Article history:Accepted 15 December 2013Available online 4 January 2014
Contemporary high-density electroencephalographic systems (hd-EEG) comprising up to 256 electrodes haveinter-electrode separations of 2–4 cm. Because electric currents of the brain are believed to strongly diffusebefore reaching the scalp surface, higher-density electrode coverage is often deemed unnecessary. We used anultra-dense electroencephalography (ud-EEG) sensor array to reveal strong potential variation at 1 cm scaleand discovered that it reflects functional brain activity. A new classification paradigm demonstrates thatud-EEG provides twice the signal to noise ratio for brain-response classification compared with contemporaryhd-EEG. These results suggest a paradigm shift from current thinking by showing that higher spatial resolutionsampling of EEG is required and leads to increased functional brain information that is useful for diverse neuro-logical applications.
The earliest EEG recordings detected electric activity of the wholebrain via a pair of sensors positioned across the head (Pravdich-Neminsky, 1913; Berger, 1929). It was soon discovered that EEG variedsubstantially over the scalp (Adrian, 1934; Adrian, 1935), which insti-gated simultaneous recordings from several EEG sensors and resultedin the standardized “10–20” electrode placement system of 21 scalpelectrodes (electrode separation N 6 cm) adopted half a century ago(Jasper, 1958). Although this system remains in wide use among clini-cians, high-density (64–256 sensors, electrode separation N 2 cm)EEG systems, which appeared two decades ago (Gevins, 1990; Tucker,1993) quickly became a popular choice for EEG scientists and havesince made their way into some clinics. Given the advances in amplifierminiaturization and wireless data transmission, EEG systems with upto 1000 sensors are well within reach for modern technology. Theincreased spatial information could significantly impact basic neurosci-ence research aswell as a broad spectrum of practical applications frombrain–computer interfaces to localization of epileptic sources. Hence,the important question: how many sensors are sufficient to capture allinformation on brain activity provided by EEG?
Theoretical and experimental analyses have shown that at least 128EEG scalp channels are necessary to meet the Nyquist requirement forspatial sampling (Srinivasan, 1998; Spitzer, 1989), but the upper limitremains unknowndue to our incomplete knowledge of the electric prop-erties of head tissues and difficulties in accurately modeling real heads.Computational modeling using simplistic head models (Ryynänen,
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2004; Ryynänen, 2006; Malmivuo, 2011) and some preeminent EEGmethods books (Srinivasan, 2005; Nunez, 2006) suggest that electrodesspaced by 2–3 cm, characteristic of hd-EEG sensor arrays, can providesufficiently dense EEG sampling, implying that further resolution isunnecessary. A more realistic head modeling based on the finite ele-ments method (FEM) applied to MRI images indicated that a muchsmaller (~0.3 cm) electrode spacing is needed for extraction of corticalpatterns from scalp EEGs in humans (Ramon, 2009). This modelingresult agrees with experimental measurements demonstrating thatelectrode spacing of 0.5–1 cm is required to capture spatial EEG patternwithout undersampling (Freeman, 2003; Odabaee, 2013). Althoughthese experiments demonstrated that human EEG contains significanthigh spatial frequencies, it remains unknown how much of the extrainformation captured at these frequencies is of practical significance,e.g., whether it provides more accurate EEG source localization orimproves discrimination between brain states. Here, we use a classifica-tion paradigm to show that sampling EEG signals at high spatial fre-quencies significantly increases classification accuracy derived fromEEG responses evoked by two visual stimuli. This demonstrates thatultra-dense (1 cm or less) electrode spacing is needed to fully capturefunctional brain information from EEG.
Methods
Paradigm
Arguably, the best way to determine the sufficient number of EEGsensors is to measure the amount of functional brain information Icontained in EEG data as a function of the number of sensors, I(n). Forsome value of n the functionmight saturate sufficiently to deem furtherincrease of the number of sensors unnecessary. However, covering the
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whole scalp with hundreds of sensors is a challenging technical task.Similarly to previous studies (Freeman, 2003; Odabaee, 2013) the com-promise we adopted here was to derive an estimate of this metric usinga small dense array of sensors. Unlike the previous studies, wheremere-ly the spatial spectral power of EEGwas estimated, we used a classifica-tion paradigm instead. In this paradigm a classification algorithm wasused to carry out binary classification of individual trials based ontheir EEG data.We hypothesized that the amount of functional informa-tion I captured by the array is amonotonically increasing function of thealgorithm's classification accuracy pc. The advantage of this approach isthat (i) it gives an estimate of functional brain information compared tomere spatial variation of EEG, and (ii) given a ‘hotspot’ of the functionalinformation relevant to the classification task on the scalp, it is sufficientto estimate I at this location as a function of sensor density, I(d), toobtain a reliable estimate of the full-scalp I(n).
