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Journal of Neuroscience Methods 166 (2007) 41–52
EEG and MEG coherence: Measures of functional connectivityat distinct spatial scales of neocortical dynamics
Ramesh Srinivasan a,c,∗, William R. Winter a,b, Jian Ding a, Paul L. Nunez b,c
a Department of Cognitive Sciences, University of California, Irvine, CA 92697-5100, United Statesb Department of Biomedical Engineering, Tulane University, New Orleans, United States
c Brain Physics LLC, Covington, LA 70433, United States
Received 9 October 2006; received in revised form 23 June 2007; accepted 25 June 2007
bstract
We contrasted coherence estimates obtained with EEG, Laplacian, and MEG measures of synaptic activity using simulations with head modelsnd simultaneous recordings of EEG and MEG. EEG coherence is often used to assess functional connectivity in human cortex. However, moderateo large EEG coherence can also arise simply by the volume conduction of current through the tissues of the head. We estimated this effect usingimulated brain sources and a model of head tissues (cerebrospinal fluid (CSF), skull, and scalp) derived from MRI. We found that volumeonduction can elevate EEG coherence at all frequencies for moderately separated (<10 cm) electrodes; a smaller levation is observed with widelyeparated (>20 cm) electrodes. This volume conduction effect was readily observed in experimental EEG at high frequencies (40–50 Hz). Corticalources generating spontaneous EEG in this band are apparently uncorrelated. In contrast, lower frequency EEG coherence appears to result frommixture of volume conduction effects and genuine source coherence. Surface Laplacian EEG methods minimize the effect of volume conductionn coherence estimates by emphasizing sources at smaller spatial scales than unprocessed potentials (EEG). MEG coherence estimates are inflatedt all frequencies by the field spread across the large distance between sources and sensors. This effect is most apparent at sensors separated by less
han 15 cm in tangential directions along a surface passing through the sensors. In comparison to long-range (>20 cm) volume conduction effectsn EEG, widely spaced MEG sensors show smaller field-spread effects, which is a potentially significant advantage. However, MEG coherencestimates reflect fewer sources at a smaller scale than EEG coherence and may only partially overlap EEG coherence. EEG, Laplacian, and MEGoherence emphasize different spatial scales and orientations of sources. 2007 Elsevier B.V. All rights reserved.e2atoia
(
eywords: Coherence; Synchrony; Volume conduction; EEG; MEG; Laplacian
. Introduction
The central goal of EEG studies is to relate various mea-ures of neural dynamics to functional brain state, determinedy behavior, cognition, or neuropathology. One of the mostromising measures of such dynamics is coherence, a corre-ation coefficient (squared) that estimates the consistency ofelative amplitude and phase between any pair of signals inach frequency band (Bendat and Piersol, 2000). Any pair of
EG signals may be coherent in some frequency bands andncoherent in others; the dependence of detailed extracranialoherence patterns on frequency and brain state is now well
∗ Corresponding author at: Department of Cognitive Sciences, University ofalifornia, Irvine, CA 92697-5100, United States. Tel.: +1 949 824 8659.
E-mail address: [email protected] (R. Srinivasan).
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165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2007.06.026
stablished (Nunez et al., 1997, 1999, 2001; Silberstein et al.,003, 2004; Srinivasan, 1999; Srinivasan et al., 1999; Nuneznd Srinivasan, 2006a). EEG coherence provides one impor-ant estimate of functional interactions between neural systemsperating in each frequency band. EEG coherence may yieldnformation about network formation and functional integrationcross brain regions.
The coherence measure is generally distinct from synchronySinger, 1999), which in the neuroscience literature normallyefers to signals oscillating at the same frequency with identicalhases. This type of synchronization in a local region of cortexs a critical factor in determining EEG amplitude in the samecentimeter scale) region. That is, each EEG signal is gener-
ted by a superposition of many brain current sources (Nuneznd Srinivasan, 2006a); the contribution of each source dependsn source and electrode locations and the spread of currenthrough the head volume conductor. Each EEG electrode signal
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eflects an average over all sources in a large region of the cor-ex (on the order of 100 cm2), and synchronous sources withinhis region produce much larger signals at each electrode thansynchronous sources. Thus, EEG amplitude in each frequencyand can be related to the synchrony of the underlying currentources (Nunez and Srinivasan, 2006a). Consistent with thisrgument, reduction in amplitude is often labeled desynchro-ization (Pfurtscheller and Lopes da Silva, 1999). Of course,eduction in amplitude may, in theory, occur as a result fromither reduction in (mesosocopic) source magnitude or reduc-ion in the surface area this synchronized (Nunez and Srinivasan,006a).
In contrast to amplitude measures, coherence is a measuref synchronization between two signals based mainly on phaseonsistency; that is, two signals may have different phases (as inhe case of voltages in a simple linear electric circuit), but highoherence occurs when this phase difference tends to remainonstant. In each frequency band, coherence measures whetherwo signals can be related by a linear time invariant transfor-
ation, in other words a constant amplitude ratio and phasehift (delay). In practice, EEG coherence depends mostly onhe consistency of phase differences between channels (Nunez,995; Nunez and Srinivasan, 2006a). High coherence betweenwo brain areas is an indicator that the relationship between theignals generated in such areas may be well approximated by ainear transformation; however, this does not necessarily implyhat the underlying neocortical dynamics is linear.
