 keV (minimum cross sec-
tion = 0.5 barn) and another at 73.9 keV (minimum cross section = 0.6 barn).
The net result is an increased attenuation length. Thus, large fuxes of low-
energy neutrons are found outside steel or iron shielding. If steel is used for
the shielding of high-energy neutrons, it must be followed by a hydrogenous
material for shielding the low-energy neutrons that are generated. Because
of the large variety of nuclear processes, including neutron capture reactions
of thermalized neutrons, steel can be highly activated (1).
17.9.4.4 Polyethylene
Polyethylene (CH
2
)
n
is used for neutron shielding. Attenuation curves in
polyethylene of neutrons from 72-MeV protons incident on a thick iron
target have been published by Teichmann (40). The thermal neutron cap-
ture in polyethylene yields a 2.2-MeV gamma ray that is quite penetrating.
Therefore, boron-loaded polyethylene can be used. Thermal neutron capture
in boron yields a 0.475-MeV gamma ray. Borated polyethylene can be used
for shielding of doors and ducts and other penetrations.
17.9.4.5 Lead
Lead is used primarily for the shielding of photons. It has a very high den-
sity (11.35 g cm
−3
) and is available in bricks, sheets, and plates. Lead is mal-
leable (2) and cannot support its own weight when stacked to large heights.
Therefore, it will require a secondary support system. Lead is transparent to
fast neutrons, and therefore it should not be used for door sills or thresholds
for proton therapy facilities where secondary neutrons dominate the radia-
tion feld. However, it does decrease the energy of higher-energy neutrons
by inelastic scattering down to about 5 MeV, making the hydrogenous mate-
rial following it, more effective. Below 5 MeV, the inelastic cross section for
neutrons drops sharply. Lead is toxic and should be protected by paint or
encased in other materials.
17.9.5 Transmission
The transmission of a given thickness of shielding material is defned as the
ratio of the dose at a given angle with shielding to the dose at the same angle
551 Basic Aspects of Shielding
without shielding. Transmission curves are useful for comparing different
shielding materials. Transmission curves for various shielding materials,
for 250-MeV protons incident on tissue have been reported by Ipe (40) for
three different production angles. Figure 17.5 shows the total particle dose
equivalent transmission (based on FLUKA calculations) of composite shields
(iron and concrete) and iron and concrete as a function of shielding thick-
ness at 20°–30° for 250-MeV protons incident on a 30-cm ICRU tissue sphere.
These transmission curves can be used to determine the composite shielding
thickness that can be used to replace large concrete thicknesses in the for-
ward direction in the treatment room and thus save space. For example, from
Figure 17.5 it can be observed that 4.65 m of concrete provides about the same
attenuation as about 2.85 m of composite shield (1.2 m of iron plus 1.65 m of
concrete), thus resulting in a space savings of 1.8 m.
References
1. NCRP. Radiation Protection for Particle Accelerator Facilities. National Council
on Radiation Protection and Measurements Report. 2003:144.
2. IAEA. Radiological Safety Aspects of the Operation of Proton Accelerators,
Technical Reports Series No. 283, International Atomic Energy Agency, Vienna,
1988.
20 to 30 degrees
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
1.00E+01
0 100 200 300 400 500 600
Shielding thickness (cm)
T
r
a
n
s
m
i
s
s
i
o
n
Concrete
30 cm Fe +Concrete
60 cm Fe + Concrete
90 cm Fe + Concrete
120 cm Fe + Concrete
Fe
FIGURE 17.5
Transmission curves for 250-MeV protons incident on 30-cm ICRU tissue sphere (20°–30°).
552 Proton Therapy Physics
3. PTCOG. Shielding Design and Radiation Safety of Charged Particle Therapy
Facilities. PTCOG Report 1, Particle Therapy Cooperative Group, 2010. Available
from: URL: http://ptcog.web.psi.ch/Archive/Shielding_radiation_protection.
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ential distributions, attenuation lengths, and source terms for proton accelerator
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Energy Agency, Organization for Economic Co-operation and Development;
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10. Agosteo S, Fasso A, Ferrari A, Sala PR, Silari M, Tabarelli de Fatis P. Double
differential distributions and attenuation in concrete for neutrons produced by
100-400-MeV protons on iron and tissue targets. Nucl Instrum Methods Phys
Res B 1996;114:70–80.
11. Agosteo S, Magistris M, Mereghetti A, Silari M, Zajacova Z. Shielding data
for 100 to 250 MeV proton accelerators: double differential neutron distribu-
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265:581–89.
12. Kato T, Kurosawa K, Nakamura T. Systematic analysis of neutron yields from
thick targets bombarded by heavy ions and protons with moving source mode.
Nucl Instrum Methods Phys Res A 2002; 480:571–90.
13. Nakashima H, Takada H, Meigo S, Maekawa F, Fukahori T, Chiba S, et al.
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14. Tayama R, Handa H, Hayashi H, Nakano H, Sasmoto N, Nakashima H,
Masukawa F. Benchmark calculations of neutron yields and dose equiva-
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213:119–31.
15. Tesch K. A simple estimation of the lateral shielding for proton accelerators in
the energy range 50 to 1000 MeV. Radiat Protect Dosim1985; 11(3):165–72.
16. Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: a multi-particle transport code.
CERN Yellow Report CERN 2005-10; INFN/TC 05/11, SLAC-R-773. CERN,
Geneva, Switzerland; 2005.
17. Birattari C, Ferrari A, Nuccetelli C, Pelliccioni M, Silari M. An extended range
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19. ICRU. Conversion coeffcients for use in radiological protection against exter-
nal radiation. International Commission on Radiation Units and Measurements
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code: description and benchmarking. In: Albrow M, Raja R, eds., Proceedings
of the Hadronic Shower Simulation Workshop 2006; 2006 Sep 6–8; Fermilab,
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calculations for a 250 MeV hospital-based proton accelerator. Nucl Instrum
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of the 2008 Mid-Year Meeting of the Health Physics Society on Radiation
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554 Proton Therapy Physics
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Protection Against Radiation 10CFR20, Code of Federal Regulations. Available
from URL: http://www.nrc.gov/reading-rm/doc-collections/cfr/part020.
35. JRPL Japanese Radiation Protection Laws (Prevention Law) 2004. Law con-
cerning Prevention from Radiation Hazards due to Radioisotopes, etc. 167.
36. IRPL (2000). Italian Radiation Protection Laws, Decreto Legislativo del Governo
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della Tutela del Territorio, Italy).
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Schutz vor Schäden durch ionisierende Strahlen (Strahlenschutzverordnung–
StrlSchV). (Bundesministerium der Justis, Germany.)
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Gamma-Ray Radiotherapy Facilities, National Council on Radiation Protection
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Particle Accelerators. Nuclear Technology Publishing, Kent, UK, 1992.
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Proton Accelerator Facilities In: Proceeedings of SATIF 8, Shielding Aspects of
Accelerators, Targets and Irradiation Facilities; 2006 May 22–24; Gyongbuk,
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41. Ipe NE. Transmission of Shielding Materials for Particle Therapy Facilities. Nucl
Technol 2009; 168(2):559–63.
555
18
Late Effects from Scattered and
Secondary Radiation
HaraldPaganetti
18.1 LateEffectsontheExampleofSecondMalignancies
Dose received by healthy tissue can lead to severe side effects, such as
infuencing cognitive function in children (1), affecting the functionality of
organs, or causing a second cancer later in life. This chapter focuses on the
CONTENTS
18.1 Late Effects on the Example of Second Malignancies .......................... 555
18.2 Volume Defnition ...................................................................................... 557
18.3 Secondary Radiation (Neutrons) in the OFV ......................................... 559
18.3.1 Physics of the Neutron Background ........................................... 559
18.3.2 Neutron Energy Distributions ..................................................... 559
18.3.3 Radiation Quality Factors and Weighting Factors .................... 560
18.3.4 Biological Effectiveness of Neutrons ........................................... 562
18.3.5 Neutron Sources in the Treatment Head .................................... 563
18.3.6 Neutron Doses as a Function of Distance to the Beam Axis .... 564
18.3.7 Field Parameters That Infuence the Neutron Field from
the Treatment Head ....................................................................... 566
18.3.8 Field Parameters That Infuence the Neutron Field
Generated in the Patient................................................................ 568
18.4 Modeling Cancer Risk ............................................................................... 570
18.4.1 Risk Parameters .............................................................................. 570
18.4.2 Low-Dose Effects (in the OFV) .................................................... 571
18.4.3 Risk Modeling Formalism in the OFV ........................................ 572
18.4.4 Results for the OFV ........................................................................ 574
18.4.5 Effects in the IFV ............................................................................ 575
18.4.6 Risk Modeling Formalism for the IFV ........................................ 576
18.4.7 Results for IFV ................................................................................ 579
Acknowledgments .............................................................................................. 580
References ............................................................................................................. 580
556 Proton Therapy Physics
latter. Criteria for a malignancy to be classifed as a radiation-induced sec-
ond tumor include, for example, that the histology of the second tumor be
different from that of the original disease. Furthermore, one needs to con-
sider a latency period of typically several years for a radiation-a ssociated
tumor. Treatment-related cancers are a well-recognized side effect in radia-
tion therapy (2–8). The SEER (Surveillance Epidemiology and End Results)
report (9) gives an overview of new malignancies after the successful treat-
ment for a primary cancer, as well as the parameters infuencing the risk
factors.
Excess risks have been reported for many treatment sites and second
tumor locations. It is known that, even 30–40 years after initial radiation
treatment, cancer survivors remain at an increased risk of developing a
second cancer (10). The cumulative risk for the development of second
cancers has been estimated to be 2–12% according to a 25-year follow-up
(11–19). The risk might level off after ~10 years for some tumor types (e.g.,
acute nonlymphocytic leukemia and non-Hodgkin’s lymphoma), whereas
for others it may increase more than 20 years after treatment (20). An
analysis of patients with pituitary adenoma resulted in an estimation of
the cumulative risk of second brain tumors of 1.9–2.4% at ~20 years after
radiotherapy and a latency period for tumor occurrence of 6 to 21 years
(15, 16, 19, 21).
The likelihood of developing second cancer depends on both the entire
irradiated volume and on the volume of the high-dose region. It has been
confrmed that the majority of second tumors occur within the margins of
the treatment volume (22). Solid cancers are mostly found within or close
to the primary cancer treatment feld (20, 23, 24), where higher doses may
cause bone and soft tissue sarcoma (19, 25). Other than carcinoma, radia-
tion induced sarcoma can be expected in high-dose regions. Low doses
delivered far outside the main feld have also been associated with second
tumors (3, 26).
When treating adults, the latent period might exceed the life expec-
tancy. Second malignancies are of particular concern for pediatric
patients (27, 28), because children, and young adults are especially prone
to the carcinogenic effects of radiation (20, 29, 30) and these patients are
likely to live longer than the average latent period. There is an increasing
risk with decreasing patient age (31, 32) due to a greater radiation effect
in humans during the period of rapid cell proliferation, for example,
during development of the thyroid gland (33). It was shown that there
is a statistically significant correlation between radiation therapy and
second tumors after childhood cancer (28). Gliomas occurred typically
within 15 years after treatment, whereas meningiomas typically occurred
beyond 15 years after treatment. The Childhood Cancer Survivor Study
presents an ongoing multi-institutional retrospective study of more than
14,000 cases (34–38). Children are preferably treated with highly confor-
mal treatment techniques (39), and there is an interest in using protons
557 Late Effects from Scattered and Secondary Radiation
because of the reduction in dose to healthy tissue compared with photon
techniques.
The knowledge about risk in medium or high dose levels for second malig-
nancies is very limited because of the scarcity of second cancer from radiation
therapy. Our understanding of radiation late effects at low doses is based on
incidence and cancer mortality data for atomic bomb survivors (29, 40–43).
However, in these cases the radiation exposure was acute over a very short
period of time, unlike in the fractionated radiation treatment. Furthermore,
the radiation feld, consisting of neutron, photons, and other particles, was
much different from those in radiation therapy. One might thus expect dif-
ferent biological damage mechanisms.
18.2 VolumeDefinition
The irradiated volume considered in treatment planning includes the tar-
get volume receiving a prescribed dose as well as the organs at risk (see
Chapter  10). The most common volume defnitions in radiation therapy
are illustrated in Figure 18.1. Target volumes might be defned as the gross
tumor volume (GTV), the clinical target volume (CTV), and the planning tar-
get volume (PTV) (44). For critical structures, the organ(s) at risk (OAR) and
the planning organ at risk volume (PRV) are defned (44). When analyzing
IFV
PRV
OAR GTV
CTV
PTV
OFV
FIGURE 18.1
Volumes considered in treatment planning as defned by the ICRU (44) for the target and for
the organ(s) at risk (OAR). Gross tumor volume (GTV); clinical target volume (CTV); planning
target volume (PTV), organ(s) at risk (OAR); planning organ at risk volume (PRV). Also shown
are the volume defnitions introduced here for the analysis of scattered and secondary doses:
in-feld volume (IFV) and out-of-feld volume (OFV).
558 Proton Therapy Physics
late effects from scattered and secondary radiation one can defne three
(overlapping) volumes in the patient:
• The target (e.g., CTV), treated with the therapeutic dose.
• OAR in the tumor vicinity that are imaged (considered) in treatment
planning that may intersect with the beam path and are allowed to
receive low-to-intermediate doses, here defned as in-feld volume (IFV).
• The rest of the patient’s body, which typically receives low doses (way
below 1% of the target dose) that are not considered, or even imaged,
for treatment planning, here defned as out-of-feld volume (OFV).
In this defnition the CTV is excluded from the IFV because presumably all
cells in the CTV will be killed during treatment. The defnitions of IFV and
OFV are arbitrary. One might also distinguish between low and intermedi-
ate dose levels. However, there is a distinct difference in dosimetry when
analyzing risk for the IFV and the OFV. With some exceptions, dose distri-
butions within the human body are not directly measurable. Organ doses
in the IFV can typically be extracted from the treatment-planning system.
On the other hand, organ doses in the OFV can typically only be calculated
using Monte Carlo simulations (see Chapter 9). Treatment-planning systems
cannot be applied for this purpose, even if whole-body computed tomog-
raphy (CT) is available, because they are not commissioned for very low
doses and do not explicitly take into account the particle type and energy
distribution of secondary radiation. Furthermore, as will be discussed later
in this chapter, the dose-response relationships and dose distributions differ
between the IFV and the OFV (i.e., the OFV and the IFV have to be consid-
ered separately).
Note that the term “integral dose” (a more correct terminology is the total
energy deposited) is often used to describe the dose deposited in the patient
including the tumor as well as all healthy tissues (target, IFV, and OFV).
Proton therapy reduces the total energy deposited in the patient by a factor of
2 to 3 compared to photon therapy. This typically causes a signifcant reduc-
tion in early and late side effects when using protons in favor of photons (1,
45). Side effects do not simply scale with total energy deposited because the
distribution of dose also plays a role. Many studies have compared different
radiation modalities regarding the potential risk of late effects (46, 47). When
comparing scattered and secondary dose from photon (intensity- modulated
radiation therapy [IMRT]) and proton (passive scattered) treatments, it seems
that, in locations far away from the target (OFV), proton therapy offers an
advantage, but within approximately 20–25 cm from the feld edge (still
OFV), the scattered photon dose in IMRT might be lower than the neutron
equivalent dose from passive scattered proton therapy (48). In total, IFV risks
seem to be higher than OFV risks, and it appears that there is an overall
advantage for proton therapy for the majority of feld arrangements (49–50).
559 Late Effects from Scattered and Secondary Radiation
18.3 SecondaryRadiation(Neutrons)intheOFV
18.3.1 Physics of the Neutron Background
Particles generated in nuclear interactions of primary protons can be very
short ranged (<1 mm; e.g., recoil nuclei, α-particles), medium ranged (less
than or equal to the range of the primary proton; secondary protons), or long-
ranged (secondary neutrons) (Chapter 17). The frst two types are included
in the planned dose distribution, as the treatment-planning system would be
commissioned for these dose levels.
Neutrons can be generated when the primary proton beam interacts with
devices in the treatment head but also when interacting inside the patient.
At low energies (<1 MeV) neutrons undergo elastic scattering processes and
cause protons and γ-rays produced by neutron capture. The most likely inter-
action in hydrogen-rich media, and thus mainly responsible for the neutrons
to lose energy, is elastic scattering. In the low/thermal energy region, there
is a decreasing probability of neutrons slowing down, as low-energy neu-
trons sparsely interact with material. For higher-energy neutrons, roughly
90% of the energy transfer (dose) occurs via secondary protons in only a few
interaction events. This process causes protons with a wide range of energies
between zero and the incident neutron energies. Secondary protons can be
produced anywhere in the human body (it is thus feasible to encounter a
proton downstream of the maximum range predicted for the primary proton
beam). As a result, an extensive part of the patient’s body may be exposed
to the secondary radiation feld. The small amount of dose and the fact that
neutrons are uncharged particles make measurements and simulations dif-
fcult and/or time consuming.
18.3.2 Neutron Energy Distributions
The biological effectiveness of neutrons depends on their energy.
Consequently, when assessing the impact of neutron doses, not only the
absorbed dose but also the neutron energy distribution is important.
Secondary neutrons can have energies up to the maximum proton energy.
Neutrons with energy in excess of 10 MeV and high-energy protons pro-
duced by an intranuclear cascade processes are mainly forward-peaked.
The majority of neutrons produced are in the energy region below 10 MeV,
produced by an evaporation process, and are emitted more isotropically.
Even though neutrons are predominantly emitted in a forward direction,
the patient might be exposed to a relatively uniform neutron feld, depend-
ing upon the distance between the patient and the neutron-emitting ele-
ments in the treatment head. Because of a 1/r
2
dependency of the neutron
fuence on the distance r, the relative position of devices in the treatment
head plays a role when analyzing the neutron dose caused by the treatment
560 Proton Therapy Physics
head. Neutrons produced in the patient, on the other hand, are generated by
protons, which have, on average, lower energies and a much wider angular
distribution. Because of the large number of elastic scatterings in soft tissue
there is a prevailing feld of low-energy neutrons inside the patient.
Neutron energy distributions in patients (or phantoms) can be calculated
using Monte Carlo simulations (51–54). Figure 18.2 shows the simulated
energy distribution of neutrons entering a water tank after being generated
in a brass block by a 200-MeV proton beam. Although the neutron energy
distribution peaks at low neutron energies, the majority of the neutron-
generated dose is deposited by high-energy neutrons. About two-thirds of
the neutron dose in a typical proton therapy scenario is deposited via neu-
trons with energy above 100 MeV (55).
18.3.3 Radiation Quality Factors and Weighting Factors
The dose from secondary radiation might be low. Nevertheless, compared
to high-dose photon radiation (the typical reference), there are concerns
because of an elevated relative biological effect (RBE) of neutrons that may
cause long-term side effects (56–58). The RBE is used when comparing dif-
ferent modalities with a reference radiation. It depends on the type of radia-
tion, the particle energy, the dose, and the biological endpoint. The rationale
behind the use of RBE and the determinants of RBE are discussed in Chapter
19. The RBE is used at a dose higher than ~0.5 Gy. The biological effectiveness
Brass H
2
O
100 cm 10 cm
Protons
0
5e-4
5e-5
5e-6
N
e
u
t
r
o
n
s
/
p
r
o
t
o
n
/
5
k
e
V
5e-7
50 100
Neutrons entering H
2
O
Neutrons undergoing
(n, xp) in H
2
O
Neutron energy [MeV]
150 200
FIGURE 18.2
Results of a Monte Carlo simulation of a 200-MeV proton beam stopping in a brass block and
the generated neutrons entering a water tank. The simulated setup is shown in the top right
with the protons indicated by an arrow and entering a 10-cm brass block, which stops all pri-
mary particles. The fgure shows the neutron energy distributions of those neutrons entering
the water tank downstream of the brass block as well as those neutrons causing a secondary
proton in a nuclear interaction, the main mechanism of dose deposition. The unit is in neu-
trons per incident proton per 5-keV bin.
561 Late Effects from Scattered and Secondary Radiation
relative to photons increases with decreasing dose, causing the difference
between photons and neutrons to be considerable at low doses. A conserva-
tive approach at low doses is to use a maximum RBE, RBE
max
, which is the
ratio of the initial slopes of the dose-response curves. This maximum RBE
value is related to conservative regulatory quantities such as the radiation
quality factors and the radiation weighting factors, which are defned inde-
pendently of dose and biological endpoint.
The equivalent dose is the average absorbed dose in an organ or tissue,
modifed by the radiation weighting factor for the type and energy of the
radiation (59–62). The radiation weighting factors, w
R
, convert the absorbed
dose in Gray (Gy) to Sievert (Sv) and are defned by the International
Commission on Radiological Protection (ICRP) (63, 64):

H Sv w D Gy [ ] [ ]. = ⋅
R
(18.1)
The ICRP recommends for photons and electrons a radiation weighting fac-
tor of 1, for protons a weighting factor of 2, and for alpha particles a weight-
ing factor of 20 (63). In the case of neutrons, the weighting factor depends on
energy, and the ICRP defnes an energy-dependent bell-shaped curve with a
maximum weighting factor of 20 at about 1 MeV (63–65). For energies above
10 MeV, however, there is a signifcant uncertainty in the radiation weighting
factors due to a lack of relevant animal studies (66). Nevertheless, a continu-
ous function is suggested by the ICRP for the calculation of radiation weight-
ing factors for neutrons (64):

w
E E
n n
R
=
+ ⋅ −
( )
<
+
2 5 18 2 6 1
5 0 17
2
. . exp [ { }] /
. .
In MeV
00 2 6 1 50
2 5 3 25
2
⋅ −
( )
≤ ≤
+ ⋅
exp [ { }] /
. .
In MeV MeV E E
n n
eexp [ { . }] / −
( )
>







In MeV. 0 04 6 50
2
E E
n n

(18.2)
Several alternative fts have been presented as well (61). The interaction prob-
ability as a function of neutron energy is important in the understanding of
the effciency of neutron radiation. Most of the dose from high-energy neu-
trons is deposited via recoil protons, whereas for low-energy neutrons most
of the dose is deposited via photons caused by neutron capture in hydrogen.
It has been shown that, for a neutron feld of 1-MeV neutrons, 25% of the dose
would be deposited by photons (67).
Most importantly, the weighting factors are only applicable for whole-
body irradiation by external radiation fields, for which they are designed.
Radiation weighting factors have also been used for internal radiation
(e.g., neutrons generated in the patient). This can cause inconsistencies
when assigning proton weighting factors for primary protons and neutron
weighting factors for protons generated by neutrons because the latter
protons would be scaled by a higher weighting factor (68). Furthermore,
because the ICRP equation is defined for an external neutron field, it
562 Proton Therapy Physics
also contains the contribution of secondary photons that might be cre-
ated in the body. For the size of a human body, however, some of the
captured gamma rays will deposit a noticeable portion of the overall dose
in the body.
The equivalent dose defned via weighting factors was originally intro-
duced to replace the “dose equivalent,” which is based on quality factors
and is defned for a point instead of an organ (65). For estimating side effects
from low doses in (proton) radiation therapy, however, the quality factor con-
cept is in fact more meaningful for the reasons discussed above. The qual-
ity factor is based on the LET (linear energy transfer), independent of the
energy-depositing particle. Thus, it allows proper consideration of internal
and external radiation (66). The dose equivalent is written as

H Sv Q D Gy [ ] [ ]. = ⋅

(18.3)
The quality factor is defned as a function of the unrestricted linear energy
transfer of charged particles in water (LET
∞
). Its maximum value is ~30 as
defned by the ICRP (63):

Q LET
LET
LET LET ( )
/
. .
∞
∞
∞ ∞
=
<
⋅ − ≤ ≤
1 10
0 32 2 2 10
keV m µ
110
300 100
keV m
keV m.
/
/ /
µ
µ LET LET
∞ ∞
>






(18.4)
For a given volume, the quality factor is obtained by integrating over the
dose-weighted contributions of charged particles:

Q
D
Q LET
dD
dLET
dLET
LET
= ⋅ ⋅
∞
=
∞
∞
∞
∞
∫
1
0
( ) .

