Cancellation of EEG and MEG signals generated by extended and distributed sources.

Abstract

Extracranial patterns of scalp potentials and magnetic fields, as measured with electro- and magnetoencephalography (EEG, MEG), are spatially widespread even when the underlying source in the brain is focal. Therefore, loss in signal magnitude due to cancellation is expected when multiple brain regions are simultaneously active. We characterized these cancellation effects in EEG and MEG using a forward model with sources constrained on an anatomically accurate reconstruction of the cortical surface. Prominent cancellation was found for both EEG and MEG in the case of multiple randomly distributed source dipoles, even when the number of simultaneous dipoles was small. Substantial cancellation occurred also for locally extended patches of simulated activity, when the patches extended to opposite walls of sulci and gyri. For large patches, a difference between EEG and MEG cancellation was seen, presumably due to selective cancellation of tangentially vs. radially oriented sources. Cancellation effects can be of importance when electrophysiological data are related to hemodynamic measures. Furthermore, the selective cancellation may be used to explain some observed differences between EEG and MEG in terms of focal vs. widespread cortical activity.

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r Human Brain Mapping 31:140–149 (2010) r
Cancellation of EEG and MEG Signals Generated
by Extended and Distributed Sources
Seppo P. Ahlfors,1,2* Jooman Han,1Fa-Hsuan Lin,1,3Thomas Witzel,1,2
John W. Belliveau,1,2Matti S. Ha ¨ma ¨la ¨inen,1,2and Eric Halgren4
1Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital/Harvard
Medical School, Charlestown, Massachusetts
2Harvard-MIT Division of Health Sciences and Technology, Cambridge, Massachusetts
3Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan
4Department of Radiology, University of California, San Diego, California
rr
Abstract: Extracranial patterns of scalp potentials and magnetic fields, as measured with electro- and
magnetoencephalography (EEG, MEG), are spatially widespread even when the underlying source in
the brain is focal. Therefore, loss in signal magnitude due to cancellation is expected when multiple
brain regions are simultaneously active. We characterized these cancellation effects in EEG and MEG
using a forward model with sources constrained on an anatomically accurate reconstruction of the
cortical surface. Prominent cancellation was found for both EEG and MEG in the case of multiple ran-
domly distributed source dipoles, even when the number of simultaneous dipoles was small. Substan-
tial cancellation occurred also for locally extended patches of simulated activity, when the patches
extended to opposite walls of sulci and gyri. For large patches, a difference between EEG and MEG
cancellation was seen, presumably due to selective cancellation of tangentially vs. radially oriented
sources. Cancellation effects can be of importance when electrophysiological data are related to hemo-
dynamic measures. Furthermore, the selective cancellation may be used to explain some observed dif-
ferences between EEG and MEG in terms of focal vs. widespread cortical activity. Hum Brain Mapp
31:140–149, 2010.
V
C 2009 Wiley-Liss, Inc.
Keywords: magnetoencephalography;
cerebral cortex; cortical patch analysis
electroencephalography;forwardmodel;inverseproblem;
rr
Contract grant sponsor: Whitaker foundation; Contract grant
number: RG-01-0294; Contract grant sponsor: NIH; Contract grant
numbers: NS57500, NS44623, and NS18741; Contract grant sponsor:
National Center for Research Resources; Contract grant number:
P41RR14075; Contract grant sponsor: MIND Research Network
(MRN); Contract grant sponsor: NIH; Contract grant numbers:
NS37462, HD40712, DA14178, EB07298; Contract grant sponsor:
National Science Council, Taiwan; Contract grant numbers: NSC
97-2320-B-002-058-MY3, NSC 97-2221-E-002-005; Contract grant
sponsor: National Health Research Institute, Taiwan; Contract
grant number: NHRI-EX98-9715EC.
*Correspondence to: Dr. Seppo P. Ahlfors, Athinoula A. Martinos
Center, Massachusetts General Hospital, 149 13th Street, Rm 2301,
Charlestown, MA 02129. E-mail: seppo@nmr.mgh.harvard.edu
Received for publication 12 August 2004; Revised 5 June 2009;
Accepted 7 June 2009
DOI: 10.1002/hbm.20851
Published online 28 July 2009 in Wiley InterScience (www.
interscience.wiley.com).
V
C 2009 Wiley-Liss, Inc.