Stimuli
The used stimuli were common English noun words rendered usingLatin and Hebrew fonts. These fonts were chosen to maximally resembleeach other in terms of character width, height, spacing, and strokeweight. The stimuliwere generated using an in-house visual psychophys-ics library (PEACH). They were viewed on a linearized 21" ViewSonicG225f monitor. The monitor resolution was set to 1600 × 1200 pixels;for the used viewing distance of 70 cm, a pixel subtended 1 minute ofarc. The monitor refresh rate was 75 Hz. The words were displayed inblack on a bright white background and positioned in the center ofthe screen. Each letter subtended 2° of visual angle. The stimuli are illus-trated in Fig. 1b. Each stimulus epoch lasted for 1 s. At the beginning ofthe epoch aword appeared and stayed on the screen for 500 ms, for thesecond half of the epoch the screen was left blank. Every 16 epochsthere was a 4 second rest interval. A fixation cross was displayed onthe white background during the rest interval. Each of the 236 wordsused was displayed once using the Latin font and once using theHebrew font, the order of words and fonts was randomized. The fullexperimental run lasted 10 min.
Fig. 1. (a) 4 × 4 ud-EEG array positioned for theword classification experiment. (b) Exemplars obars show the classification's percent correct and the corresponding signal-to-noise ratio (d′) warray. Error bars indicate one standard error. SNRs averaged over all subjects are shown on thof the experimental data (dark points). White circles mark results for 64, 128, and 256 sensors
Subjects
Twelve observers (10 males, 2 females) 20–60 years of age, withnormal or corrected visual acuity participated in the study. Six of theobservers were the authors. Most observers did not take part in EEGexperiments before. Observers were instructed to minimize head andeye muscle activity during the visual stimulation intervals and wereencouraged to blink, clear their throats, etc. during the rest intervals.Observers were also told that they could move their eyes during thevisual stimulation intervals if they needed to do so in order to read thepresented word. Otherwise, observers' eye movements were notcontrolled. Besides viewing the presented words no other task wasperformed. One subject showed excessive eye-muscle activity (blinksand eye movements) and was excluded from the study.
ud-EEG array
The custombuild ud-EEG array comprised 16 gold-coated electrodesarranged into a 4 × 4 square grid with period of 10 mm center-to-center distance. The electrodes, 3 mm in diameter, terminated with4 mm diameter cup-shaped tips. The electrodes were fixated into thesquare matrix using a PDMS silicone elastomer. The cupped tips werefilled with Spectra 360 electrode gel to lower contact impedance. Theud-EEG array was applied to the scalp by an elastic bandage, and, onceapplied,was not allowed to shift. Therewas no special scalp preparationfor the array. Given the small cup size with respect to the electrodespacing and the relatively high viscosity of the gel the probability offorming conductive bridges between the array electrodes wasminimal.We took all precautions to make sure that no such bridges occurred.Individual electrode impedances were in the 50–200 kΩ range.
Data acquisition
A pilot experiment was used to choose the placement of the 4 × 4ud-EEG array. The stimuli and task were as described above. EEG in thisexperiment was recorded using HydroCell GSN 128-channel nets, ampli-fiers (200 MΩ input impedances), and the accompanying NetStation
f the English and ‘Hebrew’word stimuli. (c) Results of the experiment for 11 subjects. Grayhen only 4 corner electrodes' data were used. Red bars show the same for the full 4 × 4e right. (d) SNR as a function of sensor density. The solid line indicates a logarithmic fit.