(18.5)
Another radiation protection quantity is the “effective dose” as the weighted
sum of various organ or tissue doses. It normalizes partial-body exposure
in terms of whole-body stochastic risk using “tissue weighting factors” (63,
65). It was developed to recommend a risk-based occupational dose limit for
radiation protection. The effective dose is not measurable or additive and
carries signifcant uncertainty in the assessed risk values because it is based
on not only radiation weighting factors but also tissue weighting factors for
specifc organs. The effective dose concept should be used only for overall
radiation protection for the general public, but not for patient-specifc radia-
tion therapy risk assessments.
18.3.4 Biological Effectiveness of Neutrons
Most second cancer risk studies have been done using the weighting factor
concept. The energy averaged neutron weighting factors in the human body
563 Late Effects from Scattered and Secondary Radiation
for a proton beam entering the patient are typically between 2 and 11 (51,
69, 70). Independent of the problems when dealing with regulatory quanti-
ties discussed above, the radiation effectiveness as a function of particle and
dose for carcinogenesis in human tissues or organs is not well known. It has
been estimated that the neutron RBE at low doses (e.g., the weighting factor)
might be about 25 for carcinogenesis (71). It is undisputed that the neutron
quality factors are subject to signifcant uncertainties (46, 62, 66, 71–75). There
is a paucity of data on RBEs at energies outside the range of about 0.1–2 MeV.
Because of the lack of high-energy neutron carcinogenesis data, extrapo-
lations have been made to much higher neutron energies (63–65, 76–79).
Furthermore, RBE values obtained at high doses might be extrapolated to
low-dose values (80).
For the atomic bomb survivor data it was estimated that the neutron RBE
for tumor induction was 70 ± 50 (81). Values up to 80 have been reported
considering several endpoints (59, 79, 82). A comprehensive study on neutron
values for RBE
max
for the induction of dicentric chromosomes found a value
of ~11 for a 60- and a 192-MeV mono-energetic neutron beam, demonstrat-
ing that the RBE is probably constant above ~20 MeV (83, 84). An RBE of 96
(relative to
60
Co) was measured for chromosome aberrations at low dose (2.5
mGy) using a neutron energy spectrum that was similar to that produced
by a clinical proton therapy nozzle (85). This may overestimate the RBE in
the patient, because the neutron energy spectrum is modifed by modera-
tion and absorption. Most experimental data are for fssion neutrons with
energies between 1 and 1.5 MeV, much lower than the energy of neutrons
responsible for most of the secondary dose in proton therapy. The RBE for
oncogenic transformation, a relevant endpoint for carcinogenesis, was mea-
sured for low-energy neutrons in vitro, resulting in values of RBE
max
relative
to x-rays of 3.7, 6.6, and 7.2 for 40-, 70-, and 350-keV neutrons, respectively (86).
The maximum RBE for induction of dicentric chromosomes was determined
to be 94 ± 39 relative to
60
Co for 0.385-MeV neutrons (corresponding to 23.4 ±
2.5 relative to 220-kV x-rays) (87).
Based on the human data from neutron dose estimates to Japanese atomic
bomb survivors (83, 88), the most likely RBE
max
for neutron-induced carcino-
genesis in humans has been estimated to be 100 for solid-cancer mortality
(89) and 63 for overall cancer incidence (90). However, the radiation feld to
which the atomic bomb survivors were exposed is much different from the
conditions in radiation therapy.
One must keep in mind that most of the neutron dose is deposited via sec-
ondary protons. Interestingly, the low-dose RBE for chromosome aberrations
induced by protons was found to be 5.7 for a proton energy of 4.9 MeV (91).
18.3.5 Neutron Sources in the Treatment Head
Neutron production depends on the nuclear interaction cross section of the
primary beam and thus on the proton beam energy and the materials in
564 Proton Therapy Physics
the beam path. The neutron production is determined mainly by the atomic
number, Z, of the material. Cyclotrons extract a proton beam with a fxed
energy. Thus, a signifcant amount of secondary radiation is produced in
the energy selection system, which includes energy degraders of variable
thickness and energy-defning slits. These degraders are usually outside the
treatment room (in the accelerator vault) and do not cause secondary dose
exposure of the patient. However, at some facilities fne-tuning of the beam
energy (range) is done directly upstream of the patient position.
High-Z materials are used in scattering devices as well as to stop the
beam around the patient aperture. Some of the materials typically used
in treatment heads are brass, steel, carbon, or nickel. Consequently, the
neutron fuence is infuenced by the treatment head design, that is, the
geometry and the materials used. Design of proton therapy beam deliv-
ery systems and treatment heads can vary considerably when comparing
different facilities. The neutron background produced by a treatment head
can be infuenced by appropriately designing the treatment head, particu-
larly for passive scattered proton beam therapy (92–94). Variable collimators
can be used to tailor the feld size upstream of the fnal patient collima-
tor. Furthermore, aperture designs can be optimized using low-Z materials
and/or preabsorbers (92).
18.3.6 Neutron Doses as a Function of Distance to the Beam Axis
Many experiments have been reported to assess secondary radiation from
therapeutic proton beams (69, 70, 94–105). Neutron detectors typically include
Bonner spheres (70, 102), thermoluminescence dosimeters (106), CR-39 plastic
nuclear track detectors (99, 102), bubble detectors (98), solid-state microdo-
simetry detectors (69, 97, 107), tissue equivalent proportional counters (104),
ionization chamber arrays (97), and other survey meters such as WENDI
(94, 108).
Bonner spheres consist of a proportional chamber flled with BF
3
gas at
the center of polyethylene sphere in diameter plus some Cd. The polyethyl-
ene moderates the neutrons to thermal energies, which are detected by the
proportional chamber via the reaction
10
B(n,α)
7
Li. The Bonner spheres can be
calibrated by measuring the response when the detector is placed a certain
distance (1 m) from an Am/Be source of known activity. These spheres can
be set up throughout the treatment room and can also be used as area moni-
tors (see Chapter 17).
Experiments to determine neutron doses can be diffcult because neutrons
are indirectly ionizing and interact only sparsely. Monte Carlo simulations
of neutron doses as a function of lateral distance to the feld edge have been
used in several studies (53–55, 95, 99, 109, 110), whereas analytical models can
be used as well (111).
The majority of published data on neutron doses as a function of dis-
tance to the feld edge is shown in Figure 18.3. The results from passive
565 Late Effects from Scattered and Secondary Radiation
scattered beams vary signifcantly because of variations in beam delivery
systems and feld specifcations. Within 5 cm of the edge of the primary
treatment feld, the reported doses vary between 0.5 and 10 mSv/Gy. At
a distance of 60 cm from the edge in lateral direction, the reported doses
vary between 0.03 and 8 mSv/Gy. Most of the studies focus on neutron
doses lateral to the feld. Because neutrons are predominantly emitted
in forward direction in the treatment head, one might expect a slightly
higher neutron dose downstream of the target. Nevertheless, neutron
equivalent doses past the distal falloff were determined to be below
2 mSv/Gy (95, 99, 107).
For scanned beams, neutron doses lateral to the feld have been mea-
sured (using a Bonner sphere and CR39 etch detectors) as below 4 mSv/Gy
outside of the target (102). Scanning reduces the equivalent dose in the OFV
by a factor of 30–45 in the entrance region. The difference decreases with
depth because internal (generated in the patient) neutrons predominate.
Because of the ratio of external (generated in the treatment head) versus
internal neutrons, the equivalent dose at 15–20 cm from the feld edge
decreases with depth in passive scattering and increases with depth for
scanning (97).
10 20 30 40
Lateral distance to the field edge [cm]
50 60 70 80 0
10
–2
10
–1
10
0
H

[
m
S
v
/
G
y
]
10
1
10
2
FIGURE 18.3
Equivalent dose per treatment dose [mSv/Gy] as a function of lateral distance to the feld. Solid
lines: measured (69, 70, 94, 97–99, 107) and simulated (53, 55, 97, 99, 110) data for a variety of
proton beam confgurations using passive scattered beam delivery. Dashed lines: results for
scanned proton beams (97, 102). If more than one confguration was reported in a given publi-
cation, two curves showing the maximum and minimum were selected. Also shown for com-
parison is the scattered photon dose for a randomly chosen 10 × 10-cm
2
intensity-modulated
photon feld using a 6-MV beam (dotted line) (181).
566 Proton Therapy Physics
18.3.7 Field Parameters That Influence the Neutron
Field from the Treatment Head
When proton treatments are delivered in passive scattering mode, various
scatterers, beam-fattening devices, collimators, and energy-modulation
devices to produce the SOBP are in the beam path. In addition, for each treat-
ment feld, individual apertures and range compensators are being used.
Doses caused by neutrons depend signifcantly on the treatment condi-
tions (i.e., the treatment facility) because of differences in position and
design of devices in the treatment head. Even for the same facility there are
huge variations between felds because the treatment head geometry and
the beam characteristics in passive scattered proton therapy are patient feld
specifc (Figure 18.3). The parameters determining the neutron contami-
nation of the primary proton beam include the characteristics of the beam
entering the treatment head (energy, angular spread), the material in the
double-scattering system and range modulator, and the feld size upstream
of the fnal patient-specifc aperture (55, 94, 98, 110). The complexity of feld
delivery in passive scattering techniques, causes considerable variations in
neutron doses and prevents the defnition of a “typical” neutron background
representing proton therapy (46, 74, 110, 112).
Neutrons are mainly generated in the modulator wheel as well as in precol-
limators and patient-specifc apertures (99, 113). Double-scattering systems
are typically designed to create a homogeneous feld with the maximum
size commissioned for treatment. The effciency of most proton therapy
treatment heads is quite low (typically between 3% and 30% depending on
the feld size). Depending on the actual required feld size for a treatment,
a high percentage of primary protons are being stopped in the treatment
head by either precollimators or the patient-specifc aperture. A systematic
experimental study on secondary neutron dose equivalent using anthro-
pomorphic phantoms confrmed that neutron dose decreased with increas-
ing aperture size and air gap, implying that the brass collimator contributes
signifcantly to the neutron dose because of its proximity to the patient (98).
Thus, the neutron dose depends on the ratio of feld size to aperture open-
ing; neutron equivalent doses due to external neutrons typically increase
with decreasing feld size (74, 98, 105, 110, 112). Figure 18.4 shows the neutron
dose equivalent as a function of the aperture opening. The neutron produc-
tion in the treatment head also depends on the beam energy, as higher beam
energies might traverse more scattering material to slow down protons in
order to cover proximal parts of the target (the proximal part of the spread-
out Bragg peak).
Neutron equivalent doses to specifc organs do depend considerably on
patient’s age and size because of the position and distance of the organ rela-
tive to the treatment head and the target. Younger patients are thus typically
exposed to a higher neutron contribution from the treatment head because of
their smaller bodies (110). For example, assuming an 8-year-old patient, the
567 Late Effects from Scattered and Secondary Radiation
dose to the brain from spinal felds ranged from 0.04 to 0.10 mSv/Gy, whereas
assuming a 9-month-old patient, the dose ranged from 0.5 to 1.0 mSv/Gy for
the same feld (114). Figure 18.5 illustrates the increase in neutron dose with
decreasing patient’s age, considering identical treatment felds.
The neutrons produced in the proton treatment nozzle are the main con-
tributor to organ equivalent doses. The ratio of internal versus external
0
0
0.05
0.15
0.2
0.25
0.3
0.35
0.1
N
e
u
t
r
o
n

d
o
s
e

e
q
u
i
v
a
l
e
n
t

(
m
S
v
/
G
y
)
10 20 30 40 50 60 70 80
Collimator area (cm
2
)
Double scattering Rectangular scanning Spiral scanning Circular wobbling
y = –0.0008x + 0.06
y = –0.0009x + 0.1906
y = –0.0009x + 0.2392
y = –0.0009x + 0.309
FIGURE 18.4
Neutron dose equivalent at a position in a water phantom as a function of the aperture open-
ing. Different delivery techniques were considered: passive (double) scattering (squares), rect-
angular scanning (diamonds), spiral scanning (triangles), and circular wobbling (circles), each
representing a different ratio of feld size versus aperture opening. (From Hecksel et al., Med
Phys., 37(6), 2910, 2010. With permission.)
0.0
0.5
1.0 H

[
m
S
v
/
G
y
]
1.5
2.0
2.5
3.0
20
Patient’s age [years]
30 40
FIGURE 18.5
Simulated organ neutron equivalent dose for thyroid (circles), esophagus (squares), lungs (tri-
angles), and liver (diamonds) as a function of patient age averaged over eight different proton
treatment felds. The simulations were based on computational phantoms resembling rep-
resentative individuals. (From Zacharatou Jarlskog et al., Phys Med Biol., 53, 693, 2008. With
permission.)
568 Proton Therapy Physics
neutron dose depends heavily on the organ and its distance to the treat-
ment target volume (51). It has been shown that for a small target volume,
the contribution of neutrons from the treatment head can reach ~99% of
the total neutron contribution, whereas for a large target volume it can
go down to ~60% (110). Beam scanning typically does not require scatter-
ing or compensating devices. Also, no feld-shaping apertures stopping
a large portion of the beam are necessary. Thus, proton beam scanning
reduces the neutron dose exposure signifcantly, particularly for small
treatment felds (i.e., small apertures in scattering systems) (97). A treat-
ment head using the passive scattering technique may show a 10-fold
secondary neutron dose disadvantage compared with the spot-scanning
technique (45, 51).
18.3.8 Field Parameters That Influence the Neutron
Field Generated in the Patient
Neutrons are also generated in the patient. Here, the bigger the target, the
more protons are entering the patient. Thus, the main parameter infu-
encing the neutron dose is the treatment volume (102). Figure 18.6 shows
the relationship of treatment volume and neutron dose from internally
created neutrons assuming different patient age. Neutron doses increase
with increasing range and modulation width (53, 110). The greater the
penetration of the beam, the greater is the overall likelihood of a nuclear
interaction producing neutrons. The treatment volume is slightly affected
by the delivery technique. One can assume that the patient generated
neutron dose for scanned beams is roughly the same as in passive scat-
tering beams.
Neutron production is not homogeneous as a function of proton penetra-
tion depth. Figure 18.7 shows the nonelastic cross section for protons on
carbon and oxygen. Clearly, the cross section is more or less independent
of proton energy down to ~100 MeV, after which it increases with decreas-
ing proton energy. The maximum is reached at ~25 MeV. To understand the
0
0.0
0.1
0.2
0.3
0.4
0.5
100 200 300
Treatment volume [cm
3
]
H

[
m
S
v
/
G
y
]
FIGURE 18.6
Simulated internally created neutron equivalent dose to the thymus as a function of treatment
volume of a brain tumor: 4-year-old patient (circles), 11-year-old patient (squares), 14-year-old
patient (triangles), and adult patient (diamonds). (From Zacharatou Jarlskog et al., Phys Med
Biol., 53, 693, 2008. With permission.)
569 Late Effects from Scattered and Secondary Radiation
neutron emission as a function of depth, one has to consider the average
proton energy as a function of depth, which is shown for a 160-MeV proton
beam in water in Figure 18.8.
Epidemiological studies require the use of organ-specifc doses for
proper risk analysis. Accurate dosimetry information exists for organs
delineated in a treatment plan. However, dosimetry for organs or tis-
sues outside the portion of the body that was imaged for treatment plan-
ning will need to be reconstructed using whole-body patient models and
Monte Carlo simulations (see Chapter 9). Many models representing male
and female adults, children, and pregnant women have been developed,
0
0.1
0.2
0.3
0.4
N
o
n
e
l
a
s
t
i
c

c
r
o
s
s

s
e
c
t
i
o
n

[
b
a
r
n
]
0.5
0.6
20 40 60 80 100 120
Proton energy [MeV]
140 160 180 200
FIGURE 18.7
Total nonelastic cross sections for protons on carbon ( ) and oxygen ( ). (Based on EXFOR/
CSISRS, Experimental Nuclear Reaction Data. International Atomic Energy Agency, Nuclear
Data Section, Vienna, Austria, 2010. (182))
0
20
40
60
80
100
120
140
160
50 0
A
v
e
r
a
g
e

p
r
o
t
o
n

e
n
e
r
g
y

[
M
e
V
]
D
o
s
e

[
r
e
l
a
t
i
v
e

u
n
i
t
s
]
100 150 200
Depth in water [mm]
FIGURE 18.8
Average proton energy for primary protons (solid line) and secondary protons from nuclear
interactions (dotted line) as a function of depth in a 160-MeV proton beam leading to the depth-
dose distribution shown as dashed line.
570 Proton Therapy Physics
mostly from segmented whole-body images (115, 116). A number of stud-
ies have used whole-body patient phantoms and Monte Carlo simulations
to calculate organ doses originating from secondary neutrons (48–51, 110,
114, 117, 118). Considering several proton felds of varying feld size, beam
range, and modulation width for the treatment of tumors in the intracra-
nial and spinal region, variations of neutron-generated dose among dif-
ferent organs for different treatment volumes and patient statures were
studied (48, 114).
To put things in perspective, assuming treatments are in the head and
neck region of an adult patient, the equivalent dose from proton therapy is
comparable to doses from a chest CT scan (110) or whole-body CT scan (99).
However, for young patients it could be in the order of more than 20 addi-
tional CT scans (110).
18.4 ModelingCancerRisk
18.4.1 Risk Parameters
Cancer risk (i.e., the probability of a disease) is either specifed as incidence
risk or mortality risk. The absolute risk (AR) is defned as the rate of a disease
among a population per capita per year. A relation between the incidence
rate in the exposed population and the incidence rate in the unexposed
population can be defned as a difference or a ratio. Relative risk (RR) is the
rate of disease in the exposed groups divided by the rate in a control group.
Excess relative risk (ERR) is defned as the rate of an effect in an exposed
population divided by the rate of the effect in an unexposed population
minus 1 (i.e., RR-1). Thus, the risk is given relative to the baseline risk. The
baseline risk is the incidence observed in a group without a specifc risk fac-
tor (e.g., the unirradiated reference population). Excess absolute risk (EAR)
is the rate of an effect in an exposed population minus the rate of the effect
in an unexposed population. In risks reported as EAR, risks are expressed
as the difference between the total risk and the baseline risk. Both, ERR and
EAR are used in risk modeling. Estimates based on ERR typically have less
statistical uncertainty. EAR models depend on the baseline risk, that is, the
area in which the person lives, the age at exposure, sex, and date of birth (9).
Estimates based on EAR are often used to describe the impact of a disease
on the population. Risks can be calculated as a function of attained age
of the individual, age at exposure, dose received, sex index, and an index
denoting population characteristics. Further, the lifetime attributable risk
(LAR) provides the probability that an individual will die from (or develop)
a disease (e.g., a second cancer) caused by the exposure during his or her
lifetime (8, 80, 119).
571 Late Effects from Scattered and Secondary Radiation
18.4.2 Low-Dose Effects (in the OFV)
Risk estimates are sometimes performed using whole-body effective doses
and organ weighting factors (see above) (65). Such tissue weighting factors
for the effective dose are gender- and age-averaged values. Effective doses
are suited for radiation protection studies but not for risk models for sec-
ond cancer, which are site specifc. Risk assessments should be based on
patient-specifc organ doses and not on population average tissue doses
(120, 121).
Interpreting clinical data on second cancers is diffcult, because accurate
organ dose information is often missing. Furthermore, because of interpa-
tient variability and the low frequency of second cancers, dose-response rela-
tionships from patient data are associated with large statistical uncertainties
(57). To establish a reliable dose-response relationship for second cancers as a
function of modality, treatment site, beam characteristics, and patient popu-
lation, progressively larger epidemiological studies are required.
Our knowledge (and the basis of low-dose epidemiological response
models) of radiation-induced tumors is largely based on the atomic bomb
survivor data (40, 41, 120–122), and models are therefore associated with
considerable uncertainties (123–125). Data on solid tumor mortality among
the atomic bomb survivors are consistent with linearity up to ~2.5 Sv (40,
42). Risks observed in the atomic bomb survivors were compared to risks
in patients after medical exposure risks (126–128). Although it was found
that the relative risk of cancer from treatment was generally less than those
in comparable subsets of the bomb survivor data, a linearity of the dose-
response curve was concluded for both series (129, 130).
Various dose-response relationships for carcinogenesis have been sug-
gested (129, 131–141), and low-dose risk models have been summarized or
developed by radiation protection bodies (6–8, 123). There is considerable
uncertainty in the shape of the dose-response curve, and linearity may not
hold for all cancers. Figure 18.9 shows the different regions of dose response.
Secondary or scattered doses in the OFV are typically well below 2 Sv where
a linear dose-response relationship for solid tumors is reasonable based
on the available data, but the slope will most likely depend on the cancer
and site. An increasing slope has been suggested as dose-effect relation-
ship for radiation-induced leukemia (42), for example, a linear-quadratic
relationship (8).
At very low doses (below ~0.1 Sv), none of the epidemiological data are suf-
fcient to predict the shape of the dose-response curve (131). Linearity is sug-
gested at least down to about 0.1 Gy (142–144). Both the BEIR VII Committee
(Biological Effects of Ionizing Radiation) (8) and the ICRP (65) recommend
a linear no-threshold (LNT) model because stochastic effects are usually
regarded as having no dose threshold. The validity of the LNT model has
been challenged (131). It has been acknowledged that for doses below ~0.1
Gy there might be a threshold effect or a nonlinear relationship (134, 135,
572 Proton Therapy Physics
145–151). A threshold in dose has been suggested for radiation-induced sar-
comas (152). This is also confrmed by atomic bomb survivor data because
no increased sarcoma risk is found there. A lack of evidence of carcinogenic
effects at low doses could be due to a dose threshold or because these effects
are too small to be detected. The situation is complex too because one often
deals with population average values. The existence of a small subpopula-
tions of individuals showing hypersensitivity would decrease the slope for
cancer mortality and incidence (136). There might also be reduced radioresis-
tance in which a small dose decreases the radiosensitivity for carcinogenesis
(138, 148). Adaptive response would cause higher risk for lower doses because
a small initial dose might decrease radiosensitivity. There might even be
hormesis (147). Pure physics considerations might support the linearity at
low doses based on the number of tracks being proportional to dose. The
argument does not hold if multiple radiation-damaged cells infuenced each
other, and bystander effects also play a role (139, 153–157). Such effects could
be relevant specifcally for higher LET because bystander effects would be
more pronounced if a small number of cells were traversed by particle tracks
at low doses (155, 156).
When estimating risks, dose-rate effects may play a role (158). Radiation
therapy is mostly delivered in multiple fractions, whereas most low-dose
weighting factors or response models are deduced from single irradiation.
Differences in tissue repair capacities of tissues are not considered. In order
to account for this effect, a dose and dose-rate effectiveness factor (DDREF)
has to be applied for doses below ~0.2 Gy (62).
18.4.3 Risk Modeling Formalism in the OFV
Risk (e.g., ERR) can be calculated as a function of attained age of the
individual (a), age at exposure (e) (or time since exposure, t), absorbed
Equivalent dose [Sv]
?
reshold
Bystander effects
Hormesis
...
?
Linear increasing
Plateau
Bell-shaped
0.05 – 2.5
C
a
n
c
e
r

r
i
s
k
FIGURE 18.9
Dose-response relationships for carcinogenesis showing a linear dose response in the dose
range of the atomic bomb exposures of ~0.05–2.5 Sv (134) and the uncertain relationships for
higher and lower doses.
573 Late Effects from Scattered and Secondary Radiation
dose (D), sex (s), and a parameter denoting population characteristics (8,
119). Low-dose models to calculate specific risks of cancer incidence and
mortality with organ-specific parameters are given, for example, in the
BEIR report (8) (there are other parameterizations by other committees
as well (6, 7)):

EAR or ERR s t a D D e a
s
( , , , ) ( ) exp( ) . = ⋅ ⋅ ⋅ ρ β γ
η

(18.6)
The BEIR committee suggests that ERR for solid cancers (except for breast
and thyroid) depends on age only for exposure under age 30, replacing e by
e* = (e-30)/10 (equals 0 for e > 30). For solid tumors ρ(D) is a linear function
of dose. Normalizing the attained age to the reference age 60 and assuming
a linear dose response leads to the following risk model for all solid cancers
except thyroid and breast:

EAR or ERR s a e D D e a
s
( , , *, ) exp( *) ( / ) = ⋅ ⋅ ⋅ β γ
η
60 .