While there has been a great deal of interest in using EEGoherence to measure functional connectivity in the brain, oneerious limitation of extracranial EEG coherence measuress contamination by volume conduction through the tissueseparating sources and electrodes. We have investigated thisffect theoretically using four-sphere models of volume con-uction consisting of an innermost sphere representing therain surrounded by three concentric spherical shells represent-ng cerebrospinal fluid (CSF), skull, and scalp (Nunez, 1981;rinivasan et al., 1998). When all cortical sources are uncor-elated, i.e., incoherent in every frequency band, this modelredicts substantial EEG scalp coherence at electrode separa-ions less than approximately 10–12 cm (Nunez et al., 1997,999; Srinivasan et al., 1998). A small volume conduction effects also predicted for very large electrode separations (>20 cm).he volume conduction effect is independent of frequency andepends only on the electrode locations and electrical proper-ies of the head. In the four-sphere model, electrodes separatedy less than about 10–12 cm are apparently recording fromartly overlapping source distributions due to volume conduc-ion. As the separation distance between electrodes decreases,he overlap in source distributions and coherence due to volumeonduction both increase. This picture is qualitatively consistentith a variety of experimental EEG data (Srinivasan et al., 1998;rinivasan, 1999; Nunez, 1981, 1995; Nunez and Srinivasan,006a). Two nearby EEG electrodes will appear coherent across
ll frequency bands because they record potentials generated byome of the same sources. In an earlier paper (Nunez et al., 1997),e defined “reduced coherence” as the difference between theeasured EEG coherence and the “random coherence”, definedtasa
ience Methods 166 (2007) 41–52
s the scalp EEG coherence due only to volume conductionxpected when cortical sources are uncorrelated. However, vol-me conduction distortions of coherence are not simply additiveut reflect spatial filtering of source activity (Srinivasan et al.,998). Reduced coherence is only a crude idea of the generalagnitude of source coherence based on a rough estimate of
olume conduction effects.We can partly overcome this problem of EEG coherence due
o volume conduction by reducing the spatial scale of scalpotentials with high-resolution EEG methods like the surfaceaplacian (Law et al., 1993; Nunez et al., 1991, 1993, 1997,999; Perrin et al., 1987, 1989; Srinivasan et al., 1996; Nuneznd Srinivasan, 2006a). The surface Laplacian is the secondpatial derivative of the scalp potential in two surface coordi-ates tangent to the local scalp. In simulations with four-sphereodels, the spatial area averaged by each electrode is reduced
rom perhaps 100 cm2 for (average reference) scalp potentialso perhaps 10 cm2 for spline Laplacians estimated from denselectrode arrays (e.g., 131 electrodes, 2.2 cm center-to-centerverage spacing, Nunez et al., 2001). Our simulations withour-sphere models indicate that all volume conduction effectsre removed from Laplacian coherence estimates at distancesreater than about 3 cm (Srinivasan et al., 1998; Nunez et al.,997, 1999; Nunez and Srinivasan, 2006a). The surface Lapla-ian isolates the source activity under each electrode that isistinct from the surrounding tissue under adjacent electrodesuch that measured Laplacian coherence can be directly relatedo coherence between these sources. However, Laplacians maylso remove genuine source coherence associated with widelyistributed source regions (very low spatial frequencies) alongith volume conduction contributions; that is, the Laplacian
patial filter cannot distinguish between source and volume con-uction effects. In other words, Laplacian coherence providesstimates of the phase consistency of sources at smaller spa-ial scales in comparison to (average reference) EEG coherenceNunez and Srinivasan, 2006a).
MEG (magnetoencephalography) is a relatively new technol-gy that potentially provides useful insights into brain sourcesHamalainen et al., 1993), especially when used as an adjuncto EEG measurements (Nunez and Srinivasan, 2006a). Oneommon but erroneous idea is that MEG spatial resolution isnherently superior to EEG spatial resolution, and that MEGhould simply replace EEG in order to extract more accuratenformation about brain source dynamics. Because of the largeistance separating the magnetometer coils from the sourcestypically 3–4 cm above the scalp), MEG also yields relativelyarge extracranial coherence even when the underlying brainources are uncorrelated due to the effects of field spread tohe sensors (Srinivasan et al., 1999; Winter et al., 2007). The
ain distinction between MEG and EEG measures is that theyre selectively sensitive to different source orientations; thisan be either an advantage or disadvantage for MEG depend-ng on application. One clear advantage of MEG over EEG is
hat much less detailed knowledge of the volume conductivend geometrical properties of the head is required to model theignals. Since normal tissue is non-magnetic (magnetic) perme-bility (μ) is constant across head tissues and free space; to first
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pproximation, the magnetic field depends only on the loca-ions and orientations of sources and sensors (Hamalainen et al.,993).
Our earlier studies (Nunez et al., 1997; Srinivasan et al.,998) using the four-sphere head model made use of exclusivelyadial dipoles sources (representing gyral surfaces) forming apherical layer. EEG is more sensitive to radial sources thanangential sources at any depth in the four-sphere model (Nuneznd Srinivasan, 2006a). Coherence due to volume conductionay be expressed analytically using the four-sphere model when
he source distribution forms a spherical layer (Srinivasan et al.,998). This analytic expression generally agrees with observedolume conduction effects in EEG recordings. Although radialipoles appear adequate for most EEG effects, tangential sourcesre essential for modeling field-spread effects on MEG coher-nce and are likely also to make contributions to EEG volumeonduction effects. The local tangential sources depend on theeometry of cortical folds; thus attendant simulations requireipoles at realistic cortical locations.
The goal of this paper is to model the relationship betweenrain source dynamics and extracranial MEG and EEG dynam-cs in order to interpret the physiological bases of measuredoherence. We use MRI to model the cortical surface in ordero realistically position and orient dipole sources in a three-llipsoid model of the head (brain, skull, and scalp). In contrast,ur previous models of volume conduction effects on EEGoherence used concentric spheres, and exclusively superficialadial dipoles. With the new ellipsoidal model and realisticource geometry, we quantify the spatial resolutions of conven-ional EEG, Laplacian, and MEG and estimate the effects ofolume conduction (EEG, Laplacian) and separation of sourcesrom sensors (EEG, Laplacian, MEG) on coherence measures.
e compare our model results to EEG, Laplacian, and MEGeasures of coherence obtained from simultaneous 148 chan-
el MEG and 127 channel EEG recordings. Our results confirmhat both the location and the spatial scale of brain networksetermine the patterns of EEG, Laplacian, and MEG coherence.
. Methods
.1. Experimental methods
Data were recorded in six subjects at the Scripps Researchoundation in La Jolla, CA: 127 EEG channels (Advancedeuro Technology, Enschede, The Netherlands) and 148 MEG
hannels (4D Neuroimaging, San Diego, USA). The EEG ampli-er was powered with a battery and placed inside the shieldedoom, and fiber-optic cables were used to transmit the EEG sig-als to the acquisition computer outside the room. The EEG andEG signals were analog filtered at 100 and 108 Hz and sampled
t 940 and 1018 Hz, respectively. Because the EEG and MEGignals were sampled by independent amplifiers and A/D cards,riggers were used to denote transitions between experimental
tates. This ensured that the two data sets had sample-to-sampleorrespondence, verified by the alignments of random triggerignals (+5 V) that were sampled by both the EEG and MEGystems during each recording.G
u
cience Methods 166 (2007) 41–52 43
.2. Procedure
The first experimental procedure consisted of a four minuteeriod with subjects resting with eyes closed followed by 4 minith resting, eyes opened. In addition, four 1 min periods of
yes closed resting were alternated with a (eyes closed) men-al arithmetic task chosen to manipulate coherence patternsNunez, 1995; Nunez et al., 2001). Each subject was given aandom two digit number X and asked to mentally sum theeries X + 1, (X + 1) + 2, (X + 1 + 2) + 3, . . . to sums of severalundred. Six subjects participated in the experiment; a high-esolution (1 mm × 1 mm × 1 mm) MRI scan was also acquiredn a separate day from three subjects.