142 Y. Petrov et al. / NeuroImage 90 (2014) 140–145
software by EGI Inc. Electrode locations on the head and head land-marks (nasion and tragi points) were measured for each subject usinga Polhemus FASTRACK digitizer and in-house software (3Digit). Thefull-head data recorded in the pilot experiment were used by a classifi-cation algorithm (VEP classification section) to determine a “mostinformative” scalp location common for all subjects. To this end the clas-sification algorithmwas applied to eachof the 128 electrodes separatelyand the location of the most informative electrode was determined. Inthe main experiment, ud-EEG data was recorded using the ud-EEGarray connected to 16 of the 128 EGI amplifiers. Subjects' earlobeswere linked and used as both ground and reference during the record-ing. Afterwards, the data was re-referenced to the average signal overthe 4 × 4 array, thus removing global EEG components. According tothe study paradigm, only the information contained in the local varia-tion of EEG over the chosen patch of the scalp was to be estimated asa function of the sensor density. Synchronously with the EEG dataacquisition the NetStation software recorded epoch markers using DINsignals generated by PEACH via the DATAPixx peripheral (VPixx Tech-nologies). The markers were generated at the beginning of the firstCRT raster sweep after theword image transfer to the screen video buff-er, and the markers were taken as the beginning of a VEP epoch in ourstudy. The stimulus rendering was completed 13.3 ms later at the endof a video frame. EEG data acquisition was externally triggered by theDATAPixx peripheral synchronously with the monitor refresh signal(75 Hz), and the trigger rate was set to 7 samples per video frameresulting in 525 Hz sampling frequency. EEG and event markers datawere saved on a hard drive and processed off-line.
EEG data pre-processing
Data processing and analysis were performed using an in-houseMATLAB software suite (Harmony). AC line noise frequencies (60 Hzand 120 Hz) and monitor refresh frequency (75 Hz) were notch-filtered out of each epoch. Constant terms were subtracted from rawepochs to remove DC components and occasional amplifier resetartifacts. Up to 15% of raw epochs were rejected due to muscle activityartifacts determined by potential thresholding. Because subjects wereencouraged to blink during the rest intervals the rejected epochs oftenincluded the first epoch after each rest interval. The remaining epochs(approximately 200 per each word type) were averaged for each sub-ject. Noisy electrodes were identified based on the proportion of therejected epochs, and, if detected, were replaced by thin-spline interpo-lating data from the remaining electrodes (Nunez, 2006). Finally, VEPswere average referenced over all channels.
ud-EEG data interpolation
Two additional sensor densities were simulated in our study. To thisend, ‘virtual’ sensors were added at new locations inside the array. Dataon these sensorswere simulated using the thin-Plate 2D-spline interpo-lation (Nunez, 2006) from the 4 × 4 array. To simulate a 5-electrodearray (emulating a square sensor grid with 3=
ffiffiffi
2p
cm period), a virtualsensor was added in the center of the 4 × 4 array and used along withthe 4 corner sensors. To simulate the 9-electrode array (emulating asquare sensor grid with 1½ cm period), the corner electrodes werecombined with 4 virtual sensors at the mid-edge points of the 4 × 4square and the central virtual sensor. In another analysis the corner sen-sors' data were interpolated to the remaining 12 sensor locations of thefull 4 × 4 array to simulate EEGdata oversampling. In this case a bilinearinterpolation was used, since the 2D thin-spline interpolation requiresdata at the minimum of 6 different spatial locations.
VEP classification
We used the cross-validation technique combined with a variant ofthe Naïve Bayes classification. Data in each epoch were averaged over
10-sample (19 ms) time bins. The length of the bin was chosen to bemuch shorter than the typical temporal scale of the observed evokedpotentials (~50 ms). Other time bin lengths were also tried (from 1 to16 samples) with little effect on the results. m sensors and n averagedtime samples constituted altogether m × n classifiers. Most of theepochs were allocated for training the classification algorithm, whilethe remaining epochs were used for testing it. The training data wereused to estimate mean and standard deviation of each classifier sepa-rately for English and Hebrew epochs. These parameters were thenused to calculate log-likelihood difference between the two conditionsfor each epoch of the testing data under the assumption of normallydistributed independent classifiers (the Naïve Bayes approach). Thesign of the difference indicated which stimulus, English or Hebrew,was more likely to evoke the given response, which determined theclassification outcome for the given epoch. Only k strongest (most pre-dictive on their own) classifiers were used in this analysis. The optimalvalue of kwas determined by an exhaustive search. For a given k, 10% ofVEP epochs chosen at randomwere allocated for testing, and the rest ofthe epochs were used for training. The proportion of correctly classifiedepochs, pc, was then calculated. Mean pc(k) and its standard deviationwere calculated by repeating this procedure 300 times. The maximumvalue, of pc(k) along with its standard deviation was used as the classi-fication accuracy of a given dataset. The optimal k value varied between50 and 100 for different subjects. Although the standard Naïve Bayesalgorithm produced qualitatively the same pattern of results, thisapproach of trimming the least informative qualifiers increased the pro-portion correct by 15–25%. The obtained pc values were converted to d′using
d′ ¼ffiffiffi
2p
norminv pcð Þ;
where norminv() stands for inverse of the cumulative density function(cdf) for normal distribution with zero mean and unit variance. Theformula is derived using the signal detection theory (Green, 1966) forthe case of 2-alternative forced choice classification (English vs. Hebrewhere), where d′ has the meaning of signal-to-noise ratio (SNR) in theclassification task.
