1IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-33, NO. 12, DECEMBER 1986

Current Source Density Estimation Using

Microelectrode Array Data from theHippocampal Slice Preparation

BRUCE C. WHEELER, MEMBER, IEEE, AND JAMES L. NOVAK, STUDENT MEMBER, IEEE

Abstract-The potentials recordable from the hippocampal slice usinga microelectrode array are described assuming a model of neural cur-rent sources. Inverse Fourier filter techniques to compute the currentsource density (CSD) are described taking into account the uncertaintyin knowledge of the height of the current source above the recordingplane. A lower bound on the minimum necessary sampling interval iscalculated as 100 Iim. Another calculation indicates it is unlikely thatcurrent sources are detectable if they are further than 250 Fsm fromthe recording array. Inverse filters with relatively short focal distancesavoid unnecessary attenuation of signals from more distant sources.

Recordings have been made using a 4 by 8 array with 200 gm elec-trode separation with an artificial current source. Spatial domainequivalent filters with nine coefficients and the five point Laplacian werefound to be good inverse filters. A demonstration of the 32 channelrecording of epileptiform activity and the application of CSD analysisis given.

I. INTRODUCTION

THE introduction of microsensor arrays into biological1 experimentation will require the use of new signal

processing techniques to take maximum advantage of theincreased available data. In this paper we describe tech-niques relevant to the use of a planar microelectrode arrayin recording evoked potentials from the hippocampal slicepreparation. The techniques have elements borrowed fromimage processing, inverse filtering, and biopotential fieldtheory, but are applied to data acquired with spatial res-olution at which it is essential to understand the processesof individual cells and of small populations of cells.The brain slice technique [1] has facilitated the study

of many of the structures of the central nervous systembecause of the ease with which many of the biologicalparameters can be varied and controlled. The typical hip-pocampal slice is 500 .um thick and can be maintained forup to 12 h. Since many brain structures, including thehippocampus, are highly stratified, it is possible to cutslices in which most of the pathways connecting the var-ious cell populations are maintained so that one may ex-periment with a section of brain tissue with considerablefunctionality but limited and controllable inputs. The hip-

Manuscript received April 5, 1986; revised September 25, 1986. Thiswork was supported by a Faculty Development Grant from the 3M Com-pany, the National Institutes of Health under Grant RR-7030, and by aGTE Fellowship Grant.

The authors are with the Department of Electrical and Computer Engi-neering, University of Illinois, Urbana, IL 61801.

IEEE Log Number 8611523.

pocampal slice preparation is used as a model system forthe study of epilepsy and memory.

Electrical recordings are usually made with one or sev-eral conventional microelectrodes, either glass pipettes orsharpened metal probes, which are positioned within theslice with the aid of micromanipulators. Recently, tech-niques have been developed for recording [2], [3] andstimulating [3] from the surface of the hippocampal slicewith planar microelectrode arrays. These early reports in-dicate not only that the slice can be maintained on thesearrays and that signals can be recorded, but also that dis-tinct signals are recorded at each electrode site, rather thanan integrated signal representing the whole of the slice.The advantages of multiple electrode arrays includegreater efficiency (more recording channels) and the pos-sibility of correlating activity at many locations. The dis-advantage of surface recording is that the electrode is ata distance from the active tissue, especially since it is gen-erally assumed that the outer 50-70 Am of the slice diesdue to the trauma of slicing [4]. Also, the potentials fromany neural source are spread out over the recording arraymaking interpretation difficult and some signal processingmandatory.Many brain structures, including the hippocampus, are

densely packed, oriented, and laminar. When synchro-nously activated, these structures can be modeled as hav-ing highly localized current sinks, typically the active ax-onal or dendritic regions, coupled with more diffuse cur-rent sources, due to passive conduction of the membranepotential [5]-[7]. Locally, the potentials produced are ad-equately represented by Poisson's equation, indicatingthat the current source density (CSD) may be inferred byestimating the Laplacian of the potential distribution [8]-[10]. Models have been constructed under- a variety ofassumptions about the geometry of the CSD and the an-isotropy of the tissue in order to explain recordings com-monly encountered when a microelectrode is advancedinto brain tissue.