.3. Surface Laplacian
The surface Laplacian was estimated from the New Orleanspline Laplacian algorithm (Law et al., 1993; Nunez et al., 1993;rinivasan et al., 1996; Nunez and Srinivasan, 2006a). The splineaplacian is based on three-dimensional interpolation of discreteamples of scalp potential with a best fit sphere to the scalp sur-ace used to estimate the two surface derivatives at each electrodeocation; its accuracy has been verified in thousands of simula-ions. Because Laplacian estimates are generally inaccurate athe locations of edge electrodes (Srinivasan et al., 1998; Nunezt al., 2001), all coherence estimates involving the 18 edge elec-rodes in simulations and genuine data were excluded from ouresults.
.4. Coherence analysis
The data were resampled to 128 Hz using the Matlab (Natick,A) resample function. Alignment of trigger signals was used
o verify alignment of EEG and MEG after resampling. The dataere divided into 2-s epochs and detrended. Estimated equip-ent and room noise were removed from the raw MEG data
y digital filtering using reference coils positioned in the dewarbove the array of MEG coils (Srinivasan et al., 1999). Ampli-ude thresholds of 70 �V for EEG and 5 pT for MEG were used toliminate epochs containing high-amplitude artifact; typically,0% of epochs were retained in each experiment with thesehresholds. The EEG data were referenced to the average poten-ial of all channels (the standard average reference potential thatpproximates potential at infinity, see Nunez and Srinivasan,006a).
The Matlab FFT algorithm was applied to each 2-s epochf data yielding Fourier coefficients with frequency resolutionf = 0.5 Hz at each of the m = 1, M channels for epochs k = 1, K,ith K = 120 epochs in each brain state. The cross-spectrum esti-ate based on the complex valued coefficients Fuk(fn),Fuk(fn) for
hannel pair (u, v) is
2 K∑ ∗ N
uv(fn) =Kk=1
Fuk(fn)Fvk(fn) n = 1,2
− 1 (1)
For single channels (u = v) the cross spectrum reduces to thesual power spectrum Pu(fn) = Guu(fn). Coherence at each fre-
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uency is the normalized cross spectrum, estimated by (Bendatnd Piersol, 2000)
2uv(f ) = |Guv(f )|2
Guu(f )Gvv(f )(2)
Coherence was calculated between all pairs of data channelsithin each of the measurement categories, EEG, Laplacian andEG.
. MRI based source models
In order to simulate EEG and MEG coherence effects due tohe separation of sensors from sources, dipoles at realistic corti-al locations are required. Sources in the three-ellipsoid modelollow the cortical surfaces obtained from MRIs of individualubjects. While mainly motivated by the need to study MEGoherence, we note that omission of tangential dipoles could pos-ibly also have important influences on our estimates of the EEGr Laplacian coherence due to volume conduction. The sourceodels used in this study were based on MRIs obtained on
hree subjects. Grid surfaces were created to represent the brainy a combination of automatic segmentation with a thresholdnd manual correction of the segmented volume on a slice-y-slice basis (Brain Voyager QX 1.6, Brain Innovation B.V.,aastricht, The Netherlands). Sources were simulated at each
oint of the grid representing the brain boundary as the currentipole moment per unit volume P(r,t) oriented perpendicularo the local cortical surface (for discussion of this mesoscopicource function in terms of synaptic microsources, see Nuneznd Srinivasan, 2006a). An example grid is shown in Fig. 1.
.1. Three-ellipsoid volume conduction model
The upper surfaces of human heads may be fit accuratelyo general ellipsoids defined by their dimensions along threerthogonal axes (Law and Nunez, 1991). For purposes ofhis study, we have constructed new head models (for three
ubjects) based on three confocal ellipsoidal surfaces (three-llipsoid models) for the following reasons: (1) the new modelsave a more realistic geometry (in comparison to sphericalodels) that may influence coherence especially at the largedom
ig. 1. (a) Electrode locations on the best fit ellipsoid to the scalp surface are shown a
ience Methods 166 (2007) 41–52
nterior–posterior electrode separations. However, we have notsed realistic head geometry (skull and scalp) in the modelartly because such models make the incorrect assumption thatesistance is proportional to thickness of the skull layer. Asiscussed in Nunez and Srinivasan (2006a), in vivo measure-ent of hydrated skull plugs and in vivo studies of skull flaps
n surgery patients provide no clear evidence that thicker skullas greater resistance. Rather, the thicker middle (spongy) skullayer appears to be a better conductor due its ability to hold fluid.he adoption of three confocal ellipsoids allows us to focus on
he issue of non-spherical head shape and make use of realisticource geometry, without introducing factors related to tissueonductivity that are not well-known.
The CSF/skull boundary was segmented to fit a general ellip-oid by means of a principal component analysis. Two confocalllipsoidal surfaces of constant thicknesses were then addedo represent outer skull and scalp surfaces. Each of the outerllipsoids was centered and oriented on the innermost ellipsoidCSF/skull boundary) as shown by the scalp surface with elec-rode positions in Fig. 1a. The thicknesses of layers were almostdentical to those used in our four-sphere model (Srinivasan etl., 1998), except for absence of the CSF layer. In general, theSF layer is thin (<1–2 mm) so that its effect on volume conduc-
ion is generally small in four-sphere models; in any case, theffect of CSF in the four-sphere model may be approximated inhe three-sphere model by increasing the effective skull conduc-ivity (Nunez and Srinivasan, 2006a). The CSF/skull boundaryas also fit to a sphere, and a three-sphere model was simi-
arly constructed. For both ellipsoidal and spherical models, theest-fit electrode positions were calculated.
The outer surface potentials for dipole sources were obtainedor the three-sphere and three-ellipsoid models using a boundarylement model (ASA 3, EEimagine, Germany). The numericalolution for outer surface potential due to a single radial dipole inhe three-sphere boundary element model was found to match theorresponding analytic solution as expected. The outer sphericalurface was also used to provide a spherical surface for the Newrleans Laplacian algorithm.
Numerical solutions for outer surface potentials due to unitipoles at each location over the folded, MRI generated modelf the cortical surface were calculated with the three-ellipsoidodel. For each subject there were approximately 100,000
s grey circles. (b) MEG coils, approximately 4 cm above the scalp, are shown.