(18.7)
The parameter β
s
denotes the ERR/Sv or the EAR/10
4
PY Sv for a person that
has been exposed to radiation at age 30 and has attained 60 years of age. The
parameter γ gives the per-decade increase in age at exposure over the range
0–30 years and expresses the fact that the ERR decreases with increasing age
at exposure for those exposed under age 30.
For breast cancer, it was recommended that (8, 159)

ERR s a D D a ( , , ) ( / ) = ⋅ ⋅
−
β 60
2

(18.8)

EARper women years D e 10 9 4 0 05 30
4
⋅ = ⋅ ⋅ − − ( ) . exp . ( ) ⋅⋅ ( / ) . a 60
η

(18.9)
For thyroid cancer, a recommended model reads (8, 33)

ERR s e D D e
s
( , , ) exp( ( )). = ⋅ ⋅ − β γ 30

(18.10)
Finally, the excess risk for leukemia can be defned as (8)

ERR s e t D D D e t
s
( , , , ) ( )exp * log( / ) = ⋅ ⋅ + ⋅ + β θ γ δ φ 1 25 ee t * log( / ) . 25 ( )

(18.11)
The LAR can be calculated by integrating ERR or EAR over the expected
lifetime for all attained ages exposed at age e with dose D. Other param-
eters are the latent period L (e.g., 5 years for solid cancers and 2 years for
leukemia), and the survival fraction (i.e., the probability at birth of reaching
a specifc age):

LAR e M D a e
S a
S e
da
e L
a
( ) ( , , ).
( )
( )
,
max
=
+
∫

(18.12)
574 Proton Therapy Physics
where S(a)/S(e) is the conditional probability for a person who was alive at
age e to reach age a and M(D, a, e) is the excess absolute risk at the a from
exposure at age e, which is defned for both EAR as well as ERR:

M D a e EAR D a e M D a e ERR D a e
c
( , , ) ( , , ) ( , , ) ( , , ) ( = = ⋅ λ
U
aa).
(18.13)
The parameter λ
c
U
(a) is the age- and gender-specifc baseline (unexposed
population U) cancer incidence rate at the attained age a (9). The preference
for one or the other method (EAR vs. ERR) depends on whether there are
differences in the baseline risks between the reference population and the
considered population. The BEIR committee has recommended that LAR be
estimated as a weighted average between the ERR and EAR models, except
in the case of breast (ERR and EAR not combined) and thyroid (only ERR). A
related parameter to LAR is REID (risk of exposure induced death), which is
considered dose dependent (6, 7).
18.4.4 Results for the OFV
Organ doses in the OFV in proton therapy have been simulated applying
Monte Carlo simulations (Chapter 9). Based on the results, risks for devel-
oping a second malignancy in patients treated with passive and scanned
proton radiation have been estimated (50, 51, 71, 114, 118, 160, 161). Whole-
body computational phantoms provide the geometries to assess adult and
pediatric organ doses, albeit not patient specifc (114, 160, 161).
It was found that young patients are subject to significantly higher
risks than adult patients. The reasons are geometric differences and
because of the age-dependency of risk models. Most of the calculated
lifetime risks were found to be below 1% and below the baseline risks.
For example, the LAR for lung and breast cancer incidences in a 4-year-
old child treated for a brain tumor were 1.1% and 1.3%, respectively,
and the corresponding values for an 8-year-old girl were 1.1% and 0.7%,
respectively (114). Risk clearly decreases with increasing age with the
risk for developing a second cancer in the thyroid, testes, and bladder
reported as ≤0.3% for a 14-year-old boy. The corresponding baseline
risks for thyroid, testes, and bladder were 0.4%, 0.4%, and 4%, respec-
tively. Furthermore, LAR values were found to be higher for the deep-
seated tumors because of large volume exposure. The LAR values for
different organs as a function of patient age are shown in Figure 18.10.
The numbers can be expected to be very similar, maybe within a factor
of 2, for photon treatments (161).
Because the majority of neutron doses are caused by scattering devices
in the treatment head, there is a big advantage of scanned proton beams
over photon beams on the incidence of treatment-induced second cancers
specifcally for pediatric patients (45, 102). It was demonstrated that with
scanned beam proton therapy there is the potential to reduce the incidence
575 Late Effects from Scattered and Secondary Radiation
of radiation-induced second cancers by a factor of 2 to 15. In another study,
craniospinal irradiation of a male patient was simulated for passively scat-
tered and scanned-beam proton treatment units, and the total lifetime risk
of second cancer due exclusively to secondary radiation was 1.5% for the
passively scattered treatment versus 0.8% for the scanned proton beam
treatment (50).
18.4.5 Effects in the IFV
Other than in the OFV, average organ doses are not meaningful in the IFV
because dose-volume effects might play a role. Furthermore, mutagenesis
is in competition with cell survival, causing the dose-response relationship
to become nonlinear, as sterilized cells will not mutate (37, 135). In addi-
tion, tissues may respond to radiation by accelerated repopulation, contrib-
uting to tissue sparing during fractionated radiation therapy. This causes
risk modeling in the IFV to be more complicated than in the OFV. Figure
18.9 shows the dose-response relationship at high doses and the potential
uncertainties.
An analysis of pediatric patients showed that a linear dose-response rela-
tionship best described the radiation response down to 0.1 Gy, whereas a
decrease or leveling of risk was apparent beyond 10 Gy (33). On the other
hand, a linear increase with dose even beyond 40 Gy was found for meningi-
oma and glioma (28, 162). This could be because the killed cells are balanced
by repopulation (163). Also, other studies have suggested a linear increase
to even higher doses in second cancers after Hodgkin lymphoma or cervical
cancer (134, 164, 165). Most human data show no decrease in risk but just a
leveling off at higher doses. There is evidence that the risk of solid tumors
might level off at 4–8 Gy (4, 166). A slight decrease after ~4 Gy has been
observed for leukemia after cervical cancer (164, 167, 168). For thyroid cancer
0.0
0.2
0.4
0.6
0.75 11 14 39
L
A
R

[
%
]

Patient age [years]
Lung
yroid
Leukemia
Esophagus
FIGURE 18.10
Lifetime attributable risk (LAR) for developing a second cancer after treatment of a brain
tumor to 70 Gy at different ages for a male patient. The risks are averages over several treat-
ment felds. (From Zacharatou Jarlskog et al., Phys Med Biol., 53, 693, 2008. With permission.)
576 Proton Therapy Physics
a bell-shaped response curve with linearity up to ~25 Gy can be deduced
(34, 162) with an eventual decrease of the risk with increasing dose (37).
Thyroid is the only organ where this effect has been seen consistently. Figure
18.11 shows experimental data illustrating linear and bell-shaped response
curves. It has been shown that second cancers are more likely in the feld
periphery than in the feld center (23), providing evidence for the bell-shaped
dose-response curves due to competing factors of cell kill and cell mutation.
The reason for organ-specifc differences might be differences in repopula-
tion rates.
18.4.6 Risk Modeling Formalism for the IFV
Linear fts to atomic bomb data cannot be used for IFV risk analysis, and
more mechanistic interpretation is necessary. Radiation-induced cancers are
rare in radiation therapy and parameterizations are thus diffcult for the IFV
(38, 57). Models do incorporate mechanistic considerations to guide param-
eter fts and radiation-induced malignancies are thus modeled consider-
ing the competing probabilities for DNA mutation and cell survival (6, 7).
The survival probability can be modeled in a linear-quadratic form using
α and β as the intrinsic radiosensitivities, and the probability for mutation
can be parameterized by mutational radiosensitivities, γ and δ (169–175). The
processes are also dependent on the kinetics of repopulation by the surviv-
ing normal and mutant cells. This can be modeled as a multistage process
assuming three compartments: the nonmutated stem cells, the one-mutant
stem cells (which are also the precursor cells of malignant transformation),
and the probability that an individual cell population has received at least
one malignant transformation in a given time interval after irradiation
(170). Stem cells are subjected to a spontaneous mutation rate, μ, causing
0
5
10
R
e
l
a
t
i
v
e

r
i
s
k
15
20
25
10 0 20 30
Dose [Gy]
40 50
FIGURE 18.11
Relative risks for a subsequent glioma ( (28)) and thyroid cancer ( (38)). The solid line shows
a linear ft to the glioma risk data, and the dashed line represents a linear-exponential ft to the
data on thyroid cancer risk.
577 Late Effects from Scattered and Secondary Radiation
one-mutant cells. The expected number of malignant transformations, N, is
then proportional to

N D D D D t ∝ − − − − − − − (exp[ ])( exp[ ])( exp[ ] α β γ δ µ
2 2
1 1 ))
(18.14)
where t is the time from conception at which the radiation dose was admin-
istered. The repopulation rate for both cell types, surviving normal stem
cells and surviving one-hit mutants (two-hit mutants are assumed to lead
to malignant transformation), is assumed to be the same. Example param-
eters are α = 0.25 Gy
−1
, β = 0.025 Gy
−2
, γ = 10
−5
Gy
−1
, δ = 10
−6
Gy
−2
, and μ = 10
−8

month
−1
(170).
When analyzing high or medium dose levels organs typically receive inho-
mogeneous dose distributions. To consider such effects, one might use the
concept of organ equivalent dose (OED), in which any dose distribution in an
organ is equivalent and corresponds to the same OED if it causes the same
radiation-induced cancer incidence. A risk factor is then applied to the OED
(173, 176, 177). For low doses, the OED represents the average organ dose.
The EAR as a function of D, a, e, and s, can be written as a product of OED
and the initial slope, that is, with a risk factor based on low-dose risk models
(175, 177). Parameters for OED are the organ-specifc cancer incidence rate at
low doses, which can be taken from the data of the atomic bomb survivors,
and cell sterilization at higher doses (174). If the true dose-response curves
for radiation-induced cancer were known for each organ and tissue, an OED
estimate would be a perfect parameter to quantify second cancers. However,
because the underlying dose-response function is not known, several mod-
els have been used. One can thus assume three dose-response relationships,
linear, bell-shaped, and plateau-shaped as follows: (using free model param-
eters α
organ
and δ
organ
)

OED
N
VD
i i
i
=
∑
1

(18.15)

OED
N
VD D
i i
i
organ i
= −
∑
1
exp( ) α

(18.16)

OED
N
V
D
i
organ i
organ
i
=
− −
( )
∑
1
1 exp[ ] δ
δ

.

(18.17)
The total volume is denoted as N, and the summation includes all voxels,
assuming that the organ volume is parameterized in a CT scan. Because
there are limited data for specifc organs, the original model parameters
to describe the high dose response were estimated by analyzing the second
cancer incidence data of patients with Hodgkin’s disease, a patient popula-
tion with considerable data on second tumors because of genetic susceptibil-
ity (178).
578 Proton Therapy Physics
Note that for small doses, the formalism assumes a linear response based
on an average organ dose, such as in the low-dose models, thus allowing
parameters to be ftted to the atomic bomb data:

OED
N
V
D
N
VD D
i
organ i
organ
i
i i
i
=
− −
= =
∑ ∑
1
1 1
1
( )
.
δ
δ

(18.18)
Tumor induction is modeled with differential equations considering the bal-
ance between cell survival, mutation, and repopulation (172). Cancer risk is
defned as the ratio of the number of mutant to the number of original cells.
One might also consider that carcinoma and sarcoma might have different
functional dose relationships. Carcinoma induction is proportional to the
sum of surviving original and repopulated cells and is expected to show a
bell-shaped pattern as long as cell repopulation is small. For sarcoma induc-
tion, only repopulated cells can form tumor cells.
Using the repopulation parameter R > 0, the dose per fraction d
F
, the
total dose D, and a cell kill parameter α′, the OED can be written as follows
(179):

OED
N
V
D
R
R R
i
i i
i
i
carcinoma

− ′
′
− +
∑
1
1 2
2
exp( )
ex
α
α
pp[ ] [ ] exp ′ − − −
′
−

¸

1
]
1
¸
¸

_
,

α
α
i i
i
i
D R
R
R
D 1
1
2

(18.19)

OED
N
V
D
R
R R
i
i i
i
i
sarcoma

− ′
′
− +
∑
1
1 2
2
exp( )
exp[
α
α
′′ − ′ − − −
′
−

¸

1
]
1
¸
¸

α α
α
i i i i
i
i
D RD R
R
R
D ] [ ] exp 1
1
2
__
,

(18.20)

′ = + ⋅ α α β
i i
D
d
D
F
.

(18.21)
The EAR, for example, can then be just the product of a risk parameter (from
low-dose response) and the respective OED.
Figure 18.12 illustrates the bell-shaped dose-response relationships for car-
cinoma and sarcoma. For small repopulation parameters, carcinoma induc-
tion shows a bell-shaped function of dose, whereas a plateau is reached with
increasing dose if high repopulation is assumed. In contrast, sarcoma induc-
tion increases with increasing dose up to a constant value.
Similar models have been proposed by others (163) and expanded by add-
ing stochastic fuctuations of premalignant cell numbers among patient pop-
ulations (180).
579 Late Effects from Scattered and Secondary Radiation
18.4.7 Results for IFV
There are fewer modeling studies for the IFV than for the OFV. One of the
reasons is the uncertainty of model parameters for the nonlinear dose-
response domain in the IFV because most IFV data from radiation therapy
do not allow the deduction of a reliable dose-response curve (57). A detailed
analysis of thyroid cancer in childhood cancer survivors revealed a linear
dose-response relationship (with a small nonlinear contribution) with an
ERR of ~1.3 per Gy for doses below 6 Gy (38). For higher doses, the analysis
resulted in a relative decrease in ERR of 0.2% per unit dose squared with
increasing dose. This lead to decreases in the ERR/Gy of 53% at 20 Gy and
95% at 40 Gy. The data for most organs indicate that the risk increases with
dose to fairly high levels where it might eventually level off. Thus, one can
assume that the risk for a second malignancy is typically higher in the IFV
compared to the OFV. For prostate patients, it has been shown that about
90% of the total risk is for the colon and bladder inside the main treatment
felds and that proton therapy offers an advantage over photon techniques
(49). Comparisons between photon and proton therapy for IFV risk show-
ing the advantage of proton therapy have also been done for craniospinal
irradiation (50).
Apparently, IMRT and proton therapy decrease the risk for second malig-
nancies in-feld when compared with 3D conformal photon therapy (175).
The reason is the improved capability for shaping the dose distribution.
Furthermore, because protons typically reduce the treated volume and
reduce the total energy deposited in the tissue, dose to organ at risk in the
IFV are typically lower compared to photon techniques (for comparable tar-
get doses). In particular for pediatric treatments it is certainly benefcial to
reduce the overall treatment volume to reduce the risk for second malignan-
cies. Even within the same modality one might infuence the cancer risk. The
0
0
20
40
60
20 40
Dose [Gy]
B
r
e
a
s
t