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INTRODUCTION
Electro- and magnetoencephalography (EEG, MEG) are
methods to study electrical brain activity by recording
scalp potentials and extra-cranial magnetic fields [Cohen
and Halgren, 2009; Gevins et al., 1995; Ha ¨ma ¨la ¨inen et al.,
1993]. EEG and MEG provide millisecond time resolution
for noninvasive detection of human brain activity, and
estimates of the locations of the underlying sources can be
constructed on the basis of the spatial distribution of the
EEG and MEG over the head [Baillet et al., 2001]. In part,
the spatial resolution in EEG and MEG source estimates is
limited by the spatial spread of the signal patterns gener-
ated even by focal sources. The spread depends on the
distance between the sources and the sensors; the mini-
mum distance is limited by the thickness of the skull and
scalp, and, in the case of MEG, the thickness of the Dewar
vessel containing the superconducting SQUID sensors.
When multiple sources are simultaneously active, their sig-
nal patterns are superimposed, and cancellation of signals
of opposite polarity may occur. Cancellation reduces the
overall signal-to-noise ratio, thereby contributing to the
difficulty of source estimation. In general, when interpret-
ing EEG and MEG data, it is important to take into consid-
eration the overall pattern of simultaneous activation
across the brain. This is different from such techniques as
functional magnetic resonance imaging (fMRI) in which
the signals from individual voxels can be observed largely
independently. Here, we attempt to characterize cancella-
tion effects in EEG and MEG signal patterns.
The sources of EEG and MEG signals are described in
terms of primary currents [Plonsey, 1969; Tripp, 1983]. The
active primary currents give rise to the electric potential
distribution, which can be measured on the scalp using
EEG. In addition, there will be associated passive volume
currents at locations where the gradient of the electric
potential differs from zero. However, the primary currents,
together with the conductivity geometry of the head,
determine the electric potentials and the volume currents;
therefore, it is convenient to express the signals conceptu-
ally as functions of the primary currents. The main contri-
bution to the primary currents detectable with EEG and
MEG comes from ionic currents in the apical dendrites of
cortical pyramidal cells, which are mostly aligned perpen-
dicular to the local cortical surface [Ha ¨ma ¨la ¨inen et al.,
1993; Lopes da Silva, 1991; Okada et al., 1999]. These cur-
rents result from both postsynaptic and active transmem-
brane currents. For symmetry reasons, the signals from
other types of active currents at the cellular level are
expected to cancel out macroscopically or generate electric
potentials and magnetic fields which fall off rapidly with
distance. These invisible currents include transmembrane
currents themselves, postsynaptic currents in stellate cells
or in the basal dendrites of pyramidal cells, as well as the
quadrupole-like current patterns associated with action
potentials [Humphrey, 1968a,b; Lorente de No, 1947].
Therefore, it is reasonable to assume that the primary cur-
rents underlying the extracranial EEG and MEG signals
are located in the cortical gray matter, oriented perpendic-
ular to the cortical surface.
In EEG and MEG source analysis, the basic element for
the primary current distribution is a current dipole, which
summarizes the net effect of the microscopic currents
within a volume of a few cubic millimeters, or a few
square mm of cortical surface. At the intermediate spatial
scale of about 1 cm and above, the folding of the cerebral
cortex adds a macroscopic geometric factor, which can be
examined using the detailed anatomical information pro-
vided by structural MRI. For example, the spatial fre-
quency spectrum of cortical gyrification has been related
to the pattern of spatial coherence in scalp EEG [Freeman
et al., 2003]. Cancellation of the EEG and MEG signals
occurs when the cortical activity extends over a region
where the surface normal, and therefore, also the orienta-
tion of the source elements, changes. In particular, cancel-
lation occurs when the activation involves opposing walls
of a sulcus or a gyrus. Figure 1A depicts simulated EEG
and MEG signals from two current dipoles of opposite
direction in the primary visual cortex in the calcarine
region, which mostly cancel out when the dipoles are
active simultaneously. Even at the spatial scale of several
centimeters, corresponding to activity distributed over
multiple regions across the whole cortex, large amount of
cancellation of spatially overlapping EEG or MEG signal
patterns can occur. Partial cancellation is illustrated in Fig-
ure 1B with sources in the inferior occipitotemporal region
of the left and right hemispheres.