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R. Srinivasan et al. / Journal of N
ipole sources per hemisphere, approximating the continuousource function P(r,t). The surface Laplacian was calculatedrom the potential distribution for each dipole source. Thisielded two matrices for the EEG (GE) and Laplacian (GL)here each row corresponded to one dipole source and each
olumn corresponded to the EEG electrode positions. Theseatrices are the numerical versions of the corresponding Green’s
unction, a concept widely used in mathematical physics andngineering (Srinivasan et al., 1998; Nunez and Srinivasan,006a).
.2. Magnetic field model
The local surface normal of the magnetic field Hn(r,t) onellipsoidal surface (passing through the MEG sensors) 4 cm
bove the scalp ellipsoid, as shown in Fig. 1b was calculatedrom the Biot-Savart law (Nunez, 1986; Hamalainen et al., 1993;unez and Srinivasan, 2006a)
n(r, t) = μ
4πan(r) ·
I∑
i=1
P(ri, t) �V × (r − ri)
|r − ri|3 (3)
ere the sum is over all I cortical dipoles P(ri,t)�V with corticalocations ri, where �V is the discrete volume element of corticalissue, an(r) is a unit vector normal to the local sensor surface,nd r is location on the sensor ellipsoid.
Numerical solutions for the radial magnetic field due to unitipoles at each location over the folded, MRI generated modelf the cortical surface were calculated. For each subject thereere approximately 100,000 dipole sources per hemisphere.his yielded a matrix (GM) where each row corresponded tone dipole source and each column corresponded to the MEGensor positions.
.3. Sensitivity distribution and half-sensitivity area
The sensitivity of each EEG or Laplacian electrode and MEGensor to dipole sources on the cortical surface was expressed inerms of a sensitivity distribution. The properties of the electricnd magnetic Green’s functions determine the sensitivity of EEGlectrodes and MEG coils as demonstrated by Malmivuo andlonsey (1995) using lead field analysis in spherical volumeonduction models. By introducing more realistically shapedolume conduction models such as ellipsoids, the sensitivitystimates are further refined by restricting the simulated sources(r,t) to be normal to the local cortical surface derived fromRI.For each electrode or sensor position the sensitivity distribu-
ion describes the relative contribution of each possible sourceo the electrode or sensor and can be obtained by normalizingach column of the Green’s function matrix (GE, GL, or GM)o its maximum magnitude on the brain surface. The sensitiv-ty function provides a simple way to visualize the locations
f brain sources that make the largest contributions to EEG,aplacian, or MEG signals. The half-sensitivity area (HSA) ishe surface area (on the brain surface) which contains all theources which contribute at least half of the strongest signal.
ofos
cience Methods 166 (2007) 41–52 45
he half-sensitivity area is similar to the half-sensitivity volumeefined by Malmivuo and Plonsey (1995) and provides a simpleetric of the spatial resolutions of EEG, Laplacian and MEGeasures.
.4. Spatial white-noise simulation
Spatial white-noise source distributions P(r,t) over the entirerain were defined as a delta correlated random process; in otherords at any frequency the cross spectrum between all pairs of
ources forms an identity matrix, KPP = I. The cross spectrumf the EEG can be calculated from the source cross-spectrumnd Green’s function matrix as KEE = G′
EKPPGE. The crosspectrum of the Laplacian and the MEG were similarly cal-ulated using the appropriate Green’s function matrix. Crosspectra were normalized to obtain the coherence using Eq. (2).n this idealized simulation (with essentially an infinite numberf epochs) any non-zero coherence observed between EEG orEG channels reflects only the effects of volume conduction or
eld spread. In simulations with finite number of epochs used tostimate coherence, small non-zero coherence is also observedue to statistical fluctuations.
. Results
.1. Sensitivity distributions of EEG, Laplacian, and MEG
Fig. 2 shows the sensitivity distributions for a fixed EEGlectrode location (yellow circle at right) and MEG coil posi-ion (green line) shown in the figure inset. We have normalizedhe Green’s function to its maximum magnitude on the brainurface in order to define the sensitivity function that describeshe contribution of each source to the electrode or sensor. Fig. 2ahows that the EEG electrode is most sensitive to sources in theyral crown closest to the electrode. Although the sensitivityunction tends to fall off with distance from the electrode, gyralrowns widely distributed throughout the cortical hemisphereontribute roughly half the potential of the sources directlyeneath the electrode. Sources along sulcal walls, even whenlose to the electrode, contribute much less to scalp potentialhan sources in the gyral crowns. Fig. 2b shows the Laplacianensitivity distribution for the same electrode position. The high-st sensitivity regions of the Laplacian and EEG are the identicalyral crown beneath the electrode as expected. The Laplacians much less sensitive to distant gyral crowns, thereby provid-ng a far more “local” measure of source activity. Fig. 2c showshe sensitivity distribution of an MEG coil whose location 4 cmbove the EEG electrodes is shown in the inset head. EachEG coil is sensitive to a large region of the cortex, consis-
ent with the very large half-sensitivity volumes reported for aingle coil magnetometer (Malmivuo and Plonsey, 1995). Theensitivity function generally exhibits local maxima on sulcalalls. Opposing sulcal walls have opposite sensitivities because
f the change in orientation of the sources; thus adjacent sur-aces with sensitivities of opposite sign are expected to makenly small or perhaps negligible contributions to the magneticensor.
46 R. Srinivasan et al. / Journal of Neuroscience Methods 166 (2007) 41–52
Fig. 2. The EEG (a), Laplacian (b), and MEG (c) sensitivity distributions fora fixed electrode location (yellow circle at right inset figure) and magnetic coilposition (green line at right inset figure) are shown. The cortical surface wasconstructed from the MRI of one subject. Simulated “dipole sources” P(r,t)(dipole moment per unit volume, 100,000 in one hemisphere) were assumednormal to the local cortical surface. Scalp surface potentials, scalp Laplacians,and surface normal magnetic fields due to each dipole were calculated at theelectrode and coil locations shown in the inset using Green’s functions (onefor each measure) based on the confocal three-ellipsoid head model. The threeGreen’s functions were normalized with respect to their maximum values so thatthe relative sensitivity of the three measured could be compared. (a) The EEGelectrode is most sensitive to gyral sources under the electrode, but this electrodeis also sensitive to large source regions occupying relatively remote gyral crownsand much less sensitive to sources in cortical folds. (b) The Laplacian is mostsensitive to gyral sources under the electrode; sensitivity falls off rapidly atmoderate and large distances. (c) The MEG is most sensitive to sources in corticalfolds that tend to be tangent to MEG coils. Maximum MEG sensitivity occursin folds that are roughly 4 cm from the coil in directions tangent to the surface.Regions in blue provide contributions to MEG of opposite sign to those ofyc
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Fig. 3. The half-sensitivity areas for the potential (a) and Laplacian (b) due totwo electrodes spaced by about 5 cm (shown in the figure inset at left) are plottedusing the three-ellipsoid head model. Half-sensitivity areas are defined as thesurface areas of the cortex containing sources that could contribute at least halfthe “maximum signal” (i.e., contributed by the strongest source location for eachelectrode or MEG sensor position). The regions of cortex associated with thehalf-sensitivity area of each electrode are indicated by the two colors. The areasassociated with the scalp potential measure are shown to overlap substantially,wms
IEosL(
ttstmdiLdtFdistant gyral surfaces. The implication is that if a source region
ellow/orange, reflecting dipoles on opposite sides of folds that tend to produceanceling magnetic fields at the coil.
