Signals

M E TH O D S 2 5 , 2 4 9 –2 7 1 2 0 0 1  
d o i:1 0 .1 0 0 6 /m e th .2 0 0 1 .1 2 3 8 , a va ila b le o n lin e a t h ttp ://www.id e a lib ra ry.co m o n
S ign a l P ro ce ssin g in M a gn e to e n ce p h a lo gra p h y
Ji ri Vrba and Stephen E. Robi nson
CTF Systems I nc., A subsidiary of VSM MedTech Ltd., 15-1750 McLean Avenue, British Columbia V3C 1M9,
Port Coquitlam, Canada
whi ch fortunatel y become avai l abl e i n 1964 (3, 4),
Th e su b je ct o f th is a rticle is d e te ctio n o f b ra in m a gn e tic fie ld s,
shortl y after the di scovery of the Josephson effect i n
o r m a gn e to e n ce p h a lo gra p h y M E G   . Th e b ra in fie ld s a re m a n y
1962 (5). These hi ghl y sensi ti ve magneti c detectors are
o rd e rs o f m a gn itu d e sm a lle r th a n th e e n viro n m e n ta l m a gn e tic
based on superconducti ng and quantum phenomena
n o ise a n d th e ir m e a su re m e n t re p re se n t a sign ifica n t m e tro lo gica l
and are cal l ed SQUI Ds (superconducti ng quantum i n-
ch a lle n ge . Th e o n ly d e te cto rs ca p a b le o f re so lvin g su ch sm a ll fie ld s
terference devi ce). SQUI Ds were fi rst used for MEG i n a n d a t th e sa m e tim e h a n d lin g th e la rge d yn a m ic ra n ge o f th e
e n viro n m e n ta l n o ise a re su p e rco n d u ctin g q u a n tu m in te rfe re n ce 1972 (6). After thi s pi oneeri ng work, the fi el d of MEG
d e vice s o rS Q U I D s  . Th e S Q U I D s a re co u p le d to th e b ra in m a gn e tic
devel oped fi rst by usi ng si ngl e-channel devi ces, fol -
fie ld s u sin g co m b in a tio n s o f su p e rco n d u ctin g co ils ca lle d flu x
l owed by somewhat l arger systems wi th 5 to 7 channel s
tra n sfo rm e rs p rim a ry se n so rs  . Th e e n viro n m e n ta l n o ise is a tte n u -
i n the mi d- 1980s, then systems wi th 20 to 40 sensor
a te d b y a co m b in a tio n o f sh ie ld in g, p rim a ry se n so r ge o m e try, a n d
arrays i n the l ate 1980s and earl y 1990s, and fi nal l y
syn th e tic m e th o d s. O n e o f th e m o st su cce ssfu l syn th e tic m e th o d s
the fi rst hel met MEG systems were i ntroduced i n 1992.
fo r n o ise e lim in a tio n is syn th e tic h igh e r-o rd e r gra d io m e te rs. H o w
Present-day MEG systems have several hundreds chan-
th e gra d io m e te rs ca n b e syn th e size d is sh o wn a n d e xa m p le s o f
nel s i n a hel met arrangement and operate i n ei ther
th e ir n o ise ca n ce lla tio n e ffe ctive n e ss a re give n . Th e M E G sign a ls
si tti ng or supi ne posi ti on. m e a su re d o n th e sca lp su rfa ce m u st b e in te rp re te d a n d co n ve rte d
in to in fo rm a tio n a b o u t th e d istrib u tio n o f cu rre n ts with in th e b ra in .
I n addi ti on to MEG, magneti c si gnal s were al so de-
Th is ta sk is co m p lica te d b y th e fa ct th a t su ch in ve rsio n is n o n -
tected from other body organs (7), e.g., heart, eye, stom-
u n iq u e . Ad d itio n a l m a th e m a tica l sim p lifica tio n s, co n stra in ts, o r
ach, smal l i ntesti ne, skel etal muscl es, peri pheral
a ssu m p tio n s m u st b e e m p lo ye d to o b ta in u se fu l so u rce im a ge s.
nerves, fetal heart, fetal brai n, l ungs. However, so far
M e th o d s fo r th e in te rp re ta tio n o f th e M E G sign a ls in clu d e th e
the most i mportant appl i cati on of bi omagneti sm has
p o p u la r p o in t cu rre n t d ip o le , m in im u m n o rm m e th o d s, sp a tia l
been to the brai n and the MEG started i ntense techno-
filte rin g, b e a m fo rm e rs, M U S I C , a n d B a ye sia n te ch n iq u e s. Th e u se
l ogi cal devel opment i n l ow-noi se mul ti channel mag-
o f syn th e tic a p e rtu re m a gn e to m e try a cla ss o f b e a m fo rm e rs  is
neti c detecti on and l ed to the establ i shment of several illu stra te d in e xa m p le s o f in te ricta l e p ile p tic sp ik in g a n d vo lu n ta ry
h a n d -m o to r a ctivity. ᭧ 2 0 0 1 E lse vie r S cie n ce commerci al suppl i ers (8–10). I t i s i nteresti ng to note
that duri ng the 22-year peri od from 1970 to 1992 onl y
about 1000 SQUI D sensors were produced and used i n
al l appl i cati ons (7) (i ncl udi ng nonbi omagneti c appl i ca-
ti ons), However, si nce the i ntroducti on of the fi rst hel -
Magnetoencephal ography (MEG) i s a di sci pl i ne con-
met systems i n 1992, nearl y 10,000 SQUI D sensors
cerned wi th detecti on and i nterpretati on of magneti c
have been i nstal l ed i n approxi matel y 60 MEG hel met
fi el ds produced by the human brai n. I t i s a rel ati vel y
systems now operati ng around the worl d.
new fi el d, even though the detecti on of el ectromagneti c
MEG measurements span a frequency range from
acti vi ty of the human brai n has a l ong hi story. The
about 10 mHz to 1 kHz (or perhaps as l ow as 1 mHz
el ectroencephal ogram was fi rst measured i n 1929 (1)
for sl eep studi es) and fi el d magni tudes from about 10
and i ts magneti c counterpart, the magnetoencephal o-
fT for spi nal cord si gnal s to about several pi cotesl a for gram, was fi rst recorded 40 years l ater, i n 1968 (2),
brai n rhythms (11). To appreci ate how smal l the MEG usi ng room temperature coi l s. Further progress i n MEG
requi red more sensi ti ve detectors of magneti c fi el ds, si gnal s are, i t shoul d be recal l ed that the Earth’s fi el d
1046-2023/01 $35.00 2 4 9
᭧ 2001 El sevi er Sci ence
Al l ri ghts reserved.
VRBA AND ROBI NSON 2 5 0
magni tude i s about 0.5 mT and the urban magneti c and e) and the radi al currents woul d produce no mag-
neti c fi el ds (Fi g. 1d). I f the magneti c detectors were noi se about 1 nT to 1 ␮T, or about a factor of 1 mi l l i on
to 1 bi l l i on l arger than the MEG si gnal s. Such l arge radi al to the head, then MEG woul d be mostl y sensi ti ve
to the i mpressed i ntracel l ul ar currents, whi l e EEG di fferences between si gnal and noi se demand noi se can-
cel l ati on wi th extraordi nary accuracy. woul d detect the return vol ume currents.
Current fl ow wi thi n a si ngl e cel l i s too smal l and MEG si gnal s are measured on the surface of the head
and they refl ect the current fl ow i n the functi oni ng cannot produce observabl e magneti c fi el ds outsi de the
scal p. For fi el ds to be detectabl e, i t i s necessary to have brai n. The cortex Fi g. 1a) contai ns wel l -al i gned pyrami -
dal cel l s, whi ch consi st of dendri tes, cel l body, and an nearl y si mul taneous acti vati on of a l arge number of
cel l s, typi cal l y 10
4
to 10
5
(15). General l y, the MEG axon and there are approxi matel y 10
5
to 10
6
cel l s i n an
area of about 10 mm
2
of cortex (12). There are many sources are di stri buted; however, acti vati on of even
l arge numbers of cel l s can often be assumed spati al l y connecti ons between vari ous parts of the brai n medi -
ated by nerve fi bers whi ch are connected to dendri tes smal l and can be model ed by a poi nt equi val ent current
di pol e (16). As an exampl e, consi der audi tory evoked and cel l bodi es vi a synapses. I n the whol e brai n there
are approxi matel y 10
10
cel l s and about 10
14
synapti c fi el ds (AEFs) as i n Fi g. 19. Such fi el ds typi cal l y yi el d
equi val ent current di pol e magni tudes i n the range 20 connecti ons.
Because of i oni c exchange between the cel l and i ts to 80 nAиm (18). I t was shown that the current di pol e
densi ty i n the brai n ti ssue i s nearl y constant and ranges surroundi ngs, the equi l i bri um between di ffusi on proc-
esses and el ectri cal forces establ i shes negati ve poten- from about 0.5 to 2 nAиm/mm
2
(17), whi ch for our AEF
di pol e magni tude transl ates to the order of 1 cm
2
of ti al s of about Ϫ70 mV wi thi n the cel l (13). Cel l sti mul a-
ti on (chemi cal , el ectri cal , or even mechani cal )can cause acti vated corti cal ti ssue. For such a rel ati vel y smal l
acti vati on area, approxi mati on of the equi val ent cur- al terati on of the cel l ’s transmembrane potenti al and
can l ead to cel l depol ari zati on (or hyperpol ari zati on). rent di pol e i s sati sfactory.
MEG measures the di stri buti on of magneti c fi el ds on Such changes can occur, e.g., at the synapse, when neu-
rotransmi tters are rel eased. Because the cel l i s conduc- the two-di mensi onal head surface. However, the re-
qui red i nformati on i s usual l y a three-di mensi onal di s- ti ve, the depol ari zati on (or hyperpol ari zati on) causes
current fl ow wi thi n the cel l (cal l ed the i mpressed or tri buti on of currents wi thi n the brai n. Unfortunatel y
the fi el d i nversi on probl em i s nonuni que and MEG data i ntracel l ul ar current) and a return current outsi de the
cel l (cal l ed vol ume or extracel l ul ar current). must be suppl emented by addi ti onal i nformati on, phys-
i ol ogi cal constrai nts, or mathemati cal si mpl i fi cati ons. The dendri ti c current due to cel l depol ari zati on (or
hyperpol ari zati on) fl ows roughl y perpendi cul ar to the One way to suppl y more i nformati on i s to al so use EEG
(see Secti on 3). Both MEG and EEG measure the same cortex. However, the cortex i s convol uted wi th numer-
ous sul ci and gyri and, dependi ng on where the cel l sources of neuronal acti vi ty and thei r i nformati on i s
compl ementary (19). Addi ti onal i nformati on to assi st sti mul ati on occurred, the current fl ow can be ei ther
tangenti al or radi al to the scal p surface (Fi g. 1b) I f the fi el d i nversi on can al so be suppl i ed by other i magi ng
techni ques. For structural i nformati on one can use brai n coul d be model ed as a uni form conducti ng sphere,
then due to symmetry, onl y the tangenti al currents magneti c resonance i magi ng (MRI ) and computed axi al
tomography (CAT) and for functi onal i nformati on one woul d produce fi el ds outsi de the sphere (14) (Fi gs. 1c
FIG. 1. Ori gi n of the MEG si gnal . (a) Coronal secti on of the human brai n. Cortex i s i ndi cated by dark col or. The pri mary currents fl ow
roughl y perpendi cul ar to the cortex. (b) The cortex has numerous sul ci and gyri and i ts convol uted nature gi ves ri se to the currents fl owi ng
ei ther tangenti al l y or radi al l y rel ati ve to the head. The head can be approxi mated by a spheri cal conducti ng medi um. (c) Tangenti al currents
wi l l produce magneti c fi el ds that are observabl e outsi de the head. (d) Radi al currents wi l l not produce magneti c fi el ds outsi de the head. (e)
Magneti c fi el ds due to corti cal sources wi l l exi t and reenter the scal p.
SI GNAL PROCESSI NG I N MEG 2 5 1
can use posi tron emi ssi on tomography (PET), si ngl e- measurement. I t i s esti mated the overal l head l ocal i za-
photon emi ssi on computed tomography (SPECT), and ti on accuracy, consi deri ng al l errors, i s about 2 or 3
functi onal MRI (fMRI ). mm. Note that duri ng the EEG measurement, the EEG
A typi cal MEG system i s a compl ex i nstal l ati on and el ectrodes are attached di rectl y to the scal p surface i n
a schemati c di agram i s shown i n Fi g. 2. The SQUI D fi xed posi ti ons rel ati ve to the head geometry and the
detectors of magneti c fi el d are housed i n a cryogeni c questi on of head l ocal i zati on for the EEG purposes i s
contai ner cal l ed a dewar, whi ch i s usual l y mounted i n not an i ssue (however, the el ectrode posi ti ons must be
a movabl e gantry for hori zontal or seated posi ti ons. The
known accuratel y and shoul d be di gi ti zed).
subject or pati ent i s posi ti oned on an adjustabl e bed or
Photographs of a 151-channel MEG system (8) for
chai r. The SQUI D system and pati ent may or may not
hori zontal and seated operati on are shown i n Fi g. 3.
be posi ti oned i n a shi el ded room. At present, the major-
The MEG measurement process i ncl udes di verse
i ty of i nstal l ati ons use shi el ded rooms; however, pro-
technol ogi es rangi ng from superconducti ng sensors, to
gress i s bei ng made toward unshi el ded operati ons. The
anal ogue and di gi tal SQUI D el ectroni cs, to computer
MEG measurement i s usual l y suppl emented by EEG
data acqui si ti on. Thi s procedure i nvol ves frequenci es
and both MEG and EEG si gnal s are transmi tted from
rangi ng from mi l l i hertz to more than a gi gahertz, as
the shi el ded room to the SQUI D and processi ng el ec-
shown i n Fi g. 4. Di fferent frequency ranges are poi nted
troni cs and the computers for data anal ysi s and archi v-
out duri ng the di scussi on of rel evant MEG system
i ng. The MEG system al so contai ns sti mul us del i very
components.
and i ts associ ated computer, whi ch i s synchroni zed wi th
The arti cl e i s organi zed as fol l ows: Detecti on of the
the data acqui si ti on. The i nstal l ati on i s compl eted wi th
brai n magneti c fi el ds i s di scussed i n Secti on 1. Secti on
a vi deo camera(s) and i ntercom for observati on of and
1.1 outl i nes pri nci pl es of SQUI D sensors and Secti on
communi cati on wi th the subject i n the shi el ded room.