Comparison with existing hd-EEG systems
For the purpose of comparisonwith the existing hd-EEG systemsweused the popular hd-EEG nets produced by Electrical Geodesics Inc.These nets are based on geodesic geometry, which is close to a regularhexagonal (triangular) grid. 128-sensor GSN nets of several sizes wereapplied to 34 subjects of both genders. Electrode positions were digi-tized and averaged across subjects. The total net area was then calcu-lated and divided by the number of electrodes. The resulting electrodedensity was 0.167 cm−2. This estimate allows an easy conversionbetween electrode densities and the corresponding number of scalpelectrodes in geodesic grids. EGI Inc. nets with 64 sensors cover aboutthe same scalp area as the 128-sensor nets. Hence, their density wastaken as 0.084 cm−2. EGI Inc. GSNnetswith 256 sensors, which are cur-rently the densest EEG nets available on the market, cover not only thescalp area, but also large portions of the cheeks. Of the 256 sensors about206 cover the scalp. This corresponds to an electrode density of0.269 cm−2.
Results
We used a prototype ud-EEG array: a square 4 × 4 grid of smalldiameter EEG electrodes with inter-electrode separation of 1 cm(Fig. 1a, Section 2.4). A signal classification paradigmwas used to dem-onstrate that the ud-EEG array provides additional information aboutbrain activity compared to hd-EEG. In this paradigm, eleven subjectsviewed images of words presented one by one on a computer monitor(Stimuli section). On each trial, a word appeared on the screen for half
Fig. 2.Visually evoked responses averaged over epochs are shown across the ud-EEG array(one subject). Dark dots indicate electrodes. Electrode potentials are shown interpolatedacross the array, hot and cold colors representing positive and negative values withrespect to the array's average. Responses on the left were evoked by English words,responses on the right — by Hebrew words. Measuring time from the stimulus onset,VEPs were similar at 200 ms, and dissimilar at 280 ms.
143Y. Petrov et al. / NeuroImage 90 (2014) 140–145
a second followed by a blank screen for another half a second. Thewords displayed were of two types: common English nouns printed incapitals such as TABLE, and ‘Hebrew’words: nonsense words producedby substituting Latin characters in the Englishwords with Hebrew char-acters with the same ASCII codes. Exemplars are shown in Fig. 1b. Allsubjects were either native speakers or fluent speakers of English. Sub-jects did not speak or read Hebrew and were not familiar with theHebrew alphabet. Over the course of a ten-minute long EEG sessioneach subject viewed 236 different words of each type randomlyinterleaved.
In a preliminary experiment (Data acquisition section), a common‘informative’ location was chosen in the parieto-occipital scalp region,approximately 6 cm above and left of the inion (Fig. 1a). The 4 × 4ud-EEG array was applied to this location for all subjects. Recordedvisually evoked potential (VEP) epochs were separated into two sets,English and Hebrew, based on which stimulus was presented in agiven epoch. Part of the data was used for training a classification algo-rithm, while the remaining data were used for testing the performanceof the trained algorithm (VEP classification section).