We follow the notion of a half-sensitivity volume (Malmivuond Plonsey, 1995) in order to define a half-sensitivity areas the surface area of the cortex that contains sources thatould contribute at least half the signal contributed by thetrongest source location for each electrode or MEG sensorosition. Across 128 electrode locations in the three subject’s
ead models, the EEG half-sensitivity areas ranged from 8 to5 cm2 (median = 13 cm2); across 148 sensor positions, MEGalf-sensitivity area ranged from 5 to 26 cm2 (median = 11 cm2).ias
hereas the scalp Laplacians at these two electrodes are shown to be sensitiveainly to distinct local gyral crowns reflecting the Laplacian’s much improved
patial resolution.
n contrast to the widespread sensitivity areas of conventionalEG or MEG, the sensitivity area of high-resolution EEGbtained with the surface Laplacian is limited to very localources within a small distance to the electrode. In our study,aplacian half-sensitivity areas ranged from 0.8 to 5.1 cm2
median = 1.5 cm2).Fig. 3a shows the half-sensitivity distribution for the poten-
ial due to two electrodes spaced by about 5 cm as shown inhe figure inset. The regions of cortex associated with the half-ensitivity area of each electrode are indicated by the two colors;hey are shown to overlap substantially. The dramatic improve-
ent in spatial resolution afforded by high-resolution EEG isemonstrated by comparing these results with the correspond-ng surface Laplacian sensitivity plot in Fig. 3b. The surfaceaplacians at these two electrodes are shown to be sensitive toistinct local gyral crowns. The highest sensitivity for each elec-rode is at the same location in the cortex as for the potential inig. 3a, but the surface Laplacian is much less sensitive to more
s localized within a small dipole layer in a specific gyral surfaces indicated in the figure, the surface Laplacian will isolate theignal corresponding to that source in a single electrode. In con-
R. Srinivasan et al. / Journal of Neuros
Fig. 4. Simulated coherence is shown as a function of tangential electrode (orMEG coil) separation for EEG, Laplacian, and MEG for uncorrelated corticalsources, that is, spatial white noise at arbitrary temporal frequency. Sensor sep-aration is defined on the simulated scalp surface (ellipsoidal). These coherencefall-offs with sensor separation were calculated using our three-ellipsoid headmodel. Simulated cortical dipoles P(r,t) are distributed over the entire foldedcwT
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ortical surface with locations in gyri and cortical folds. P(r,t) is assumed every-here normal to the local cortical surface, as obtained from one subject’s MRI.he grey lines plot the average coherence at each sensor separation.
rast, the same source will contribute substantially to potentialsecorded at both electrodes.
.2. Spatial white-noise simulations of EEG, Laplacian,nd MEG coherence
Fig. 4 shows simulated coherence as a function of tangen-ial electrode (or MEG coil) separation for EEG, Laplacian,nd MEG for uncorrelated cortical sources (spatial white noiset arbitrary temporal frequency) as obtained from our three-llipsoid head model in one subject. The simulated corticalipoles are distributed over the entire folded cortical surfaceith locations in gyri and cortical folds assumed normal to the
ocal cortical surface, obtained from the subject’s MRI.At small to moderate electrode separations (<10–12 cm) EEG
ppears to be somewhat coherent even when the underlyingources are uncorrelated as shown in Fig. 4a. This effect is inde-endent of temporal frequency and only reflects the overlap inensitivity distribution of closely spaced electrodes as shown by
he example in Fig. 3. This volume conduction effect is mostlyemoved by the surface Laplacian where only nearest neighboroherences appear elevated as shown in Fig. 4b. MEG shows aimilar elevated coherence at short and moderate sensor separa-anes
cience Methods 166 (2007) 41–52 47
ions due to the field spread from the sources to sensors as shownn Fig. 4c. The magnitude of this effect is less easily predicted by
EG sensor separation because it depends on the orientationsf the coils and folded geometry of the cortex.
The EEG coherence increase at large distances (>20 cm)s due to the fact that potentials due to single radial dipolesall to zero at large distances on spherical or ellipsoidal sur-aces and then become progressively more negative, producingon-zero coherence at very large distances due only to vol-me conduction. By comparison, tangential sources contributeess potential at these large distances than radial sources.
EG coherences are higher than EEG coherences at inter-ediate distances (10–20 cm) but no similar rise is observed
t large distances. field-spread effects on MEG coherence areot simply related to separation distance as they also dependn the relative orientations of coils and dipole sources in theortex.
.3. Comparison of white-noise simulation toigh-frequency EEG/MEG data
Volume conduction effects in EEG and field-spread effectsn MEG are independent of temporal frequency over the band-idth of recordable scalp EEG (Nunez and Srinivasan, 2006a).hus, in experimental EEG spectra we expect that any frequencyand exhibiting minimal genuine source coherence will produceatterns of EEG coherence on the scalp due only to volume con-uction. Since most scalp EEG power is below about 15–30 Hz,e conjectured that source activity in the brain above 30 Hz isot generally coherent at the cm scale, thereby contributing veryittle signal. Thus, at high frequencies we expect the source dis-ributions underlying the EEG and MEG signals to be similar tohat of spatial white noise; that is, we expect observed extracra-ial coherence to be mostly generated by volume conductionnd passive field spread.