1.2 i ntroduces fl ux transformers and compares thei r
Even though the subject’s head i s i nserted i n the
performance. Secti on 1.3 di scusses how the processi ng
MEG hel met, there i s sti l l freedom to move i t, and
el ectroni cs works, expl ai ns how SQUI Ds are control l ed
accurate measurement of the head posi ti on rel ati ve to
by the el ectroni cs and what preprocessi ng and real -
the MEG sensors i s necessary (the posi ti on i nformati on
ti me processi ng tasks are performed by the el ectroni cs,
i s used to regi ster the MEG resul ts rel ati ve to the brai n
and di scusses data col l ecti on i ssues and exampl es. Sec-
anatomy, e.g., to MRI i mages). To accompl i sh accurate
ti on 1.4 descri bes the cryogeni cs requi red for the opera-
l ocal i zati on, vari ous 3D di gi ti zi ng methods may be
ti on of SQUI D sensors. Envi ronmental noi se cancel l a-
used, e.g., (20), or the MEG system i tsel f may be used
ti on i s necessary for successful MEG operati on. Noi se
for the head posi ti on determi nati on. I n that case three
cancel l ati on methods and the system requi rements for
smal l coi l s are mounted on the subject’s head at the
thei r successful performance are di scussed i n Secti on
nasi on and preauri cul ar poi nts. The coi l s are energi zed
2. Secti on 3 bri efl y outl i nes EEG and i ts i ntegrati on
from the computer; thei r magneti c si gnal s are detected
wi th MEG. Secti on 4 di scusses what i s done wi th the
by the MEG system and used to determi ne the head
measured MEG data and how the i nformati on about
posi ti on. The measuri ng procedure has submi l l i meter
sources wi thi n the brai n i s extracted.
accuracy; however, the l argest errors are caused by i n-
The materi al presented i n thi s arti cl e has general
accurate coi l pl acements or by head moti on duri ng the
val i di ty; however, when di scussi ng speci fi c detai l s of
the i nstrumentati on CTF’s MEG system (8) i s used as
an exampl e because the authors are most fami l i ar
wi th i t.
1 . S E N S I N G O F M AG N E TI C FI E LD S
Hi gh-qual i ty detecti on of brai n magneti c fi el ds i s the
fi rst step i n the MEG si gnal processi ng chai n. The
measured brai n fi el ds are smal l and the onl y detectors
wi th adequate sensi ti vi ty are SQUI D sensors. A sche-
mati c di agram of a typi cal SQUI D magnetometer i s
shown i n Fi g. 5.
SQUI D sensors exhi bi t hi gh sensi ti vi ty to magneti c
fi el ds; however, thei r confi gurati on i s not best sui ted FIG. 2. Schemati c di agram of an MEG i nstal l ati on (8).
VRBA AND ROBI NSON 2 5 2
for the di rect detecti on of brai n fi el ds. SQUI Ds are cou- model ed as a superconducti ng ri ng i nterrupted by two
pl ed to the brai n fi el ds by means of fl ux transformers. resi sti vel y shunted Josephson juncti ons as i n Fi g. 6a
SQUI Ds and thei r fl ux transformers are superconduct- (3). Josephson juncti ons are superconducti ng quantum
i ng and must be operated at l ow temperatures, usual l y mechani cal devi ces that al l ow passage of currents wi th
i mmersed i n cryogen (ei ther l i qui d He for l ow-T
c
zero vol tage, and when vol tage i s appl i ed to them, they
SQUI Ds or l i qui d N
2
for hi gh-T
c
SQUI Ds). The cryogen exhi bi t osci l l ati ons wi th frequency to vol tage constant
i s contai ned i n a thermal l y i nsul ated contai ner (dewar), of about 484 MHz/␮V. The resi sti ve shunti ng causes the
whi ch must be el ectromagneti cal l y transparent so that Josephson juncti ons to work i n a nonhystereti c mode,
the brai n si gnal s can reach the fl ux transformers and whi ch i s necessary for l ow-noi se operati on (21). The
the SQUI D detectors. SQUI D si gnal s are transmi tted
SQUI D sensors are usual l y made of thi n fi l ms, even
to room temperature and ampl i fi ed, before bei ng sub-
though i n the past vari ous 3D structures were used.
jected to processi ng by the SQUI D el ectroni cs. The si g-
An exampl e of a thi n-fi l m dc SQUI D, consi sti ng of a
nal s from the SQUI D el ectroni cs may be preprocessed
square washer and Josephson juncti ons near the out-
i n real ti me before they are acqui red and mani pul ated
si de edge, i s shown i n Fi g. 6b (22, 23).
by a computer. SQUI D el ectroni cs and real -ti me proc-
The SQUI D ri ng (or washer) must be coupl ed to the
essi ng el ectroni cs may be combi ned i n one el ectroni cs
external worl d and to the el ectroni cs that operates i t
system. Vari ous el ements of SQUI D magnetometers are
(see Fi g. 7a). Because the SQUI D i mpedance i s l ow, i t i s
di scussed i n more detai l i n the fol l owi ng secti ons.
usual l y matched to the room temperature preampl i fi er
ei ther by a cool ed transformer (24) (shown i n Fi g. 6a),
or a cool ed resonant ci rcui t (25). The i mpedance of the
1 .1 . S Q U I D S e n so rs matchi ng el ements i s desi gned to opti mi ze the noi se
temperature of the preampl i fi er. When the dc SQUI D
The SQUI D sensor i s the heart of the MEG system
i s current bi ased, i ts I –V characteri sti cs i s si mi l ar to
and i t provi des hi gh-sensi ti vi ty detecti on of smal l MEG
that of a nonhystereti c Josephson juncti on and i ts cri ti -
si gnal s. The most popul ar types of SQUI Ds are dc and
cal current I
0
i s modul ated by magneti c fl ux external l y
rf SQUI Ds, deri vi ng thei r names from the method of
appl i ed to the SQUI D ri ng. The modul ati on ampl i tude
thei r bi asi ng. The operati on of SQUI Ds i s descri bed
i s roughl y equal to ⌽
0
/L (21), where ⌽
0
i s the fl ux quan-
bri efl y i n thi s secti on; a more detai l ed descri pti on of
tum wi th magni tude Ϸ2.07 ϫ10
Ϫ15
Wb and L i s i nduc- thei r operati on can be found i n the l i terature [see, e.g.,
tance of the SQUI D ri ng. The cri ti cal current i s maxi - an excel l ent revi ew (21)].
mum for appl i ed fl ux ⌽ ϭ n⌽
0
and mi ni mum for ⌽ ϭ The modern commerci al MEG i nstrumentati on uses
(n ϩ 1/2)⌽
0
, and the dc SQUI D I –V characteri sti cs are dc SQUI Ds i mpl emented i n l ow-temperature supercon-
ducti ng materi al s (usual l y Nb). The dc SQUI D can be represented by heavy l i nes i n Fi g. 7b. When the SQUI D
FIG. 3. Photograph of a 151-channel MEG system (8). (a) Hori zontal operati on. (b) Seated operati on.
SI GNAL PROCESSI NG I N MEG 2 5 3
i s bi ased by a dc current I
DC
Ͼ I
0
, the average val ue of of gi gahertz. The osci l l ati ons are hi ghl y asymmetri c
and thei r average vol tage i s not zero. Al l vol tages di s- the resul ti ng vol tage across the SQUI D i s modul ated
by external l y appl i ed fl ux between two extreme val ues cussed i n connecti on wi th Fi g. 7 correspond to these
average vol tages. V
1
and V
2
i n Fi g. 7b. For monotoni cal l y i ncreasi ng fl ux
the average SQUI D vol tage osci l l ates as i n Fi g. 7c wi th The rf SQUI Ds were popul ar i n the earl y days of
superconducti ng magnetometry because they requi red peri od equal to 1 ⌽
0
. The maxi mum magni tude of the
vol tage modul ati on i s approxi matel y ⌬V ϭ ⌽
0
R/(2L), onl y one Josephson juncti on; however, i n the majori ty
of l ow-T
c
commerci al appl i cati ons, rf SQUI Ds have been where R/2 i s the paral l el resi stance of the two shunt
resi stors i n Fi g. 6a. Thus the SQUI D fl ux-to-vol tage di spl aced by dc SQUI Ds. I n recent years, i nterest i n rf
SQUI Ds has been renewed i n connecti on wi th hi gh-T
c
transfer functi on i s a mul ti val ued peri odi c si nusoi dal
functi on and the SQUI D i s typi cal l y operated on i ts superconducti vi ty. The rf SQUI D consi sts of a super-
conducti ng i nductor i nterrupted by one nonhystereti c steep part where the magni tude of the transfer coeffi -
ci ent V
⌽
ϭ ѨV/Ѩ⌽ i s maxi mum. Josephson juncti on, as i n Fi g. 7d. The SQUI D i s coupl ed
to a tank ci rcui t and the average vol tage on the tank Because the SQUI D i s bi ased above i ts cri ti cal
current, there i s a vol tage appl i ed to the Josephson ci rcui t i s a measure of the fl ux appl i ed to the SQUI D
(26, 27). juncti ons. The appl i ed vol tage causes the juncti ons to
produce hi gh-frequency osci l l ati ons at Josephson fre- The behavi or of rf SQUI D current and fl ux i s espe-
ci al l y si mpl e for LI
0
⌽
0
. Assume that the SQUI D quency (5), whi ch for typi cal dc SQUI Ds i s of the order
has been cool ed to the superconducti ng state i n zero
external fi el d and the current and fl ux i n the SQUI D
i nductor are zero (zero fl ux state, n ϭ 0). Appl i cati on
of a smal l fl ux to the SQUI D wi l l gi ve ri se to a screeni ng
current i n the SQUI D i nductor, but the fl ux i nsi de the
SQUI D ri ng wi l l remai n essenti al l y zero. As the appl i ed
fl ux sl owl y i ncreases, the magni tude of the screeni ng
current al so i ncreases, whi l e the fl ux remai ns cl ose to
FIG. 4. Frequenci es needed for MEG si gnal processi ng. The brai n
zero. When the screeni ng current reaches the cri ti cal
si gnal s range from mi l l i hertz to ki l ohertz, the magneti c SQUI D detec-
tors contai n frequenci es i n the gi gahertz range, and the SQUI D el ec- val ue I
0
of the Josephson juncti on, the juncti on momen-
troni cs operates wi th frequenci es i n the hundreds of ki l ohertz and
tari l y swi tches i nto a resi sti ve state and the SQUI D
tens of megahertz. The shaded bar i n the “MEG si gnal s” i ndi cates
jumps from the state n ϭ 0 to n ϭ 1. For a monotoni c
the range where the spontaneous MEG can be seen above the sensor
fl ux i ncrease thi s process repeats i tsel f and resul ts i n
noi se wi thout any processi ng or averagi ng.
peri odi c i nserti on of more fl ux quanta i nto the
SQUI D i nductor.
Consi der a SQUI D ri ng threaded by fl ux ⌽
S
and i n-
ducti vel y coupl ed to a tank ci rcui t. The tank ci rcui t i s
exci ted at i ts resonant frequency by current I
rf
and the
current through the tank ci rcui t i nductor, L
T
, i s propor-
ti onal to QI
rf
, where Q i s the tank ci rcui t qual i ty factor.
For smal l I
rf
the rf fl ux coupl ed to the SQUI D i s smal l
and the SQUI Dscreeni ng current osci l l ates around zero
and the fl ux through the SQUI D i nductor remai ns
FIG. 5. Schemati c di agram of a typi cal SQUI D magnetometer.
roughl y constant. I n thi s regi me the vol tage V
rf
on the
tank ci rcui t i ncreases proporti onal l y to I
rf
, as i n Fi g. 7e
for smal l I
rf
. As the bi as I
rf
i ncreases, i t reaches a l evel
at whi ch the i nduced SQUI D screeni ng current magni -
tude at the rf peak reaches the cri ti cal current I
0
, the
fl ux transi ti on occurs, and 1 ⌽
0
i s ei ther added or sub-
tracted from ⌽
S
. The fl ux transi ti on wi l l di ssi pate en-
ergy from the tank ci rcui t and wi l l reduce the tank
ci rcui t vol tage magni tude and therefore the i nduced
FIG. 6. Di agram of a typi cal thi n-fi l m dc SQUI D. (a) Schemati c
screeni ng current i n the SQUI D ri ng.
di agram i ndi cati ng i nductance of the SQUI D ri ng and shunti ng resi s-
I t takes many rf cycl es to repl eni sh the di ssi pated
tors to produce nonhystereti c Josephson juncti ons (the Josephson
energy and to restore the rf current through L
T
to i ts
juncti ons are i ndi cated by ϫ’s). (b)Di agram of a si mpl e SQUI Dwasher
wi th Josephson juncti ons, JJ, near the outer edge. ori gi nal val ue, before the next quantum transi ti on i n
VRBA AND ROBI NSON 2 5 4
the SQUI D ri ng i s tri ggered. For l arger I
rf
bi ases, the where S
⌽
( f ) i s the spectral densi ty of the fl ux noi se.
For dc SQUI Ds the energy sensi ti vi ty was shown by current i n the L
T
recovers i n fewer rf cycl es; however,
the average tank ci rcui t vol tage wi l l remai n constant si mul ati ons to be ␧ ϭ 9k
B
TL/R (31). For typi cal dc
SQUI Ds [e.g., i n commerci al bi omagnetometers (29)] (hori zontal part of the V
rf
vs I
rf
characteri sti cs i n Fi g.