We refer to local patches of activity as extended sources,
whereas distributed source patterns may consist of multiple
local foci or patches of activity in separate regions of the
cortex. This terminology is useful also in the context of
source estimation: on one hand, a single equivalent dipole
is usually an adequate model, not only for very small foci,
but also for moderately extended source patches, such as
those corresponding to various types of sensory evoked
responses. On the other hand, distributed source models
are particularly useful for widely spread activation that
consists of multiple simultaneously active functional areas,
as is often the case, e.g., with language-related activity. In
the present study, we explore the cancellation effects in
EEG and MEG signals using a realistic reconstruction of
the cortical surface [Dale et al., 1999; Dale and Sereno,
1993; Fischl et al., 1999]. For quantitative analysis, we cal-
culated a measure of cancellation for multiple randomly
distributed source dipoles across the cortex as well as for
locally extended patches of activity.
MATERIALS AND METHODS
Forward Model
The forward model is used to calculate the signals in a
set of sensors, due to dipolar source elements of unit mag-
nitude. The relationship between the EEG and MEG signals
rCancellation of MEG and EEG Signals r
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(signal vector v, with the dimension equaling the number
of sensors) and the source amplitudes (source vector q,
with the dimension equaling the number of dipole ele-
ments) is linear: v ¼ A q, where A is the forward matrix, of-
ten also called the lead-field matrix. The column vectors aj
of A correspond to the signal patterns generated by a single
source element of unit amplitude whereas each row of A
contains samples of the lead-field or sensitivity pattern of a
given sensor. To calculate A, one needs to specify the loca-
tion and orientation of each source element, the electromag-
netic properties of the tissues within the head (in
particular, the conductivity geometry), and the location, ori-
entation, and configuration of the sensors. Here, we re-
strictedthe sourcestobe
reconstruction of the cortical surface, oriented perpendicu-
lar to the surface, used the boundary element model (BEM)
for the conductivity geometry of the head, and chose com-
monly used whole-head EEG and MEG sensor array
configurations.
The forward model was based on data from a 42-year-old
male volunteer subject. The procedures were approved by
the Massachusetts General Hospital Institutional Review
Board. High-resolution structural T1-weighted magnetic
resonance images (MRIs) were acquired on a 1.5 T Siemens
scanner (TR ¼ 2530 ms, TE ¼ 3.25 ms, flip angle ¼ 7, 128
sagittal slices, slice thickness ¼ 1.3 mm, voxel size ¼ 1.3 3
1.0 3 1.3 mm3). A surface representation for the cerebral
cortex was constructed from the MRI using the FreeSurfer
software [Dale et al., 1999; Fischl et al., 1999]. A mesh of
about 300,000 vertices was created, with an average distance
of about 1 mm between neighboring source points. Each
vertex on the surface corresponding to the gray-white mat-
ter border was selected to represent the location of an MEG
and EEG source element (current dipole). Selecting the inner
surface of the cerebral cortex, rather than, e.g., the middle of
the gray matter, helped to avoid numerical instabilities that
can occur if the dipoles are very close to the brain-skull
interface, where the conductivity change is large. In our for-
ward model, sources were included also in the noncortical
medial regions corresponding to corpus callosum and thala-
mus that complete the closed surface representation of each
hemisphere. The orientation of each source element was
assumed to match the local surface normal.
The conductivity geometry of the head was modeled
using a boundary element model with three compart-
ments: the brain, the skull, and the scalp. The boundaries
were determined from the MRI by identifying the inner
and outer surfaces of the skull and the outer surface of the
skin [Hamalainen and Sarvas, 1989; Oostendorp and van
Oosterom, 1989]. Each surface consisted of 5,120 vertices;
the linear collocation method was used in the BEM calcu-
lations [Mosher et al., 1999]. This provides a reasonable ac-
curacy for most cortical source locations [Yvert et al.,
1996]. The accuracy of the forward model for the most su-
perficial sources close to the inner surface of the skull may
suffer from the sparseness of the BEM vertices [Fuchs et
al., 2001]. However, these inaccuracies are expected to
have only small effect on the cancellation explored in the
present study, except if very large values for the elements
of the forward matrix are obtained because of numerical
instabilities in the BEM calculations. To exclude this possi-
bility, we checked that there were no outliers (very large
values) among the elements of the forward matrix. The
conductivity ratios of 1:0.0125:1 were assumed for brain:
skull:scalp [Geddes and Baker, 1967].
locatedonarealistic
Figure 1.