We examined experimental EEG, Laplacian and MEG coher-nce at frequencies ranging from 40 to 50 Hz in three differentrain states—resting eyes closed, resting eyes open, and (eyeslosed) mental calculations. Fig. 5 shows coherence at 45 Hzlotted versus sensor or electrode separation for each brain stateaveraged over the six subjects). The upper row indicates thathe EEG has elevated coherence at short electrode separationsalling to a minimum at around 12 cm in all three experimen-al conditions. The rise at larger distances is also observed inll three cases. The grey curve superimposed on each scatterhows the average value at each distance. Although there areome differences between coherence estimates in the three EEGcatter plots, the main factor determining EEG coherence in the5 Hz band is the pattern imposed by volume conduction, sug-esting that the underlying sources are indeed approximatelypatial white noise as we conjectured. This conclusion is sup-orted by the Laplacian coherence (middle graphs) at 45 Hzhich shows very low coherence in all three brain states except
t very close (<3 cm) electrode separations. In the spatial white-oise simulation, Laplacian coherence is also essentially zeroxcept at very closely spaced surface locations. The lower rowhows recorded MEG coherence at 45 Hz, which indicates ele-
48 R. Srinivasan et al. / Journal of Neuroscience Methods 166 (2007) 41–52
Fig. 5. Experimental coherence at 45 Hz plotted is vs. sensor or electrode sep-aration in each column for each of three brain states (eyes closed resting, eyesclosed computation, eyes open resting) and for the three measures in each row.Coherence was calculated for all possible pairs of the 127 electrodes and 148magnetic coils (8001 and 10,878 coherence estimates, respectively). The 18 edgeelectrodes were omitted from the Laplacian estimates yielding 5886 coherences.The grey curves superimposed on each scatter show the average coherence ateach distance. The EEG (upper row) has elevated coherence at short to moderateelectrode separations falling to a minimum at around 12 cm in all three experi-mental conditions with the rise at higher distances also observed in all three cases(due to negative potentials generated by radial dipoles). The Laplacian coher-ence (middle row) shows very low coherence in all three brain states except atvery close (<3 cm) electrode separations. MEG coherence (lower row) repre-sb
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Fig. 6. (a) The average (over the 40–50 Hz range) coherence–distance relation-ship is plotted in one subject for the EEG (upper), Laplacian (middle) and MEG(lower) measures. The grey curve is the simulated coherence for this subjectbased on his (MRI estimated, white noise) dipole source orientations in thetob
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bMibboralower alpha band (Nunez et al., 2001; Nunez and Srinivasan,
ents the intermediate case; it falls off somewhat faster than the EEG coherence,ut slower than the Laplacian coherence.
ated coherence at short distances again generally consistentith the three-ellipsoid model with spatial white-noise sources.Fig. 6a shows the average coherence–distance relationship
or each unit frequency in the 40–50 Hz range for the EEGupper), Laplacian (middle) and MEG (lower) measures forne subject. In each case the curves are essentially identicalt each frequency, and at all frequencies Laplacian coherences negligible at moderate or large distances. The grey curvesre the simulated coherences for the same subject obtainedith the three-ellipsoid model with white-noise sources. Fig. 6b
hows that the coherence–distance relationship averaged overhe 40–50 Hz band is very similar across our six subjects.
Fig. 7 demonstrates the behavior of coherence in differentrequency bands (for the three brain states) in one subject. Allix subjects’ coherency showed similar behavior. In contrast toxperimental coherences in the 40–50 Hz band, similar curvesn the theta to alpha bands (Fig. 7) show elevated coherence at all
istances, and strong dependences of coherence on brain statend temporal frequency in EEG, Laplacian, and MEG suggest-ng substantial genuine source coherence effects. Coherence is2ta
hree-ellipsoid head model. (b) The coherence–distance relationship averagedver the 40–50 Hz band in each of the six subjects showing very little differenceetween subjects.
levated over a wide range of frequencies during resting andomputation states in each measure. When the subject has eyespen at rest, only the EEG alpha frequencies near the 9.5 Hz peakaintain the high coherence similar to the other brain states. By
ontrast, the MEG and Laplacian coherences, which are alsoargest at the alpha peak of 9.5 Hz during eyes closed at restnd computation, are small when the eyes are opened. This sug-ests the high coherence observed at 9.5 Hz takes place in aource distribution that is readily recorded by the EEG but nothe Laplacian or MEG. These data are consistent with the ideahat the alpha peak represents a large-scale source distributionpanning very large regions of the cortex as discussed in Nuneznd Srinivasan (2006a).
In this subject, the EEG exhibits relatively minimal changesetween (eyes closed) resting and computation, whereas theEG and Laplacian show more robust differences between rest-
ng and computation. Such differences in coherence patternsetween rest and computation are not very obvious in Fig. 7ecause we have presented the average coherence as a functionf separation distance. Mental calculations occur with specificegional coherence increases in theta (especially frontal), upperlpha, or both bands, together with coherence reductions in the
006a). We do not provide such detailed coherence patterns inhis paper in order to focus on the issue of volume conductionnd comparisons between measures.
R. Srinivasan et al. / Journal of Neuros
Fig. 7. Experimental coherence (in one subject) at several frequencies is plottedversus electrode (or MEG coil) separation in each column for each of three brainstates (eyes closed resting, eyes closed computation, eyes open resting) and forthe three measures of coherence in each row. The grey curve is the simulatedcoherence for this subject based on his (MRI estimated, white noise) dipolesource orientations in the three-ellipsoid head model. This figure is similar toFig. 5 except that the multiple curves represent the average coherence at eachsensor separation for the frequencies 9.5, 9, 10, 8.5, 10.5, 5.5, 8, 11, 4, 4.5, 6, 5,7.5, 11.5, 6.5, 7, 12 Hz. This frequency order (top to bottom) applies to the EEGresting plot. While there are minor differences in the ordering of frequencies, allplots with large coherences over moderate and large distances are for frequenciesntc
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ear the alpha peak at 9.5 Hz. Comparison of these plots with Figs. 4–6 indicateshat neocortex produces source activity P(r,t) that is moderately to stronglyorrelated in the theta and (especially) alpha bands in the two eyes closed states.
Coherence changes are often observed in the Laplacian andEG but not in the EEG. Such differences in coherence pat-
erns appear to involve localized alpha sources in sulcal wallsdetected by MEG) and on gyral crowns (detected by the Lapla-ian). Simultaneously, the large-scale (global) alpha sourcectivity detected by the EEG may exhibit only minimal coher-nce changes. This general pattern was observed across all ourix subjects in this study, though the details of frequencies andize of the effects varied across subjects. These data are consis-ent with our earlier studies suggesting that the alpha band gen-rally consists of combinations of global dynamic and local net-ork activity that may or may not overlap in frequency (Andrew
nd Pfurtscheller, 1997; Nunez, 2000a,b; Nunez et al., 2001;unez and Srinivasan, 2006a, 2006b; Srinivasan et al., 2006a,b).