7e). More detai l ed anal ysi s reveal s that as a functi on of the energy sensi ti vi ty may be ␧ Ϸ10
Ϫ31
–10
Ϫ32
J/Hz and
for typi cal rf SQUI Ds operated i n 30- to 50-MHz range the tank ci rcui t bi as I
rf
, the V
rf
-versus-I
rf
characteri sti cs
exhi bi t a seri es of pl ateaus and ri sers (21). Si mi l ar to ␧ Ϸ 5 ϫ 10
Ϫ29
J/Hz (28, 31). Thus, for typi cal appl i ca-
ti ons, the fi el d sensi ti vi ty of dc SQUI Ds i s more than 10 the dc SQUI Ds, the l evel at whi ch the tank ci rcui t i s
stabi l i zed al so depends on the dc fl ux threadi ng the ti mes better than that of rf SQUI Ds. Energy sensi ti vi ty
achi eved for experi mental dc SQUI Ds cool ed to 0.3 K SQUI D ri ng, bei ng maxi mum for appl i ed fl ux ⌽ ϭ n⌽
0
and mi ni mum for ⌽ ϭ (n ϩ 1/2)⌽
0
. I n between the two was ␧ Ϸ 3 ϫ 10
Ϫ34
J/Hz Ϸ 3 ប (30), and for rf SQUI Ds
usi ng cool ed hi gh-el ectron-mobi l i ty transi stors as a pre- extreme fl ux l evel s the tank ci rcui t vol tage changes
l i nearl y wi th the fl ux. For monotoni cal l y i ncreasi ng ap- ampl i fi er, ␧ Ϸ 3 ϫ 10
Ϫ32
J/Hz (32).
I n recent years, there has been si gni fi cant progress pl i ed fl ux, the tank ci rcui t osci l l ates between i ts two
extreme l evel s and the rf SQUI D transfer functi on i s i n the devel opment of hi gh-T
c
SQUI Ds, both dc and rf.
These devi ces are usual l y constructed from a tri angul ar peri odi c functi on of appl i ed fl ux wi th peri -
odi ci ty of 1 ⌽
0
, as shown i n Fi g. 7f. The magni tude of YBa
2
Cu
3
O
7Ϫx
cerami cs. Hi gh-T
c
SQUI D magnetome-
ters were shown to achi eve noi se l evel s bel ow the vol tage tri angl es i n Fi g. 7f i s (21) ⌬V ϭ ␻
rf
L
T
⌽
0
/
(2M), where ␻
rf
i s the rf frequency and M i s mutual 10 fT/ΊHz (33); however, thei r poorer l ow-frequency
performance and di ffi cul ti es wi th reproduci bl e l arge- i nductance between the tank ci rcui t coi l L
T
and the
SQUI D ri ng. I f LI
0
Ϸ ⌽
0
, the vol tage tri angl e hei ght i s vol ume manufacturi ng do not yet make them sui tabl e
for l arge-scal e MEG appl i cati ons. opti mi zed for k
2
Q Ն ␲/4, where k i s the coupl i ng con-
stant between the SQUI D i nductor L and the tank i n-
ductor L
T
, k ϭ M/ΊLL
T
.
The magneti c fi el d resol uti on of SQUI D sensors i s
1 .2 . Flu x Tra n sfo rm e rs
gi ven by thei r noi se performance whi ch can be conve-
The purpose of fl ux transformers i s to coupl e the
ni entl y characteri zed i n terms of the noi se energy per
SQUI D sensors to the measured si gnal s and to i ncrease
uni t bandwi dth (21) (or energy sensi ti vi ty)
overal l magneti c fi el d sensi ti vi ty. Fl ux transformers are
superconducti ng and consi st of a pi ckup coi l (s) whi ch
i s exposed to the measured fi el ds, l eads, and a coupl i ng ␧( f ) ϭ
S
⌽
( f )
2L
, [1]
FIG. 7. SQUI D sensors and thei r operati ng characteri sti cs. (a) dc SQUI D and i ts coupl i ng ci rcui try; the Josephson juncti ons i n the SQUI D
are assumed to be resi sti vel y shunted. (b) Current–vol tage characteri sti cs of a dc SQUI D. (c) Fl ux (or fi el d)-to-vol tage transfer functi on of
a dc SQUI D. (d) rf SQUI D and i ts coupl i ng ci rcui try; (e) Mean tank vol tage versus rf bi as characteri sti cs of a rf SQUI D. (f) Fl ux-to-vol tage
transfer functi on of a rf SQUI D.
SI GNAL PROCESSI NG I N MEG 2 5 5
coi l whi ch i nducti vel y coupl es the fl ux transformer to di pol ar magneti c source. The fi el d of a di pol e decays
the SQUI D ri ng (see the l eft-hand i nductors i n Fi gs. 7a wi th di stance, R, as 1/R
3
. The fi rst gradi ent decays as
and 7d). Because the fl ux transformers are super- 1/R
4
, and for each i ncrease of the gradi ent order by 1
conducti ng, they do not generate noi se and thei r gai n
the decay exponent al so i ncreases by 1. Thus the gradi -
i s noi sel ess.
ents due to di stant sources are reduced far more than
The fl ux transformer pi ckup coi l s can have di verse
the fi el ds, whi l e for the near (brai n) sources the gradi o-
confi gurati ons (Fi g. 8). A si ngl e l oop of wi re acts as a
meters and magnetometers have comparabl e sensi ti vi -
magnetometer and i s sensi ti ve to the magneti c fi el d
ti es. Al so, the attenuati on of di stant sources i s better
component perpendi cul ar to i ts area (Fi gs. 8a and 8b).
when the gradi ent order i s hi gh.
Two magnetometer l oops can be combi ned wi th opposi te
For these purposes the earl y si ngl e channel MEG
ori entati on and connected by the same wi re to the
detectors used second- or thi rd-order hardware gradi o-
SQUI D sensor. Such confi gurati on i s sensi ti ve onl y to
meters, Fi gs 8f–8h. However, the hardware gradi omet-
the magneti c fi el d changes across the devi ce di mensi on
ers are bul ky, di ffi cul t to manufacture accuratel y, and
and the pi ckup coi l s are cal l ed fi rst-order gradi ometers,
al so parti al l y reduce the MEG si gnal s. For these rea-
(Fi gs. 8c–8e). Si mi l arl y, fi rst-order gradi ometers can be
sons, l arge-scal e MEG i nstruments use onl y magnetom-
combi ned wi th opposi ng pol ari ty to form second-order
eters or fi rst-order gradi ometers as pri mary sensors,
gradi ometers (Fi gs. 8f and 8g) and second-order gradi o-
and for effecti ve noi se cancel l ati on, the hi gher-order
meters can be combi ned to form thi rd-order gradi omet-
gradi ometers are synthesi zed i n software or fi rmware
ers (Fi g. 8h). Other confi gurati ons are possi bl e but not
(35).
wi del y used i n MEG practi ce (tangenti al gradi ent of
Mai n types of hardware fl ux transformers used i n
tangenti al fi el d, e.g., (c) or (d) ti pped to i ts si de, paral l el
commerci al practi ce as pri mary sensors are magnetom-
pl anar gradi ometers). The pl anar structures i n Fi gs.
eters (Fi g. 8a), radi al gradi ometers (Fi g. 8c), and pl anar
8a, 8b, 8d, and 8e permi t thi n-fi l m constructi on and
gradi ometers (Fi g. 8d). Thei r responses toan equi val ent
i ntegrati on wi th the SQUI D sensor on the same chi p.
current di pol e, (Fi g. 9) were computed assumi ng that
The fl ux transformers i n Fi g. 8 are cal l ed hardware
the current di pol e i s l ocated bel ow the poi nts i ndi cated
fl ux transformers, because they are di rectl y constructed
by bl ack arrows and the respecti ve devi ces are scanned
i n hardware by i nterconnecti ng vari ous coi l s. I n Secti on
i n a pl ane above the di pol e.
2 syntheti c gradi ometers are di scussed.
The radi al magnetometer produces a fi el d map wi th
An i mportant functi on of fl ux transformers i n MEG
one maxi mum and one mi ni mum, symmetri cal l y l o-
appl i cati ons i s to hel p reduce envi ronmental noi se. I n
cated on the di pol e si des (Fi g. 9a). The separati on of
an i deal noi sel ess si tuati on, i t woul d be suffi ci ent to
the extrema, d, can be used to determi ne the di pol e
use magnetometers as i n Fi gs. 8a and 8b. However, the
depth as d/Ί2 (36). Di rectl y above the di pol e the radi al
magnetometers are sensi ti ve not onl y to the near-fi el d
fi el d i s zero. The radi al gradi ometer i n Fi g. 9b produces
MEG si gnal s but al so to the fi el ds generated by di stant
si mi l ar fi el d pattern as the magnetometer, except that noi se sources. For these reasons, the MEG systems usu-
al l y empl oy some ki nd of gradi ometer as a pri mary
sensor. The gradi ometers attenuate si gnal s from di s-
tant sources and i n effect behave as spati al hi gh-pass
fi l ters (34). Thi s can be understood by consi deri ng a
FIG. 9. Response to a poi nt current di pol e of the most frequentl y
used hardware fl ux transformers. A tangenti al di pol e i s posi ti oned
2 cm deep i n a semi -i nfi ni te conducti ng space bounded by x
3
ϭ 0
pl ane and i ts fi el d i s scanned by the fl ux transformers posi ti oned i n
x
3
ϭ 0 pl ane. Di mensi ons of each map are 14 ϫ 14 cm. Schemati c FIG. 8. Exampl es of hardware fl ux transformers for bi omagneti c
appl i cati ons. The fl ux transformer ori entati on assumes that the scal p top vi ew of the fl ux transformers i s shown i n the upper part of each
fi gure. Sol i d and dashed l i nes i ndi cate di fferent fi el d pol ari ti es. (a) surface i s at the bottom of the fi gure. (a) Radi al magnetometer. (b)
Tangenti al magnetometer. (c) Radi al fi rst-order gradi ometer. (d) Pl a- Radi al magnetometers, Fi g. 8a. (b) Radi al gradi ometers wi th 4-cm
basel i ne, Fi g. 8c. (c) Pl anar gradi ometers wi th 1.5-cm basel i ne, Fi g. nar fi rst-order gradi ometer. (e) Radi al gradi ometer for tangenti al
fi el ds. (f) Second-order symmetri c gradi ometer. (g) Second-order 8d, al i gned for maxi mum response. (d) Pl anar gradi ometers wi th 1.5-
cm basel i ne, Fi g. 8d, al i gned for mi ni mum response. asymmetri c gradi ometer. (h) Thi rd-order symmetri c gradi ometer.
VRBA AND ROBI NSON 2 5 6
the pattern i s spati al l y ti ghter. Thi s i s because the grad- because di fferent sensors measure contri buti ons from
i ometer subtracts two fi el d patterns measured at di ffer- the same regi ons of the brai n. I n many si tuati ons, how-
ent di stances from the surface of the scal p. The pl anar
ever, the background brai n acti vi ty i s consi dered the
gradi ometer fi el d patterns i n Fi gs. 9c and 9d are qui te
si gnal and the argumentati on based on the brai n noi se
di fferent from those of radi al devi ces. I f the two coi l s
i s i rrel evant. I f the envi ronmental noi se were the onl y
of the pl anar gradi ometer were al i gned perpendi cul ar
noi se acti ng on the detector, the pl anar gradi ometers
tothe di pol e, as i n Fi g. 9c, the pl anar gradi ometer woul d
woul d cl earl y be subopti mal because thei r basel i nes are
exhi bi t a peak di rectl y above the di pol e; i f the two coi l s
too short (about 1.4–1.6 cm) (see Fi g. 10c).
were al i gned paral l el to the di pol e, the pl anar gradi o-
To compare the performance of radi al and pl anar
meter woul d read zero di rectl y above the di pol e and the
gradi ometers for whi te sensor noi se and brai n noi se, i t
map of i ts response woul d exhi bi t a weak, cl overl eaf
i s assumed that the gradi ometer arrays are used to
pattern. I f two orthogonal pl anar gradi ometers were
l ocal i ze one equi val ent current di pol e source (14) and
posi ti oned at the same l ocati on, thei r two i ndependent
the standard devi ati on of the source posi ti on, ␴, i s used
components woul d determi ne ori entati on of the current
as a measure of the devi ce performance. ␴ i s di rectl y
di pol e l ocated di rectl y under the gradi ometers (37).
connected to confi dence i nterval s and i t i s al so rel ated
I n the absence of noi se, the detected fi el d patterns
to the S/N rati o (i nversel y proporti onal to i t). When
i n Fi g. 9 coul d be transformed from one to another
onl y the random sensor noi se acts on the gradi ometers,
and there woul d be no practi cal di fference between the
␴ val ues are shown i n Fi g. 10d as a functi on of the
devi ces. However i n the presence of noi se (Secti on 2)
the si tuati on i s more compl i cated and the si gnal -to-
noi se rati os of di fferent devi ces can di ffer si gni fi cantl y,
resul ti ng i n si gni fi cant performance di fferences. The
i deas behi nd compari ng di fferent devi ces on the basi s
of thei r S/N rati os are i l l ustrated i n Fi g. 10.