c
a
n
c
e
r

r
i
s
k

[
/
1
0
0
0
0
P
Y
]
0.0
0.5
1.0
1.5
2.5
2.0
S
a
r
c
o
m
a

r
i
s
k

[
/
1
0
0
0
0
P
Y
]
60 80
Rf = 99%
Rf = 80%
Rf = 60%
Rf = 40%
Rf = 20%
Rf = 10%
Rf = 0%
0 20 40
Dose [Gy]
60 80
Rf = 99%
Rf = 80%
Rf = 60%
Rf = 40%
Rf = 20%
Rf = 10%
Rf = 0%
FIGURE 18.12
Calculated absolute risk for breast carcinoma (left) and for sarcoma (right) assuming different
repopulation factors. The three data points on the left represent data on breast cancer after
radiation therapy for Hodgkin’s disease. (From Schneider, Med Phys., 36(4), 1138, 2009. With
permission.)
580 Proton Therapy Physics
choice of beam angles and the number of felds can infuence the risk for
a second malignancy because of different distribution of dose. When ana-
lyzing the risk for a radiation-induced cancer, treating a smaller volume to
higher doses might seem benefcial compared to treating a larger volume
with, on average, lower doses. However, this has to be balanced against
other side effects that might deserve higher attention, for example, radiation-
induced reduction in cognitive function in the case of brain dose (1).
Acknowledgments
The author thanks Dr. X. George Xu, Dr. Uwe Schneider, and Jocelyn Woods
for proofreading and Clemens Grassberger for help with some of the fgures.
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19
The Physics of Proton Biology
HaraldPaganetti
19.1 Introduction
There is no simple relationship between dose and biological effect. Even
the exact knowledge of the underlying energy deposition (i.e., the macro-
scopic physics) might not be suffcient to predict the effect of radiation on
tissues, as is evidenced by the fact that different radiation modalities show
different dose–response relationships. The reason for using dose as a clini-
cal prescription is our lack of understanding of biological effects and the
fact that we base treatments on clinical experience with specifc dose levels.
CONTENTS
19.1 Introduction ................................................................................................ 593
19.2 Mechanisms of Radiation Action ............................................................ 594
19.2.1 DNA Damage ................................................................................. 594
19.2.2 Energy Deposition Events and DNA Damage .......................... 595
19.2.3 Ionization Event Distribution and Lesion Complexity ............ 596
19.3 Dose–Response Relationships ................................................................. 597
19.4 The Relative Biological Effectiveness ...................................................... 600
19.5 Rationale for the Clinical Use of 1.1 as Proton RBE .............................. 600
19.6 Variations of RBE ....................................................................................... 602
19.6.1 LET Dependency of RBE ............................................................... 602
19.6.2 Dose Dependency of RBE ............................................................. 606
19.6.3 Endpoint Dependency of RBE ..................................................... 606
19.7 Modeling Cellular Radiation Effects....................................................... 608
19.8 Biophysical Models of Radiation Action on Cells ................................. 609
19.8.1 LET-Based Models ......................................................................... 609
19.8.2 Microdosimetric Models ............................................................... 609
19.8.3 Lesion Interaction Models ............................................................ 610
19.8.4 Lesion Induction and Repair Models .......................................... 611
19.8.5 Track Structure Models ................................................................. 613
Acknowledgments .............................................................................................. 617
References ............................................................................................................. 617
594 Proton Therapy Physics
Some biological aspects are discussed in this chapter. A detailed discussion
of subcellular mechanisms, repair pathways, and genetic effects of radiation
damage and repair is beyond the scope of a book on proton therapy physics.
Radiation action on living cells is a complex sequence of physical, biochemi-
cal, and physiological events.
19.2 MechanismsofRadiationAction
19.2.1 DNA Damage
Radiation interacts with tissue atoms. Ionizations lead to cellular and then
to molecular effects. Radiation also causes molecules to go into excited states
leading to vibrations producing heat. In fact, more than 95% of the energy in
radiation therapy goes into heat. Nevertheless, the most important impact of
radiation is caused by ionizations.
The cell nucleus with a diameter of typically about 10 μm contains the
main genetic information within the double-helical DNA macromolecules.
The DNA resembles the biggest target although its diameter of about 2 nm
(and a length of about 2 m) accounts for only a few percent of the total mass
of the nucleus. The rest is composed of other structures, particularly water.
Although all molecules in the cell are affected by ionizing radiation, there
is substantial evidence that damage to the DNA molecules is the decisive
lesion for mutation induction, carcinogenic transformation, and killing
of most cell types. Aside from damage to other cellular structures, DNA
damage is directly related to cell death. Although there are multiple cop-
ies of most molecules and those are undergoing fast turnover, only two
copies exist of the DNA, and the turnover is limited. DNA is central to all
cellular functions.
The initial damage caused by a proton would typically be a strand break. If
DNA strand breaks are in close proximity it can cause double-strand breaks
(DSBs) either directly or during the strand break repair process. Only a small
portion of the initial biochemical damage leads to a cellular effect because
the damage is either nonsignifcant or can be repaired.
Damaged DNA undergoes transformations that invoke different repair
mechanisms. Unrepaired DSBs lead to the dysfunction and loss of genetic
material. Pieces of DNA may join to form chromosomal aberrations, which
can cause cell death. The term cell death is usually used for loss of reproduc-
tive capacity, although this defnition might not be relevant for all cell types
and tissues. For some cell types, apoptosis or programmed cell death may
also be initiated by damage to the cell membrane. Although cell death via
necrosis increases exponentially with increasing dose, induction of apopto-
sis saturates with increasing dose.
595 The Physics of Proton Biology
19.2.2 Energy Deposition Events and DNA Damage
If an electron originating from an ionization event has enough energy to
cause further ionizations, it is called a δ-electron. For protons with energy
between ~0.5 and ~100 MeV, ~70% of the energy lost is transferred to and
then transported by secondary electrons, ~25% is needed to overcome their
binding potential, and the residual 5% produces neutral excited species (1).
Each photon or proton track is associated with δ-electrons of widely differ-
ent energies. Therefore, the spatial pattern of energy deposition is complex.
There are ionizations and excitations that can be considered independently
as well as clusters of ionizations and excitations caused by track-ends of low-
energy δ-electrons.
Ionizations in water are responsible for the type of damage that leads to
chemical reactions threatening the DNA via highly reactive radicals (indi-
rect effects). This has to occur within a few nanometers of the DNA, that
is, within the diffusion distance of the radicals. In addition, radiation can
cause lethal damage from the direct deposition of energy (direct effects) in
the DNA. For low-LET (linear energy transfer) radiation, effects are caused
mainly via δ-electrons creating free radicals. Direct hits become more pro-
nounced at higher LET. Figure 19.1 illustrates different interaction channels.
The number of energy depositions per cell per Gray is quite substantial.
Assuming a 100-keV electron, there will be more than ~500 energy deposi-
tion events with energies larger than 10 eV in a 6-nm
2
target but less than 10
with energies larger than 150 eV (2). Table 19.1 shows the approximate num-
ber of events in a mammalian cell following different radiation felds after a
dose of 1 Gy (3, 4). Interestingly, the number of ionizations per cell nucleus is
about the same. Even the initial yield of DSBs shows little variation with ion-
ization density. Importantly, the number of residual breaks at 8 h after cel-
lular repair substantially differs. The same number of initial DSBs gives rise
to a substantially larger number of chromosome aberrations after high-LET
~ 2 mm
H
H
O
OH*
~ 2 nm
direct
indirect
FIGURE 19.1
Direct and indirect (via diffusion of free radicals) radiation effects on the DNA. The dashed
lines show two potential particle paths leading to the two interaction types. The insert illus-
trates the size of a proton track with ionization events and δ-electrons (white tracks).
596 Proton Therapy Physics
versus low-LET irradiation. Furthermore, higher-LET radiation increases the
frequency of complex aberrations.
19.2.3 Ionization Event Distribution and Lesion Complexity
The number of initial DSBs is not directly proportional to cellular dam-
age. The number of DSBs per cells typically increases with dose linearly
(Figure 19.2). Even if two different modalities, for example, photons and pro-
tons, cause the same number of DNA DSBs per unit dose, the distribution of
the DSBs can differ substantially. It is not so much the type of DSBs but the
spatial distribution of DNA lesions within the cell that determines radiation
effects (5). The key to understanding radiation effects lies in the spatial distri-
bution of energy deposition events and the complex lesions this may cause.
The spatial distribution of lesions might be random for low-LET radiation
but follows more closely specifc particle tracks at high-LET values (6). With
increasing LET more DSBs are predicted within dimensions of several base
pairs (7). Clustering of radiation damage is assumed to be responsible for the
effectiveness of high-LET radiation (7, 8). Lesion complexity is not restricted
to DSB but can also involve single-strand breaks. It can involve more than
two strand breaks (9) or damage enhanced by damaged bases. Thus, lesions
from protons might be more complex than those from photons (10). This
complexity increases with LET due to higher energy delivered in direct hits
(5, 11–13) together with an LET dependence of the DSB repair kinetics (14–16).
The resulting cluster of strand breaks that are more concentrated in space
and the associated damage is believed to render the lesions less amenable
TABLE 19.1
Average Yield of Damage in a Single Mammalian Cell after 1 Gy Delivered
by Photons (low-LET) or Low-Energy α Particles (high-LET)
Radiation Low-LET High-LET
Tracks in nucleus 1000 2
Ionizations in nucleus 10
5
10
5
Ionizations in DNA 1500 1500
Base damage 10
4
10
4
DNA single-strand break 700–1000 300–600
DNA double-strand breaks (initially) 18–60 70
DNA double-strand breaks (after 8 h) 6 30
Chromosome aberrations 0.3 2.5
Complex aberrations 10% 45%
Lethal lesions 0.2–0.8 1.3–3.9
Cells inactivated 10–50% 70–95%
The assumed nucleus has a diameter of 8 μm, and the energy deposition per ioniza-
tion is set to 25 eV.
Source: Adapted from Goodhead, Can J Phys., 68 ,872, 1990; and Nikjoo et al., Int J
Radiat Biol., 73, 355, 1998.
597 The Physics of Proton Biology
to repair, or, rather, to competent repair (17). Furthermore, clustered strand
breaks increase the likelihood of mis-joining, which can cause chromosome
aberrations.
The importance of understanding lesion complexities and repair mecha-
nisms in order to understand radiation effects is illustrated by the fact that
the difference between protons and photons with respect to DSB induction as
a function of dose is smaller than the one for cell reproductive death or chro-
mosomal aberrations (18). Cell kill and cell mutation show different depen-
dencies on dose and energy deposition pattern. Because repair depends on
the spatial distribution of lesions (19), one interesting consequence might be
that the difference in radiation sensitivity among different cell lines might
be, at least in part, due to different spatial orientation of the DNA.
19.3 Dose–ResponseRelationships
If we assume a single particle crossing a radiosensitive volume and no varia-
tion in energy deposition characteristics, Poisson statistics defne the mean
number of effective hits per unit dose. The probability of fnding a nucleus
with ω lethal events if an average of Ω lethal events per nucleus is produced
in the whole population is

P( ) exp( ). ωΩ
Ω
ω!
Ω
ω
= −

(19.1)
10000
D
S
B
s

p
e
r

c
e
l
l
1000
100
10
1
0.1
0.01
0.001 0.01 0.1 1 10 100
Dose (Gy)
FIGURE 19.2
DSB induction in MRC-5 cells showing a rate of approximately 35 DSBs per cell per Gray. (From
Rothkamm and Loebrich, Proc Natl Acad Sci USA, 100, 5057, 2003. With permission.)
598 Proton Therapy Physics
Because only cells without lethal events will survive, the survival probabil-
ity as a function of absorbed dose, D, with N
0
being the initial number of cells
and N being the number of unaffected cells, is given as

N
N
D P
0
0 ( ) ( , ) exp . = = − ( ) Ω Ω( ) D

(19.2)
The response of a biological system to dose is typically visualized in a dose-
response curve, for example, cell survival as a function of dose. Cell survival
curves represent the number of cells that have lost the ability for unlimited
proliferation. The assumption that there are individual single targets requir-
ing a single hit (i.e., that it requires one hit by a particle to inactivate a sensi-
tive area) would result in a straight line on the logarithmic dose-response
plot. However, the dose-response relationship typically results in a sigmoi-
dal curve. A linear-quadratic parameterization is the simplest mathematical
formulation to ft most survival curves (20, 21):

N
N
D
0
( ) exp . = − −
( )
α β D D
2

(19.3)
Accordingly, a biological effect can be defned as (with either the dose D
delivered at once or in n fractions of d):

E D D D n d d ( ) = + = +
( )
α β α β
2 2
.

(19.4)
The linear quadratic form of the cell survival curve could be due to dual
lesion interactions (e.g., two particles from two tracks, leading to a quadratic
term in dose) or because of competing effects in lesion induction linear with
dose and the dose-dependent depletion of repair enzymes. The likelihood of
radiation lesion from two tracks occurring at a short distance from each other
is quite small within the dimensions of the DNA molecule. Consequently,
biophysical models that include repair have been more successful in inter-
preting experimental results (see Section 19.7).
Figure 19.3 shows two dose-response curves. The curvature, or shoulder, of
a survival curve can be interpreted based on lesion repair capacity or lesion
induction mechanisms, that is, by the α/β ratio. For a given end point, the
dose-response curves from proton radiation are steeper than the ones from
photon radiation, indicating perhaps that the likelihood for repair of lesions
is decreasing. If the proton energy is decreasing, that is, increasing LET, the
response curve becomes steeper (reduction of the width of the shoulder of
the response curve) up to a limit after which it may be reversed (see Section
19.6.1). Specifcally, α typically increases with increasing LET, whereas β is
not signifcantly affected (22–25).
599 The Physics of Proton Biology
A more general form of the linear-quadratic equation also takes into
account the dose rate and time-dependent repair. It can be written including
the Lea-Catcheside dose protraction factor, G (26):

N
N
D
0
( ) exp . = − −
( )
α β D GD
2
(19.5)
The dose-response relationship is not simply related to killing a fraction of a
given number of cells. The linear-quadratic equation is only an approxima-
tion to a more general description using a number of sensitive sites in a cell
nucleus, which in contrast to the pure linear-quadratic formulation has an
exponential asymptote for high doses (27, 28). The linear-quadratic formal-
ism is typically only valid roughly in the dose region from ~1 to ~10 Gy
(depending on the end point), and when ftting α and β to a response curve,
one has to keep in mind that the result may depend on the dose range con-
sidered (29, 30).
Although the linear-quadratic function is the most common in radia-
tion therapy, dose–response curves can also be described with other math-
ematical equations, for example, the multitarget/single-hit equation with
the parameters D
0
(intrinsic radiosensitivity) and n. The parameter n is the
extrapolation number representing the ability to accumulate and repair sub-
lethal damage:

N
N
D
D
0 0
1 1 − − −

¸

1
]
1
¸
¸


_
,


exp .
n

(19.6)
When interpreted mechanistically, the multitarget formalism assumes that
from a collection of targets in the cell nucleus, n have to be hit at least k times
each to inactivate the cell (k is set equal to 1 in the equation above).
1
0.1
0.01
0.001
0 1 2
Dose (Gy)
N
/
N
0
3 4 5 6
FIGURE 19.3
Example of two dose-response curves. The solid line might resemble the response after photon
irradiation, and the long dashed line might be caused by low-energy proton irradiation. The
relative biological effectiveness (RBE) at 10% survival would be ~2.55/1.3 = 1.96, whereas at 1%
survival it would be ~4.15/2.4 = 1.73 (short dashed lines).
600 Proton Therapy Physics
19.4 TheRelativeBiologicalEffectiveness
Protons are more biologically effective than photons, that is, a lower dose is
required in order to cause the same biological effect. The relative biological
effectiveness (RBE) of protons is defned as the dose of a reference radiation,
D
x
, divided by the proton dose, D
p
, to achieve the same biological effect (see
Figure 19.3):

RBE
D
D
x
p
( int) . endpo =

(19.7)
The RBE adjusted dose is defned as the product of the physical dose and the
respective RBE. The prescribed dose to the target, dose constraints to critical
structures, and fractionation schemes are largely based on clinical experi-
ence gained mostly by treating patients with photon beams. For consistency
in the clinic and in order to beneft from the large pool of clinical results
obtained with photon beams, prescription doses are defned as photon doses.
Proton therapy patients receive a 10% lower prescribed dose than would be
prescribed using photons, thus assuming an RBE of 1.1. Before 2008 proton
doses were given in Cobalt Gray Equivalent (CGE), and then it was changed
to reporting D
RBE
as Gy(RBE) (31).
Because the RBE is defned for a given level of effect, one can easily deduce
the RBE for a given proton dose as a function of the proton, p, and reference, x,
radiation parameters from the linear-quadratic dose-response relationship:

RBE D
D D
p x x p p
x x p p p p x
, , , , α β α β
α β α β α
β
( )
=
+ +
( )
−
2
4
2
xx p
D
.

(19.8)
Note that for treatment-planning considerations not only the total dose but
also fractionation needs to be taken into account. Fractionation effects (32,
33) are beyond the scope of this chapter and are, by defnition, not included
in the RBE formalism.
19.5 RationalefortheClinicalUseof1.1asProtonRBE
Proton therapy is based on the use of a single RBE. The value of 1.1 is mainly
based on animal experiments performed in the early days of proton therapy
(34–37). There are obvious advantages of using a generic RBE. Converting pho-
ton doses into proton doses for clinical trials is straightforward. Furthermore,
clinical dosimetry is based on homogeneous dose distributions in the target.
601 The Physics of Proton Biology
On the other hand, a generic value disregards the dependencies of the RBE
on various physical and biological properties (e.g., proton beam energy,
depth of penetration, biological endpoint, dose per fraction, position in the
spread-out Bragg Peak [SOBP], and particular tissue). It is well-known that
the RBE is not a constant, but there are no clinical data indicating that the
use of a generic RBE of 1.1 is unreasonable (i.e., that it leads to unexpected
side effects). On the other hand, clinical data cannot confrm that the RBE of
1.1 is correct because not only the effect but also the dose distributions differ
between photon and proton irradiations.
As shown in Figure 19.4 for in vivo and in vitro data, measured proton RBE
values show signifcant variations of the RBE (38). The measured RBE values
using colony formation as the measure of cell survival in vitro indicate a
substantial spread between the diverse cell lines (38). The average value at
mid-SOBP over all dose levels is about 1.2, ranging from 0.9 to 2.1. The aver-
age RBE value at mid-SOBP in vivo is about 1.1, ranging from 0.7 to 1.6 (38).
The majority of RBE studies have been done with in vitro systems and V79
cells inhibiting a low α/β ratio, whereas most of the in vivo studies were
performed in early-reacting tissues with a high α/β ratio.
Importantly, the magnitude of RBE variation with physical or biological
parameters is usually small relative to our abilities to determine RBE values.
The required number of animals to measure a 5% RBE difference (1.10 vs.
1.15) for one endpoint can be several hundred (38).
To implement RBE variations in treatment planning, we need to under-
stand the relationships between LET, dose, and biological endpoint.
Systematic quantitative statements regarding therapeutic situations are still
diffcult because of the experimental uncertainties, the specifc experimen-
tal arrangements used, and the different biological endpoints chosen in the
experiments. At present, there seems to be too much uncertainty in the RBE
value for any human tissue, for example, to propose RBE values specifc for
tissue, dose/fraction, and proton energy.
2.5
2.0
R
B
E
1.5
1.0
0.5
2.5
2.0
R
B
E
1.5
1.0
0.5
1 10
Dose (Gy)
in vitro in vivo
1 10
Dose (Gy)
FIGURE 19.4
Experimental proton RBE values (relative to
60
Co) as a function of dose/fraction for cell inacti-
vation measured in vitro (left) and in vivo (right). (From Paganetti et al., Int J Radiat, Oncol, Biol
Phys., 53, 407, 2003. With permission.)
602 Proton Therapy Physics
19.6 VariationsofRBE
19.6.1 LET Dependency of RBE
The LET is the energy transferred to the absorbing medium per unit track
length of the particle. Note that the region of maximum energy transfer is not
occurring at the Bragg peak but downstream of the Bragg peak (Figure 19.5).
The reason for the Bragg peak is a combination of LET and decreasing proton
fuence. Biologically, the increase in LET can cause an increase in both the
amount of damage and its complexity. Both can infuence the ability of the
cellular system to repair itself, either because of the frequency or the severity
of damage.
When describing energy loss on a cellular level, the LET concept is only a
crude approximation because the track structure and micro- or even nano-
dosimetric effects play a role. The LET is a macroscopic rather than micro-
scopic parameter and deals with energy loss per unit path length rather than
energy loss in subcellular volumes. At a given LET protons are in fact more
effective than carbon ions (5, 25, 39). This is because protons have smaller
track radii (as defned by the range of δ-electrons), implying higher ioniza-
tion density in the submicrometer range, ultimately leading to more com-
plex and potentially clustered DSBs (40). Radiation is more effective per unit
dose when the energy deposition is more concentrated in space. Figure 19.6
shows how the dose is distributed in a cell. Because of the huge number of
tracks and ionization events to deliver 1 Gy of low LET photon irradiation,
the distribution is basically homogeneous. For a given particle (e.g., a proton)
it becomes more and more heterogeneous as the energy deposition per path
length increases.
16
L
E
T

[
k
e
V
/
µ
m
]
14
12
10
8
6
4
2
0
0 50
Depth [mm]
100 150 200
100%
D
o
s
e

[
a
r
b
i
t
r
a
r
y

u
n
i
t
s
]
FIGURE 19.5
Dose (dotted line; right axis scale) and dose-averaged LET (left axis scale) as a function of
depth in a water phantom for a 160-MeV beam. The dashed line shows the total dose-averaged
LET (primary and secondary particles), and the solid line shows the dose-averaged LET for the
primary protons only.
603 The Physics of Proton Biology
Considering one particle type only, the RBE increases with increasing LET
up to a certain maximum (3). If the LET is further increased, far fewer tracks
are required to deposit the same dose. This leads to saturation of the effect in
small regions and eventually to a decrease of RBE with increasing LET. For
protons, the maximum RBE occurs at extremely low proton energies where
the contribution to the dose in a clinical scenario is negligible. Thus, we can
safely assume that RBE increases with LET, with the slope depending on
the biological endpoint. Low-energy protons can have high RBE values (24,
41–50). RBE values for cell survival for near-mono-energetic proton beams of
<8.7 MeV are presented in Figure 19.7. These low-energy protons contribute
100
80
60
F
r
a
c
t
i
o
n

o
f

n
u
c
l
e
u
s

[
%
]
40
20
0
0.1 1 10
Maximum dose [Gy]
100
FIGURE 19.6
Dose distribution within a cell after photon and proton irradiation. The graph shows the inte-
gral dose distribution for 5-MeV protons at a macroscopic dose of 3 Gy (solid line), 5 Gy (long-
dashed line), and 7 Gy (short-dashed line). Also shown are the limits for infnitesimal low-LET
for 3, 5, and 7 Gy (dashed-dotted). (From Paganetti, Med Phys., 32, 2548, 2005. With permission.)
5
4
R
B
E
3
2
1
1 10
Proton energy [MeV]
FIGURE 19.7
Experimental RBE values (relative to
60
Co; various dose levels) as a function of proton energy
for cell inactivation measured in vitro for near mono-energetic protons. Open circles refer to
human tumor cell lines at 2 Gy. (From Paganetti et al., Int J Radiat, Oncol, Biol Phys., 53, 407,
2003. With permission.)
604 Proton Therapy Physics
typically less than ≈1% to the total dose within an SOBP but illustrate the
LET dependency nicely.
Because of protons slowing down, the LET increases, resulting in an
increasing RBE with depth in an SOBP (23, 51–64). The results of a study
using a 70-MeV 2.5-cm SOBP beam with a high-precision cell sorter assay
system are shown in Figure 19.8 (64). The RBE clearly increases with increas-
ing depth. One might expect, on average, an increase in RBE of ≈5% at 4 mm
and ≈10% at 2 mm from the distal edge, relative to the mid-SOBP RBE (38).
Although diffcult to measure in vivo, an increase of RBE with depth has
been seen using mouse thorax and gut.
The increase in LET at the end of range (i.e., at the Bragg peak and beyond)
is more pronounced in pristine Bragg curves than in SOBPs because of the
contribution of several pristine peaks and the mix of proton energies (63, 65).
1.6
a
80% Survival
50% Survival
3% Survival
Dose-
averaged
LET
Spread-out
Bragg peak
Calculated
Bragg peak
Measured
Bragg peak
b
c
1.4
1.2
1.0
8
6
4
2
0
1.0
0.8
0.6
0.4
0.2
0.0
0 5 10 15 20
Depth (mm of H
2
O)
R
e
l
a
t
i
v
e