. Discussion
.1. EEG and MEG are sensitive to distinct sources
EEG and MEG are shown here to be generally sensitive toidely distributed cortical sources; many of these sources are
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cience Methods 166 (2007) 41–52 49
ocated at large distances from each sensor as demonstrated inigs. 2 and 3. Radial dipoles (normal to local scalp surface) arestimated to be roughly three times more efficient than tangentialipoles (of the same strength and depth) in generating scalpEG; the effect of dipole depth in the cortical folds increases
his preference for radial dipoles in EEG (Nunez and Srinivasan,006a). In addition, radial dipole layers covering large areasf superficial cortex (spanning several or perhaps many gyralrowns) make a much larger contribution to scalp potentials thanmaller dipole layers (Nunez, 1995). Since deep dipole layersfor instance, in the thalamus) make much smaller contributionso scalp potentials due to the greater distance between sourcesnd electrodes, we can plausibly conclude that most EEG isenerated by radial sources in the gyral crowns forming dipoleayers, and that larger synchronous dipole layers generate largerEG signals. We note that although time averaging of evokedotentials (including Fourier methods), can be used to extractignals generated by smaller dipole layers from the backgroundEG, these signals are similarly sensitive to dipole layer size.
Large dipole layers, spanning several sulci, are unlikely toake strong contributions to MEG (except at the edges) because
f a dipole cancellation effect. That is, MEG is preferentiallyensitive to sources in the sulcal walls (to the extent that sulcire tangent to MEG coils), thus dipole layers that extend overpposing sulcal walls are expected to generate minimal MEGignals (Nunez, 1995). Tangential dipoles in each wall tend toe oriented in opposite directions, and the radial sources in theyral crowns principally generate minimal radial magnetic fieldassuming the gyral dipole moments are normal to MEG coils).hese large radial dipole layers are the strongest generators ofEG signals. MEG is preferentially sensitive to small dipole lay-rs limited to one sulcal wall and not extending to the opposingulcal wall. Thus, EEG and MEG are preferentially sensitive toifferent source orientation and source spatial scale, even withinhe same region of the brain.
MEG simulations and data were obtained here with mag-etometer coils; the point-spread functions of EEG andagnetometer-based MEG are typically in the same general
ange (Malmivuo and Plonsey, 1995; Nunez and Srinivasan,006a). MEG systems based on gradiometer coils can bexpected to dramatically improve spatial resolution, subject todditional issues associated with noise and coil geometry; welan future studies of gradiometer-based MEG to address thesessues.
.2. The surface Laplacian is sensitive to smaller sourceegions than EEG
The Laplacian acts as an EEG spatial filter that can substan-ially improve spatial resolution by removing the very low spatialrequencies associated with volume conduction as demonstratedn Figs. 2 and 3. Another advantage of the Laplacian (and MEG)s that they are reference-free, whereas EEG depends on the
ocations of both recording and reference electrode (Nunez andrinivasan, 2006a). However, with large numbers of electrodes,or instance 128 in these studies, average reference potentialslosely approximate absolute potentials (“at infinity”) in simu-
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ations (Srinivasan et al., 1998; Nunez and Srinivasan, 2006a).espite its advantages demonstrated here, the Laplacian shouldot be viewed as a panacea; Laplacian and other high-resolutionEG estimates have practical limitations associated with noise,lectrode density, and the removal of genuine source activity byhe spatial filter algorithm; issues examined in some depth inunez and Srinivasan (2006a).
.3. Coherence due to volume conduction and field spread
We calculated the coherence between EEG electrodes andEG sensors due to volume conduction and field spread using
ur three-ellipsoid head models and uncorrelated dipole sourcesistributed over the cortical surface. In the models, the mainactor determining the magnitude of these coherence effects ishe separation distance between sensors. EEG electrodes sep-rated by less than 10 cm show substantial effects of volumeonduction that become larger as the separation between elec-rodes decreases. In addition, electrodes separated by more than0 cm also exhibit a small volume conduction effect due to theurved geometry of the head. MEG sensors separated by lesshan 15 cm produce substantial field-spread effects of on coher-nce that depend on both separation distance and the orientationsf the magnetometer coils. By contrast to the EEG, more widelyeparated MEG sensors show very little field-spread effects onoherence. This difference between EEG and MEG coherencet large distance occurs because EEG and MEG are mainly sen-itive to radial and tangential dipoles, respectively, and the radialources contribute more signals at large distances in the curvedead geometry. Although EEG head models have accuracy lim-ted by our knowledge of tissue conductivity and geometry, theredicted relationship between coherence and electrode separa-ion is not very sensitive to head model errors. The EEG andaplacian coherence estimates presented here using the three-llipsoid models with realistically positioned sources are similaro results obtained with a four-sphere model and only radialources (Srinivasan et al., 1998).
Volume conduction is largely independent of frequency andrain state (Nunez and Srinivasan, 2006a). The models then pro-ide theoretical estimates of coherence effects that are expectedo correspond to brain states and frequency bands in which corti-al sources have minimal or perhaps zero coherence. Such EEG,aplacian, and MEG coherence was observed here for all fre-uencies in the range 40–50 Hz, and was largely independentf brain state (see also Nunez et al., 1997, 1999; Nunez andrinivasan, 2006a). Across six subjects, the pattern of coher-nce versus distance was very similar in the 40–50 Hz range; inhree subjects with MRI-based head models, model coherenceas qualitatively similar to the 40–50 Hz data. This suggests
hat the general features of volume conduction and field-spreadffects of coherence are likely to be similar across other subjects,mplying that the predicted relationship presented here can bextended to other subjects even in the absence of head mod-
ls. Moreover, in any subject the high-frequency (40–50 Hz orotentially higher) data can itself be used to gauge volume con-uction effects; a pattern of coherence versus distance that doesot change with frequency and brain state provides a reasonable2wdt
ience Methods 166 (2007) 41–52
stimate of volume conduction when accurate head models areot available.
Application of spline Laplacian algorithms to either sim-lated white-noise sources in volume conductor models orenuine EEG data at frequencies greater than 40 Hz generallyields very low (<0.1) coherence estimates at tangential dis-ances greater than about 3–4 cm. These data are in sharp contrasto alpha and some theta rhythms, which can easily yield Lapla-ian coherences >0.5 between many electrode pairs separated by0–25 cm (Nunez, 1995; Srinivasan, 1999; Nunez et al., 2001),lso shown in Fig. 7. Such data can only be explained in termsf substantial long-range source coherence in these frequencyands due perhaps to some combination of corticocortical net-orks and global synaptic action fields (Nunez and Srinivasan,006a, 2006b).