Fi rst, consi der radi al devi ces and ask whether we
want gradi ometers or magnetometers (the magnetome-
ters can be thought of as gradi ometers wi th i nfi ni tel y
l ong basel i ne) and what shoul d the opti mum gradi o-
meter basel i ne (separati on between the coi l s) be. I t can
be shown that the magni tude of the detected brai n si g-
nal i ncreases wi th gradi ometer basel i ne (Fi g. 10a) and
the magni tude of the detected envi ronmental noi se al so
i ncreases wi th i ncreasi ng basel i ne (Fi g. 10b) (38). Both
the detected brai n si gnal and detected envi ronmental
noi se i ncrease wi th i ncreasi ng basel i ne, but si nce thei r
functi onal dependenci es are di fferent, the S/N rati o
peaks at a certai n opti mum basel i ne, (Fi g. 10c). Si nce
FIG. 10. Opti mi zati on of fl ux transformer noi se performance and
the S/N rati o i s the most i mportant operati ng parame-
compari son of di fferent fl ux transformer types: 150 channel s, sensor
shel l radi us r ϭ11 cm, head radi us r
head
ϭ9.1 cm. (a–c) Opti mi zati on ter of MEG sensors, we shoul d choose basel i nes corres-
of the radi al gradi ometer basel i ne: (a)radi al gradi ometer brai n si gnal
pondi ng to thi s opti mum basel i ne, whi ch i s i n the range
as a functi on of basel i ne l ength; (b) envi ronmental noi se detected by
of about 3 to 8 cm. Thus magnetometers are not opti mal
the radi al gradi ometer as a functi on of the basel i ne l ength; (c) si gnal -
because thei r “basel i ne” i s too l ong and as a resul t thei r
to-noi se rati o as a functi on of the basel i ne. An opti mum operati ng
poi nt exi sts at rel ati vel y short basel i nes. (d–f) Compari son of the
S/N performance i s i nferi or to that of radi al gradi omet-
standard devi ati on of the di pol e l ocal i zati on error, ␴, for pl anar and
ers wi th opti mum basel i ne.
radi al gradi ometers i n the presence of random or correl ated brai n
To deci de between radi al and pl anar gradi ometers,
noi se; (d) pl anar and radi al gradi ometers, random noi se, n
w
ϭ 5 fT
the noi se has to be agai n consi dered. There are three
rms/͌Hz, bandwi dth ϭ 100 Hz; (e) pl anar and radi al gradi ometers,
correl ated brai n noi se, bandwi dth ϭ 100 Hz, number of averages ϭ
major types of noi se acti ng on the detector: whi te noi se
100, brai n noi se densi ty detected by radi al gradi ometers, n
b
ϭ 30 fT
of the sensors, envi ronmental noi se, and brai n noi se.
rms/͌Hz, and pl anar gradi ometers, n
p
ϭ 15 fT rms/͌Hz; (f) di ffer-
The brai n noi se i s the brai n si gnal due to the extended
ence between pl anar and radi al standard devi ati ons of the l ocal i zati on
background brai n acti vi ty. Thi s background si gnal can accuracy. The upper curve corresponds to the random sensor noi se,
the l ower curve to the correl ated brai n noi se. When the di fference i s
be consi dered a noi se when a speci fi c l ocati on i n the
posi ti ve, the radi al gradi ometers gi ve smal l er l ocal i zati on errors, and
brai n i s i nvesti gated and si gnal s from other brai n re-
when the di fference i s negati ve, the pl anar gradi ometers gi ve smal l er
gi ons are of no i nterest (e.g., duri ng studi es of evoked
l ocal i zati on errors. The shaded band i ndi cates the mechani cal uncer-
tai nty of the l ocal i zati on and regi strati on. responses) (37). The brai n noi se i s spati al l y correl ated,
SI GNAL PROCESSI NG I N MEG 2 5 7
di pol e depth bel ow the scal p surface. For al l i nvesti - pi ckup l oop, L
P
i s the pi ckup l oop i nductance, k i s cou-
pl i ng constant between the SQUI D and the fl ux trans- gated depths the standard devi ati on ␴ i s l arger for pl a-
nar gradi ometers than for radi al gradi ometers. The per- former coupl i ng coi l , ␮
0
i s permeabi l i ty of vacuum, and
␧ i s the SQUI D energy sensi ti vi ty (Eq. [2]). I t was as- formance of pl anar gradi ometers i n thi s regi me i s worse
than that of radi al gradi ometers because pl anar gradi o- sumed duri ng deri vati on of the ri ght-hand si de of Eq.
[2] that the i nductance of the pi ckup l oop can be approx- meter si gnal strength decays faster wi th depth than
radi al gradi ometers si gnal strength. i mated by L
P
Ϸ 5␮
0
r (31). Eq. [2] i ndi cates that the
magnetometer resol uti on can be made arbi trari l y smal l The magni tude of brai n noi se detected by di fferent
sensor types scal es wi th the sensor abi l i ty to see more by i ncreasi ng the radi us r of the pi ckup coi l . For a
typi cal DC SQUI Ds (e.g., i n commerci al MEG systems) di stant sources. Thus pl anar gradi ometers wi th about
1.5-cm basel i ne wi l l see about 50% of the brai n noi se the energy sensi ti vi ty may be ␧ Ϸ 10
Ϫ31
to 10
Ϫ32
J/Hz,
k Ϸ0.7 and the magnetometer wi th 1-cm di ameter l oop that radi al gradi ometers wi th about 5-cm basel i ne see
(37). I f brai n noi se was used for cal cul ati on of ␴, then woul d exhi bi t sensi ti vi ty of ␦B
mag
Ϸ 1 to 3 fT/ΊHz. The
method of gradi ometer sensi ti vi ty opti mi zati on i s si mi - the resul t woul d be as i n Fi g. 10e. I n thi s case, because
of the l ower brai n noi se, the pl anar gradi ometer ␴ i s l ar and terms descri bi ng i nducti ve effects of vari ous
coi l s i n the gradi ometer fl ux transformer must be i n- smal l er than the radi al gradi ometer ␴ for source depths
smal l er than Ϸ5 cm. For deeper sources pl anar gradi o- cl uded i n Eq. [2] (42). To enhance the fl ux transformer –
SQUI D resol uti ons, asymmetri cal fl ux transformers as meter ␴ becomes l arger than radi al gradi ometer ␴,
agai n because pl anar gradi ometers l ose si gnal strength i n Fi g. 8g can be constructed, and i f mul ti turn coi l s are
used, the turns can be spaced to reduce the i nducti ve faster than radi al gradi ometers. Even though pl anar
gradi ometers produce smal l er posi ti oni ng errors than l oadi ng.
Pri mary hardware gradi ometers were di scussed as- radi al gradi ometers for sources l ess than 5 cm deep,
the di fferences between the two devi ces are smal l . Thi s sumi ng that they are manufactured perfectl y. Real
gradi ometers, however, are subject to di fferent manu- i s emphasi zed i n Fi g. 10f, where the di fference ␴
pl anar
Ϫ
␴
radi al
i s pl otted as a functi on of depth for both the ran- facturi ng errors: thei r coi l s may not have equal areas,
coi l s coul d be ti l ted, there are parasi ti c l oops i n the dom sensor and correl ated brai n noi se. When the di ffer-
ence i s negati ve, pl anar gradi ometers produce the bet- gradi ometer l eads, or there coul d be pi eces of bul k su-
perconductor or normal metal i n thei r vi ci ni ty. Al l these ter resul t (dashed l i ne); when the di fference i s posi ti ve,
radi al gradi ometers produce the better resul t (sol i d factors conspi re to make the gradi ometers sensi ti ve not
onl y to the desi gned gradi ents, but al so to magneti c l i ne). Al so shown by the shaded band i s the range of
head posi ti oni ng and MRI regi strati on i naccuraci es fi el ds and/or thei r deri vati ves. These errors are cal l ed
common mode and eddy current errors and they must (Ϯ0.2 cm). The pl anar gradi ometer advantage i s over-
shadowed i n thi s regi on of posi ti oni ng i naccuracy and be el i mi nated ei ther by hardware or software bal anci ng
(42). Di scussi on of these probl ems and of correcti ve ac- i s not real l y i mportant.
Based on envi ronmental noi se, i t was shown that ti ons i s outsi de the scope of thi s arti cl e.
magnetometers have poorer S/N performance than ra-
di al gradi ometers. The consi derati on of brai n noi se,
1 .3 . S Q U I D E le ctro n ics
when appl i cabl e, makes the magnetometer even more
di sadvantaged because they see about 30% more brai n The SQUI D transfer functi on i s peri odi c (Fi g. 7c) and
to l i neari ze i t, the SQUI D i s operated i n a feedback l oop noi se than radi al gradi ometers wi th about 5 cm base-
l i ne. as a nul l detector of magneti c fl ux (25). Most SQUI D
appl i cati ons use an anal og feedback l oop, as shown i n To concl ude thi s secti on, the desi gn of hardware grad-
i ometers for opti mum coupl i ng to SQUI D sensors i s Fi gs. 11a and 11b. A modul ati ng fl ux wi th Ϯ1/4 ⌽
0
ampl i tude i s appl i ed to the SQUI D sensor through the bri efl y outl i ned. To opti mi ze a fl ux transformer, i t i s
requi red that fl ux transferred to the SQUI D l oop (e.g., feedback ci rcui try. The modul ati on, feedback si gnal ,
and fl ux transformer output are superposed i n the Fi g. 7a) be maxi mi zed. To i l l ustrate the opti mi zati on,
consi der a si mpl e magnetometer fl ux transformer. The SQUI D, ampl i fi ed, and demodul ated i n a l ock-i n detec-
tor fashi on. The demodul ated output i s i ntegrated, am- opti mum fi el d resol uti on i s gi ven by (31)
pl i fi ed, and fed back as a fl ux to the SQUI D sensor to
mai ntai n i ts total i nput cl ose to zero. The modul ati on
fl ux superposed on the dc SQUI D transfer functi on i s ␦B
mag
ϭ
2Ί2␧L
p
kA
Ϸ
2(␮
0
␧)
1/2
kr
3/2
, [2]
shown i n Fi g. 11d. and the modul ati on frequenci es are
typi cal l y several hundreds of ki l ohertz.
The anal og feedback l oop i s not al ways adequate for where A i s the pi ckup l oop area, r i s the radi us of the
VRBA AND ROBI NSON 2 5 8
MEG operati on. Even though MEG si gnal s are rel a- i ntegrator to ensure opti mum i nterchannel matchi ng
ti vel y smal l and wel l behaved, the MEG system i s al so (41) (see Fi g. 11c). The extensi on of the dynami c range
exposed to envi ronmental noi se, whi ch i ncreases de-
by usi ng the fl ux peri odi ci ty of the SQUI D transfer
mand on the MEG el ectroni cs system performance. Ex-
functi on works i n the fol l owi ng manner: The l oop i s
ami nati on of the range of envi ronmental si gnal s ob-
l ocked at a certai n poi nt on the SQUI D transfer functi on
served duri ng ei ther shi el ded or unshi el ded operati ons
and remai ns l ocked for the appl i ed fl ux i n the range of
i ndi cates that for sati sfactory MEG operati on the
Ϯ1 ⌽
0
, (Fi g. 11d). When thi s range i s exceeded, the l oop
SQUI D system must exhi bi t l arge dynami c ranges, ex-
l ock i s rel eased and the l ocki ng poi nt i s shi fted by 1 ⌽
0
cel l ent i nterchannel matchi ng, good l i neari ty, and sati s-
al ong the transfer functi on. The fl ux transi ti ons al ong
factory sl ew rates. The exact parameters depend on
the transfer functi on are counted and are merged wi th
whether the pri mary sensors are magnetometers or
the si gnal from the di gi tal i ntegrator to yi el d a 32-
gradi ometers and whether the system i s operated un-
bi t dynami c range. The l i neari ty of the system was
shi el ded or shi el ded (39). Typi cal l y, the dynami c ranges
measured to be better than 10
Ϫ6
at a si gnal ampl i tude
requi red for gradi ometer pri mary sensors are about 22
of 1000⌽
0
(i t i s not known whether the l i neari ty l i mi t
and 27 bi ts for shi el ded and unshi el ded operati on, re-
i s due to the SQUI Ds, el ectroni cs system, or measuri ng
specti vel y. Si mi l ar numbers for magnetometer pri mary
apparatus). The fl ux sl i ppi ng concept can al so be i mpl e-
sensors are 27 and 31 bi ts. The i nterchannel matchi ng
mented usi ng four-phase modul ati on (47), where the
i s especi al l y i mportant when the pri mary sensors are
feedback l oop jumps by ⌽
0
/2 and can al so provi de com-
magnetometers, where for the shi el ded operati on tens
pensati on for the vari ati on of SQUI D i nductance wi th
of mi croseconds, and for unshi el ded several 100-nano-
fl ux changes (whi ch mi ght be i mportant for hi gh-T
c seconds, synchroni ety i s requi red.
SQUI D sensors).
To accommodate the above requi rements, the dy-
MEG systems contai n l arge numbers of MEG, EEG,
nami c range of the SQUI D feedback l oop was extended
and auxi l i ary channel s and the archi tecture of the di gi - by usi ng the fl ux peri odi ci ty of the SQUI D transfer
functi on (40) and the l oop was compl eted wi th a di gi tal tal el ectroni cs must be desi gned to accommodate them.
FIG. 11. SQUI D wi thi n a feedback l oop. (a) Coupl i ng of SQUI D sensor to the ampl i fi er. (b) Anal og feedback l oop. (c) Di gi tal feedback l oop
usi ng di gi tal si gnal processor (DSP). (d) Feedback l oop modul ati on.
SI GNAL PROCESSI NG I N MEG 2 5 9
A bl ock di agram of such a system i s shown i n Fi g. 12 el ectroni cs archi tecture provi des powerful processi ng
capabi l i ti es, i ncl udi ng real -ti me fi l teri ng, resampl i ng, (43). The el ectroni cs consi sts of four major parts: MEG,
EEG, peri pheral i nterface uni t (PI U), and DSP proces- hi gher-order gradi ometer synthesi s (Secti on 2), di spl ay,
and real -ti me executi on of numerous other computa- sor uni t. The MEG uni t i s organi zed i n banks; each
bank can have up to 192 MEG channel s (Fi g 12 shows ti onal l y i ntensi ve functi ons (such as covari ance up-
dates, cross-power updates, coherence cal cul ati ons, two banks wi th 384 MEG channel s). The banks contai n
SQUI D el ectroni cs as di scussed above, control for spati al fi l teri ng). The el ectroni cs computati onal power
can al so be used for fast off-l i ne processi ng of previ ousl y SQUI Ds, automated tuni ng and di agnosti cs, heaters,
data communi cati on i nterface, and di gi tal processors col l ected data.