d
o
s
e
L
E
T

(
k
e
V
/
µ
m
)
R
B
E
25 30 35 40 45
FIGURE 19.8
(a) Proton RBE for different cell survival levels of V79 Chinese hamster cells measured in
an SOBP. (b) Dose-averaged LET as a function of depth in the SOBP. (c) Depth–dose distri-
bution at position of cell samples ( ). (From Wouters et  al., Radiat Res., 146, 159, 1996. With
permission.)
605 The Physics of Proton Biology
Furthermore, there can be additional dilution in the patient because of fre-
quent interfaces between different materials in the beam path and signif-
cant scatter in the bone. At the trailing edge of the distal most Bragg peak of
the SOBP, the dose falls very rapidly with increasing depth. The rise in LET
and RBE results in an extension of the biologically effective range by 1-2 mm
(23, 51, 57–59, 61, 64, 66). Although there is a greater absolute RBE effect for
lower-energy beams, this shift is smaller because of the sharper falloff (58).
The clinical consequence of the increasing RBE and the uncertainty of the
distal edge position of the Bragg peak is the avoidance of beams that place
the distal edge close to critical structures.
LET distributions in a patient geometry can be calculated with analyti-
cal methods (67), using interpolations based on Monte Carlo calculations in
homogeneous media (68) or using Monte Carlo simulations in a patient CT
geometry (see Chapter 9) (69). For the dose-averaged LET (LET
d
), the LET is
averaged in such a way that the contribution of each particle is weighted
by the dose it deposits. This concept is valid for proton beams where the
number of particle tracks crossing a subcellular structure is quite large (70).
However, one should keep in mind that, for high-LET ion beams, the number
of tracks per subcellular target may be much smaller and the track aver-
aged LET might become more meaningful. This illustrates the limitations of
the LET concept when, at low fuence, the track structure becomes increas-
ingly important (71). Figure 19.5 shows distributions of dose and LET
d
in
a water tank, whereas Figure 19.9 illustrates the distributions in a patient.
LET
d
values in patient geometries can be more than 10 keV/μm in the distal
falloff, but only between 1.5 and 4 keV/μm in the target, using typical beam
arrangements (69).
6
100%
5
4
3
2
1
FIGURE 19.9
(See color insert.) Dose distribution and distribution of dose-averaged LET (LET
d
) for an
intensity-modulated proton therapy (IMPT) treatment plan. The contour for the GTV is shown
in blue. Right: dose in percent of prescribed dose. Left: LET
d
distribution in keV/μm. The LET
distribution is a potential measure of biological effectiveness. See (69) for more details.
606 Proton Therapy Physics
19.6.2 Dose Dependency of RBE
Because of the more pronounced shoulder in the x-ray survival curve com-
pared to the proton survival curve (Figure 19.3), the RBE depends on dose;
for example, the RBE is higher at a cell survival level of 80% than at 3%
(64). Both in vitro and in vivo data indicate a statistically signifcant increase
in RBE for lower doses per fraction (38). Specifcally, there is experimental
evidence that RBE increases with decreasing dose for cell survival (51, 52,
62, 64, 72) and for induction of dicentrics (73). The RBE increases more rap-
idly with decreasing dose for late-responding tissues (low α/β) compared
to early-responding tissues (high α/β) (74). No dose dependency is seen for
cells that inhibit a linear dose-response curve. Figure 19.10 shows the RBE as
a function of dose for the inactivation V79 cells in vitro. Most experimental
RBE studies in vivo have used large doses for which an RBE effect may be
expected to be minimal.
19.6.3 Endpoint Dependency of RBE
The RBE is defned for a given level of effect. There is a difference between
the radiation response of normal and malignant cells due to differences
in repair mechanisms and cell repopulation. Furthermore, there is greater
resistance to radiation in regions of low oxygen that are often found in
tumors, hindering the creation of free radicals (Figure 19.1). At the same
time, there is an increased repair capacity in the presence of oxygen because
the damage from free radicals can be fxed in the presence of oxygen. The
latter plays a role in high-LET radiation therapy with an increased likeli-
hood of direct actions infuencing the oxygen-enhancement ratio (75). Many
different endpoints can be scored based on radiation damage, for example,
2.0
1.8
1.6
1.4
1.2
1.0
0 2 4 6 8 10 12
Proton dose [Gy]
Total
Proximal
Distal
Distal edge
R
B
E
FIGURE 19.10
Proton RBE as a function of dose for cell survival levels of V79 Chinese hamster cells mea-
sured at different positions in an SOBP. (From Wouters et al., Radiat Res., 146, 159, 1996. With
permission.)
607 The Physics of Proton Biology
inactivation (cell survival) and chromosomal aberrations or mutations. For
assessing the biological effectiveness in the target, one is mainly interested
in the RBE for cell death. Other effects are also important, in particular
when considering organs at risk that might not receive suffcient dose to
cause signifcant cell inactivation. RBE values for cell death and mutation
have been compared, and most studies fnd that the RBE values are com-
parable. For example, the RBE for mutation at the HGPRT locus at various
proton energies was found to be approximately equal compared to cell kill-
ing the LET for protons at the maximum mutation induction in the range of
25–30 keV/µm (76, 77).
The dependency of the RBE on the α/β ratio has been studied using exper-
imental data (74) and theoretical models (29). RBE for late damage seems
to be higher than for early damage (78). Figure 19.11 shows theoretical RBE
values plotted as a function of the tissues’ α/β. A strong tendency toward
an increased RBE in cells exhibiting smaller α/β ratios is apparent at the
lower dose levels. Thus, the biggest variation in RBE can be expected in late-
responding normal tissues. This in turn predicts an advantage of proton
therapy when treating, for example, prostate carcinoma (79), but it might also
increase the risk for side effects for other treatment sites if the spinal cord,
another tissue with a low α/β ratio, has to be partially irradiated to achieve
suffcient tumor coverage.
Differences seen between in vivo and in vitro (Figure 19.4) are most likely
due to the different endpoints used in the experiments (i.e., the larger shoul-
der seen in the survival curves for the endpoints used in vitro). In vitro
studies have predominantly used Chinese hamster ovary and especially
V79 cells, which exhibit large shoulders on their x-ray response curve and
low α/β ratios. Most in vitro experiments use as their endpoint the killing
of single cells of one cell population (colony formation). On the other hand,
most in vivo RBE studies have used early-reacting tissues having a high
2.4
2.2
2.0
1.8
1.6
1.4
R
B
E
1.2
1.0
0 2 4
α/β [Gy]
6 8 10 12 14
FIGURE 19.11
Calculated RBE values as a function of α/β for 2 Gy ( ) and 6 Gy ( ). RBE values were deter-
mined in the middle of the SOBP or averaged over the entire SOBP. (From Paganetti et al., Int J
Radiat Biol., 76, 985, 2000. With permission.)
608 Proton Therapy Physics
α/β ratio. The in vivo response refects the more complex expression of the
integrated radiation damage to several tissue systems and various biologi-
cal processes (e.g., mutation). Figure 19.7 shows the RBE measured in vitro
for low-energy protons on human tumor cell and V79 Chinese hamster cell
data. In the studies with low-energy beams, the data on human cells (41, 46)
are signifcantly lower than the RBE values determined for hamster cells (24,
42, 48, 49, 80, 81).
19.7 ModelingCellularRadiationEffects
The frequencies of energy deposition by protons in small subcellular tar-
gets have been studied extensively (82–86), for example, using Monte Carlo
(see Chapter 9). Subsequently, there are chemical processes, biochemical
processes, and fnally, a macroscopic cellular response leading to a molec-
ular response. Of particular interest is the impact of radiation damage on
the DNA macromolecule and subsequent cellular response. At the DNA
level, the energy deposition events are extremely nonuniform, depending
on the properties of the incident ionizing particles. Even a complete under-
standing of the energy deposition events may give only limited insight
into the biological consequences because of the different types of direct
and indirect reactions that can lead to radiation-induced effects and the
complicated repair phenomena. Most experimental data only give a mac-
roscopic view.
Biophysical models relate the biological effect of ionizing radiation to the
physical properties of the incident radiation feld. Modeling radiation action
mechanistically is diffcult because the radiation feld can be complex with
primary and secondary particles and because the biological target (i.e., the
cell nucleus containing the DNA molecule) is highly structured. Mechanistic
approaches to DNA damage and early chemistry have made much progress
in describing the initial events produced by radiation (87), but no truly mech-
anistic model exists for describing biological endpoints such as cell killing
(88). Most models are in fact mechanistic when considering the underlying
physics but take a phenomenological approach toward the biology. Some
of the model assumptions, in particular the ones on hypothetical cellular
subtargets, are rather unrealistic. Furthermore, the defnitions of lesions or
sublesions are often a mathematical necessity rather than a description of
true biological phenomena. The knowledge about subcellular physics cer-
tainly exceeds the knowledge about subcellular or molecular biological
mechanisms.
Biological model parameters are typically obtained from cell survival
experiments because models are typically based on the description of the
shoulder in the dose-response curve caused by the interaction of sublesions
609 The Physics of Proton Biology
and/or by repair kinetics (89, 90). Some assume a nonlinear increase of lesions
or certain kinds of repair saturation where the shape of the survival curve is
determined by a dose-dependent rate of repair. The following section gives a
brief, but not comprehensive, overview of some of the models.
19.8 BiophysicalModelsofRadiationActiononCells
19.8.1 LET-Based Models
The LET is a macroscopic parameter and does not take into account the track
structure. Nevertheless, LET-based models, although entirely phenomeno-
logical, can be a valuable approximation because they can be based on only
a few parameters. To calculate dose-averaged LET distributions, analytical
functions (67) or Monte Carlo calculations (69) can be used.
The biological part is described by the linear quadratic dose-response
curve. Unfortunately, not many α and β values for relevant tissues in vivo are
known. Most experimental data in vitro are based on V79 (low α/β ratio, i.e.,
~2 Gy) and SQ20B and C3H10T1/2 cells (high α/β ratio, i.e., ~10 Gy). One solu-
tion is to use a linear relationship between LET and the α value, for example,
of the following form:

α α λ
0
= + LET
d
.

(19.9)
One might assume that β is independent of LET (63, 91–93), which is moti-
vated by experimental data (22, 23, 25). By knowing α and β from photon
data and as a function of LET, one can thus predict the cell survival curve
and the RBE. For mixed radiation felds (e.g., for broad proton energy distri-
bution) dose-averaged means of α and √β have to be applied.
A related phenomenological approach is to combine measured RBE values
from various low-energy proton beams with the proton energy distribution
as a function of location in the irradiated volume (94).
19.8.2 Microdosimetric Models
In the framework of microdosimetry a radiation feld is characterized by
energy deposition in a small subcellular volume, that is, by the energy
imparted, z. Dose is related to the probability density function of z in a
set of cellular targets. Another important parameter is the frequency dis-
tribution of the energy deposited, y. It is the energy deposited in a volume
divided by the mean chord length and is related to the macroscopic quan-
tity of LET. Note that LET is defned for a track segment, whereas the lineal
energy y considers energy deposition in a volume. The microdosimetric
610 Proton Therapy Physics
quantities, energy imparted and lineal energy, are both measureable in
small proportional counters with low-density gas mimicking micrometer
volumes (see Chapter 7).
Microdosimetric models are purely phenomenological. The biological
effect is described by experimentally determined response functions (56, 72,
95–97). A response function describes a cumulative probability that a sub-
cellular target structure will respond to a specifc target-averaged ionization
density (96). A microdosimetry spectrum (e.g., the measured dose distribu-
tion in lineal energy d(y)) can be convolved with a biological response func-
tion r(y) to obtain biological effectiveness as a function of y (59, 96–99):

RBE y r y d y dy ( ) ( ) ( ) . =
∫

(19.10)
The response functions can be obtained experimentally by measuring bio-
logical effect as a function of y. The concept fnds application in radiation
protection (100).
The initial formalism of the model was valid only for single-event distribu-
tions, that is, interactions of a single particle track with the sample volume.
This limits the concept to low doses and low dose rates. The formalism can
also be extended to include multiple events.
Although phenomenological, the model is convenient because both the
biological part (i.e., dose-response curves) and the physical part (i.e., micro-
dosimetric energy loss spectra) are measurable (53, 56, 72, 101). This, for
example, makes the model suitable for intercomparison studies of relative
effect between proton therapy installations (53, 59, 99).
19.8.3 Lesion Interaction Models
Lesion interaction models, for example, the dual radiation action model
(DRA) (102), represent a step further toward mechanistic description of
radiation action. The assumption is that nonlethal sublesions are produced
proportional to the energy absorbed in a radiosensitive volume, z. Lesion pro-
duction is then proportional to z
2
. This theory is linked to microdosimetry
because the radiosensitive volume can be associated with a microdosimetric
volume and the energy imparted in it, z
1D
(i.e., the dose-mean specifc energy
for a single event). The model results in linear-quadratic dose-response rela-
tionships of the following form (with a constant k):

N
N
k z D D
D
0
1
2
= − +




( )
exp .

(19.11)
Initially, the model assumed that a pair of sublesions could interact with
constant probability if within a distance of ~0.4 μm. This lead to RBE val-
ues exceeding those seen experimentally specifcally at low doses and for
611 The Physics of Proton Biology
high-LET radiation. Furthermore, lesions were seen experimentally that
could not be related to long-range sublesion interactions. Consequently, the
model was refned by introducing a sublesion interaction probability that
depends on the distance between sublesions (103, 104). Thus, the gener-
alized DRA uses a distance model, whereas the original approach was a
site model.
A shortcoming of the concept is the fact that the interaction of two suble-
sions is extremely unlikely at typical dose levels because of the low prob-
ability of two independent particle tracks causing a single-strand break in
close enough proximity to form a DSB. It is more likely that a single track
causes clustered damage. For high-LET values, the probability of multiple
ionizations or excitation in close proximity is increased (105). For protons
below 10 MeV, there is a high probability of fnding two δ-electrons causing
independent lesions close to each other. In contrast, for high-energy protons
(160 MeV; low LET), the probability of fnding two energy deposition events
within 2 nm is almost zero.
Related to the theory of DRA is the stochastic track structure–dependent
approach (106, 107). It also contains a proximity concept where the probabil-
ity of misrepair increases with decreasing distance of sublesions.
19.8.4 Lesion Induction and Repair Models
The lethal-potentially lethal (LPL) model (108) is based on lesions that are
either repairable or nonrepairable. Nonrepairable lesions are responsible for
the linear part of the dose-response curve, whereas repairable lesions include
repair and binary misrepair. Different effects are caused by the amount of
energy deposited locally. Lesions that cannot be repaired (lethal lesions) are
formed proportional to dose and a parameter η
L
. Repairable, or potentially
lethal, lesions are formed proportional to dose and a parameter η
PL
. These
lesions are categorized into two groups: a slow- and a fast-repairing com-
ponent. The slowly repairing lesions (repair rate ε
PL
) can either turn lethal
(fxed) or interact with another potentially lethal lesions to form a lethal
lesion (rate 2ε
2PL
; binary misrepair). The resulting dose-response curve for
cell survival becomes

N
N
D
D
t
L PL
PL
PL PL
PL
0
1 1 − + [ ] ( )
+ − − exp exp η η ×
η
ε ε
ε
2
rr
PL PL
{ ¦
¸
1
]
¸
¸

_
,

ε ε
2
.

(19.12)
The time t
r
is the time after irradiation and it determines the repair rate. The
model converges to the linear-quadratic formulation at low doses. Note that,
unlike in the DRA model, individual lesions can be lethal without the need
of sublesion interaction. This is accomplished by fxation.
Related to the LPL model is the repair-misrepair (RMR) model, which
assumes that there are linear repair processes and quadratic misrepair
612 Proton Therapy Physics
processes (109, 110). Further, the saturable repair model assumes that repair
becomes saturated with increasing dose (111). This can be either because the
complexity or number of lesions increases or because the supply of repair
enzymes is limited. The saturable repair approach assumes that repair
capability depends on the total number of lesions, the time for repair, and
the availability of repair enzymes. This is different from other approaches
including repair (e.g., the LPL model) where repair capability solely depends
on the damage concentration. Saturable repair models do explain the curva-
ture of survival curves without the need for multitrack action. The increasing
RBE with LET is due to more effcient production of less repairable lesions.
The fnal slope of the survival curve is a measure of the number of critical
lesions produced before repair.
Another ansatz is the two-lesion kinetic model, which provides a direct
link between the biochemical processing of DSBs and cell survival (112). All
DSBs are subdivided into simple and complex DSBs, each with a unique
repair characteristic. It can be transformed into linear-quadratic formalism
for therapeutic doses and dose rates (113).
The microdosimetric-kinetic model (MKM) (114–118) uses principles of the
DRA, the LPL model, and the RMR model. It also uses microdosimetric con-
cepts via the dose mean lineal energy, y
D
. It is assumed that the sensitivity of
cells to low-LET radiation is largely determined by their vulnerability to the
formation of lethal unrepairable lesions from single potentially lethal lesions
(PLL) but not due to forming them from pairwise combination of two PLL.
As in other models, differences in radiation action are due to differences
in the energy deposition characteristics. MKM predicts the β value in the
linear-quadratic equation to be independent of LET and results in RBE val-
ues to increase with decreasing α/β. The cell nucleus is divided into subvol-
umes, called domains, and each particle track deposits dose in one or several
domains. A domain can be thought of as a sphere of unit density. The size
of a domain is a unique property of a cell type, and the DNA content may
vary from domain to domain. The dose absorbed in a domain is z, the energy
imparted. The specifc energy of a domain is the sum of the contributions
from each track. The MKM model assumes a linear-quadratic dose-response
relationship in each domain with two types of lesions: lethal (proportional
to z) and repairable. The diameter of a domain is inversely related to the rate
of repair of a PLL. The maximum travel distance of a PLL is limited by the
domain, that is, there is a restriction in the distance of PLL interactions (note
the relation to DRA). The domains are just a mathematical concept to defne
the proximity of two lesions in order to have a chance of connecting. A PLL
may be repaired, or it may combine with another PLL in the same domain
to form an unrepairable lesion. In addition, the PLL may turn into a lethal,
unrepairable lesion.
The MKM model, as it is based on subcellular domains, deals with y
D

instead of LET, and it assumes a direct relationship between a dose-weighted
z, the energy imparted, and cell survival.
613 The Physics of Proton Biology
Let D
d
be the absorbed dose in one of the p domains within the nucleus.
Then, the average number of lethal lesions, per domain is given as

N D D
d d
= + α β
0
2
.

(19.13)
A parameter α can be defned as

α = α β
∗
0 1
+ z
D
.

(19.14)
The number of lethal lesions depends on the average number of lethal lesions
that form per cell per Gray from conversion of a single PLL and on the aver-
age number of lethal lesions created per cell per Gray from combination of
pairs of PLL created from passage of a single charged particle through or
near the nucleus. Here, z
1d
*
is the saturation-corrected dose-mean specifc
energy of a domain. The actual model parameters are thus α
0
and the radius
of the domain (e.g., ~0.3 μm).
Another approach combining some of the RMR and LPL concepts is the
repair-misrepair-fxation (RMF) model (119). It is a kinetic reaction-rate
model and relates DSB induction and processing to cell death. It links radio-
sensitivity parameters in the linear-quadratic equation to DSB induction
and repair and explicitly accounts for unrejoinable DSB, misrepaired DSB,
and exchanges formed through intra- and intertrack DSB interactions. The
linear-quadratic parameters are parameterized as follows:

α Σ θ Σ η λ γ θ)( Σ)
β = (η/ [2λ])
2
= − + + − ( ) ( / )( 1 f f z f
R R
F
R
((γ − θ)( Σ)
2
f
R
.

(19.15)
Here f
R
denotes the fraction of potentially rejoinable DSBs, λ the rate of DSB
repair, η the rate of binary misrepair, Σ the expected number of DSBs per
Gray per cell, θ the probability of a DSB lethally misrepaired/fxed, and γ the
probability of a lethal exchange-type aberration. The three terms adding to α
stand for the unrejoinable and lethal damage, the lethal misrepair and fxa-
tion, and the intratrack DSB interaction, respectively. The β term describes
intertrack DSB interaction. Note the microdosimetric parameter z
F
, the fre-
quency-mean specifc energy per radiation event and that z
F
× f
R
× Σ gives the
DSBs per track per cell.
19.8.5 Track Structure Models
Track structure models are based on the physical details of a particle track,
including its secondary particles. Because the main goal is to calculate rela-
tive biological effects (i.e., RBE values), biological phenomena are treated in
a purely phenomenological way, as relative effects. Track structure theory
ignores the actual mechanisms of energy deposition and repair mechanisms,
614 Proton Therapy Physics
for example, whether the curvature of the response curve has its origin in
the interaction of sublesions or if it is due to some mechanism like dose-
dependent repair processes. The key assumption is that the difference in
biological effciency, when comparing photons with protons, is caused by dif-
ferent microscopic dose deposition patterns (i.e., track structure). Radiation
is more effective per unit dose when the energy deposition is more concen-
trated in space.
Track structure theory (120–123) assumes a simplifed biological target and
a simplifed particle track. The target is assumed to be an infnitely thin disc
to ensure that there is no LET variation within the target (track segment con-
dition). A proton track is characterized by its radial dose distribution origi-
nating from δ-electrons emitted in ionization events. The track’s δ-electron
halo (i.e., the dose as a function of distance to the track center) is approxi-
mated by a smooth radial distribution. One can think of each particle track
as an amorphous track with a certain diameter (124). Various models and
parameterizations were published to calculate this radial deposited energy
(120, 125–128). Generally, the dose deposited as a function of the distance, r,
to the ion path can be written as a function of 1/r
2
up to a limit determined
by the maximal radial penetration of δ-rays. Track structure theory involves
some simplifcation. The track volume for protons is mostly empty with only
a few δ-ray events on the scale of the cell nucleus size. The stochastic nature
of particle-induced events is not taken into account when applying a contin-
uous radial dose distribution defning the track shape. The higher the mean
free path of the ion, the more important will be statistical fuctuations such
as the stochastic δ-ray emission (129–131).
For equal absorbed dose, the microscopic response due to δ-electrons from
protons is assumed to be identical to that due to δ-electrons from photons.
Based on this assumption, the knowledge of both the response of a medium
to photons and the spatial distribution of the dose yield the spatial distribu-
tion of response around the path of a particle. The effciencies of different
types of radiation result solely from different dose deposition patterns.
In the initial track structure model approach, the biological effect is cal-
culated from the overlap of the track with the target, considering local
energy depositions in subtargets (120–123). The subtarget concept is similar
to the MKM model. The saturation value of the action cross section of the
cell nucleus, σ
0
, is not necessarily equal to the geometrical size of the target.
A set of cellular subtargets have to be activated or inactivated in order to
achieve a given effect. The sensitive target radius, a
0
, is characterized by a
dimensionless variable κ. The radius of the subtargets is calculated using
D
0
(intrinsic radiosensitivity in the multitarget/single-hit formalism) and κ.
Each biological endpoint is characterized by a set of four radiosensitivity
parameters: n, D
0
, σ
0
, and κ (132). The parameters can be obtained by a ft on
a set of response curves for the considered endpoint measured in different
radiation felds (122, 133, 134). Photon dose-response curve data are needed
to obtain the parameters n and D
0
.
615 The Physics of Proton Biology
Two modes of interaction are considered: single-track action (called ion-
kill) and multitrack action (called γ-kill). Differences in biological effect
between two radiation modalities are due to different probabilities for these
two reaction channels. Ion-kill is described by the single-hit/single-target
relationship for cell response. Thus, in the case of cell inactivation, it is pos-
sible to inactivate a biological target by a single particle track. It usually dom-
inates at low fuence and high-LET. The initial slope of the dose-response
curve is attributed to the ion-kill mode because, at low doses, particles are
so far apart that it is unlikely that their δ-rays overlap in the nucleus. If the
cell is not inactivated in this mode, the remaining dose can still lead to an
inactivation due to the overlapping of several particle tracks. The γ-kill is
defned by a multitarget/single-hit equation where a set of subtargets has to
be inactivated. The term γ-kill underlines the analogy to photon inactivation.
The γ-kill mode is responsible for the shouldered response curve. Because
there is usually a mixture of the ion-kill and γ-kill components, the cell inac-
tivation is a product of single-target/single-hit and multitarget/single-hit
components (120, 135).
Protons, due to their generally low LET, are usually limited to ion-kill
probabilities much lower than 1 (136). With increasing LET, the action mode
passes from predominantly γ-kill to predominantly ion-kill. When the LET
is further increased, the action cross section increases over σ
0
, and the so-
called track-width region is reached. The radiation action is now due to long-
range δ-rays, which pass the target although the ion does not. The dose is
now deposited almost completely by ion-kill. The central part of the track
has saturated the biological effect, and the width of the track determines
the probability of biological effects. At high LET the action cross section
decreases due to a decreasing track radius from low-energy δ-rays (137).
Within this concept, one integrates the dose deposited in the subtarget
over the radial dose distribution. Next, the effect produced by this average
dose is calculated, and the effects are integrated over impact parameters. A
dose-response relationship can be written as

N
N
D
dE
dx
D
D
0 0
1 1 1 −
¸
¸

_
,

− − − −
¹
,
¹
¹
¹
exp exp σ ×
σ
σ
0
¹¹
,
¹
¹
¹

¸


1
]
1
1
¸
¸


_
,


n
.