.4. Implications for studies of neocortical dynamics withEG and MEG coherence
The problem of volume conduction effects on EEG coherencestimates has been sufficiently severe that, at least as late as theid 1990s, many EEG scientists and physiologists were skepti-
al that large or even moderate extracranial coherence could beeliably associated with brain source coherence. Such skepticismas bolstered by intracranial recordings in epileptic patients and
nimals. For example, subdural coherence measured with 2 mmiameter electrodes was reported to fall to zero at all frequen-ies for electrode separations greater than about 2 cm (Bullockt al., 1995a,b). This picture is in sharp contrast to scalp EEGoherence at the peak alpha frequency in the eyes closed rest-ng state, which can easily be greater than 0.5 and even close to.0 between pairs of electrodes separated by 10–25 cm (Nunez,995; Srinivasan, 1999; Nunez et al., 1999, 2001; Nunez andrinivasan, 2006a), also indicated in Fig. 7.
This apparent discrepancy concerning cortical source coher-nce may be understood by noting that in any complex system,or which human brains provide the pre-eminent examples, weenerally expect dynamic measures to be scale-dependent. Amm diameter subdural electrode is sensitive to cortical sourcesovering perhaps 10 mm2 of cortical surface. By contrast, a 1 cmiameter scalp electrode records from sources covering perhaps0–100 cm2 of cortical surface (Nunez, 2000a,b; Nunez et al.,997, 2001). We may describe this approximate idea in termsf cortical macrocolumns (3–10 mm2); scalp recordings aver-ge over 1000 or more macrocolumns. The implication is thate cannot predict scalp dynamic behavior from small or evenoderate numbers of cortical electrodes. Such predictions might
equire perhaps 10,000 or more mm scale cortical electrodes. Ifmaller cortical electrodes are used, even more spatial samplesre required for scalp predictions.
We have characterized neocortical dynamics as consistingf (local and regional) cortical and thalamocortical networksmbedded in global fields of synaptic action (Nunez, 1989,
000a,b; Nunez and Srinivasan, 2006a, 2006b). In this mannere are able to make convenient connections between neocorticalynamic theory and experiment. For example, a purely globalheory predicts traveling and standing waves of synaptic action
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Nunez, 1974, 1995), a prediction having experimental supportor both spontaneous EEG and steady state visually evokedotentials (Burkitt et al., 2000; Nunez, 1995, 2000a,b; Nuneznd Srinivasan, 2006a). The global theory predicts large-scaleource distributions consisting of coherent source activity span-ing several (or many) gyral surfaces, which are the dominantources of EEG. One the other hand, this global theory ignoresritical network effects and must, at best, represent a vast over-implification of genuine neocortical dynamics. Some of theetwork dynamics in gyri may be observed at scales smallerhan that of the global fields with the Laplacian measure. Inddition, networks that occupy one side of a cortical fold (orny cortical tissue tangent to MEG coils) may be best observedith MEG.
.5. Implications for localization studies
The simulations of Figs. 2 and 3 also have implications forEG and MEG dipole localization studies. It is well known that
he inverse solution has no unique solution; a very large num-er of source distributions can be fit to any external data setNunez and Silberstein, 2001; Nunez and Srinivasan, 2006a).or this reason, inverse solutions require additional informationor assumptions) about the nature of brain sources. The tradi-ional assumption has been one of a small number of localizedources. Alternate constrains (or assumptions) on inverse solu-ions involve restriction to (MRI based) neocortex or temporal orpatial smoothness of the source function P(r,t). We have arguedhat most spontaneous EEG is generated by distributed sourcest multiple spatial scales for which traditional inverse methodsre mostly inappropriate (Nunez and Srinivasan, 2006a). Therigins of evoked or event related potentials are less clear; oneay guess that the later the latency from the stimulus, the moreidely distributed the sources as a result of the spreading of
ynaptic action from primary sensory cortex. The distinctionetween distributed and localized sources is, of course, essen-ially a quantitative argument based on the threshold criterionsed to distinguish “substantial” from “negligible” magnitudesf the source function P(r,t), which can be expected to be gen-rally non-zero at any brain location where synaptic actionccurs.
For purposes of argument, let us first assume a relativelyocalized source region occupying a single gyral crown and aontiguous sulcal wall. In this idealized example, EEG and MEGocalization methods (used either together or separately) mayuccessfully locate the source region. If, however, both sides ofcortical fold become active so as to produce dipole cancella-
ion, MEG localization may fail to identify this region. Similarly,f the synaptic action occurs only in the folds, EEG localization
ay fail. When the genuine source function P(r,t) is widelyistributed, Fig. 2 implies that dipole localization methods mayometimes pick out a few discrete locations with large sensitivi-ies to most sensors, especially gyral crowns in the case of EEG,
hereby providing an erroneous picture of distributed sources asocalized. An MEG signal, on the other hand, is inherently moreikely to be explained by a small number of sources (on singleides of cortical folds) due to its insensitivity to cortical sourcesB
cience Methods 166 (2007) 41–52 51
n the gyri that may dominate EEG in many brain states (Nunez,995; Nunez and Srinivasan, 2006a).
Attempts to “undo” the volume conduction problem in EEGor MEG) by estimating source activity before estimating coher-nce have not yet been evaluated with the formalism appliedere and are a potentially significant future use of our model.owever, we note that such source reconstructions have theirwn biases that depend on the inversion method. For instance,olutions that impose maximal smoothness on cortical sourcectivity are biased towards low spatial frequencies (Lehmann etl., 2006), much like conventional EEG, and will underestimatehe focal source activity identified with the Laplacian or MEG.
. Summary
EEG and MEG coherence measures apparently reflect differ-nt aspects of neocortical dynamics. EEG coherence is mostlyensitive to large-scale source distributions spanning several (orerhaps many) gyral crowns and is subject to significant volumeonduction effects influencing about 60% of electrode pairs,oth moderately (<10 cm) and widely (>20 cm). Almost all ofhese volume conduction effects on coherence are removed byhe surface Laplacian; however, the Laplacian spatial filter alsoemoves large-scale source activity. MEG is sensitive to a differ-nt set of sources, mainly small isolated dipole layers in sulcalalls, and is also subject to significant field-spread effects influ-
ncing about 50% of sensor pairs typically separated by lesshan 15 cm. Widely separated MEG sensors show very littleeld-spread effects, which is a potentially significant advantagef MEG. However, since MEG records from different sets ofources than EEG, MEG coherence may only partly overlapEG coherence. An MEG signal is inherently more likely to bexplained by a small number of sources, not because of superiorccuracy, but rather due to its insensitivity to cortical sourceshat may dominate the EEG in many brain states. The EEG,aplacian, and MEG coherence measures provide selective
nformation about generally distinct neocortical source activ-ty. Thus, we generally expect a more comprehensive picture ofortical source distributions when all three measures are applied.
cknowledgments
The authors are grateful for the support of the NIMH, R01-H68004.
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