MEG systems col l ect l arge quanti ti es of data. Toi l l us- for real -ti me computati on tasks. MEG el ectroni cs and
SQUI Ds were desi gned for robust operati on, exhi bi ti ng trate thi s poi nt, consi der, e.g., a system wi th 200 MEG
channel s, 64 EEG el ectrodes, 16 ADC/DAC channel s hi gh i mmuni ty to rf i nterference, i mmuni ty to fl uxi ng,
and “set and forget” tuni ng. and 4 mi scel l aneous channel s. Each MEG and EEG
channel data word i s 4 bytes l ong, correspondi ng to The EEG subsystem has a si mi l ar modul ar desi gn
and can contai n mul ti pl e channel uni ts, each accommo- 1056 bytes, and the ADC/DAC and mi scel l aneous chan-
nel s are onl y 2 bytes l ong, correspondi ng to 40 bytes. dati ng up to 32 EEG channel s (composed of 24 uni pol ar
channel s and 8 ei ther bi pol ar or uni pol ar channel s). Therefore, one sampl e of MEG system output i s 1096
bytes l ong. I f the sampl e rate was 4000 sampl es/s, then The EEG i s di gi ti zed to 21 bi ts (usi ng oversampl i ng)
and for conveni ence, si mi l ar to MEG, the EEG data the data rate woul d be about 4.4 Mbyte/s. Consi der
speci fi c experi ments. For exampl e an evoked fi el d ex- word i s al so 4 bytes. The PI U i s desi gned to accept or
transmi t si gnal s to the peri pheral equi pment, sti mul a- peri ment (such as, e.g., AEF di scussed before) may be
col l ected wi th sampl e rate of 625 sampl es/s, 1.5-sec du- ti on equi pment, head posi ti oni ng, head shape di gi ti za-
ti on, and EEG el ectrode posi ti on measurement. The rati on per tri al , and a total of 100 tri al s, resul ti ng i n
103 Mbyte of data. Epi l epsy moni tori ng at a sampl e DAC uni ts al so doubl e as functi on generators for a
range of waveforms. Si gnal s from the MEG, EEG, and rate of 2000 sampl es/s for 10 mi n woul d resul t i n 1.3
Gbyte of data. I f 10 to 15 pati ents were exami ned per PI U are transmi tted by fi beropti c l i nks to the DSP uni t
for preprocessi ng before the data are acqui red by a host day, the data vol ume woul d be 1 to 20 Gbyte per day.
computer. The system al l ows for sampl e rates of up
to 4 kHz wi th a total of 450 channel s (hi gher sampl e
rates up to 12 kHz are possi bl e for smal l er subsets
1 .4 . C ryo ge n ics
of channel s).
The MEG sensi ng el ements (SQUI Ds, fl ux transform-
A more general i zed bl ock di agram of the MEG el ec-
ers, and thei r i nterconnecti ons) are superconducti ng
troni cs, emphasi zi ng i ts real -ti me and off-l i ne proc-
and must be mai ntai ned at l ow temperatures. Si nce al l
essi ng capabi l i ti es, i s shown i n Fi g. 13 (8). The Pro-
commerci al MEG systems use l ow-temperature super-
grammabl e Gate Array/Di gi tal Si gnal Processor MEG
conductors, they must be operated at l i qui d He temper-
atures. The He temperatures can be achi eved ei ther
wi th cryocool ers or wi th a cryogeni c bath i n contact
wi th the superconducti ng components. The cryocool ers
are attracti ve because they el i mi nate the need for peri -
odi c refi l l i ng of the cryogeni c contai ner; however, they
FIG. 12. Bl ock di agram of the di gi tal MEG/EEG el ectroni cs archi -
tecture, shown wi th two banks for up to 384 SQUI D channel s, and
a custom number of EEG and ADC/DAC channel s (8). dc SQUI D FIG. 13. Bl ock di agram of the di gi tal MEG system el ectroni cs (8)
wi th capabi l i ty for real -ti me preprocessi ng of MEG/EEG si gnal s, real - ampl i fi er uni ts contai n 8 channel s per uni t, the MEG “channel uni ts”
contai n 16 channel s per uni t, and the EEG contai n 32 channel s per ti me computati on of numeri cal l y extensi ve tasks, and off-l i ne capabi l -
i ty as a fast processor. uni t. PGA, programmabl e gate array; DSP, di gi tal si gnal processor.
VRBA AND ROBI NSON 2 6 0
contri bute l arge magneti c i nterference and are not sui t- tens of them. The col d gases from the evaporati ng He
abl e for sensi ti ve MEG i nstrumentati on [EMI i nterfer- carry out energy that i s captured i n the dewar neck and
ence, vi brati onal noi se, thermal fl uctuati ons, and
conducted by heat shi el ds back i nto the dewar vacuum
Johnson noi se from metal l i c parts (44)]. The present
space to hel p reduce the thermal gradi ent between the
commerci al MEG systems rel y on cool i ng by l i qui d He
l i qui d He and the envi ronment. Agai n, onl y one heat
bath contai ned i n a dewar. An exampl e of how the com-
shi el d i s shown i n Fi g. 14b, but several shi el ds may be
ponents may be organi zed wi thi n the dewar i s shown
empl oyed. The overal l dewar desi gn takes i ntoconsi der-
i n Fi g. 14a (8). The pri mary sensi ng fl ux transformers
ati on heat l osses through radi ati on, conducti on, and
(radi al gradi ometers i n thi s case) are posi ti oned on He
convecti on and mi ni mi zes them by usi ng refl ecti vi ty,
surface of the dewar hel met area. The reference system
i nsul ati on, and energy extracti on from the escapi ng He
for the noi se cancel l ati on (Secti on 2) i s posi ti oned cl ose
vapors. The dewar desi gns are hi ghl y effi ci ent and the
to the pri mary sensors and the SQUI Ds, wi th thei r
present commerci al MEG systems consume l i qui d He
shi el ds l ocated some di stance from the references, al l
at a rate of approxi matel y 10 l i ters per day.
i mmersed i n l i qui d He or col d He gas.
The dewar i s a compl ex dynami c devi ce that i ncorpo-
rates vari ous forms of thermal i nsul ati on, heat conduc-
2 . N O I S E C AN C E LLATI O N ti on, and radi ati on shi el di ng. An excel l ent revi ew of the
i ssues associ ated wi th dewar constructi on i s presented
i n (44); onl y a qual i tati ve descri pti on of the dewar oper-
Noi se at the output of MEG sensors i s a combi nati on
ati on i s gi ven here. A schemati c di agram of the dewar
of sensor whi te noi se, brai n noi se, and envi ronmental
i nner structure i s shown i n Fi g. 14b. Si mi l ar to the
noi se. Sensor noi se can be mi ni mi zed to acceptabl e l ev-
standard coffee thermos fl asks, the He dewar i s an
el s by careful desi gn of the SQUI D and pri mary fl ux
evacuated doubl e-wal l ed vessel . Because the thermal
transformers, and brai n noi se (i f i t i s consi dered noi se
di fferenti al between the envi ronment and the He l i qui d
and not si gnal ) can be control l ed or reduced by spati al
i s about 300ЊC (whi l e for the coffee i t may be onl y about
fi l teri ng methods. Envi ronmental noi se i s caused by
50ЊC), thermal radi ati on l osses (whi ch are proporti onal
vari ous movi ng magneti c objects (cars, peopl e, trai ns,
to T
4
) are an i mportant factor i n the overal l dewar
etc.)or by el ectri cal equi pment (power l i nes, computers,
heat budget. To protect the cryogen from the thermal
vari ous machi nery, etc.). I t i s usual l y generated at
radi ati on mul ti pl e l ayers of superi nsul ati on (thi n met-
l arger di stances from the MEG system and the mag-
al l i zed myl ar foi l ) are pl aced i nto the dewar vacuum
neti c i nterference magni tudes at urban l ocati ons or space. Onl y two superi nsul ati on l ayers are shown i n
Fi g. 14b; however, i n real dewars there may be several even at rural areas are many orders of magni tude l arger
FIG. 14. Schemati c di agram of cryogeni cs used for MEG. (a) Pl acement of vari ous MEG components rel ati ve to the cryogeni c dewar. (b)
Pri nci pl es of the dewar operati on.
SI GNAL PROCESSI NG I N MEG 2 6 1
than the magneti c fi el ds of the brai n (42). I t was sug- hi gher-order gradi ometers or adapti ve systems. I f refer-
ences are not used, spati al fi l teri ng methods (si gnal gested i n Secti on 1.2 that the pri mary MEG sensors
coul d be hardware gradi ometers to hel p reduce the ef- space projecti on or beamformers) are empl oyed. Spati al
fi l teri ng i s often a part of the si gnal i nterpretati on and fect of the envi ronmental noi se. Even though such an
approach i s benefi ci al , i t i s not suffi ci ent, and addi ti onal i s di scussed i n more detai l i n Secti on 4. The di scussi on
i n thi s secti on concentrates on noi se cancel l ati on by methods for envi ronmental noi se el i mi nati on have been
the subject of i ntense study duri ng MEG hi story. Envi - usi ng references.
When cancel i ng noi se usi ng references, a l i near com- ronmental noi se reducti on by shi el di ng, acti ve noi se
compensati on, syntheti c gradi ometers, adapti ve meth- bi nati on of the reference outputs i s subtracted from the
MEG pri mary sensor output and the coeffi ci ents of the ods, and spati al fi l teri ng i s di scussed or touched on i n
thi s secti on. l i near combi nati on are sel ected to reduce envi ronmen-
tal noi se. The subtracti on coeffi ci ents may be chosen Encl osi ng the MEG system wi thi n a shi el ded encl o-
sure (shi el ded room) i s the most strai ghtforward ei ther to mi mi c a hi gher-order gradi ometer component
or on the basi s of some other requi rement (e.g., mi ni - method for reducti on of envi ronmental noi se. The si m-
pl est shi el di ng can be accompl i shed by eddy currents mum noi se). The advantage of synthesi zi ng hi gher-or-
der gradi ometers i s that thei r coeffi ci ents are trul y uni - usi ng a thi ck l ayer of hi gh-conducti vi ty metal (54), but
such shi el di ng i s not effecti ve at l ow frequenci es. versal ; they can be factory predetermi ned and are
i ndependent of the noi se character or dewar ori entati on Shi el di ng usi ng hi gh-permeabi l i ty materi al s provi des
l ow-frequency attenuati on and i s often al so suppl e- (43). I n contrast, the coeffi ci ents determi ned by adapta-
ti on for mi ni mum noi se are not uni versal because they mented by eddy current shi el di ng to enhance the
hi gher-frequency attenuati on. Typi cal shi el ded rooms depend on the noi se character and dewar ori entati on
(48). Thus even though the adaptati on coeffi ci ents can for MEG exhi bi t a l ow-frequency shi el di ng factor of 50
to 100 and the shi el di ng factor i ncreases i n proporti on provi de l ower noi se than the syntheti c gradi ometer co-
effi ci ents, the frequent need for readaptati on for every to frequency above about 0.1 or 0.2 Hz (45). Shi el ded
␮-metal rooms wi th hi gh attenuati on i n excess of about dewar ori entati on or change of the noi se character
makes them l ess desi rabl e than the gradi ometer coeffi - 10
4
at l ow frequenci es have al so been constructed, but
they are expensi ve and are used mostl y for experi men- ci ents. However, i n MEG systems equi pped wi th suffi -
ci ent number of references, the swi tch between the tal purposes [the recentl y constructed shi el ded room i n
Berl i n i s desi gned for l ow-frequency attenuati on of Ϸ gradi ometer or adapti ve coeffi ci ents i s a software opera-
ti on and both methods can be si mul taneousl y avai l - 3 ϫ10
4
wi thout acti ve shi el di ng (46)]. The hi gh l evel s of
shi el di ng can al so be accompl i shed by superconducti ng abl e (43).
Si nce the syntheti c gradi ometers provi de stabl e and shi el ds, an exampl e bei ng the whol e-body hi gh-temper-
ature superconducti ng Bi
2
Sr
2
Ca
1
Cu
2
O
x
shi el d wi th at- excel l ent noi se cancel l ati on whi ch i s addi ti ve to the
attenuati on of the shi el ded rooms, thei r synthesi s i s tenuati on approachi ng 10
8
(49).
The envi ronmental magneti c noi se of shi el ded or un- di scussed i n greater detai l . The pri nci pl e of syntheti c
gradi ometer operati on i s si mi l ar for al l gradi ometer shi el ded systems can be reduced by acti ve noi se com-
pensati on (50, 51). The acti ve compensati on consi sts of orders, and the method i s i l l ustrated on si mpl e exam-
pl es of fi rst- and second-order gradi ometers (42). Fi rst, a reference detector of magneti c fi el d, feedback el ec-
troni cs, and a set of compensati ng coi l s and i s usual l y consi der a fi rst-order gradi ometer synthesi zed from a
magnetometer pri mary sensor and a three-component operated onl y at l ow frequenci es. The sensors can be
ei ther SQUI Ds, fl uxgate magnetometers, or coi l s ex- vector magnetometer reference, as i n Fi g. 15a. The pri -
mary magnetometer detects the magneti c fi el d compo- posed to the envi ronmental magneti c fi el ds. I f the sen-
sors are l ocated wi thi n a di stance of about 1 m from nent paral l el to i ts coi l normal , p (uni t vector). I f the
magnetometer gai n was ␣
p
and the envi ronmental fi el d the detecti on area, attenuati on better than about 40
dB can be real i zed. was B, the pri mary magnetometer woul d detect m
p
ϭ
␣
p
(pB). The three reference magnetometers are orthog- Hardware noi se cancel l ati on (shi el di ng or acti ve
noi se cancel l ati on) i s usual l y not suffi ci ent and addi - onal and have i denti cal gai ns ␣
r
and thei r outputs wi l l
be r
k
ϭ ␣
r
B
k
, k ϭ 1, 2, 3, where B
k
are components of ti onal methods, i mpl emented i n software or fi rmware,
are empl oyed. These addi ti onal methods ei ther use ref- B. The components r
k
form a vector of the reference
magnetometer output, r. Then, by expandi ng the mag- erence magneti c sensors (other than the pri mary MEG
sensors) or operate di rectl y on the MEG sensors (wi th neti c fi el d i nto a Tayl or seri es about the ori gi n, defi ni ng
gradi ometer basel i ne b as a vector connecti ng the pri - or wi thout the references). The references are typi cal l y
a combi nati on of SQUI D magnetometers and gradi o- mary magnetometer center and the reference center,
and projecti ng the reference output to the di recti on p, meters and the noi se i s cancel l ed by synthesi zi ng ei ther
VRBA AND ROBI NSON 2 6 2
the syntheti c fi rst-order gradi ometer, g
(1)
, can be de- Equati on [4] shows that the syntheti c second-order
ri ved as gradi ometer i s a projecti on of the second gradi ent tensor
i nto the coi l ori entati on vector p and basel i ne vectors
qand b. Agai n, i f p, q, and bori entati ons are general ,
g
(1)
ϭ m
p
Ϫ
␣
p
␣
r
(pr) Ϸ ␣
p
pGb, [3]
the syntheti c second-order gradi ometer output wi l l
be a l i near combi nati on of the second gradi ent tensor
components.
where G i s the fi rst gradi ent tensor at the coordi nate
The above di scussi on i l l ustrates the approach to
ori gi n. Note that i n thi s and al l subsequent deri vati ons,
hi gher-order gradi ometer synthesi s. The procedure can
the gradi ometer output i s expressed as fi el d; i .e., the
be general i zed and i t can be shown that second- or
gradi ent tensor components are mul ti pl i ed by the rel e-
thi rd-order gradi ometers can be synthesi zed from
vant gradi ometer basel i nes. Equati on [3] states that
magnetometers, or fi rst-order gradi ometers, or thei r
the syntheti c fi rst-order gradi ometer i s a projecti on of
combi nati ons.
the fi rst gradi ent tensor to the pri mary magnetometer
The syntheti c hi gher-order gradi ometers substan- ori entati on, p, and the basel i ne, b. I f p and b ori enta-
ti al l y reduce the envi ronmental noi se and yet, from the ti ons are general , the syntheti c gradi ometer i n Eq. [3]
MEG si gnal poi nt of vi ew, they behave nearl y l i ke the consi sts of a l i near combi nati on of the fi rst gradi ent
pri mary sensors on whi ch they are based. Speci fi cal l y, tensor components.