Examples of cancellation of EEG and MEG signals. A: Simulated
data generated by two current dipoles in the primary visual cor-
tex of the left and right hemispheres. The maps depict spatial
patterns of signals over the occipital region when each dipole is
active alone (LH: left hemisphere, RH: right hemisphere), and
when the two dipoles are active simultaneously. Top: EEG iso-
contour maps; red and blue indicate positive and negative scalp
potentials, respectively. Middle: MEG magnetometer isocontour
maps; red and blue indicate positive and negative radial compo-
nent of the magnetic field. Bottom: MEG gradiometer signals;
each arrow depicts the signal in a pair of planar gradiometers.
The arrows have been rotated by 90 degrees from orientation
of the actual gradient vectors, to match the orientation of the
arrows with the direction of underlying source currents. The
locations (green dots) and orientations (green lines) of the
dipoles are indicated in coronal and sagittal MRI slices. This
example illustrates how cancellation can occur in all three types
of sensor arrays, when sources of opposite orientation are close
to each other. B: Maps of MEG magnetometer signals for bilat-
eral inferior temporal sources. For this particular source config-
uration, the cancellation is specific to mid-occipital MEG
magnetometer sensors. [Color figure can be viewed in the
online issue, which is available at www.interscience.wiley.com.]
rAhlfors et al. r
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We used existing MEG and EEG sensor configurations
based on actual experimental setup, with a 306-channel
MEG system (VectorView, Elekta Neuromag) and an EEG
cap with 60 scalp electrodes. Of the MEG sensors, 102
were magnetometers, measuring the magnetic field com-
ponent approximately radial to the surface of the head,
and 204 were planar first-order gradiometers, measuring
the tangential derivative of the radial component of the
magnetic field. The location and orientation of the MEG
sensor array with respect to the head were determined
with the help of small marker coils approximating mag-
netic dipoles attached to the head. The position of the
marker coils and the EEG electrodes with respect to ana-
tomical landmarks (nasion, preauricular points, and sev-
eral additional points on the scalp and face) were
determined with a 3D digitizer (Polhemus).
Cancellation Index
To quantify cancellation effects, we compared the length
of the signal vector generated by n simultaneous sources
aðnÞ ¼
Xn
jaj
???
???
???
??? ¼
XM
j
Xn
jaij
??2
??1=2
;
(1)
with the sum of the signal vector lengths for the same
sources when active individually
bðnÞ ¼
Xn
j
aj
????????¼
Xn
j
XM
ia2
ij
hi1=2:
(2)
Here aijare the elements of the forward matrix, M is the
number of sensors. For cortical patch analysis, the forward
solution ajfor each source element in Eqs. (1) and (2) was
scaled by the area ?jassociated with the source, i.e., ajwas
replaced by ?jaj.
The cancellation index ICwas defined as:
lCðnÞ ¼ 1 ? aðnÞ=bðnÞ;
(3)
which ranges from 0 to 1. If the net signal pattern for si-
multaneous sources is zero, then ? ¼ 0 and IC¼ 1, corre-
sponding to full (100%) cancellation. If there is no overlap
between the signal patterns of the individual sources, then
? ¼ ? and IC¼ 0, indicating absence of cancellation.
Simulated Source Patterns
We calculated the cancellation index for two types of
source configurations: (1) individual source elements (cur-
rent dipoles) distributed randomly across the cortical sur-
face and (2) patches of uniform activity within the cortex.
For the distributed dipole configuration, the number n
of simultaneous source elements ranged from a single
dipole up to the total number of vertices in the recon-
structed cortex representation. The amplitudes for the
source elements were derived from a random zero-mean
Gaussian distribution. The cancellation index IC(n) was
estimated by averaging the values obtained for 1,000 ran-
dom selections of n dipoles.
The cortical patches consisted of neighboring source ele-
ments within a given distance (‘‘radius’’) from the center
of the patch. The distances were computed along the corti-
cal surface using the Dijkstra algorithm [Lin et al., 2006].
The radius of a patch was varied from 1 to 50 mm (the
largest patches corresponding to n ¼ 15,000 dipole ele-
ments). Two hundred locations for the patches were cho-
sen randomly on the cortical surface.