The percentage of correctly classified trials (pc) varied among sub-jects from 52% to 78%. The large variation is not surprising given thesmall ud-EEG array size, and that the array was positioned at the samespot on each subject's head without making any attempt to accommo-date individual differences in VEP distribution across the scalp. In thiscase one would expect to land on the individual ‘informative’ spotwith a varying degree of accuracy for different subjects. The percent cor-rect values were converted to d′ values, i.e., to the signal-to-noise ratio(SNR) of the classification analysis (Green, 1966) using d′ ¼
ffiffiffi
2p
norminv pcð Þ, where norminv() stands for inverse of the cumulativedensity function (cdf) for normal distribution with zero mean and unitvariance (VEP classification section). The SNR and pc for each subjectare plotted along the y-axes in Fig. 1c; error bars show one standarddeviation. When all 16 electrodes were used (data shown by redbars), the SNR was 0.47 ± 0.02 on average. When only the 4 cornerelectrodes of the array were used for the same analysis (data shownby gray bars) the average SNR dropped to 0.27 ± 0.02. Hence, samplingEEG at 1 cm scale on average offers almost twice the amount of func-tional brain signals as compared to sampling at 3 cm scale. Individually,the improvement was significant for 10 of the 11 subjects. The cornerelectrodes, at 0.11 cm−2 sensor density, emulate a full-scalp EEG arraywith approximately 84 sensors. This is comparable with the 64- and128-sensor hd-EEG systems most common today. The full 4 × 4 array,at 1 cm−2 sensor density, emulates an ud-EEG scalp array with 766sensors. SNR for two intermediate sensor densities was estimated byinterpolating the 4 × 4 array data to square arrays with 5 and 9 elec-trodes, thus emulating full-scalp EEG arrays of 168 and 336 sensorsrespectively. SNR as a function of the sensor density grew approximate-ly logarithmically (Fig. 1d). An adequate fit (χ2 = 3.69, p b 0.3) wasobtained by linear least squares and is given by the following formula:
SNR ¼ 0:476þ 0:086 log dð Þ;
where d is the density of sensors: 0.11, 0.22, 0.44, and 1 cm−2 for 4, 5, 9,and 16-electrode ud-EEG array configurations respectively.
To understand the SNR increase due to theultra-dense EEG samplingwe examined the spatial distribution of the evoked responses. VEPs for arepresentative subject are shown in Fig. 2. Data were averaged overstimulation epochs, interpolated between electrodes in the 4 × 4array, and shown as color maps. The electrode locations are markedby black dots. Responses to English and Hebrew stimuli are shown onthe left and right respectively. Snapshots for the two time points, asindicated by the time arrow, demonstrate functional variation of theresponses between the two conditions: while evoked responses werealike at 200 ms from the stimulus onset, they became quite different80 ms later. The VEP differences between English and Hebrew stimuli,dVEP = VEPEnglish − VEPHebrew, are shown in the top panel of Fig. 3
for the five subjects with the strongest effects of electrode density onthe classification accuracy. For each subject, the electrodewith the larg-est observed dVEP is marked by a green dot. dVEP time course of thiselectrode is plotted below each snapshot. The red dot above each plotindicates the time when the corresponding snapshot was taken. Theobserved dVEP variations across the ud-EEG array were highly signifi-cant and formed local hotspots: the potential variations betweenEnglish and Hebrew stimuli were as high as 2 μV/cm for some subjects.Time courses of the hotspots have well-defined peaks. This indicatesthat the hotspots reflect evoked brain responses rather thanmeasurement-related noise. The hotspots are made particularly con-spicuous by their absence in dVEPs interpolated using corner electrodesonly. This is shown in the bottom panel of Fig. 3; the corner electrodesused for interpolation are marked in magenta. There was strong varia-tion in spatial patterns and time courses among subjects. This variationis not surprising given that the arraywas positioned at the same spot oneach subject's head without making any attempt to accommodate indi-vidual local differences in VEP distribution across the scalp. Note alsothat the shown data reflects local variation of VEP measured withrespect to the array's average and thus may look very different fromconventional VEPs recorded using global reference.
The observed classification SNR improvement of ud-EEG on hd-EEGmay result from: (i) an increased number of independent signals, asreflected by the dVEP hotspots in Fig. 3, or (ii) decreased noise due tonoise averaging among nearby ud-EEG electrodes. In order to test thislatter mechanism, we repeated the classification analysis while limitingthe number of classifiers to the single most informative electrode. Thisprecluded any noise averaging between nearby electrodes. The averageSNR for the full array dropped from 0.47 ± 0.02 to 0.25 ± 0.02, butthe 4-corner SNR decreased proportionally from to 0.27 ± 0.02 to0.15 ± 0.02. This demonstrates that noise averaging cannot explainthe observed improvement in classification accuracy.
One could also argue that the improvement might be due to someartifact of the classification algorithm benefiting from a larger numberof input signals, even if the number of independent signals remained
Fig. 3. Top panel: Snapshots of dVEP variation across the ud-EEG array for 5 subjects. Electrodes closest to the hotspots are marked by green dots. Middle panel: The time course of eachsuch electrode. Red dots indicate the timing of the corresponding snapshot. Error bars indicate one standard error of themean. Bottom panel: Snapshots of dVEPs interpolated using onlythe corner electrodes shown by the magenta dots.