(19.16)
To calculate the response to a mixed radiation feld, a calculation for each
energy and particle type must be done (122, 138–140).
It has been demonstrated that for n = 2, as well as in the case of low dose
and low-LET, the LPL model and the track structure model converge and can
be converted into a linear-quadratic formula (138).
The track structure approach was implemented in a different fashion in
the form of the local effect model (LEM) (141, 142). Compared to the origi-
nal track structure model, the unrealistic concept of subtargets was initially
dropped. The whole cell nucleus is assumed to be the critical target for which
616 Proton Therapy Physics
local effects are averaged, rather than averaging local doses in subtargets.
The biological target, that is, the cell nucleus, is assumed to be a thin disc
covering an area A
nucl
. Each track is described as the path of the primary ion
and its associated δ-rays.
If the dose is not averaged over subvolumes, the 1/r
2
-dependent radial
dose distribution shows infnite values for the local dose at r = 0. Because in
this model approach local effects have to be determined, a cutoff for small
radii must be introduced and a normalization constant adjusted, so that an
integral overall track radii will yield the unrestricted LET.
A linear-quadratic dose response is assumed. However, it is a poor
approximation for high doses as encountered locally in a subcellular tar-
get. Consequently, a modifed formulation of the linear-quadratic equation
is used to parameterize the photon dose-response curve where a parameter
D
t
denotes the transition point from the shouldered low-dose region to an
exponential tail for high doses, thus ensuring that there is an exponential
asymptote at high doses.
The biological input parameters are the geometrical cross section (i.e.,
the size of the cell nucleus) and the photon dose-response curve with the
parameters α, β, and D
t
. The diameter of the cell nucleus can be determined
microscopically. The parameter D
t
is diffcult to measure because values in
the range of several hundreds or thousands of Gray can occur. Therefore,
the transition point between the linear-quadratic and the exponential shape,
D
t
, must often be an estimated endpoint dependent on the predicted ion
response curves.
Because there are no subtargets, the response of the biological target is
determined by the responses due to local dose deposition events (i.e., point-
like targets). The concept of track structure is that, for a proton radiation feld,
one can derive the mean number of lethal events by integrating the survival
over the cell nucleus volume assuming local photon dose response. Based
on a photon survival parameterization, the mean number of lethal events
produced per cell can be calculated and the effect be determined based on
Poisson distribution of the mean.
Several tracks can contribute to the local dose at a specifc position inside
the nucleus so that the effect is based on the total deposited dose. The super-
position of dose from different tracks leads to an enhanced effciency for the
production of lethal events. The average number of lethal events does not
increase linearly with the particle fuence, and this leads to a shouldered
response curve. The relative enhancement is highest when small doses are
superimposed, so it is mostly the outer parts of the track that contribute to
the shoulder. Shouldered dose-response curves after charged particle irra-
diation can only be expected if the track diameters and particle fuences are
suffciently large that they obtain a signifcant fraction of energy deposition
by superposition of local doses from several tracks.
Dose-response curves can be determined by Monte Carlo simulation of
the stochastic process of irradiation. For cell inactivation, the total number
617 The Physics of Proton Biology
of lethal events is determined, and the survival probability is calculated
according to

N
N
Y A D r r t A
nucl
local
j j j nucl
j
0
−
( )

exp , ( ), ( , , Φ
00
hits
∑
¸
¸

_
,


¸


1
]
1
1
.

(19.17)
The average number of lethal events, Y, is a function of the number of lethal
particle hits, the nuclear area and the local dose caused by the radial dose
distribution, D
local
(Φ describes the overlap between particle track and cell
nucleus). Every simulated track deposits a certain local dose in a small, ide-
ally infnitesimal, voxel, and the considered number of tracks depends on
the macroscopic dose to be delivered to the cell nucleus.
The two track structure approaches described above have been compared
(71), as have the LEM and the MKM model (143). There are quite a few com-
monalities. By introducing subvolumes to the LEM (via MKM) a high dose
cutoff in the track center can be avoided. In the MKM, the cell survival
curve for photons determines the local dose response in a subvolume, and
the summation of the effect in all subvolumes determines the cell survival
probability.
The LEM has been modifed several times to improve the agreement
with experimental data (144, 145). For example, one modifcation takes into
account cluster effects at high local doses leading to greater damage at the
track center (144). Additionally, the radial dose distribution can be modifed
to take into account the radical diffusion length in mammalian cells. The
most recent version includes a more mechanistic description of the spatial
distribution of DSBs (146).
Because a full model calculation can be time consuming, specifcally in a
clinical setting, approximations to the model have been introduced (141, 142,
147, 148).
Acknowledgments
The author thanks Dr. Leo Gerweck, Dr. Alejandro Carabe Fernandez, and
Jocelyn Woods for proofreading.
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627
20
Fully Exploiting the Benefts of Protons:
Using Risk Models for Normal Tissue
Complications in Treatment Optimization
PetervanLuijkandMarcoSchippers
20.1 Introduction
For many cancers radiotherapy is a common and effective treatment aiming
at sterilizing tumor cells using radiation. At present, roughly 45–50% of all
patients receive radiotherapy at some stage of their treatment. For most cancers,
CONTENTS
20.1 Introduction ................................................................................................ 627
20.2 Radiotherapy: Patient Characterization for Individualized
Tailoring of Treatment Technology ......................................................... 628
20.3 The Development of Radiation-Induced Normal Tissue Damage ..... 631
20.4 Methodology of Model Development ..................................................... 632
20.4.1 Choice of Endpoint ........................................................................ 632
20.4.2 Data Gathering ............................................................................... 634
20.4.3 Fitting a Model to Binary Data .................................................... 634
20.4.4 Testing Model Validity .................................................................. 635
20.4.5 Cross-Validation ............................................................................. 638
20.5 Available Models for the Risk of Normal Tissue Damage ................... 639
20.5.1 The Sigmoid Curve: The Shape of the Population
Distribution of the Tolerance ........................................................ 639
20.5.2 Logistic Regression Analysis: Identifying Predictive Factors ...... 640
20.5.3 Lyman-Kutcher-Burman (LKB) Model ....................................... 641
20.5.4 Functional Subunit-Based Models .............................................. 643
20.5.5 Including Clinical and Patient Characteristics: Logistic
Regression Models ......................................................................... 645
20.6 Developments and Future Directions ..................................................... 646
20.7 Applicability to Proton Therapy .............................................................. 649
Acknowledgments .............................................................................................. 650
References ............................................................................................................. 650
628 Proton Therapy Physics
however, normal tissues are inevitably coirradiated. This often leads to toxicity
and a reduction of the quality of life (QoL) of the patient. For some tumors, such
as lung cancer, the dose that can be administered safely to the tumor and con-
sequently the effcacy of the treatment are limited by the risk of severe toxicity.
Because the risk of toxicity depends on radiation dose and the amount of
irradiated normal tissue, technological developments such as proton therapy
are aimed at minimizing the dose and amount of normal tissue that is coir-
radiated. Protons indisputably have a superior physical dose distribution
compared to classically used photons, because they lose most of their energy
in a small region called the Bragg peak that can be positioned in the target
volume (see Chapter 2 for details on the depth–dose distribution of protons).
Optimal use of proton therapy, however, requires the (1) selection of patient
populations for which use of protons may offer advantages, (2) comparison
to alternative treatment techniques, and (3) individualized optimization
of the selected technique (e.g., using optimization techniques described in
Chapter 15). Each of these optimizations requires the ability to quantify the
quality of a treatment (plan) by a fgure-of-merit related to tumor control
and normal tissue toxicity. Therefore an important prerequisite of optimized
use of proton therapy is the availability of accurate models for the relation
between the dose distribution and the risk of complications.
In all current evaluation methods the physical quantity “dose” plays
a major role. This is partly due to the fact that this quantity can be calcu-
lated, adjusted, measured, and compared with great accuracy. However, one
should keep in mind that it is the biological or clinical effect (tumor control
or the occurrence of a complication) that determines the treatment outcome,
and not the dose; “dose” is only a surrogate for what is clinically important
(1). In this chapter we will describe the attempts that are currently being
made to determine the relationship(s) between dose and toxicity.
Because relatively little data are available on complications occurring after
proton therapy, at present this relation can only be estimated from data obtained
after treatment with photons. However, the shapes of dose distributions that
can be achieved using protons differ considerably from those obtained using
photon-based techniques (see also Chapters 10 and 11). As such, extrapolating
photon-based experience to proton therapy by using normal tissue complication
probability (NTCP) models ftted to photon data is not trivial. In this chapter an
overview of various aspects of development and use of risk models for the pre-
diction of responses to proton therapy as well as their limitations will be given.
20.2 Radiotherapy:PatientCharacterizationfor
IndividualizedTailoringofTreatmentTechnology
Different types and stages of tumor are treated using different treatment
modalities such as fractionated photon therapy using a linear accelerator
629 Fully Exploiting the Benefts of Protons
(linac), single fraction stereotactic radiotherapy, proton therapy, or brachy-
therapy using implanted radiation sources, all with the aim to maximize the
probability of curing the patient while limiting toxicity to normal tissues.
The choice of treatment modality is based on the clinical characteristics of
the patient as well as the radiobiological characteristics of the tumor and
surrounding normal tissues. As such the choice for proton therapy is based
on for example, differences in expected risks of normal tissue complications.
Therefore optimized selection of a treatment modality and specifcally the
choice for proton therapy is a very important feld for the application of risk
models for normal tissue damage.
Each treatment modality possesses many parameters that can be used to
optimize its application. For example, in external radiotherapy (linac-based
photon therapy, proton therapy) the choice of number and shape of the beams
and their angles with respect to the patient facilitate optimization of the dose
to the tumor and normal tissues. Again based on the general location of the
tumor and adjacent normal tissues, class solutions (treatment techniques) are
developed for specifc groups of patients. The development and optimiza-
tion of these treatment techniques therefore represent a second level of treat-
ment optimization where risk models for normal tissue damage are used.
Though these treatment techniques can serve as starting points for whole
classes of patients, variability in patient anatomy necessitates individual-
ized tailoring of this technique to each patient (treatment plan optimization).
Factors determining the fnal treatment plan include the size, shape, and posi-
tion of the tumor and the exact anatomy of adjacent organs. In this fnal opti-
mization step imaging plays a pivotal role. The most-used imaging modality
in radiotherapy is x-ray computed tomography (CT) scanning. In addition
imaging modalities such as positron emission tomography (PET), single pho-
ton-emission CT (SPECT), or magnetic resonance imaging (MRI) are used to
facilitate the identifcation of the most active parts of the tumor (e.g.,
18
FDG
PET), most functional parts of the lung (
99m
Tc SPECT) or to improve the vis-
ibility of different brain regions (MRI). As an example, Figure 20.1A shows
the CT scan of a patient with a lung tumor. To distinguish better between
normal structures within the lung and extensions of the tumor, an
18
FDG
PET scan was made and superimposed on the CT scan. The available images
can be imported in a treatment-planning system that contains a dose model
of the treatment machine. Based on the CT and PET scan, the tumor and
adjacent critical organs (e.g., the lung) are contoured. By varying treatment
parameters such as beam angles, weights, and shapes, the treatment plan
can be optimized (see also Chapters 10, 11, and 15). Figure  20.1B shows an
example of the beam angles used in this patient. Based on the dose model,
the treatment plan, and the patient geometry, the dose distribution in the
patient can be calculated (Figure 20.1C).
Direct comparison of three-dimensional (3D) dose distributions of alterna-
tive treatment plans is very inconvenient. Therefore the present practice is to
summarize the 3D dose distribution in a dose-volume histogram. For each
630 Proton Therapy Physics
(relative) dose level, this histogram gives the volume that receives that dose
(Figure 20.1D). In practice the cumulative dose-volume histogram (DVH),
giving the volume receiving more than a certain dose as a function of that
dose, is reported by treatment-planning systems (Figure 20.1E). Even though
a DVH discards a lot of information compared with the 3D dose distribution,
at present this DVH is the starting point for the derivation of fgures-of-merit,
based on which the treatment plan can be optimized. Classically, individual
DVH points, the mean dose or generalized forms of the mean dose are used
A)
Imaging Planning
Dose calculation
Dose-volume histogram (DVH)
Cummulative DVH
Dose (Gy)
PTV
30
20
10
0
0
50
100
V
o
l
u
m
e

(
%
)
V
o
l
u
m
e

(
%

p
e
r

G
y
)
0 20 40 60
0 20 40 60
Myelum Lung Heart
B)
C)
D)
E)
FIGURE 20.1
(Seecolorinsert.) Tailoring modern radiotherapy technology to the patient requires charac-
terization of the patient using imaging (A). The anatomy of the patient is characterized using a
CT scan (gray scale). In addition to better distinguish between normal and tumor tissue
18
FDG-
PET scanning was used (color scale). The gross tumor volume is identifed (green contour) and
expanded with a margin to account for microscopic extensions, patient positioning, and tumor
motion uncertainties to yield the planning target volume (red contour). Moreover, the critical
organs are contoured (e.g., white contour for the lung). Subsequently in a treatment-planning
system a treatment technique is applied to the patient (B) and the resulting dose distribution
is calculated (color scale, C). Next dose-volume histograms (DVHs) are constructed of dose
deposited in the target volume and critical organs (D). In practice these differential DVHs
are converted in cumulative DVHs, giving the volume receiving more than a specifc dose
as a function of that dose (E). Based on these dose-volume histograms, the technique may be
further adapted to the patient.
631 Fully Exploiting the Benefts of Protons
for this. However, because the relation of these fgures-of-merit to clinical
outcome is not trivial, large efforts have been made to develop and use risk
models explicitly describing normal tissue damage instead.
20.3 TheDevelopmentofRadiation-
InducedNormalTissueDamage
To be able to fully appreciate the complexity of events that risk models need
to describe, a brief overview of the different events that lead from dose depo-
sition to tissue damage and possibly clinical complications will be given.
In the presence of oxygen, photon irradiation leads to the formation of
reactive oxygen species. These induce sparse DNA lesions such as single-
and double-strand breaks dispersed through the cell nucleus. In comparison
with photon irradiation, particle beams act more directly on the DNA and
produce dense ionization tracks that cause clustered DNA damage which
are, especially in the Bragg peak region, more diffcult to repair for a cell (see
Chapter 19 for details.)
Cell death is primarily determined by nonrepairable double-strand breaks.
Normal tissue damage, however, also depends strongly on other stress
responses. Besides death, in normal tissue cells DNA-damage may also lead
to differentiation or proliferation of specifc cells, cell-cycle arrest, initiating
immune responses, changed metabolism, collagen and extracellular matrix
deposition, and other fbrotic reactions, in response to activation of cytokines
and upregulation of profbrotic genes.
How these local effects are translated into clinical complications, how-
ever, strongly depends on organ or even endpoint-specifc mechanisms; for
example, in the parotid gland, late loss of function is mostly due to a loss of
repopulating primitive cells, whereas in the lung, late loss of function is due
to excessive deposition of extracellular matrix material. Moreover, whether
damage to tissue within the organ actually leads to a complication may
depend on dose to other organs. Examples of these are dose to the heart,
increasing the risk and severity of loss of pulmonary function after lung irra-
diation (2, 3) and the risk of patient-rated xerostomia (dry-mouth) depend-
ing on dose to the parotid gland as well as on dose to the submandibular
gland (4). Moreover, the relationship between DVH parameters and compli-
cation risk may also infuenced by other factors. For example, the relation-
ship between dose and complication risk after irradiation for prostate cancer
depends on whether or not abdominal surgery has been performed (5). As
such each endpoint depends on a unique chain of events leading from initial
dose deposition and local damage to the fnal clinical endpoint. Therefore
NTCP models describing these endpoints need to be tailored to the organ
and endpoint studied.
632 Proton Therapy Physics
20.4 MethodologyofModelDevelopment
For the application of new techniques, obtaining an NTCP estimate from an
NTCP model is in fact extrapolating from current knowledge (the data). This
extrapolation, however, heavily depends on the assumptions of the NTCP
model. As such it is critical to realize that the estimates obtained from the
model are as good as the data and the assumptions on which it was built.
Therefore in this section various stages of model development, such as the
collection of data, describing the data with a model, and testing the applica-
bility of this model, are given.
20.4.1 Choice of Endpoint
Because the application of NTCP models is to optimize the treatment with
respect to normal tissue toxicity, the exact type of toxicity (or endpoint) to be
described by the model has to be chosen carefully. Roughly three classes of
endpoints can be distinguished.
First, toxicity can be determined objectively in terms deterioration of
organ function or changes in tissue, visualized by imaging. This type
of  endpoint has the advantage that it depends on direct measurements
of changes in organ function (e.g., lung capacity, saliva production), and
therefore it allows an objective determination of radiation effects. Moreover,
because this type of measurement can also be performed in animal mod-
els, modeling this type of endpoint can beneft from mechanistic insight
obtained from radiobiology studies. For most of these endpoints, however,
it is unclear what the clinical impact is: although loss of 75% of parotid
gland saliva production or density changes in the lung visible on CT clearly
demonstrates damage to the parotid gland and lung, respectively, by itself,
it does not establish a clinical impact that can be weighed against toxicity in
other organs or tumor control.
Second, toxicity can be reported in terms of a clinical complication. As an
example the Common Terminology Criteria for Adverse Events (CTCAE v4.0)
defnes for each complication a grade between 1 and 5, where 1 indicates tox-
icity that remains asymptomatic or results in mild symptoms not requiring
intervention and 5 indicates death related to the complication. Though using
this system complications can be classifed according to clinical impact, this
inherently also introduces some subjectivity; for example, radiation pneu-
monitis is classifed as a grade 2 based on the need to administer steroids.
Whether or not steroids are prescribed may, however, vary between phy-
sicians. Moreover, the observed clinical complication may originate from
damage and/or functional problems in multiple organs (4). As such, accurate
prediction of clinical complications requires a good insight into the doses to
which organs potentially contribute to the clinical symptoms. Consequently,
modeling this type of endpoint requires the inclusion of a large number of
633 Fully Exploiting the Benefts of Protons
dosimetric predictors and a large dataset with many events to support the
model.
Finally, because the ultimate aim of (the optimization of) the radiotherapy
treatment is to cure the patient while preserving or improving the QoL of
the cancer patient, the impact of a treatment on QoL can also be used as
an endpoint. QoL is generally measured using questionnaires (e.g., EORTC
QLQ-C30 (6)).
The results of a number of studies clearly showed an inverse relationship
between the presence and severity of radiation-induced side effects and the
more general dimensions of QoL. Similar to scoring of clinical symptoms,
changes in QoL, may result from radiation effects in many organs as well as
from the clinical status of the patient and/or comorbid diseases; for example,
in head and neck cancer, the clinical complication xerostomia is the most
frequently reported late side effect, which is also considered by patients to
affect their QoL. However, in a recent study, radiation-induced swallow-
ing dysfunction appeared to be more important with regard to the effect
on QoL compared to xerostomia (7). Thus, changes in QoL may result from
multiple clinical complications that in turn may result from dose to multiple
organs. As such including dosimetric information on all organs that may
be involved in the reduction of QoL requires an enormous amount of data.
Moreover, the QoL could ignore clinically relevant toxicity that has limited
impact on the QoL. When basing treatment optimization of QoL, these toxic-
ities would not be taken into account. In conclusion, choosing between these
classes of endpoints is making a trade-off between specifcity and relevance
to the patient (8).
The optimization of a treatment will usually involve multiple end-
points. Normal tissue damage has to be weighed against the risk of not
curing the patient. Moreover, for many disease sites the patient is at risk
for developing more than one type of toxicity. Simultaneous optimization
of a treatment with respect to multiple endpoints requires that compa-
rable fgures-of-merit are used for each separately. A solution to this is
to specify which amount of function loss, what grade of clinical com-
plication, or what loss of health-related QoL is considered clinically rel-
evant. Based on criteria such as loss of 75% of parotid saliva production,
a grade 2 or higher radiation pneumonitis, or loss of more than 10 points
in QoL, these endpoints can be converted to a binary endpoint that speci-
fes whether or not the complication occurred. Now the treatment can
be optimized with respect to these binary endpoints, using tumor con-
trol probability and NTCP models. Though probabilities are suitable to
compare nonequivalent types of endpoints, care should be taken to use
binary endpoints that specify equally severe complications. Optimizing
the occurrence of a grade 1 (asymptomatic) radiation pneumonitis against
the probability of tumor control would compromise a lethal complica-
tion (not achieving tumor control) too much in favor of an asymptomatic
complication.
634 Proton Therapy Physics
20.4.2 Data Gathering
Because a model is in essence a summary of previously made observa-
tions, the quality of the data used for the development of the model is
critical to its applicability. As such when collecting data to facilitate the
development of NTCP models to be used in treatment optimization with
respect to some clinical endpoint, it is important that the data collected at
least contains the candidate predictors that can be expected to be related
to this endpoint. Because many clinical endpoints (e.g., swallowing disor-
ders, xerostomia, and radiation pneumonitis) are multiorgan endpoints,
it is imperative that a dataset used for their predictive modeling includes
clinical and dosimetric parameters of all organs involved. Moreover,
though 3D dose distributions are generally reduced to dose-volume his-
tograms, from the endpoint’s perspective dose-volume histogram points
may not be the most sensible choice. In addition, because the risk of many
complications depends on a combination of dosimetric and other clini-
cal, treatment, or demographic factors, such as the addition of concurrent
chemotherapy to radiation and age, it is imperative to collect these param-
eters and include them in the analysis as candidate predictors. Because
models built on such a multitude of predictive factors require an amount
of data that is generally beyond the capacity of individual centers, data
gathering requires extensive collaborations such as the U.S. QUANTEC
collaboration (9).
Finally, because a model in principle summarizes the data used to con-
struct it, the quality of a model critically depends on the quality of these
data. As such the quality of a model is infuenced strongly by the accuracy
by which endpoints are scored, consistency in organ delineation, and the
accuracy of the estimated dose distribution.
20.4.3 Fitting a Model to Binary Data
After the data has been collected, a model has to be selected to describe
them. For models with a fxed set of predictors and parameters such as the
Lyman-Kutcher-Burman (LKB) model, critical-element and critical-volume
models, or logistic regression models with a known set of predictors (see the
next section for descriptions), parameter values can be determined by ftting
the model to the data. Because the model describes a process with binary
outcome (the occurrence or absence of a complication), the most appropriate
ftting method is the maximum-likelihood ft (10). In this approach the model
parameters are selected for which the model prediction maximizes the prob-
ability that the experimental data would be observed. This in general cor-
responds to maximizing

L m e NTCP m e NTCP m
i i i i
i
( ) = ⋅ ( ) ( ) + − ⋅ − ( ) ( ) ln ( ) ln 1 1
∑∑
. (20.1)
635 Fully Exploiting the Benefts of Protons
L indicates the logarithm of the likelihood, e
i
indicates the outcome (0 or 1)
for patient i, and NTCP
i
(m) indicates the estimate of the NTCP for the para-
meter set m. For testing the consistency between model and data (see below
in this section) patients need to be grouped based on similarity of treatment
with respect to the predictors in the model. The likelihood function to be
optimized then becomes

L m r NTCP m n r NTCP m
i i i i i
( ) = ⋅ ( ) ( ) + − ⋅ − ( ) ( ) ln ( ) ln 1
ii
∑
. (20.2)
Here n
i
and r
i
indicate the number of patients and the number of compli-
cations in group i, respectively. As an example Figure 20.2A shows the
incidence of a reduction to 25% saliva production compared to the pretreat-
ment level in patients treated in the head-and-neck region (11). Using the
maximum-likelihood method given by Equation 20.2, a logistic model (see
Equations 20.6 and 20.7) was ftted to these data (curves).
20.4.4 Testing Model Validity
Though ftting a model to data will always produce a set of parameters that
makes the model correspond to the data as well as possible, this does not
imply that the model accurately describes the data. Different ways to assess
the quality of the model put emphasis on different aspects such as corre-
spondence between model and data or the ability to correctly distinguish
between responding and nonresponding patients. As a frst measure of how
well the data are described by the model, the likelihood L(m) (Equation 20.1
or 20.2) can be used. Although higher values of L(m) indicate a better ft of the
model to the data, by itself it does not provide a means to determine whether
the model predictions are consistent to the data and can be used for a specifc
task. Derived from the likelihood, various information criteria have been
developed.
These criteria also depend on the number of model parameters and as such
provide a means to determine whether the addition of a new parameter in
a model can be justifed by the improvement in the likelihood. Examples of
these are Akaike’s or the Bayesian information criteria (AIC/BIC):

AIC k L = ⋅ − ⋅ 2 2 (20.3)

BIC k n L = ⋅ ( ) − ⋅ ln 2 . (20.4)
Here k indicates the number of model parameters and L the natural logarithm
of the likelihood obtained from the maximum likelihood ft. By comparing
Equations 20.3 and 20.4, the difference between the BIC and the AIC can be
seen to be in the penalization of the addition of a model parameter. In the
BIC this penalty depends on the logarithm of the number of samples, which
leads to more conservative models, for datasets larger than six samples.
636 Proton Therapy Physics
A)
1
0.8
0.6
0.4
0.2
N
T
C
P
0
0 20 40
Mean dose (Gy)
Fit model to training data Model & cross validation data
Difference model / training data Difference model / cross validation data
ROC analysis ROC analysis cross-validation data
Mean dose (Gy)
60 0 20 40 60
0 10 20
p=0.043
60 patients 31 patients
Area under the curve: 0.72 Area under the curve: 0.62
Deviance Deviance
30 0 10 20 30
0 0.2 0.4 0.6 0.8
False positive rate False positive rate
1 0 0.2 0.4 0.6 0.8 1
1
0.8
0.6
0.4
0.2
N
T
C
P
0
1
0.8
0.6
0.4
0.2
P
r
o
b
.