To relate the cancellation index for patches with the
local curvature properties of the cortex, we computed an
orientation nonuniformity index IO, defined as:
lOðnÞ ¼ 1 ? g ðnÞ=D ðnÞ;
(4)
where
gðnÞ ¼
Xn
jdjnj
???
???
???
???
(5)
is the averaged dipole moment vector within a patch, and
DðnÞ ¼
Xn
jdj
(6)
is the area of the patch; ?jis the area associated with a sin-
gle vertex and njis the corresponding surface normal vec-
tor. If all dipole elements within a patch have the same
orientation, then IO¼ 0. If the dipole moment vectors are
oriented such that their sum is zero, then IO¼ 1. This is
analogous to a ‘‘closed source’’ configuration, in which the
net dipole moment cancels out, resulting in minimal meas-
urable signal when distance between the sensors and the
patch is large compared with the size of the patch.
RESULTS
Randomly Distributed Dipoles
As shown in Figure 2, the mean cancellation index ICfor
randomlydistributeddipoles
increased monotonically as a function of the number of
source elements. Notable cancellation occurred even with a
small number of sources: ICreached the value of about 0.5
with only five simultaneous dipoles. A small difference
between EEG and MEG was seen for n \ 100, with ICbeing
larger for EEG than for MEG. For large values of n, IC
approached unity; e.g., with 10,000 dipoles ICwas ?0.99, sug-
gesting that substantial cancellation of EEG and MEG signals
takes place when many sources are simultaneously active.
onthecorticalsurface
Extended Patches of Activity
An example of EEG and MEG signal patterns generated
by uniformly activated cortical patches of two different
sizes is shown in Figure 3. The signal pattern due to a
small patch is likely to be similar to that of a single dipole
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(Fig. 3A), whereas substantial cancellation is expected to
occur when the patch is large enough to extend to oppo-
site walls of a sulcus or a gyrus (Fig. 3B,C). To emphasize
the cancellation effect per source element, the maps in Fig-
ure 3 were scaled by the patch area. Note, however, that
the absolute peak signal magnitudes in this example were
larger for the large patch than for the small patch, though
only by a factor of about seven for EEG and two for MEG,
i.e., much less than 25, which was the ratio of the areas.
The mean value of the cancellation index ICfor patches
of different sizes is depicted in Figure 4. For very small
patches, ICwas close to zero, consistent with neighboring
dipole elements having a similar orientation and conse-
quently the signal patterns summating with little cancella-
tion in either EEG or MEG. For intermediate patches (radii
between 2 and 10 mm), ICincreased rapidly as a function
of the patch size, reaching IC¼ 0.5 for a radius of 10 mm;
this suggests that the local curvature affected the orienta-
tion of the dipole elements within a patch, resulting in
partial cancellation of the signals patterns. For large
patches, the cancellation index depended only weakly on
the size of the patch, reaching IC¼ 0.9 for MEG and ?0.8
for EEG for patches with a radius of 50 mm. Thus, in con-
trast to the case of randomly distributed dipoles (cf. Fig.
2), there appeared to be a prominent difference between
EEG and MEG in the cancellation of signals from large
patches of uniform cortical activity. Note that it is essential
here that all the dipole elements within a patch have the
same polarity, corresponding to currents flowing either
outward or inward with respect to the cortical surface.
The relationship between the cancellation index IC for
cortical patches and the corresponding orientation nonuni-
formity index IOis shown in Figure 5. ICis a measurement
of the actual cancellation of the EEG and MEG signals,
whereas IO only takes into account the mean dipole
moment vector across the source elements within a patch,
ignoring the location of each element. Figure 5 indicates
that ICand IOwere highly correlated. In the case of EEG,
the two indices were close to being equal for most of the
patches, suggesting that the cancellation effects in EEG can
be well approximated by the orientation nonuniformity,
i.e., the cancellation was proportional to the net dipole
moment obtained by summing the individual dipole
moment vectors. For MEG, however, there were many
patches for which IC[ IO, i.e., points that were above the
diagonal in Figure 5. For smaller patches, for which IC¼
0.2–0.6, the occasional large values of ICfor MEG can be
understood in terms of the orientation of the net dipole
moment being radial, resulting in very little MEG signal,
i.e., a ¼ 0 in Eq. (1). For large values of the indices, the
Figure 3.