Synthesi s of a second-order gradi ometer i s si mi l ar the syntheti c gradi ometers do not i ncrease the whi te
(see Fi g. 15b). Assume that there are two fi rst-order noi se l evel s (because the references are desi gned wi th
gradi ometers wi th paral l el basel i nes band bЈ, and par- hi gher gai n than the pri mary sensors) and they do not
al l el coi l ori entati on uni t vectors p and pЈ, and the substanti al l y reduce the MEG si gnal ; i n fact they can
output of each gradi ometer i s gi ven by Eq. [3] as g
(1)
and sl i ghtl y i ncrease i t or reduce i t, dependi ng on the exact
g
(1)
’. The second-order gradi ometer basel i ne, q, connects
confi gurati on of the MEG sources and references (52).
the two gradi ometer centers. The second-order gradi o-
Thi s i s i l l ustrated i n Fi g. 16 where an audi tory evoked
meter, g
(2)
, i s synthesi zed si mi l ar to the fi rst-order grad-
fi el d for one channel i s di spl ayed for a pri mary hard-
i ometer by scal i ng the gai ns and basel i nes and sub-
ware fi rst-order gradi ometer and a syntheti c thi rd-
tracti ng fi rst-order gradi ometer outputs (42),
order gradi ometer based on the same pri mary sensor.
I n thi s exampl e the syntheti c thi rd-order gradi ometer
si gnal ampl i tude i s sl i ghtl y l arger than that of the hard-
g
(2)
ϭ g
(1)
Ϫ
␣
g
␣
gЈ
b
bЈ
g
(1)
Ј Ϸ ␣
g
pG
(2)
qb, [4]
ware fi rst-order gradi ometer.
The l ow noi se and smal l effect on the MEG si gnal s
for syntheti c gradi ometers are very di fferent from what where ␣
g
i s the fi rst-order gradi ometer gai n and G
(2)
i s
the second gradi ent tensor at the coordi nate ori gi n. i s usual l y observed for hardware gradi ometers of the
FIG. 15. I l l ustrati on of gradi ometer synthesi s. (a) Synthesi s of a fi rst-order gradi ometer from a pri mary magnetometer sensor and a vector
magnetometer reference. (b) Synthesi s of a second-order gradi ometer from two hardware fi rst-order gradi ometers.
SI GNAL PROCESSI NG I N MEG 2 6 3
same order and approxi mate di mensi ons. Hardware whi l e the effect of syntheti c gradi ometers on MEG si g-
hi gher-order gradi ometers provi de l arge i nducti ve l oad- nal i s smal l and they can ei ther i ncrease or reduce i t
i ng on the SQUI D sensor and reduce overal l sensi ti vi ty
(52) (Fi g. 16).
(42), whi l e syntheti c hi gher-order gradi ometer sensi ti v-
Envi ronmental noi se reducti on by the syntheti c grad-
i ty i s typi cal l y i ndi sti ngui shabl e from that of the pri -
i ometers i s i l l ustrated i n Fi g. 17a for a 151-channel
mary sensor. Si mi l arl y, hardware hi gher-order gradi o-
MEG system operated wi thi n a shi el ded room. The gray
meters are known to strongl y reduce MEG si gnal s,
traces show noi se spectra of al l channel s, the bl ack l i nes
overl yi ng the gray show rms noi se computed over al l
channel s. Note that the spectral l i nes at about 1.8 and
7 Hz are compl etel y el i mi nated by syntheti c thi rd-order
gradi ometers. At l ow frequenci es, syntheti c thi rd-order
gradi ometers reduce the pri mary fi rst-order hardware
gradi ometer sensor noi se by about two orders of magni -
tude and reduce magnetometer noi se by about four or-
ders of magni tude (43). The effect of a shi el ded room
i s addi ti ve to the syntheti c gradi ometer noi se reducti on.
I f shi el ded room attenuati on at l ow frequenci es were
about a factor of 70, the combi ned shi el ded room and
syntheti c thi rd-order gradi ometer attenuati on of the
envi ronmental noi se woul d be about 7 ϫ 10
5
.
FIG. 16. Syntheti c hi gher-order gradi ometers do not reduce si gnal .
Exampl e of audi tory evoked fi el ds measured wi th hardware fi rst- Syntheti c gradi ometers al so dramati cal l y reduce
order gradi ometer and syntheti c thi rd-order gradi ometer, 100 aver-
MEG system sensi ti vi ty to vi brati onal noi se. Thi s i s
ages, measured i n shi el ded room. I n thi s exampl e, the syntheti c thi rd-
i l l ustrated i n Fi g. 17b, where measurement duri ng pa-
order gradi ometer si gnal magni tude i s l arger than that of the fi rst-
order hardware gradi ometer. ti ent head moti on i s shown. Head moti on i s cl earl y
FIG. 17. Exampl es of syntheti c gradi ometer performance. (a) Noi se spectra of magnetometers, hardware fi rst-order gradi ometer pri mary
sensors, and syntheti c thi rd-order gradi ometers for al l channel s of 151-channel MEG system wi th 29 references, operated wi thi n a shi el ded
room (43) (b) I l l ustrati on of syntheti c thi rd-order gradi ometer i mmuni ty to vi brati ons. The pati ent head moti on arti facts are compl etel y
el i mi nated by the syntheti c thi rd-order gradi ometer.
VRBA AND ROBI NSON 2 6 4
vi si bl e i n the references and the pri mary fi rst-order measurements can be confi gured so that there i s l i ttl e
contri buti on from vol ume currents.
1
By contrast, bi oe- hardware gradi ometer sensor, but i t i s compl etel y el i mi -
nated by the syntheti c thi rd-order gradi ometer. l ectri c potenti al measures vol ume currents onl y. As
such, source current determi nati on from EEG measure-
ments al so requi res accurate knowl edge of the conduc-
ti vi ty di stri buti on. Si nce MEG measurements have onl y
3 . E E G
weak dependence on ti ssue conducti vi ty, pri mary cur-
rent sources are readi l y l ocal i zed, wi thout havi ng
El ectri c potenti al s (EEG) and magneti c fi el ds (MEG)
knowl edge of ti ssue conducti vi ty or i ts boundari es.
are rel ated because they both detect the same current
The overal l goal s of MEG anal ysi s are twofol d: fi rst,
generators. Whi l e radi al magneti c fi el ds are generated
enhancement of si gnal -to-noi se rati o of el ectrophysi o-
mostl y by the i ntracel l ul ar current, the EEG measures
l ogi cal si gnal s sothat they may be readi l y i denti fi ed and
vol ume currents. Magneti c fi el d maps and el ectri c fi el d
cl assi fi ed; second, determi nati on of where the si gnal s
patterns on the surface of the scal p are orthogonal (Fi g.
ori gi nate. I n thi s secti on, we outl i ne onl y the quanti ta-
18a), and an experi mental demonstrati on of EEG/MEG
ti ve aspects of MEG anal ysi s, and focus on the func-
orthogonal i ty for mechani cal sti mul ati on of the ri ght
ti onal i magi ng method, syntheti c aperture magnetome-
i ndex fi nger can be found i n (53). The EEG and MEG
try (SAM). Quanti tati ve MEG i mpl i es deri vati on of
must be measured si mul taneousl y to take advantage
objecti ve i ndi ces of the si gnal s bei ng measured. The
of the compl ementary i nformati on. EEG el ectrodes and
fol l owi ng categori es are exampl es of quanti tati ve
al l thei r connecti ons must be nonmagneti c to avoi d cre-
techni ques:
ati on of MEG arti facts. A vi ew of a subject wi th EEG
el ectrodes attached i s shown i n Fi g. 18b.
1. Time-amplitude analysis: Automated character-
i zati on of waveforms, i ncl udi ng epi l epti c spi ke i denti fi -
cati on, appearance or suppressi on of brai n rhythms
4 . D ATA I N TE R P R E TATI O N
such as ␣(8–13 Hz)and ␤(15–30 Hz), and i denti fi cati on
of hemi spheri c asymmetri es.
Much of the si gnal anal ysi s used for MEG has been
2. Frequency–amplitude analysis: Esti mati on of
i nheri ted from EEG appl i cati ons. However, MEG i s
MEG frequency content usi ng Fouri er transform or
more commonl y used for quanti tati ve assessment of
maxi mum entropy methods.
brai n acti vi ty, especi al l y for source l ocal i zati on. El ectro-
3. Coherence analysis: Esti mati on of correl ati on of
physi ol ogi cal acti vi ty i s characteri zed by a pri mary
i oni c current, fl owi ng wi thi n cel l bodi es (the “source
current”), and a vol ume or return current, fl owi ng i n the
1
The normal component of the magneti c fi el d at the surface of a
extracel l ul ar space. Bi omagneti c sensors are coupl ed
conducti ng body wi l l have the mi ni mum contri buti on of vol ume
currents. mai nl y to the pri mary current sources; bi omagneti c
FIG.18. EEG. (a) Orthogonal rel ati onshi p between EEG and MEG si gnal s. (b) A subject wi th attached EEG el ectrodes before head i nserti on
i nto the MEG hel met.
SI GNAL PROCESSI NG I N MEG 2 6 5
an MEG si gnal channel wi th other channel s (MEG, Si gnal averagi ng does not make use of the i nforma-
ti on avai l abl e from l arge MEG sensor arrays. The unav- EEG, or measured events).
4. Averagedevokedresponse: The averaged MEG si g- eraged MEG si gnal s exhi bi t spati al and temporal corre-
l ati on. Thi s correl ati on may be used to advantage i n nal — synchronous wi th an external sti mul us or vol un-
tary motor event. i mproved separati on of source si gnal s from the noi se
and the l ocal i zati on of acti vi ty. 5. Topographicmappingof signal and power: Di stri -
buti on of band-l i mi ted si gnal power, mapped to the sen- The three-di mensi onal source esti mati on method wi l l
be i l l ustrated usi ng SAM. I t i s a robust method, provi d- sor surface.
6. Forward and inverse solutions: Computati on of i ng excel l ent spati al resol uti on, and i s sui tabl e for anal -
ysi s of nonaveraged MEG si gnal s. SAM uses the spati al fi el ds from a current source model , wi th adjustment
of model parameters for best fi t to the observed fi el d and temporal correl ati on of a MEG array. Consi der an
array of M sensors, wi th i nstantaneous measurements pattern. Model s i ncl ude si ngl e and mul ti pl e equi val ent
current di pol es (ECDs) (55) and conti nuous current di s- m ϭ {m
1
, m
2
,…, m
M
}. Each sensor responds to ti me-
varyi ng bi oel ectri c currents J (r) wi thi n the brai n. The tri buti ons (mi ni mum norm) (56).
7. Spatial filters: Wei ghted l i near combi nati ons of response of each sensor to the current i s gi ven by the
vol ume i ntegral , measurements that separate si gnal s by thei r spati al
ori gi n.
8. Three-dimensional mappingof sourcepower: Esti -
m
i
(t) ϭ
Ύ
⍀
J (r) G
i
(r)dv ϩ n
i
(t) [5]
mati on of source power or a stati sti cal deri vati ve. Not
to be confused wi th i nverse sol uti on. Methods i ncl ude
SAM (57), l i near beamformi ng (58), and MUSI C (59).
where G
i
(r)i s Green’s functi on
3
descri bi ng that sensor ’s
Hi stori cal l y, MEG data anal ysi s has focused on the
response to current at each coordi nate r. The measure-
ubi qui tous averaged evoked response paradi gm. The
ment may al so have added i nstrumental noi se n
i
(t). To
underl yi ng assumpti on of thi s method i s that the acti -
use the enti re sensor array to esti mate source acti vi ty
vati on of some areas of the brai n i s ti me-l ocked to exter-
S
ˆ
␪
(t) at voxel ␪ wi thi n the head, l et us form a wei ghted
nal events, ei ther to a sti mul us or to a motor outfl ow.
l i near combi nati on of al l measurements:
Averagi ng the MEG or EEG si gnal s enhances the si g-
nal -to-noi se rati o of the ti me-l ocked fracti on of brai n
S
ˆ
␪
(t) ϭ W
T
␪
m(t). [6]
acti vi ty. Thi s, i n turn, permi ts reproduci bl e quanti ta-
ti ve measures of that speci fi c acti vi ty. For exampl e, a
The coeffi ci ents W
␪
are to be sel ected so that they
map of the averaged evoked response to transi ent tone
emphasi ze acti vi ty at ␪, and attenuate si gnal s from
bursts reveal s a characteri sti c two-di pol e pattern at
al l other l ocati ons, i ncl udi ng envi ronmental magneti c
100-ms l atency rel ati ve to sti mul us onset (see Fi g. 19b).
i nterference. The opti mal coeffi ci ents may be found by
Unfortunatel y onl y a smal l porti on of the brai n i s acces-
mi ni mi zi ng the total power over ti me, whi ch can be
si bl e to thi s method. Pri mary sensory and motor areas
expressed as W
T
␪
RW
␪
, where R i s the M ϫM correl ati on
acti vate synchronousl y wi th external events. However,
matri x of the measurements. The SQUI D sensors used
regi ons servi ng hi gher cogni ti ve functi ons have much
for MEG have an unknown dc basel i ne, dependi ng on
more vari abl e l atency. The averaged si gnal s of ti me-
the nearest fl ux quantum for whi ch the fl ux-l ocked l oop
vari abl e events cannot fai thful l y reproduce the charac-
acqui red l ock. The basel i ne offset occupi es one degree of
ter of thei r sources.
freedom i n the correl ati on matri x, and i s not a probl em,
The advent of l arge MEG sensor arrays wi th whol e-
provi ded that a suffi ci ent number of ti me sampl es have
head coverage has al tered the strategy of si gnal anal y-
been i ntegrated i nto the correl ati on matri x. To el i mi -
ses. Let us consi der the averaged evoked response para-
nate thi s bi as, one can substi tute the covari ance matri x
di gm: The i ncrease i n channel count has decreased the
C for correl ati on matri x R, gi vi ng
ti me requi red to map an evoked response, but has not
yi el ded addi ti onal i nformati on. I n fact, the evoked re-
W
␪
ϭ C
Ϫ1
B
␪
[B
T
␪
C
Ϫ1
B
␪
]
Ϫ1
. [7]
sponse mapped by a l arge whol e-head array wi l l be
i denti cal to that detected by seri al mul ti pl e pl acement
An esti mate of the mean-squared source power at
and measurement by a si ngl e-channel MEG sensor at
␪ can, i n fact, be determi ned wi thout computi ng the
the same si tes.