D
e
n
s
.
0
1
0.8
0.6
0.4
0.2
P
r
o
b
.

D
e
n
s
.
0
1
0.8
0.6
0.4
0.2
T
r
u
e

p
o
s
i
t
i
v
e

r
a
t
e
0
1
0.8
0.6
0.4
0.2
T
r
u
e

p
o
s
i
t
i
v
e

r
a
t
e
0
B)
C)
D)
E)
F)
p=0.45
FIGURE 20.2
Overview of methods and their use in an example. Data on reduction >75% of parotid
gland saliva production at 6 weeks and 1 year (11) are modeled using the mean parotid
gland dose in a logistic model (Equation 20.6). The model is fitted to two-thirds of the
data using the maximum likelihood method (Equation 20.2, A). (B) The expected dis-
tribution of the deviance, determined by fitting to 10
5
alternative outcomes that were
obtained using a Monte Carlo technique (Section 20.4.4). The dotted line indicates the
deviance obtained in the real study. Based on these, the probability of finding larger
deviances is 45%. As such the differences between model and data are not significant
(p = 0.45), and the model is not rejected by the data. To determine to what extent the
model distinguishes between responders and nonresponders, an ROC analysis was per-
formed (C). For internal cross-validation the fitted model shown in A was compared to
the unused one-third of the data (validation dataset, D). New Monte Carlo datasets were
generated to determine the deviance distribution for the validation data (E). The dif-
ference between the model fitted in (A) and the validation data, however, is significant.
(F)  ROC analysis showing that the performance of the model in the validation data is
lower than in the training set.
637 Fully Exploiting the Benefts of Protons
Many other statistical methods exist to quantify correspondence between
model and data and to what extent the model separates patients with com-
plications from patients without complications.
The most elementary test of the model is whether ranking of patients
according to their predicted risk corresponds to ranking them according to
the incidence of the complication. To this end, Spearman’s rank correlation
coeffcient can be used (12). Though a high correlation coeffcient indicates
that the model can be used to optimize the plan based on this model, it also
does not test whether the probabilities are quantitatively correct. Treatment
optimization based on risks of multiple endpoints (e.g., tumor control, xero-
stomia, and dysphagia), however, requires quantitatively correct NTCP val-
ues. Biases in the individual models would inadvertently infuence plan
selection (13). Therefore, in addition to testing the ability of a model to rank
plans with respect to a specifc endpoint, also checking the accuracy of the
NTCP values obtained from the model is desired.
For large datasets with normally distributed uncertainties generally the χ
2

test is used to test whether differences between model and data are larger
than expected based on the statistical properties of the data. A similar
method suitable for smaller datasets and binary outcome data is based on the
likelihood given by Equation 20.1 or 20.2 (10). The data themselves are used
as the best possible model, also called “the full model” (14). Subsequently it
is tested whether the likelihood of the ftted model has signifcantly dete-
riorated compared with that of the full model. The expected distribution of
the difference between model and data is determined using a Monte Carlo
method. The likelihood of obtaining the data if the model NTCP values are
given by the data themselves can be obtained by substituting NTCP
i
= r
i
/n
i

in Equation 20.2 to yield

L r
r
n
n r
r
n
i
i
i
i
i r
i
i
0
1 = ⋅






+ − ( ) −





 ∑
ln ln
. (20.5)
Now it can be tested whether the decrease of L(m) with respect to L
0
signif-
cantly exceeds the amount expected based on the statistical noise in the data.
Usually in this analysis the deviance, given by −2 ∙ (L(m) − L
0
), is used since
for large datasets the distribution of the deviance resembles the χ
2
distri-
bution  (14). However, the probability distribution of the deviance has to be
known so that one can set a maximum decrease of the ftted models deviance
with respect to the full model at which the model is considered to signifcantly
deviate from the data. This distribution can be determined based on alterna-
tive study outcomes obtained using the ftted model and a Monte Carlo tech-
nique (10). In this approach for each data point the NTCP is calculated using
the ftted model. Subsequently for each patient included in this data point
a random number between 0 and 1 is drawn and compared to the NTCP. If
the random number is lower than the NTCP, for the simulated outcome the
638 Proton Therapy Physics
patient is scored as showing the complication. Using this procedure a large
number of alternate datasets that could have occurred given that the ftted
NTCP model is obtained. Subsequently L
0
can be recalculated and the NTCP
model reftted for each of these datasets. This results in a large number of
alternate values of the deviance and their distribution. Finally, from this dis-
tribution it can be determined which fraction of the fts to the Monte Carlo
datasets resulted in a larger deviance than the ft to the experimental data.
Because larger values indicate a larger difference between model and data,
a small fraction (e.g., <5%) indicates that the difference between model and
actual outcome is unlikely (e.g., probability <5%) to occur based on the sta-
tistical spread in the data, which is a good reason to reject the model. Figure
20.2B shows the deviance distribution for the model ft shown in Figure 20.2A.
The difference between the model and data is not signifcant.
Besides testing whether the ftted model actually corresponds to the data, it
is important to assess its ability to distinguish between responding and non-
responding patients. This aspect of performance, called discrimination, can
be characterized by the Receiver Operating Characteristic (ROC) curve (15).
The ROC plot is a plot of true positive vs. false positive rates for all pos-
sible NTCP threshold values (see e.g., Figure 20.2C). For a random prediction
(lowest performance) the area under this curve is 0.5. For better performing
models this area increases up to a maximum of 1.
20.4.5 Cross-Validation
The fact that a model was developed based on a dataset does not automatic-
ally imply that it is capable of predicting normal tissue toxicity in a new group
of patients receiving the same type of treatment, let alone that its results can
be extrapolated to other treatment modalities. Testing the ability of a model
to predict the response in new patients can be done by cross-validation. Two
stages of cross-validation can be distinguished. Internal cross-validation can
be performed to test the predictive power within the patient population and
treatment type the model was developed in. In internal cross-validation the
dataset is split into a “training set” used to develop (i.e., determine predictive
factors and/or ft model parameters) the model and a “validation set” to test
the model performance in an independent set of data. In fact for the model
fts shown in Figure 20.2A, only two-thirds of the available data was used as
a training set. Every third patient was saved for a cross-validation. Figure
20.2D shows the original model curves copied from panel A, together with
the cross-validation data. Here it can be seen that, though the model follows
the data, it appears to underestimate the risk at higher dose levels. Similar
to Figure 20.2B, the signifcance of the difference between model and data
can be tested. Because the deviance depends on L
0
and thus on the dataset,
the deviance distribution has to be redetermined by generating alternative
outcomes and calculating the deviance using Equation 20.1 or 20.2, and the
model must be ftted to the training set. The resulting distribution is shown
639 Fully Exploiting the Benefts of Protons
in Figure 20.2E. The difference between the model and the cross-validation
datasets is indeed signifcant. As also expected, the performance of the
model assessed by the ROC curve is reduced (Figure 20.2F).
One should be aware that this approach to cross-validation may be sensi-
tive to the specifc selection of development and cross-validation datasets.
This sensitivity can be reduced by using bootstrapping. In bootstrapping
multiple validation sets are sampled by randomly selecting patients from
the original dataset (12). The ability of the model developed in the original
dataset to predict the outcomes in the bootstrapping datasets can now be
assessed by the previously described methods, such as the ROC curve or
Spearman’s correlation.
A successful internal cross-validation does not imply that it is accurate
beyond the domain specifed by the dataset on which it was based (e.g.,
other new treatment techniques or modalities). Therefore, any extrapola-
tion to other patient populations or treatment techniques/modalities should
be regarded as a hypothesis that needs to be tested prospectively in a new
dataset that was obtained in this new patient population or using the new
treatment technique. To this end again the previously described methods
(see “testing model validity” section) can be applied to test consistency or
performance of the model in new datasets. This procedure is called external
cross-validation.
20.5 AvailableModelsfortheRiskofNormalTissueDamage
For a long time efforts have been made to create predictive models for the
beneft of treatment optimization. Only during the past two decades evolu-
tion of treatment techniques and technology made the systematic collection
of dose distribution and response data, and consequently the development
of models describing their relation, possible. In the following subsections a
selection of these models will be described. In addition, in Table 20.1 a sum-
mary of these models, their properties, and typical applications is given.
20.5.1 The Sigmoid Curve: The Shape of the Population
Distribution of the Tolerance
Already in 1924 in the feld of toxicology it was recognized that the dose
dependence of “poisoning can be described by an S-shaped curve, and that
such a curve is properly conceived as an expression of the variation, either
in sensitiveness or in resistance, of organisms, tissues or cells toward a given
poison” (16). Though radiation can be regarded similar to poison, the nor-
mal tissues are generally not receiving a uniform dose. Therefore one of the
challenges in NTCP modeling is to recognize what predictive factor, derived
640 Proton Therapy Physics
from the dose distribution applied to the patient, best characterizes the vari-
ation of the resistance to the treatment (population tolerance distribution).
20.5.2 Logistic Regression Analysis: Identifying Predictive Factors
Classically the description of the relation between (candidate) predictive
factors and outcome are the domain of the epidemiologist. Though in this
feld many possible modeling techniques are available, logistic regression
analysis is still one of the most commonly used tools. The logistic regression
model is given by

NTCP
e
z
=
+
−
1
1
. (20.6)
Here z is the predictive factor representing the stimulus of which the popu-
lation tolerance distribution can be used to predict outcome. This predictive
factor z can be a single variable (e.g., mean dose) or a function of multiple
predictive variables. Though any type of function is possible, usually a lin-
ear function such as

z x x = + ⋅ + ⋅ + β β β
0 1 1 2 2
… (20.7)
TABLE 20.1
Overview of Models and Their Properties
Model Parameters Remarks
Logistic regression Depending on model composition Classical epidemiology
approach
Lyman-Kutcher-
Burman (LKB)
n volume effect (Figure 20.3)
D
50
(1) tolerance to whole-organ
irradiation
m relative slope
Most generally used specialized
NTCP model at present
Critical element P(1, D) Dose–response to
whole-organ irradiation
Designed for so-called “serial
organs”
Critical volume Tolerance dose and slope of
dose-response curve of the
function subunit
v
r
functional reserve
σ
r
population spread of v
r
Designed for so-called “parallel
organs”
Relative seriality P(1, D) Dose–response curve to
whole-organ irradiation
s relative seriality
parameter
Designed for mixed behavior.
Parameter s describes the
extent to which the organ
behaves serially or parallel.
Extended
multivariate logistic
regression modeling
framework
Depending on model composition Approach rather than a model.
Most versatile allowing
combining different types of
predictive factors
641 Fully Exploiting the Benefts of Protons
is used. In Equation 20.7 the parameters β
i
represent regression coeffcients
and x
i
the corresponding predictive variables, such as points from the dose-
volume histogram, mean dose, or clinical parameters such as pretreatment
pulmonary function. Though Equation 20.7 shows a linear function of inde-
pendent predictive factors, each of these factors may depend on (combi-
nations of) dose, volume, or clinical factors via a nonlinear function. The
advantages of this type of model are the wide availability of methods for
ftting it to data in statistics software packages and its intrinsic capability of
combining a very heterogenic set of predictive factors, such as dose-related
and patient factors.
20.5.3 Lyman-Kutcher-Burman (LKB) Model
In the clinical physics feld efforts have been made to create mathematical
formalisms that summarize 3D dose distributions in a single predictive fac-
tor. Because mechanisms underlying normal tissue damage vary by organ
and even type of toxicity within the organ, the optimal strategy by which the
3D dose distribution is reduced to a single predictive factor is organ depen-
dent. One of the frst and still the most-often used model in this class is the
LKB model (17). In this model the nonuniform dose distribution is reduced
to a uniform dose distribution that is assumed to be equivalently effective
as the original nonuniform one. To this end the relative contribution of each
subvolume of the organ to the uniformly irradiated volume is assumed to be
proportional to a power function of its relative dose:

v
D
D
v
N
D
D
eff
i
n
i
i
i
n
i
=






⋅ =





 ∑ ∑
max max
1 1
1
. (20.8)
Here D
i
indicates the dose in relative subvolume of size v
i
in the original,
nonuniform dose distribution. If equally sized subvolumes (e.g., voxels in
the 3D dose distribution) are used, the second formulation can be used. Here
N indicates the number of subvolumes. Depending on the value of para-
meter n subvolumes contribute only to the effective volume if they contain
a dose close to the maximum dose (n→0), proportionally to the relative dose
(n = 1), or already starting at a low dose (n >> 1). Irradiation of a volume v
eff

to a dose D
max
is assumed to result in the same clinical outcome as irradia-
tion with the original dose distribution. Furthermore the parameter D
50
, also
called the tolerance dose, is assumed to depend on the effective irradiated
volume and the tolerance to irradiation of the whole organ D
50
(1) following
a power law:

D v
D
v
eff
n
50
50
1
( ) =
( )
.
(20.9)
642 Proton Therapy Physics
Finally, by assuming that this D
50
(v) is normally distributed over the popu-
lation with a relative uncertainty (i.e., standard deviation) m, the NTCP is
given by

NTCP
D D v
m D v
=
− ( )
⋅ ( )






Φ
max 50
50
(20.10)
where Φ represents the cumulative normal distribution and is given by

Φ x e dy
y x
( ) = ⋅ ⋅
−
−∞
∫
1
2
2
2
π
. (20.11)
Altogether, by specifying the parameter n, organ-specifc behavior can be
introduced (see Figure 20.3). For small values of n the tolerance dose will
hardly depend on irradiated volume and the NTCP is determined mostly by
the D
max
of the dose distribution. For n = 1, however, the contribution of all
subvolumes to the effective volume is proportional to dose and changes in
irradiated volume will result in a proportional change in tolerance dose. At
large values of n (>>1) any subvolume receiving even a low dose contributes
fully to the effective volume. The tolerance dose, however, rises steeply if
part of the organ is spared. Because this type of volume dependence might
arise if subvolumes of the organ function independently and only a small
functional subvolume is required for the organ to perform its function, this
type of behavior is often characterized as “parallel,” as opposed to “serial”
behavior occurring for n << 1, where damaging even the smallest subvolume
renders the organ dysfunctional.
0
n=0.05
n=0.5
n=1
n=2
n=5
n=10
D
50
(1)
D
5
0
(
v
)
0.2 0.4 0.6 0.8
Relative volume
1
FIGURE 20.3
Dependence of the relation between the tolerance dose and irradiated volume on the value
of parameter n of the Lyman model. For small values of n, the tolerance dose hardly depends
on irradiated volume, in contrast to large values of n leading to a strong volume dependency.
643 Fully Exploiting the Benefts of Protons
At present treatment optimization is still most-often performed based on
dose metrics such as DVH points and mean dose, rather than NTCP models.
One of the fgures-of-merit often used in such dose-based optimization is the
generalized equivalent uniform dose (gEUD) (18):

gEUD
N
D
i
a
i
a
=






∑
1
1
(20.12)
where N represents the number of equivalently sized subvolumes in the organ
at risk and a is a free parameter. The formulation of the EUD is very similar
to the effective volume of the LKB model. In fact by substituting a = 1/n in
Equation 21.12, the LKB model can be reformulated in terms of the gEUD:

NTCP
gEUD D
m D
=
− ( )
⋅ ( )






Φ
50
50
1
1
(20.13)
showing that the gEUD is in fact equivalent to the dosimetric predictor
underlying the LKB model.
20.5.4 Functional Subunit-Based Models
The serial and parallel types of behavior were modeled explicitly in a class
of models assuming that organs consist of independent substructures, called
functional subunits, and that the organ response is determined by the orga-
nization and response of these functional subunits to radiation (19). Initially
three of these models have been developed, assuming a serial (critical-
element model [20]), parallel (critical-volume model [21]), or a mixed (relative
seriality [22]) organization. All three models start with the assumption that
the risk of failure of this substructure (p) as a function of dose is given by
a sigmoid curve. Many formulations (e.g., logistic, Poisson, and cumulative
normal distribution) for this type of curve are available. As such the logistic
regression model of Equation 20.6 could be used with dose as a predictive
factor. Alternatively it could be assumed that the tolerance dose of functional
subunits is distributed according to the normal distribution. In this case the
dose-response curve is given by the cumulative normal distribution (see
Equation 20.11). Finally, the Poisson distribution that describes the number of
rare events (e.g., a lethal hit to a cell) occurring in a large sample size (e.g., all
dose deposition events in the cell) could be used. Although the underlying
assumptions differ, it is important to note that for all practical applications
these models perform similarly.
The critical-element model is based on the assumption that damage to any
subvolume of the organ will result in failure of the entire organ (20). Because
the probability of preserving function in subvolume i is given by

1− ( ) p D
i
(20.14)
644 Proton Therapy Physics
and the probability of preserving function in all subvolumes is obtained by
multiplication over all subvolumes, the risk of organ failure is given by

NTCP p D
i
i
= − − ( ) ( )
∏
1 1
(20.15)
where D
i
indicates the dose in FSU i. Similar to the Lyman model, also the
critical element model can be expressed in terms of the response to whole-
organ irradiation:

NTCP P D
j
v
j
j
= − −
( ) ( ) ∏
1 1 1,
(20.16)
where P(1, D
j
) equals the NTCP after irradiation of the whole organ to a dose
D
j
and (D
j
, v
j
) represents the dose-volume histogram.
In contrast, the critical-volume model is based on the assumption that the
organ possesses some spare capacity. Organ failure is assumed to occur only
if the damaged fraction of the organ exceeds this spare capacity. Therefore,
to estimate the NTCP, frst an estimate of the damaged volume has to be
obtained:

v v p D
d i i
i
N
= ⋅ ( )
=
∑
1
(20.17)
where v
i
indicates the relative volume of subvolume i and N is the total num-
ber of subvolumes. Assuming a normal distribution for the spare capacity,
the risk of the damaged volume exceeding the spare capacity is then given by

NTCP
v v
d r
r
=
− 





Φ
σ
(20.18)
where v
r
and σ
r
indicate the spare capacity and its population spread,
respectively.
A model that combines both types of behaviors and allows the type of
response (i.e., the degree of seriality) to be determined by a ft parameter is
the relative seriality model:

NTCP p D
FSU
s
i
i
s
= − − ( )
( )






∏
1 1
1
(20.19)
where the parameter s determines whether the volume dependency of the
tolerance dose follows a parallel (s << 1) or serial (s = 1) behavior (Figure 20.4).
645 Fully Exploiting the Benefts of Protons
Similar to the LKB and critical-element models also the relative seriality
model can be expressed in the response after whole-organ irradiation:

NTCP P D
s
j
v
j
s
j
= − −
( ) ( )