Examples of EEG and MEG signals for extended patches of uniform
cortical activity. A patch with a 4-mm (A) and 20-mm (B) radius
in the left parietal cortex is shown in red on a cortical surface rep-
resentation reconstructed from anatomical MRI. The dots and
squares indicate the locations of the EEG scalp electrodes and the
MEG triple-sensor units (one magnetometer and two gradiome-
ters), respectively. Cancellation is illustrated by the signal per unit
source element, obtained by plotting the maps for the 20-mm
patch normalized by the ratio of the areas of the two patches (C).
[Color figure can be viewed in the online issue, which is available
at www.interscience.wiley.com.]
Figure 2.
Cancellation index IC for randomly distributed sources. The
index was computed for an array of 60 EEG electrodes, 102
MEG magnetometers, and 204 MEG gradiometers. The mean
and standard deviation over 1,000 random selections of n
dipoles are shown. For clarity, the standard deviation bars are
plotted one-sided only. [Color figure can be viewed in the online
issue, which is available at www.interscience.wiley.com.]
rAhlfors et al. r
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points for MEG clustered around IC¼ 0.9 and IO¼ 0.8
instead of the diagonal, suggesting that there was more
cancellation than would be predicted simply by the net
dipole moment vector. Inspection of the distribution as a
function of the patch size indicated that these points corre-
spond to the largest patches. These off-diagonal points
found for MEG but not for EEG are presumably related to
selective cancellation of tangential as compared with radial
source components.
DISCUSSION
We quantified cancellation effects in EEG and MEG sig-
nal patterns due to cortical sources using an anatomically
accurate model of the cortex. Substantial cancellation was
found both for randomly distributed sources and for
extended patches of activity. Later, we discuss implica-
tions of signal cancellation that depends on the distribu-
tion and extent of cortical activation to the interpretation
of EEG and MEG data, particularly in terms of the integra-
tion of multimodal brain imaging data and different char-
acteristics of EEG and MEG.
Relevance of Signal Cancellation in EEG
and MEG Studies
Several sources of data suggest that both spontaneous
and event-related cortical activity is likely to be spatially
extended [Halgren, 2004]. The cortex is highly intercon-
nected, with each neuron receiving and sending ?10,000–
100,000 synapses with other neurons. A variety of data,
including direct intracranial EEG recordings obtained in
subjects undergoing diagnostic procedures prior to surgi-
cal therapy for epilepsy [Halgren et al., 1998], indicates
that cortical activity can spread widely in less than 30 ms.
This suggests that with the possible exception of early sen-
sory evoked responses, patterns of activation are often suf-
ficiently widespread that the effects of cancellation are
relevant to interpretation of EEG and MEG data.
Figure 5.
Comparison of the cancellation index ICand the orientation non-uniformity measure IOfor cort-
ical patches. Data from simulated patches with different radii up to 50 mm are shown for EEG
(A), MEG magnetometers (B), and MEG gradiometers (C). [Color figure can be viewed in the
online issue, which is available at www.interscience.wiley.com.]
Figure 4.
Cancellation index ICfor cortical patches. The mean and stand-
ard deviation over 200 randomly located simulated patches of
uniform activity for each of the different radii shown. [Color fig-
ure can be viewed in the online issue, which is available at
www.interscience.wiley.com.]
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Prominent cancellation is expected when the two walls
of a sulcus are simultaneously active. Functional areas of-
ten cover both sides of a given sulcus. A well-known
example is the primary visual cortex, which is organized
so that visual stimuli extending across the horizontal me-
ridian will produce sources that cancel across the calcarine
fissure. Cancellation may also occur where the opposite
sides of the sulcus belong to distinct neurocognitive sys-
tems. For example, in the Sylvian fissure, primary and
association auditory cortices in the ventral bank are con-
trasted with somatosensory and other cortices dorsally
[Hari et al., 1993]. Also, bilateral activation of regions fac-
ing the interhemispheric fissure may produce cancellation
(cf. Fig. 1A); such regions include the visual medial occipi-
tal, cingulate, and supplementary motor areas [Lang et al.,
1991].