2
wei ghti ng coeffi ci ents as
2
Wi thi n the reproduci bi l i ty of the averaged evoked response,
and assumi ng that the subject’s state of attenti on to the sti mul us
3
I n the el ectrophysi ol ogy l i terature, Green’s functi on i s often re-
ferred to as the “l ead fi el d.” i s mai ntai ned.
VRBA AND ROBI NSON 2 6 6
Q
ˆ2
␪
ϭ [B
T
␪
C
Ϫ1
B
␪
]
Ϫ1
. [8] buti on of sensor noi se to the power i s the wei ghted
sensor noi se for that voxel :
I n pri nci pl e, an i mage of the source power di stri buti on
␯ˆ
2
␪
ϭ W
␪
T
⌺W
␪
. [10] i n three di mensi ons coul d be generated by appl yi ng the
l atter equati on to coordi nates on some gri d of poi nts
i n the head. Thi s i s referred to as “source scanni ng.”
4
The normal i zed voxel val ue becomes
However, the si gnal -to-noi se rati o of the source esti -
mate decl i nes wi th depth and di stance from the sensors.
Z–
2
␪
ϭ
Q
ˆ
␪
2
␯ˆ
␪
2
. [11]
Furthermore, due to the l i mi ted spati al sel ecti vi ty of
the process, unwanted source power may “l eak” i nto
the source esti mate. Near the center of the head, the
The symbol Z– (pronounced pseudo-Z) denotes the anal -
total noi se power may be so l arge as to obscure source
ogy of thi s quanti ty to the cl assi c Z devi ate of descri p-
acti vi ty. One can readi l y compensate for the noi se by a
ti ve stati sti cs.
normal i zati on process.
We i l l ustrate thi s anal ysi s wi th an exampl e of source
To i mpl ement such normal i zati on, l et us consi der the
acti vi ty mappi ng, usi ng Z–, i n Fi g. 20a; the SAMZ–i mage
i nstrumental noi se vari ance of an array of sensors:
i s shown superi mposed on the MRI i mage. A 143-chan-
nel whol e-cortex MEG (CTF Systems I nc. [8]) was used
to measure epi l epti c spi ke acti vi ty i n an 8-year-ol d pa-
ti ent. A total of 100 s of MEG si gnal (as ten 10.0-s
⌺ ϭ
΄
␯
2
1
0
␯
2
2
O
0 ␯
2
M
΅
. [9]
epochs) was acqui red at a sampl e rate of 625 Hz.
5
The
si gnal was band-l i mi ted from 30 to 55 Hz, pri or to SAM
anal ysi s, to excl ude the contri buti on of the domi nant
Assumi ng that al l sensors have equal noi se, the noi se ␣- and ␤-band brai n rhythms to the i mage. The regi ons
matri x can al so be represented by ⌺ ϭ ␯
2
I. The contri - of i nteri ctal spi ke generati on are characteri zed by hi gh-
frequency acti vi ty. These appear as bri ght regi ons of
4
One di sti ngui shes source scanni ng from i nverse sol uti ons i n that
acti vi ty i n the SAM Z– i mage.
the l atter i nvol ves fi tti ng a model to the observed fi el d, by adjusti ng
the parameters of the model so as to mi ni mi ze a di stance functi on
such as ␹
2
. Scanni ng methods (i ncl udi ng the MUSI C al gori thm) are
5
Data were col l ected i n the open envi ronment, wi thout magneti c
shi el di ng, usi ng thi rd-order syntheti c gradi ometer sensors. not i nverse sol uti ons for source.
FIG. 19. Exampl e of averaged event-rel ated MEG data anal ysi s. The fi el d maps can be i nterpreted by di screte ECDs, shown by whi te
arrows. (a) One-di pol e map correspondi ng to somatosensory (SEF) sti mul ati on of the medi an nerve. (b) Two-di pol e fi el d map correspondi ng
to audi tory evoked fi el ds.
SI GNAL PROCESSI NG I N MEG 2 6 7
The anal ogous true Z-devi ate i mage (rati o of aver- most easi l y i denti fi ed by subtracti on of the common-
mode brai n acti vi ty. To accompl i sh thi s, MEG data are aged source power to i ts standard devi ati on, for mul ti -
pl e epochs) al so provi des normal i zati on for the i ncrease col l ected duri ng both task performance, acti ve (a), and
background acti vi ty, control (c). The si mpl e power di f- i n i mage power wi th depth. Thi s i s shown i n Fi g. 20b.
However, the true Z devi ate does not convey source ference,
i nformati on i n the same manner as i ts pseudo-Z ki n.
⌬Q
ˆ
␪
2
ϭ
(a)
Q
ˆ
␪
2
Ϫ
(c)
Q
ˆ
␪
2
, [12] Epi l epti c spi ke events occur at random throughout the
MEG recordi ng. Each of the ten 10.0-s epochs contai ned
di fferent rates of spi ke acti vi ty. Hence, the Z-devi ate suffers from the same noi se degradati on as does the
si ngl e-state SAM source i mage. Once more, we appl y score appears l owest (dark, i n the i mage) at the spi k-
i ng l oci . the noi se normal i zati on to each voxel to compute i ts
pseudo-T val ue: Source acti vi ty rel ated to performance of a task i s
FIG. 20. SAM i mages of MEG recordi ng of i nteri ctal spi ke acti vi ty, fused to the pati ent’s MRI . The three orthogonal vi ews i ntersect at a
common poi nt i n the head. Acti vi ty i s mapped for the 30 to 55-Hz band. (a) The i nteri ctal spi ke source acti vi ty shown by outl i ne as SAM
pseudo-Z val ue (peak val ue Z–
max
ϭ 10.4). (b) The same MEG data are al so mapped usi ng the Z– devi ate. The spi ke l oci appear dark (marked
by whi te dot), because they have hi gh stati sti cal vari abi l i ty.
VRBA AND ROBI NSON 2 6 8
for one-handed squeezi ng i s l ocal i zed to the hand regi on
T–
␪
ϭ
(a)
Q
ˆ
␪
2
Ϫ
(c)
Q
ˆ
␪
2
(a)
␯ˆ
␪
2
ϩ
(c)
␯ˆ
␪
2
. [13]
of the central sul cus.
The true T stati sti c can be computed from mul ti pl e-
tri al SAM i mages of acti ve and control acti vi ty,
To i l l ustrate thi s, a si mpl e vol untary motor study was
performed. A subject was di rected by voi ce command
T
␪
ϭ
(a)
Q
ˆ
␪
2
Ϫ
(c)
Q
ˆ
␪
2
Ί␴
2
/N
, [14]
to squeeze a sponge wi th one hand for 10 s and rel ax
the hand for 10 s. Ten tri al s of MEG data were acqui red,
wi th each tri al consi sti ng of squeezi ng and then re- where ␴
2
i s the pool ed vari ance and N the total number
of i nstances of both the acti ve and control events. A l axi ng. Data were col l ected at 625-Hz sampl e rate i n the
open envi ronment, usi ng a 143-channel whol e-cortex SAM source power i mage i s generated for each i nstance
of acti ve and control acti vi ty. The mean acti ve, mean MEG [CTF Systems I nc. (8)] wi th syntheti c thi rd-order
gradi ometer sensors. A pseudo-T SAM i mage was control , and thei r pool ed standard error are used to
compute Student’s T val ue for each voxel . Li ke the mapped for ␤-band (15–30 Hz) acti vi ty. Thi s i s shown
i n Fi g. 21a. Vol untary motor movement i s accompani ed pseudo-T val ue thi s procedure compensates for the i n-
crease i n noi se power wi th depth i n the head. The stati s- by event-rel ated suppressi on of ␤-band acti vi ty. As can
be seen i n these i mages, the source of the suppressi on ti cal probabi l i ty of each voxel can al so be computed
FIG. 21. SAM i mages of MEG recordi ng duri ng vol untary hand motor acti vi ty (squeezi ng). Ten tri al s, each wi th 10.0 s of squeezi ng and
10.0 s of rel axati on, were recorded. (a) The pseudo-T i mage (T–
max
ϭ 6.5) shows a focal regi on of ␤-band suppressi on i n motor cortex i n the
hemi sphere opposi te the hand that was squeezi ng. (b) Student’s T– stati sti c i mage (T
max
ϭ 10.4) of the same data reveal s a weaker i psi l ateral
suppressi on, i n addi ti on to the contral ateral si te found wi th pseudo-T.
SI GNAL PROCESSI NG I N MEG 2 6 9
from the true T stati sti c. A T i mage of the motor MEG current sources. Second, the changes i n i oni c source
data i s shown i n Fi g. 21a. The peak T val ue i n the i mage currents can be studi ed on a ti me scal e of l ess than 1 ms.
i s 10.39 (19 degrees of freedom). Thus, the regi ons of Thus, MEG can be used for functi onal neuroi magi ng of
acti vati on are hi ghl y si gni fi cant. events that are not accessi bl e ei ther to functi onal MRI
Student’s T i mages show acti vi ty i n si mi l ar l ocati ons or to nucl ear i magi ng methods. Let us retrace the fun-
to the pseudo-T i mages. Thi s di ffers from the SAM i m- damental s of MEG from i ts ori gi n as el ectrophysi ol ogi -
ages of epi l epti c acti vi ty shown i n Fi g. 20. I t i ndi cates cal i oni c source currents wi thi n the brai n to the presen-
that the suppressi on of ␤-band acti vi ty i s reproduci bl y tati on of anal yzed resul ts.
present duri ng each of the acti ve-state (squeezi ng) tri - We have shown that the magneti c fi el d of the brai n
al s, si nce the vari ance over tri al s i s smal l . Thi s con-
i s many orders of magni tude smal l er than fl uctuati ons
trasts wi th the epi l epti c acti vi ty for whi ch i nteri ctal
of the envi ronmental magneti c fi el d. Thi s i mpl i es the
spi kes occurred sporadi cal l y, resul ti ng i n l arge vari ance
need for hi ghl y sensi ti ve sensors as wel l as sophi sti -
and therefore l ow Z-devi ate scores.
cated noi se cancel l ati on techni ques.
At present, the most sensi ti ve magneti c detectors are
based on the SQUI D (superconducti ng quantum i nter-
ference devi ce). Other cl asses of magneti c detectors are 5 . C O N C LU S I O N S
too noi sy to characteri ze the spontaneous (unaveraged)
MEG or have poor frequency response. Modern SQUI D- The rati onal e for usi ng magnetoencephal ography to
based MEG sensors can achi eve a noi se densi ty of a study the brai n i s twofol d: Fi rst, the physi cs of magneti c
measurement permi t three-di mensi onal l ocal i zati on of few femtotesl a per root hertz, i n a bandwi dth from dc
FIG. 22. Overvi ew of the MEG si gnal processi ng chai n. The MEG si gnal s ori gi nate i n the brai n neurons. Acti vati on of the i ndi vi dual
neurons i s not detectabl e and onl y the col l ecti ve acti vati ons of l arge number of neurons are detected by the pri mary SQUI D sensors (Secti on
1). I n addi ti on to the brai n si gnal s, the SQUI D sensors are al so exposed to the envi ronmental and body noi se. To el i mi nate the envi ronmental
noi se, references sensors, posi ti oned farther from the scal p, are often used. The reference si gnal s are subtracted from the pri mary sensor
outputs to reduce the detected noi se; the process can be understood as spati al hi gh pass fi l teri ng. The SQUI D desi gn and opti mi zati on of
the pri mary sensor fl ux transformers were di scussed i n Secti on 2 and the noi se cancel l ati on was outl i ned i n Secti on 3. After the noi se
reducti on, the detected si gnal s are processed to the requi red bandwi dth and the data are acqui red. The data processi ng and acqui si ti on by
the di gi tal SQUI D el ectroni cs were di scussed i n Secti on 2.3. The acqui red data represent magneti c fi el d on the scal p surface and must be
i nterpreted to yi el d i nformati on about the brai n sources. Thi s process requi res addi ti onal i nformati on about the anatomi cal structure,
forward model s of the brai n sources, and methods for source esti mati on from the measured fi el ds. These steps were di scussed i n Secti on
5. The brai n magneti c fi el ds were generated by a speci fi c di stri buti on of the neuronal currents as shown i n the upper l eft si de of thi s fi gure.
After the measurement, processi ng, and i nterpretati on, a smoothed esti mate of the neuronal acti vi ty i s obtai ned, as shown i n the l ower
ri ght si de of the fi gure.
VRBA AND ROBI NSON 2 7 0
to several ki l ohertz. The pri nci pl es of SQUI D operati on
R E FE R E N C E S
have been outl i ned, showi ng how SQUI Ds are coupl ed
to the brai n magneti c fi el d usi ng superconducti ng fl ux
1. Berger, H. (1929) Arch. Psychiat. Nervenkr. 7, 527–570.
transformers. Condi ti oni ng el ectroni cs are requi red to
2. Cohen, D. (1968) Science161, 784–786.
transform the quantum peri odi c si gnal s of the SQUI Ds
3. Jakl evi c, R., Lambe, R. C., Si l ver, A. H., and Mercereau, J. E.
i nto a l i near representati on of the magneti c fi el d. The
(1964) Phys. Rev. Lett. 12, 159–160.
peri odi c nature of the SQUI D response al l ows re-
4. Zi mmerman, J. E., and Si l ver, A. H. (1964) Phys. Lett. 10, 47–48.
cordi ngs wi th a dynami c range of 192 dB (32 bi ts) or
5. Josephson, B. D. (1962) Phys. Lett. 1, 251–253.
greater. SQUI D el ectroni cs i s parti al l y di gi tal and i s 6. Cohen, D. (1972) Science175, 664–666.
i nti matel y coupl ed to the fast di gi tal si gnal processi ng 7. Wi kswo, J. P., Jr. (1995)I EEE Trans. Appl. Supercond. 5,74–120.