144 Y. Petrov et al. / NeuroImage 90 (2014) 140–145
constant (i.e., when VEP is oversampled). The “most informative elec-trode” analysis described in the previous paragraph also applies hereto refute this argument, since only one electrode was used in bothcases. However, we also carried out a more straightforward test: inter-polated raw VEP data on the corner electrodes over the remaining12 electrodes of the 4 × 4 array (ud-EEG data interpolation section,snapshots in Fig. 3, bottom panel) and applied the classification analysisto the interpolated 16-electrode dataset. There was no significantincrease in average classification accuracy across subjects between theinterpolated 4 × 4 dataset (pc = 0.58 ± 0.04) and the original 4-corner dataset (pc = 0.57 ± 0.04). Hence, the higher classificationaccuracy for the full 4 × 4 array appears to be a genuine advantage ofsampling EEG at 1 cm resolution.
Discussion
The importance of a higher spatial resolution is becoming increas-ingly appreciated. Our results are consistent with a recent study,where a linear ultra-dense array (2.5 mm inter-electrode spacing)was used to demonstrate that sensor distances 6–10 mm are requiredto capture the full spatial texture of EEG signal on neonatal scalp(Odabaee, 2013). While one could argue that large fontanels overwhich the linear array was positioned could cause the increased spatialvariation of EEG for neonatals, our results clearly indicate that thisaspect of EEG applies to adults as well. This confirms an earlier studyfrom the same group, where a similar linear array was used on adultsubjects (Freeman, 2003). In this study, spatial power spectral densities(PSDs) were calculated for open-eyes and closed-eyes EEG data forcomparison with earlier analyses of intracranial EEG. As expectedfrom electric current diffusion due to brain–skull and skull–scalpconductivity gradients, scalp spectra decreased more rapidly thanthese recorded intracranially. However, spatial spectral peaks in scalpPSDs suggested that optimal scalp electrode spacingwas approximately
1 cm. An even finer spatial sampling scale was indicated based on theresults of a modeling study in which scalp and intracranial PSDs weresimulated using a fairly accurate FEM head model (Ramon, 2009).Cortical PSDs showed a broad peak from 0.08 to 0.32 cycles/cmand other two peaks within the range of 0.32 to 0.9 cycles/cm.These peaks were attributed to the gyri structures and associatedlarger patterns on the cortical surface. Smaller peaks in the range of1–3 cycles/cm were also observed which were possibly due to sulcistructures. Correspondingly, scalp PSDs showed two broad peaks, onefrom 0.05 to 0.22 cycles/cm and the other from 0.22 to 1.2 cycles/cm.These results implied that the practical Nyquist frequency for samplingscalp EEGs should be 3.0 cycles/cm and an optimal electrode spacing ofabout 3 mm is needed for extraction of cortical patterns from scalp EEGsin humans.
The EEG variations observed at high spatial frequencies not merelyreflect cortical folds and inhomogeneity of the skull but can carry func-tional information on brain activity. Because dipole sources of EEG arebelieved to reside within pyramidal cells, which are primarily orientedperpendicularly to the cortical surface, source shifts along the cortexwill be often accompanied by a strong change of the source orientation.This would produce corresponding changes in EEG at the spatial scalesof 0.5–1 cm following the Ramon (2009) study. Analytical modeling ofskull inhomogeneity (Nunez, 2006; Ollikainen, 1999; Flemming, 2005)provides another possible explanation. Scalp electric potential above acortical source is very sensitive to the local skull conductivity. In partic-ular, it increases approximately proportionally to the conductivity, ifthere is a ‘hole’, i.e., an area of high conductivity above the source. Thisimplies that the location of a source with respect to the ‘hole’ makes astrong impact on the resulting scalp potentials, increasing them whenthe source happens to be below the hole (Nunez, 2006), and distortingthem when the source moves off-center (Ollikainen, 1999; Flemming,2005). Variations of skull conductivity at a given spatial scale areexpected to produce EEG variations at about the same spatial scale,
145Y. Petrov et al. / NeuroImage 90 (2014) 140–145
when the source shifts its position on the cortex, hence producing theobserved functional EEG variations. Skull inhomogeneity is pronouncedacross suture lines, where the conductivity increases approximatelytwo-fold, and also across individual skull bones due to variation intheir thickness, morphology, and electrical conductivity. The surface ofthe lower compact layer of the bones has depressions, furrows, andforamina to accommodate cerebral convolutions and numerous bloodvessels. The spongiform bone layer is strongly variable in structure(with marrow pores ranging from 3 mm in diameter to microscopicsize), distribution, density, and mechanical properties (McElhaney,1970). Studies of cadaver and live human skull showed, that the con-ductivity of spongiform and lower compact layers of the bones variedmore than two-fold (Akhtari, 2000; Akhtari, 2002; Law, 1993), whilebulk skull conductivity could vary ten-fold (Law, 1993). The absenceof the spongiform bone layer (e.g., in temporal bones) decreased bulkbone conductivity 2–3 fold (Law, 1993). Importantly, bone thicknessand density, which were indicative of conductivity, varied significantlyat 1 cm scale, as can be seen from X-ray and optical images of the sam-ples used in these studies (Ollikainen, 1999; McElhaney, 1970; Akhtari,2002).