An important goal of many MEG and EEG studies is to
determine the spatiotemporal patterns of source activity
underlying the measured signals. Characterization of can-
cellation effects, combined with sensitivity analyses [de
Jongh et al., 2005; Goldenholz et al., 2009; Hillebrand and
Barnes, 2002], can provide valuable insights into what can
and cannot be detected with EEG and MEG. The present
study was based on the properties of the forward matrix
only; thus, the results are not specific to any particular
source estimation method. In the calculation of the electric
potentials and magnetic fields, we assumed a piecewise
homogeneous conductor of arbitrary shape and imple-
mentedthecomputations
method, commonly used for EEG and MEG source estima-
tion. More detailed head models that take into account
local variations in conductivity and its anisotropy are not
expected to change the major patterns of the forward solu-
tions [Haueisen et al., 2002], and thus not to change much
the cancellation measures.
Thecancellationindex
expected to depend somewhat on the design of the sensor
array. For example, the overlap of signals, and therefore
also the cancellation index IC, for sources located far apart
is likely to be smaller for differential sensors, such as pla-
nar MEG gradiometers compared with magnetometers, or
bipolar or Laplacian EEG derivation compared with a ref-
erential derivation. In general, meaningful comparisons
between different sensor array designs require that the sig-
nal-to-noise ratio of the measurements is taken into
account [Ahonen et al., 1993], which was beyond the scope
of the present study. The similarity of the graphs for MEG
magnetometers and gradiometers in Figure 2, however,
suggest that the cancellation index is not overly sensitive
to the specific sensor configuration.
Also, the exact number of sensors in the array does not
have a major effect on the cancellation analysis. For exam-
ple, the cancellation index in Figures 2 and 4 were almost
identical for MEG gradiometers and MEG magnetometers,
even though the number of gradiometers was twice the
number of magnetometers. It appears that the arrays used
here adequately captured those spatial frequencies that
withaboundary-element
fordistributedsourcesis
dominate the signal patterns and, therefore, also the can-
cellation effects. Increasing the sensor density would result
in signals that are similar in neighboring sensors; this is
expected to affect the cancellation index minimally, as its
definition was such that, e.g., doubling the number of sen-
sors by including each channel twice does not alter the
value of the index. It is unlikely that the differences seen
between EEG and MEG were due to the differences in the
number of sensors. As will be discussed below, the main
differences in the cancellation effects found between EEG
and MEG are consistent with selective cancellation of ra-
dial vs. tangential source components, which is independ-
ent of the specific sensor arrays used.
Implications for Multimodal Spatiotemporal
Brain Imaging
Cancellation effects are of concern when electrophysio-
logical EEG and MEG data are compared with hemody-
namic measures (fMRI, positron emission tomography,
optical imaging) [Dale and Halgren, 2001] or with invasive
intracranial recordings [Halgren et al., 1998; Lu and Wil-
liamson, 1991]. At the spatial scale of up to a few square
millimeters of cortical surface, the net signal from a com-
plex pattern of microscopic neural currents was repre-
sented by a single current dipole element in our forward
model. This is adequate in practice, as only the dipolar
term of the multipole expansion for a complex pattern of
microscopic source currents contributes significantly to the
recorded potentials and fields when the distance from the
source to the sensors is much larger than the extent of the
source [Nunez, 1995]. Details of the local current patterns
and microscopic cancellation effects are beyond the spatial
resolution of presently available non-invasive imaging
techniques. Thus, detailed quantitative comparisons with
electrophysiological and hemodynamic measures have to
rely on information provided by invasive intracranial
recordings [Schroeder et al., 1998; Ulbert et al., 2001;
Vaughan, 1982] and biophysical modeling [Jones et al.,
2007; Murakami and Okada, 2006].
At the intermediate spatial scale of a few square centi-
meters of cortex, represented here by patches of extended
activity, anatomical information about the local folding of
the cortical surface can be used to estimate cancellation
effects. In addition, information provided by fMRI about
the spatial extent of local regions of activity could be
incorporated in the cancellation analysis. Assumptions
about activity within cortical patches can also be incorpo-
rated in inverse modeling [Fuchs et al., 1999; Han et al.,
2007; Kincses et al., 1999; Lapalme et al., 2006; Lin et al.,
2006].
At the whole-cortex scale, cancellation of EEG and MEG
can be large even for randomly distributed simultaneous
sources. The reduction in the signal-to-noise ratio per
source element due to cancellation may result in some
active areas being detected with fMRI but not with EEG or
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MEG. This does not appear to be a serious problem, how-
ever, for approaches in which fMRI is used to suggest
likely locations for the EEG and MEG sources: simulation
studies have indicated that the inclusion of such noncon-
tributing regions as fMRI priors have only little effect on
the EEG and MEG source estimates [Ahlfors and Simpson,
2004; Im et al., 2005; Liu et al., 1998].