8. CTF Systems I nc., 15-1750 McLean Ave, Port Coqui tl am, BC, usi ng DSPs and PGAs to provi de effi ci ent preprocessi ng
Canada.
of the MEG data before acqui si ti on and anal ysi s by the
9. 4D Neuroi magi ng, 9727 Paci fi c Hei ghts Bl vd., San Di ego, CA
col l ecti on computers. A typi cal MEG system may have
92121-3719.
several hundred pri mary sensors di sposed about the
10. Yokogawa El ectri c Corp., MEG Busi ness Center, 2-9-32 Nakacho,
head and can generate data vol umes of up to several
Musashi no-ci ty, Tokyo, 180-8750, Japan.
tens of gi gabytes per day.
11. Nakaya, Y., and Mori , H. (1992) Clin. Phys. Physiol. Meas. 13,
For an i nstrument to measure MEG i n the open envi - 191–229.
12. Carpenter, M. B. (1985) Core Text of Neuroanatomy, Wi l l i ams & ronment (wi thout a magneti cal l y shi el ded room), i t
Wi l ki ns, Bal ti more London.
must possess sensors and el ectroni cs capabl e of han-
13. Partri dge, L. D., and Partri dge, L. D. (1993)The Nervous System,
dl i ng a very l arge dynami c range (approachi ng 30 bi ts).
I ts Functi on and I ts I nteracti on wi th the Worl d, A Bradford Book,
Furthermore, the i mpul se response of al l pri mary sen-
MI T Press, Cambri dge.
sors and thei r reference channel s must be accuratel y
14. Sarvas, J. (1987) Phys. Med. Biol. 32, 11–22.
matched and have l ow di storti on, to obtai n effecti ve
15. Wi kswo, J. P., Jr. (1989) in Advances i n Bi omagneti sm (Wi l l i am-
son, S. J., et al., Eds.), Pl enum, pp.1–18, New York/London. envi ronmental noi se cancel l ati on and for accurate
16. Wi l l i amson, S. J., and Kaufman, L. (1981) J . Magn. Magn. Mater. data anal ysi s.
22, 129–201.
I nterpretati on of MEG data i s compl i cated by the
17. Okada, Y. C., Papuashvi l i , N., and Xu, C. (2000) in Bi omag96:
fact that the sol uti on for the three-di mensi onal source
Advances i n Bi omagneti sm Research (Ai ne, C., et al., Eds.),
current di stri buti on i n the brai n from any array of
Spri nger-Verl ag, Berl i n, i n press.
sensors outsi de the head i s nonuni que. Useful source
18. Nakasato, N., Fuji ta, S., Seki , K., Kawamura, T., Matani , A.,
esti mates can be obtai ned onl y after i ncorporati on of Tamura, I ., Fuji wara, S., and Yoshi moto, T. (1995) Electroenceph-
alogr. Clin. Neurophysiol. 94, 183–190.
constrai nts, pri or assumpti ons, and mathemati cal si m-
19. Vi eth, J., Kober, H., Grummi ch, P., Pongratz, H., Ul bri cht, D.,
pl i fi cati ons. The spati al fi l teri ng approach offers an al -
Bri gel , C., and Daun, A. (1995) in Bi omagneti sm: Fundamental
ternati ve to i nverse sol uti on by i sol ati ng si gnal s from
Research and Cl i ni cal Appl i cati ons (Baumgartner, C., et al.,
di fferent parts of the brai n.
Eds.), pp. 50–54, El sevi er Sci ence, I OS Press, Amsterdam/New
York.
We now summari ze i n Fi g. 22 the steps i n functi onal
20. Pol hemus I nc., 1 Hercul es dri ve, PO Box 560, Col chester, VT
brai n i magi ng by MEG, l eadi ng from the el ectrophysi o-
05446.
l ogi cal source currents wi thi n the brai n to i nterpreta-
21. Cl arke, J. (1993) inThe New Superconducti ng El ectroni cs (Wei n-
ti on of the resul tant magneti c si gnal s. Brai n acti vi ty i s
stock, H., and Ral ston, R. W., Eds.), pp. 123–180, Kl uwer Aca-
associ ated wi th el ectrochemi cal events that resul t i n
demi c, Dordrecht.
pri mary and secondary i oni c currents. These currents
22. Jaycox, J. M., and Ketchen, M. B. (1981) I EEE Trans. Magn.
MAG-17, 400–403.
gi ve ri se to magneti c fi el ds whi ch, together wi th the
23. Ketchen, M. B., and Jaycox, J. M. (1982)Appl. Phys. Lett. 40,736–
envi ronmental magneti c noi se, are detected by super-
738.
conducti ng fl ux transformers. The envi ronmental noi se
24. Ketchen, M. B., Goubau, W. M., Cl arke, J., and Donal dson, G.
i s attenuated usi ng reference sensors that are remote
B. (1978) J . Appl. Phys. 44, 4111–4116.
from the head, and the data acqui si ti on i n the desi red
25. Cl arke, J., Goubau, W. M., and Ketchen, M. B. (1976) J . Low
bandwi dth i s performed. The acqui red magneti c fi el d Temp. Phys. 25, 99–144.
i s combi ned wi th anatomi cal i nformati on, forward mod- 26. Zi mmerman, J. E., Thi ene, P., and Hardi ng, J. T. (1970) J . Appl.
Phys. 41, 1572–1580.
el s, and anal ysi s procedures for source esti mati on. Be-
27. Gi ffard, R. P., Web, R. A., and Wheatl ey, J. C. (1972) J . Low.
cause the sensors cannot detect the acti vati on of i ndi -
Temp. Phys. 6, 533–610.
vi dual neurons (due to the spati al and fi el d ampl i tude
28. Tesche, C. D., and Cl arke, J. (1977) J . LowTemp. Phys. 27, 301–
condi ti ons) and because the i nversi on probl em i s non-
331.
uni que, the procedure yi el ds a smoothed “esti mate” of
29. Vrba, J., Betts, K., Burbank, M. B., Cheung, T., Fi fe, A. A., Hai d,
G., Kubi k, P. R., Lee, S., McCubbi n, J., McKay, J., McKenzi e, D., the ori gi nal neuronal acti vati on.
SI GNAL PROCESSI NG I N MEG 2 7 1
Spear, P., Tayl or, B., Ti l l otson, M., Cheyne, D., and Wei nberg, H. McKay, J., McKenzi e, D., Noni s, D., Paz, J., Rei chl , E., Ressl , D.,
Robi nson, S. E., Schroyen, C., Sekachev, I ., Spear, P., Tayl or, B., (1993) I EEE Trans. Appl. Supercond. 3, 1878–1882.
Ti l l otson, M., and Sutherl i ng, W. (1999) in Recent Advances i n
30. Ketchen, M. B, Stawi asz, K. G., Pearson, D. J., Brunner, T. A.,
Bi omagneti sm (Yoshi moto, T., et al. Eds.), pp. 93–96, Tohoku
Hu, C.-K., Jaso, M. A., Manny, M. P., Parsons, A. A., and Stei n,
Uni v. Press.
K. J. (1992) Appl. Phys. Lett. 61, 336–338.
44. ter Brake, H. J. M. (2000) in Appl i cati ons of Superconducti vi ty
31. Cl arke, J. (1996) in H. Wei nstock (ed.), SQUI D Sensors: Funda-
(Wei nstock, H., Ed.), pp. 561–639, Kl uwer Academi c, Dordrecht.
mental s, Fabri cati on and Appl i cati ons (Wei nstock, H., Ed.), pp.
45. Vacuumschmel ze GmbH, Hanau, Germany, shi el ded room Model 1–62, Kl uwer Academi c, Dordrecht.
AK-3.
32. Muck, M. (1993) I EEE Trans. Appl. Supercond. 3, 2003–2010.
46. Koch, H., PTB, Berl i n, Germany, pri vate communi cati on.
33. Bragi nski , A. I ., Krause, H.-J., and Vrba, J. (2000) in Supercon-
47. Robi nson, S. E. (2000) in Bi omag96: Advances i n Bi omagneti sm ducti ng Devi ces, A Vol ume of Handbook of Thi n Fi l m Devi ces:
Research (Ai ne, C., et al. Eds.), pp. 103–106, Spri nger-Verl ag, Fronti ers of Research, Technol ogy and Appl i cati ons (Francombe,
Berl i n/New York. M., and Broussard, P. Eds.), Academi c Press, San Di ego, i n press.
48. Vrba, J. (2000) in Appl i cati ons of Superconducti vi ty (Wei nstock,
34. Vrba, J., Fi fe, A. A., Burbank, M. B., Wei nberg, H., and Bri ckett,
H., Ed.), pp. 61–138, Kl uwer Academi c, Dordrecht.
P. A. (1982) Can. J . Phys. 60, 1060–1073.
49. Matsuba, H., Shi ntomi , K., Yahara, A., I ri sawa, D., I mai , K.,
35. Vrba, J., Betts, K., Burbank, M., Cheung, T., Cheyne, D., Fi fe,
Yoshi da, H., and Sei ke, S. (1995) in Bi omagneti sm: Fundamental
A. A., Hai d, G., Kubi k, P. R., Lee, S., McCubbi n, J., McKay, J.,
Research and Cl i ni cal Appl i cati ons (Baumgartner, C., et al.,
McKenzi e, D., Mori , K., Spear, P., Tayl or, B., Ti l l otson, M., and Xu,
Eds.), pp. 483–489, El sevi er Sci ence, I OS Press, Amsterdam.
G. (1995) in Bi omagneti sm: Fundamental Research and Cl i ni cal
Appl i cati ons (Baumgartner C. et al. Eds.), pp. 521–525, El sevi er 50. Kel ha, V. O., Pukki , J. M., Pel tonen, R. S., Pentti nen, V. J.,
Sci ence, I OS Press, Amsterdam. I l moni emi , R. J., and Hei no, J. J. (1982) I EEE Trans. Mag. 18,
260–270.
36. Wi l l i amson, S. J., and Kaufman, L. (1981) J . Magn. Magn. Mater.
22, 129–201. 51. ter Brake, H. J. M, Huonker, R., and Rogal l a, H. (1993) Meas.
Sci. Technol. 4, 1370–1375.
37. Knuuti al , J. E. T., Ahonen, A. I ., Hamal ai nen, M. S., Kajol a, M.
J., Petteri Lai ne, P., Lounasmaa, O. V., Parkkonen, L. T., Si mol a, 52. Vrba, J., Cheung, T., Tayl or, B., and Robi nson, S. E. (1999) in
J. T. A., and Tesche, C. D. (1993) I EEE Trans. Mag. 29, 3315– Recent Advances i n Bi omagneti sm (Yoshi moto, T. et al., Eds.),
3321. pp.105–108, Tohoku Uni v. Press.
53. Cheyne, D., Roberts, L. E., Gaetz, W., Bosnyak, D., Wei nberg, 38. Vrba, J. (1997) Basel i ne opti mi zati on for noi se cancel l ati on sys-
tems, inProceedi ngs of the 19th I nternati onal Conference I EEE– H., Johnson, B., Nahmi as, C., and Deecke, L. (2000) Bi omag96:
Advances i n Bi omagneti sm Research (Ai ne, C., et al., Eds.), pp. EMBS, Chi cago, I L, Oct. 30 to Nov. 2, pp. 1240–1243.
1130–1133, Spri nger-Verl ag, Berl i n/New York.
39. Vrba, J., and McKay, J. (1998) Appl. Supercond. 5, 431–439.
54. Zi mmerman, J. E. (1977) J . Appl. Phys. 48, 702–710.
40. Vrba, J., Fi fe, A. A., and Burbank, M. B. (1981)inSQUI DAppl i ca-
55. Scherg, M., and von Cramon, D. (1985) Electroencephalogr. Clin. ti ons to Geophysi cs (Wei nstock, H., and Overton, W. C. Eds.), pp.
Neurophys. 62, 290–299. 31–34, Soc. of Expl orati on Geophysi ci sts, Tul sa, OK.
56. Hamal ai nen, M. S., and I l moni emi , R. J. (1984) I nterpreti ng
41. McKay, J., Vrba, J., Betts, K., Burbank, M. B., Lee, S., Mori ,
measured magneti c fi el ds of the brai n: Esti mates of current di s-
K., Noni s, D., Spear, P., and Uri el , Y. (1993) I mpl ementati on
tri buti ons, Report TKK-F-A559, Low Temperature Laboratory,
of mul ti channel bi omagneti c measurement system usi ng DSP
Hel si nki Uni versi ty of Technol ogy, SF-02150 Espoo 15, Fi nl and.
technol ogy, in Proceedi ngs of 1993 Canadi an Conference on El ec-
tri cal and Computer Engi neeri ng, Vol . 2, pp. 1090–1093. 57. Robi nson, S. E., and Vrba, J. (1999) Recent Advances i n Bi omag-
neti sm (Yoshi moto, T., et al., Eds.), pp. 302–305, Tohoku Uni v.
42. Vrba, J. (1996)inH. Wei nstock (ed.), SQUI D Sensors: Fundamen-
Press.
tal s, Fabri cati on and Appl i cati ons (Wei nstock, H., Ed.), pp. 117–
178, Kl uwer Academi c, Dordrecht. 58. Van Veen, B. D., Van Drongel en, W., Yuchtman, M., and Suzuki ,
A. (1997) I EEE Trans. Biomed. Eng. 44, 867–880.
43. Vrba, J., Anderson, G., Betts, K., Burbank, M. B., Cheung, T.,
Cheyne, D., Fi fe, A. A., Govorkov, S., Habi b, F., Hai d, G., Hai d, 59. Mosher, J. C., Lewi s, P. S., and Leahy, R. M. (1992) I EEE Trans.
Biomed. Eng. 39, 541–557. V., Hoang, T., Hunter, C., Kubi k, P. R., Lee, S., McCubbi n, J.,