 ∏
1 1 1
1
, . (20.20)
During the last decade the number of available models has increased
enormously. Most of these recent models, however, share the most critical
assumptions of the aforementioned models, and until now their beneft over
the previously described ones has not been demonstrated experimentally.
20.5.5 Including Clinical and Patient Characteristics:
Logistic Regression Models
The LKB, critical element, critical volume, and relative seriality models are
exclusively based on the entire dose distribution. Their formulation does
1
0.8
0.6
0.4
Critical element
Critical volume
Serial (s = 1)
Parallel (s = 0.05)
0.2
0
N
T
C
P
1
0.8
0.6
0.4
0.2
0
Dose (a.u)
Dose (a.u)
Critical element/volume model
Relative seriality model
B)
A)
N
T
C
P
FIGURE 20.4
Behavior of FSU-based models illustrated by dose-response curves expected after irradiation of
100%, 67%, and 33% of the organ. The curves of the critical-element model and the relative seriality
model in its serial limit demonstrate the characteristic small effect of irradiated volume on tolerance
dose for low risk levels. In contrast the critical volume model and the relative seriality model in its
parallel regime show a strong dependence of tolerance dose on irradiated volume for all risk levels.
646 Proton Therapy Physics
not generally facilitate the inclusion of clinical parameters (e.g., addition
of chemo or pre-existing morbidity), which would improve the accuracy of
NTCP models. Alternatively, however, this can be achieved using a multi-
variate logistic regression model in which, for example, the damaged volume
for the critical-volume model, or the effective volume and dose for the LKB
model are used as predictors. Establishing the optimal combination of pre-
dictors resulting in the most accurate prediction of normal tissue toxicity is,
however, not trivial. El Naqa et al. (12) gave an overview of methods that can
be used to achieve this using a multivariate modeling approach combined
with methods to test model robustness and prevent overftting. The develop-
ment of such a model involves (1) determining which parameter combina-
tions result in a good description of the data, (2) determining the number
of parameters that can be supported by the data without overftting, and (3)
determining the robustness of parameter selection.
First, determining combinations of candidate predictors that result in an
accurate description of the data by testing all possible combinations is not
feasible, especially if large numbers of candidates are considered. Therefore,
two possible alternative approaches are sequentially adding the candidate
that most improves the performance of the model or starting with all candi-
dates and sequentially leaving out the one that leads to the least deteriora-
tion of model performance. Both approaches will result in a series of models
with a number of predictors ranging from a single parameter to all candidate
predictors. Subsequently the optimal model order needs to be determined.
To this end various criteria, such as the AIC or BIC (Equations 20.3 and 20.4),
can be used. Finally the stability of the selection of predictive factors can be
assessed by performing this procedure on alternative datasets, for example,
sampling by bootstrapping. For each bootstrap dataset the selection of pre-
dictive factors as described above can be repeated, and for each factor the
number of times it is selected can be determined, giving an indication of
which factors are generally selected, independent of statistical fuctuations
in the data.
Because in many studies it was demonstrated that accurate prediction
of normal tissue damage requires combining clinical and dosimetric fac-
tors, optimized multivariate modeling is a promising approach to NTCP
modeling.
20.6 DevelopmentsandFutureDirections
NTCP model development was initially inspired by improvements in radio-
therapy technology allowing sparing of normal tissues. Because both clinical
data relating 3D dose distributions to clinical outcome and the knowledge
of mechanisms underlying the irradiated-volume dependence of the risk
647 Fully Exploiting the Benefts of Protons
of toxicity were sparse, the models described in the previous section were
based on abstract assumptions. To test the validity of these assumptions to
allow improvement of the accuracy of NTCP models, many radiobiological
studies have been performed, leading to new insights in the development of
normal tissue damage and providing directions for improving and develop-
ing predictive NTCP models.
All previously described models share a set of assumptions. First, the risk
of damaging a subvolume (or functional subunit) is assumed to depend on
dose to that subvolume alone. As such, damage in the tissue is assumed to be
independent of events occurring elsewhere. Second, the radiation response
of all subvolumes is assumed to be identical. Third, it is assumed that organ
failure is the result of inactivation of a single type of target. To test these
assumptions, during the past two decades numerous studies have been per-
formed on the lung, parotid gland, and spinal cord. Already in the 1990s it
was demonstrated in the mouse lung that the response of the lung to irradia-
tion of the apex differed from that after irradiation of the base (23), indicat-
ing that the either the functional consequence of dose may vary with the
location at which it is deposited within the organ. Similarly, experiments
in the rat spinal cord demonstrated that laterally located white matter is
more radiosensitive than centrally located white matter (24), leading to large
regional differences in tolerance dose for paralysis. Finally, also in the rat
parotid gland the response to irradiation of the cranial parts of the gland
differed from irradiation of the caudal parts of the glands (25). All together
these results demonstrate that, in contrast to current model assumptions, the
response of organs to irradiation is not uniform.
Moreover, in the rat spinal cord the tolerance dose for irradiation of 8-mm
cord length was found to be only 56% of the tolerance to a split-feld dose dis-
tribution consisting of two segments of 4 mm (26), demonstrating irradiated
volume is not generally the determinant of toxicity. In addition, the tolerance
of the spinal cord to irradiation of a small subvolume (shower) was strongly
reduced by a subtolerance dose (e.g., 20% of ED
50
) administered to a larger,
surrounding volume (bath) (26) (Figure 20.5A). Interestingly, this bath-and-
shower effect was also observed in the rat parotid gland, showing that this is
not an isolated fnding, unique to the spinal cord (27) (Figure 20.5B). In addi-
tion, it has been long recognized that the response of the lung is not limited
to its irradiated parts (28). Taken together these observations demonstrate
that the occurrence of tissue damage does not only depend on local dose.
In fact, in the rat lung it was demonstrated that radiation-induced loss of
pulmonary tissue strongly depended on the dose administered to the heart,
showing that in fact the response of an organ may depend on the dose dis-
tribution in other organs (2).
Though the exact mechanisms underlying these nonlocal effects are not
fully characterized, taken together these observations all demonstrate that
the functional response of an organ to irradiation is not trivially related
to local dose. Moreover, even though this was demonstrated by looking at
648 Proton Therapy Physics
organ-specifc effects, mostly in animal models, the fact that nonlocal effects
were observed in virtually any organ that was studied suggests that these
nonlocal effects are likely to be the rule rather than an exception. More
importantly, these effects have been shown to have a strong impact on toler-
ance doses and responses. This indicates that accounting for these effects in
NTCP models will greatly enhance their accuracy.
Improvement of NTCP models by choosing predictors based on these
nonlocal mechanisms requires an approach that is more organ-specifc than
has been done so far. Because inclusion of full mathematical descriptions
of biological mechanisms would likely lead to overly complex models with
too many parameters, an epidemiological approach (i.e., logistic regression
100
80
60
40
20
E
D
5
0

(
G
y
)
L
o
s
s

o
f

s
a
l
i
v
a

p
r
o
d
u
c
t
i
o
n

(
%
)
0
60
B)
A)
50
40
30
20
10
0
0 5
Spinal cord
Parotid gland
10
Bath dose (Gy)
15 20
0 2 4 6
Bath dose (Gy)
8 10
FIGURE 20.5
The effect of irradiation of a small subvolume can be strongly modulated by coirradiation of
larger volumes to a low dose. (A) The tolerance dose for irradiation of a 2-mm section of the cer-
vical spinal cord of the rat in the center of a 20-mm section irradiated to a low dose (bath dose).
Though the tolerance dose for irradiation of 20 mm of the spinal cord is 19.7 Gy, a dose of only
4 Gy already reduces the tolerance dose in the 2-mm section from 87.5 to 56 Gy. Similarly the
reduction of the rat parotid saliva production after irradiation of the caudal 50% of the parotid
gland to 50 Gy was increased by ~15-30% when adding a bath dose to the cranial 50%. (After
van Luijk et al., Int J Radiat Oncol Phys., 73(4), 1002, 2009; van Luijk et al., Int J Radiat Oncol
Phys., 61(3), 892, 2009; and Bijl et al., 64(4), 1204, 2006.)
649 Fully Exploiting the Benefts of Protons
analysis) that uses the biological mechanisms to select candidate predictors
may be preferable over mechanistic modeling approaches that were used
classically. Moreover, to allow testing of candidate predictors in a clinical
setting, the data gathering needs to be expanded from the widespread prac-
tice of collecting dose-volume histograms to actually storing 3D dose distri-
butions to allow the extraction of these biology-based candidate predictors.
20.7 ApplicabilitytoProtonTherapy
The development of NTCP models was inspired by the development of new
techniques that allowed dose reductions in the normal tissues surrounding
the target volume and the question of how to optimally put this new technol-
ogy to use. As an example the introduction of advanced techniques such as
proton therapy provided the clinic with an unprecedented control over the
dose distribution. However, the most generally used dosimetric predictors,
such as dose-volume histogram points and mean organ dose, were selected
exclusively from available clinical data, which were mostly obtained in
photon-based treatments. In such an analysis, only predictors showing both
impact on outcome and strong variability in the dataset are selected. Because
of this variability criterion, however, this does not necessarily yield those
parameters that best describe the biological processes underlying the toxic-
ity with respect to which the treatment is to be optimized. Consequently,
optimization of novel treatment techniques using a thus-selected predictor
is not necessarily minimizing toxicity. Moreover, new treatment modalities,
such as particle therapy, allow controlling more and other characteristics of
the dose distribution than was possible with the modalities that the models
were based on. As such when optimizing these new modalities based on a
model solely based on data obtained in old treatment techniques, unique
properties of the new treatment modality are not used to their full potential.
Thus, when using NTCP models developed in photon-based datasets for the
optimization of proton therapy treatment it is important to realize that these
models may not optimize unique features of proton therapy and NTCP esti-
mates will be biased. As such the NTCP model can only be used routinely
for proton therapy after prospective testing against actual data on the effect
of proton therapy.
These issues might be avoided by using independent mechanistic informa-
tion obtained in preclinical studies, because this may allow the identifcation of
predictive factors describing the underlying biological processes, independent
of the extent to which their effect was the most prominent effect in existing
photon-based data. As such using these biology-based factors for treatment
optimization is expected to better optimize for the biological effect and use
new treatment modalities such as proton therapy to their full potential.
650 Proton Therapy Physics
Acknowledgments
The authors thank Dr. R. P. Coppes, Dr. C. Schilstra, and Dr. J. A. Langendijk
for critically reading the manuscript. Moreover, they also thank numerous
colleagues in the feld for the fruitful discussions that contributed to the
insights presented in this chapter.
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Infuence of adjacent low-dose felds on tolerance to high doses of protons in rat
cervical spinal cord, Int. J. Radiat. Oncol. Biol. Phys., 2006; 64(4):1204–10.
0 –15
–15 –10 –5 5 10 15 0
–10
–5
y

(
c
m
)
0
5
10
15
200
400
600
800
1000
1200
1400
1600
1800
2000
x (cm)
sigmaY
sigmaX
position (x, y)
dose
FIGURE 6.21
20 40
80
60
40
20
–
1
0
.
0
–
8
.
0
–
6
.
0
–
4
.
0
–
2
.
0
0
.
0
2
.
0
4
.
0
6
.
0
8
.
0
1
0
.
0
[cm]X
[cm]Y 100% = 35.5875 cGy
A
B
60
11.0
10
50
96
98
100
102
105
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
–1.0
–2.0
–3.0
–4.0
–5.0
–6.0
–7.0
–8.0
–9.0
–10.0
–11.0
FIGURE 6.8
100
5 10 15 20
Dose [Gy]
CTV Spinal cord
25 30 35
Dose [Gy]
40 30 20 10
Nominal
1MU repainted
1MU skipped 80
60
40
20
%

V
o
l
u
m
e


Dose (Gv)
0
30 32 34 36 38 40 42
100
80
60
40
20
%

V
o
l
u
m
e


Dose (Gv)
0
20 22 24 26 28 30 32
FIGURE 6.23
a)
1 mm
2
3
1
Disp. Width: +29.7 mm
Center: (+3.1, +9.1)
Disp. Width: +36.8 mm
Center: (-2.2, +6.7)
1 mm
1
4
3
2
Dose %
100
90
70
50
30
10
Scale: 5.389 : 1 Scale: 4.345 : 1
b)
FIGURE 10.8
105 %
95 %
50 %
20 %
rough
Patch

r
o
u
g
h

b
e
a
m

Target Volume
P
a
t
c
h

b
e
a
m

Target Volume
Patch Volume

r
o
u
g
h

b
e
a
m

Patch Volume
P
a
t
c
h

b
e
a
m

d)
a)
f)
g)
e)
b)
c)
105 %
95 %
50 %
20 %
105 %
95 %
50 %
20 %
FIGURE 10.6
2
4
6
8
10
12
14
16
–10 –5 0
Y [cm]
Measurement Eclipse Difference eclipse - measurement
5 10
–10
–5
0
Y [cm]
5 10
–10 –5 0
Y [cm]
5 10
–10 –5 0
Y [cm]
5 10
D
e
p
t
h

[
c
m
.
H
2
O
]
2
4
6
8
10
12
14
16
D
e
p
t
h

[
c
m
.
H
2
O
]
2
4
6
8
10
12
14
16
D
e
p
t
h

[
c
m
.
H
2
O
]
120
100
80
60
40
20
120
100
80
60
40
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
20
0
20
10
Depth
[cm.H
2
O]
0
–10
–5
0
Y [cm]
5 10
120
100
80
60
40
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
20
0
20
–40
–20
20
40
0
10
Depth
[cm.H
2
O]
0
–10
–5
0
Y [cm]
5
10
20
10
Depth
[cm.H
2
O]
0
120
100
80
60
40
20
30
20
10
0
–10
–20
FIGURE 8.10
450
400
200
100
f)
rough

r
o
u
g
h

P
a
t
c
h

r
o
u
g
h
P
a
t
c
h
P
a
t
c
h
P
a
t
c
h
5200
100
90
80
70
60 Spinal Cord
GTV
Brainstem
50
V
o
l
u
m
e

(
%
)
Dose (cGy * RBE)
0
5
0
0
1
0
0
0
1
5
0
0
6
0
0
0
5
5
0
0
5
0
0
0
4
5
0
0
4
0
0
0
3
5
0
0
3
0
0
0
2
5
0
0
2
0
0
0
40
30
20
10
0
5000
4750
3000
2000
g)
a)
1 2
3 3
b)
h)
2250
2200
2000
1000
c)
Anterior
Posterior
R
i
g
h
t
L
e
f
t

1100
1000
900
400
d)
1100
1000
900
400
e)
FIGURE 10.9
a)
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
95%
50%
20%
b)
c)
d)
e)
f )
g)
h)
FIGURE 10.10
%
a
112
95
90
80
70
60
50
30
0
%
b
100
40
25
18
12
9
7
5
0
%
c
106
95
90
80
70
60
50
30
0
%
d
100
40
25
18
12
9
7
5
0
%
e
112
95
90
80
70
60
50
30
0
%
f
100
40
25
18
12
9
7
5
0
FIGURE 11.2
Dose %
104
90
80
70
60
50
40
30
0
FIGURE 11.1
%
a
100
40
25
18
12
9
7
5
0
%
b
100
40
25
18
12
9
7
5
0
%
c
112
95
90
80
70
60
50
30
0
%
d
112
95
90
80
70
60
50
30
0
FIGURE 11.6
Dose %
Combined distributon
F3
F1 F2
F4
107
90
80
70
60
50
40
30
0
FIGURE 11.7
Dose %
Combined distributon
F3
F1 F2
F4
122
90
80
70
60
50
40
30
0
FIGURE 11.8
Dose %
a b
c
10%
2
0
.
0
%
2
5
.
0
%
3
0
.
0
%
3
5
.
0
%
4
0
.
0
%
4
5
.
0
%
5
0
.
0
%
5
5
.
0
%
12%
D
1
0
5
-
D
9
5

(
P
T
V

a
t

l
e
v
e
l

o
f

p
a
r
o
t
i
d
s
)
14%
16%
18%
20%
22%
24%
26%
117
110
90
80
70
60
50
30
0
Dose %
123
110
90
80
70
60
50
30
0
Mean bilateral parotid dose
IMRT - 5 Fields
IMRT - 9 Fields
IMPT - 3 Fields
IMPT - 5 Fields
IMPT - 9 Fields
FIGURE 11.9
a b c
d e
2500 spots per field
IMPHNT_CTO_TO IMPHNT_CTO_TO IMPHNT_CTO_TO
150 spots per field 120 spots per field
f
FIGURE 11.10
%
108
105
95
90
80
70
50
30
0
%
131
105
95
90
80
70
50
30
0
%
110
105
95
90
80
70
50
30
0
%
121
105
95
90
80
70
50
30
0
b a
d c
FIGURE 11.13
%
109
105
99
90
80
70
50
D
2
= 106%
D
98
= 99%
D
2
= 106%
D
98
= 97%
30
0
a
%
109
105
99
90
80
70
50
30
0
b
FIGURE 11.14
%
a b
c d
106
SFUD plan
D
o
s
e

d
i
s
t
r
i
b
u
t
i
o
n
C
o
m
p
o
s
i
t
e

e
r
r
o
r
-
b
a
r
IMPT plan
105
95
90
80
70
50
30
0
%
123
105
95
90
80
70
50
30
0
43
Diff-%
20
16
13
10
7
4
1
43
Diff-%
20
16
13
10
7
4
1
FIGURE 11.15
%
a b
c d
e f
107
95
90
80
70
60
50
30
0
%
107
95
90
80
70
60
50
30
0
%
114
95
90
80
70
60
50
30
0
%
114
95
90
80
70
60
50
30
0
%
110
95
90
80
70
60
50
30
0
%
110
95
90
80
70
60
50
30
0
FIGURE 11.17
%
a b
c d
e f
110
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
%
116
95
90
80
70
50
60
30
0
%
116
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
%
110
95
90
80
70
50
60
30
0
FIGURE 11.18
10
30
50
70
90
95
100
102
1
3
5
7
9
9.5
10
FIGURE 12.9
1 Gy(RBE)
3 Gy(RBE)
5 Gy(RBE)
7 Gy(RBE)
9 Gy(RBE)
11 Gy(RBE)
13 Gy(RBE)
15 Gy(RBE)
17 Gy(RBE)
FIGURE 12.10
–10
0
20
40
60
R
e
l
a
t
i
v
e

d
o
s
e

[
%
]
80
100
120
5 cm
2
4
6
8
10
12
14
D
e
p
t
h

[
c
m
.
H
2
O
)
20
40
60
80
100
120
–10 –5 0 5 10
Y [cm]
Measurement
6 cm.H
2
O 3 cm.H
2
O
Depth 8.7 cm
Eclipse (raw)
Eclipse (convolved)
Measurement (diode)
–5 0 5 10
Y [cm]
FIGURE 13.3
100
0.0
0 1000 2000 3000
Dose (cGy)
4000 5000 6000
Lower
bound
95%
0.1
0.2 N
o
r
m
.

v
o
l
u
m
e
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
80
60
40
20
0
0 1 2 3 4
Case 1
Case 2
5 6 7
Dose uncertainty (%)
(a)
(b)
(c)
Dose volume histogram
Upper
bound
FIGURE 13.7
a) b) c)
FIGURE 14.2
T 0%
S
I
L R
T 10% T 20% T 30% T 40%
15
(mm-WEL)
7.5
0
T 50% T 60% T 70% T 80% T 90%
FIGURE 14.4
(a) (b)
Stationary, CTV Stationary, ITV
R
T = 4s, ϕ = 0°
T = 4s,
ϕ = 90°
T = 4s,
ϕ = 0°
T = 4s, ϕ = 90°,
90% etr.
T = 4s, ϕ = 90°
50%
95%
105%
T = 4s, ϕ = 90°, 90% extr.
75
100
80
60
40
20
V
o
l
u
m
e

[
%
]
0
80 85 90 95
Dose [%]
100 105 110 115
Stationary
(d) (e)
(f )
(c)
FIGURE 14.5
No motion 1 rescan 4 rescans 6 rescans 8 rescans
max: 103.2%
100.0%
90.0%
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
a) b) c) d) e)
FIGURE 14.6
A B C
D E F
G
20 30 40 50
Dose [%]
60 70 80 90 100
100
80
60
40
20
0
100
80
60
40
20
0
100
80
60
40
20
0
0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100
H
Dose [%]
Spinal
cord
Stomach
Target
Liver
V
o
l
u
m
e

[
%
]
Dose [%] Dose [%]
I
FIGURE 15.2
B
C D E
A
FIGURE 15.3
Planned dose
mGy
Port-1
Dose Activity (2.5 GyE) Activity (32.5 GyE)
Bq/ml Bq/ml Bq/ml
–1500 –200 –150 –100 –50 200 –1000–500 0 0 0 50 100 150
–150 –100 –50 0 50 100 150
Day 1
Day 4
Day 7
Day 13
–100
R
e
l
a
t
i
v
e

a
c
t
i
v
i
t
y

n
o
r
m
a
l
i
z
e
d

a
t

I
.
C
.

[
%
/
1
0
0
]
–50 50 100
Depth [mm]
0
500 1000 1500
Physical MC PET MC PET + washout PET/CT Meas.
FIGURE 16.10
Target Dose
Homogeneity
OAR Sparing
FIGURE 15.5
A B
FIGURE 15.7
a) b)
Beam direction
10
20
30
40
50 GyRBE
0
0
–0.1
–0.05
0
0.05
0.1
0.15
0.2
0.25
5 10 15 20 25
Radiation dose (GyRBE)
N
o
r
m
a
l
i
s
e
d

s
i
g
n
a
l

i
n
t
e
n
s
i
t
y
30 35 40 45 50
123 cm
36 GyRBE
c)
FIGURE 16.14
6
100%
5
4
3
2
1
FIGURE 19.9
Dose
100
0
5961.3
0
PG
(
%
)
(
C
o
u
n
t
s
/
c
G
y
)
268.3
0
(
C
o
u
n
t
s
/
c
G
y
)
PET
with washout
FIGURE 16.12
A)
Imaging Planning
Dose calculation
Dose-volume histogram (DVH)
Cummulative DVH
PTV
30
20
10
0
0
50
100
V
o
l
u
m
e

(
%
)
V
o
l
u
m
e

(
%

p
e
r

G
y
)
0 20 40 60
0 20 40 60
Myleum Lung Heart
B)
C)
D)
E)
FIGURE 20.1
PROTON THERAPY
PHYSICS
SerieS editorS: John G WebSter, Slavik tabakov, kWan-hoonG nG
Edited by
Harald Paganetti
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a
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PROTON THERAPY PHYSICS
Physics
K11646
A TAYL OR & F RANCI S BOOK
ISBN: 978-1-4398-3644-6
9 781439 836446
90000
Proton Therapy Physics goes beyond current books on proton therapy to
provide an in-depth overview of the physics aspects of this radiation therapy
modality, eliminating the need to dig through information scattered in the
medical physics literature.
After tracing the history of proton therapy, the book summarizes the atomic and
nuclear physics background necessary for understanding proton interactions
with tissue. It describes the physics of proton accelerators, the parameters
of clinical proton beams, and the mechanisms to generate a conformal dose
distribution in a patient. The text then covers detector systems and measuring
techniques for reference dosimetry, outlines basic quality assurance and
commissioning guidelines, and gives examples of Monte Carlo simulations in
proton therapy.
The book moves on to discussions of treatment planning for single- and
multiple-feld uniform doses, dose calculation concepts and algorithms, and
precision and uncertainties for nonmoving and moving targets. It also examines
computerized treatment plan optimization, methods for in vivo dose or beam
range verifcation, the safety of patients and operating personnel, and the
biological implications of using protons from a physics perspective. The fnal
chapter illustrates the use of risk models for common tissue complications in
treatment optimization.
Along with exploring quality assurance issues and biological considerations,
this practical guide collects the latest clinical studies on the use of protons
in treatment planning and radiation monitoring. Suitable for both newcomers
in medical physics and more seasoned specialists in radiation oncology, the
book helps readers understand the uncertainties and limitations of precisely
shaped dose distribution.
K11646_COVER_final.indd 1 10/31/11 3:21 PM