The unique advantage of our study is that for the first time it directlydemonstrated that the high spatial frequency variations of electricpotential captured by ud-EEG provide practically significant informa-tion on brain states. The observed two-fold improvement in the SNRof the classification paradigm is immediately relatable to many brain–computer interface (BCI) applications. Similarly, significant improve-ments may be expected for the localization of EEG sources. In thiscase, however, the above discussion of the effects of cortical folds andskull inhomogeneities makes it clear that to succeed the accuracy ofhead modeling must be on par with the dense spatial sampling ofud-EEG. Clearly, spherical headmodels and boundary elementmethods(BEM) are inadequate for this task, because they cannot reflect inhomo-geneities of electrical conductivity along the skull surface. Instead,methods based on fine 3Dmeshing of head volume, such as FEM or sim-ilar, must be used. While modern computers are sufficiently powerfulfor creating such sophisticated models, measurements of head conduc-tivity tensor at high spatial resolution required to complete the modelare still challenging. Diffusion tensor imaging (DTI) can be used forthis purpose (Tuch, 2001), but the method's spatial resolution needsto be very high (~1 mm3 voxels) in order to accurately representanisotropies and high conductivity gradients within skull bones.
The logarithmic fit of information yield versus channel density(Fig. 1) shows the asymptotic nature of the yield with increasing chan-nel density: the greatest amount of improvement is at the lower densi-ties (e.g., 45% from 16 to 64 sensors), but there is continuing yield at thehigher sensor densities even though increasing numbers of sensorsmust be added for a constant increment in information. In particular,the classification SNR increased by 31% from 256 sensors (currently,the highest density hd-EEG) to 766 sensors (corresponding to the sen-sor density in our study). Considering the cost–benefit tradeoff forincreasing sensor density, the optimal number of sensors will, likely,be determined not by the price of the associated electronics and hard-ware, which is quite low, but by the particular solution to the problemof placing hundreds or even thousands of sensors in good electricalcontact with the scalp without creating electrical bridges between thesensors at the same time. This challenging engineering task is yet tobe solved.
Summary
To summarize, we observed surprisingly strong variations of VEPs at1 cm scale. This result explains a nearly two-fold increase in the classi-fication SNRbetween themost commonly used hd-EEG sensor densities(~0.1 cm−2, see the Comparisonwith existing hd-EEG systems section)
and the density of sensors in our prototype ud-EEG array (1 cm−2).Given the advances in amplifierminiaturization andwireless data trans-mission, ud-EEG helmets with 700–800 sensors needed for full scalpcoverage at 1 cm−2 sensor density are well within reach for moderntechnology. One can expect that reduction in sensor noise will lead toeven larger improvements than observed in this work (Ryynänen,2006). The increased spatial information,when combinedwith accuratehead models and inversion algorithms, will be essential for precisesource localization of brain activity. Thus, the potential exists for EEGto supplement ECoGwith the advantage of non-invasive measurement.We expect that ud-EEG will significantly impact basic neuroscienceresearch as well as a broad spectrum of practical applications frombrain–computer interfaces to localization of epileptic sources.
Acknowledgments
This work was supported by NSF-IIP-1264216, NSF-DGE-0965843and a Northeastern University Tier1 award grants.
Conflict of interest
The authors declare that they have no competing financial interests.
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