Differences Between EEG and MEG in
Cancellation of Signals From Extended Sources
The cancellation analysis with extended patches of activ-
ity indicated a systematic difference between EEG and
MEG that may have interesting implications to the inter-
pretation of combined recordings of EEG and MEG. If a
patch of uniform activity extends over multiple sulci and
gyri, selective cancellation of signals from sources of par-
ticular orientation can occur. The dipole moments of
source elements in the two walls of a sulcus point to oppo-
site directions, resulting in strong cancellation of extracra-
nial signals, whereas the sources on the crown of a gyrus
and the bottom of a sulcus have the same direction and,
thus, produce similar signal patterns that summate with
minimal cancellation. In the lateral, dorsal, frontal, and
posterior regions of the cerebral cortex, the canceling sour-
ces in sulcal walls are mainly tangentially oriented,
whereas the noncanceling ones are radial. Since MEG is
insensitive to radially oriented sources [Grynszpan and
Geselowitz, 1973], strong cancellation is expected for MEG,
whereas the radial sources will still generate prominent
EEG signals [Eulitz et al., 1997; Freeman et al., 2009].
The roles of tangential and radial sources are inter-
changed in the ventral and medial parts of the cortex. For
these regions, the main orientation of the nonopposing
gyral source elements is tangential, whereas the canceling
sources in the sulcal walls have a predominantly radial
orientation. Therefore, signals from extended sources in
these regions should be present in both EEG and MEG.
However, as mentioned above, bilateral activity of func-
tional areas in the medial wall of the cerebral hemispheres
is likely to result in strong cancellation [Lang et al., 1991].
Selective cancellation of radial vs. tangential sources
could underlie some of the differences seen between EEG
and MEG in cognitive event-related responses [Eulitz
et al., 1997]. For example, the amplitude of the P300 com-
ponent is typically large in central scalp EEG electrodes,
whereas in MEG the P300 is often small and scattered
across sensors [Siedenberg et al., 1996]. This is consistent
with signal patterns generated by large patches of activity,
for which the EEG is expected to mostly reflect the super-
ficial radial sources on the top of the gyri, but the corre-
sponding MEG only reflects the residual signals remaining
from incomplete cancellation of tangential sources. A
widely distributed pattern of cortical activity related to the
P300 has also been observed in intracortical recordings
[Halgren et al., 1998] and in fMRI [Kiehl and Liddle,
2003]. The difference in the selective cancellation of EEG
and MEG signals could also be helpful in identifying the
presence of extended regions of synchronized oscillatory
activity [Freeman et al., 2009].
Selective cancellation of spontaneous background activ-
ity is also likely to contribute to differences in the SNR of
event-related activity in EEG and MEG. For example,
inter-ictal epileptogenic discharges are sometimes detected
either in EEG or in MEG but not necessarily in both [Iwa-
saki et al., 2005; Knake et al., 2006; Lin et al., 2003]; expla-
nation for this may lie in the combination of differential
sensitivity of EEG vs. MEG to the source of interest [de
Jongh et al., 2005; Goldenholz et al., 2009; Hillebrand and
Barnes, 2002] as well as in the selective cancellation of
widespread background brain activity [de Munck et al.,
1992]. These considerations support the view that EEG
and MEG provide complementary information of human
brain activity [Cohen and Cuffin, 1983; Hari and Ilmo-
niemi, 1986; Wood et al., 1985] and that these two closely
related measures should be combined for optimal results.
Both experimental [Sharon et al., 2007] and theoretical
[Molins et al., 2008] results have suggested that the accu-
racy of source estimates can improve beyond the capabil-
ities of EEG or MEG alone by combining data acquired
with the two methods.
CONCLUSIONS
Substantial amount of cancellation can occur in extracra-
nial EEG and MEG signals generated by simultaneously
active sources. For extended patches of activity, selective
cancellation of signals due to sulcal vs. gyral sources can
result in a systematic difference between EEG and MEG.
These effects are independent of the source estimation
method employed and can be important in explaining dif-
ferences in experimental data obtained with EEG and
MEG.
ACKNOWLEDGMENTS
The authors thank David Cohen, Anders Dale, Ksenija
Marinkovic, Maria Mody, and Suresh Narayanan for use-
ful discussions and comments.
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