Recently, CSD analysis has been applied to brain slices[11], [12]. In one method several microelectrodes are po-sitioned in the tissue, evoked responses are averaged, thenthe electrodes are moved and the process is repeated untila sufficient number of spatial sample points have beenused. CSD analysis can be done with the planar electrode

0018-9294/86/1200-1204$01.00 © 1986 IEEE

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WHEELER AND NOVAK: CURRENT SOURCE DENSITY ESTIMATION USING MICROELECTRODE ARRAY DATA

Fig. 1. Photograph of the hippocampal slice preparation on top of theplanar electrode array. The position is that of the recordings in Fig. 8.

array by using a two-dimensional estimate of the Laplac-ian. The primary advantage is efficiency, since the slicecan be positioned once relative to a large number of elec-trodes and all potential recordings can be done simulta-neously.

Since the recordings are done in a plane some distancefrom the current source, there is always some ambiguityin the reconstruction of the CSD from the array record-ings. The problem can be thought of as an image pro-cessing problem by assuming that current sources are con-fined to a plane and cast an image, the potentialdistribution, upon the plane of the electrode array. Therecorded potential image is a linear transformation of thecurrent source density image, and, if the medium is ho-mogeneous, the transformation can be described by a pointspread function (PSF) or its Fourier transform equivalent,the modulation transfer function (MTF). The originalCSD image can be reconstructed using a number of tech-niques borrowed from the image processing discipline.The finite difference estimate of the Laplacian is one of aclass of image sharpening techniques.EEG signals are more accurately modeled as resulting

from dipolar sources [13]. For the hippocampal slice, theinterelectrode separations and the recording plane toneural source separation are equal to or smaller than thecharacteristic electrotonic distance which describes thepassive decline of a potential within nerve processes. EEGelectrodes are further from the sources and spaced morewidely. Recordings from the surface of the brain are takenabove tissue composed of perpendicularly oriented di-poles, whereas in the typical hippocampal slice the di-poles lie parallel to the recording plane with a relativelylarge source to sink separation. EEG signal analysis hasbeen approached using Laplacian operators and Fourierand matrix inverse or deconvolution filters [13].

Freeman [141 reported a deconvolution technique ofparticular relevance in which he assumed vertically ori-ented dipolar sources for the potentials he recorded witha hand-fabricated electrode array placed on the surface ofthe rabbit olfactory bulb. The image deconvolution tech-nique was described as a software lens with a variablefocal depth to compensate for the variable but unknowndepth of the bipolar sources. The technique appeared tobe robust and effective in sharpening the two-dimensionalresponse plots.Below we describe the nature of the potentials record-

able from an array in terms of the current source modeland methods for the reconstruction of the CSD pattern andtheir limitations. We then demonstrate the application ofCSD reconstruction to data recorded with an array in ourlaboratory.

II. EXPERIMENTAL METHODSThe hippocampal slice was obtained using the method

of [4], in which the hippocampus of a 100-150 gSprague-Dawley rat was sliced into 500 i.m thick slices,which were allowed to equilibrate in artificial cerebrospi-nal fluid (ACSF) and placed on the electrode array in aHaas type chamber [15]. The ACSF was maintained at35°C, oxygenated (5 percent CO2), and allowed to flowslowly over the slice. 60 zM picrotoxin was added to in-duce epileptiform activity. Recordings were obtained forup to 3 h on the array, and for up to 10 h with a micro-pipette electrode placed in the center of the slice.A test current source consisted of a glass micropipette,

broken to a 10 jum diameter, passing 100 nA rms at 100Hz. It was positioned with a Narishige MO-103 micro-manipulator while viewed microscopically to an accuracyof ± 10 jam relative to the electrode array in a hippocam-pal slice bathed in ACSF.

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-33, NO. 12, DECEMBER 1986

Fig. 1 shows a hippocampal slice on top of the array,whose fabrication has been described [16]. It consists ofa 3 in by 3 in glass substrate upon which gold conductorshave been deposited, patterned, and covered by a poly-imide insulation everywhere but at the electrode sites andthe connector pads. There are 32 electrodes in a 4 by 8array, separated by 200 ,um. Each electrode is 25 Am indiameter and is plated with platinum so that a 10 kQimpedance at 1 kHz is achieved.The electronic system consists of 32 channels of JFET

buffer amplifiers, track/hold artifact suppression, pream-plifiers (gain of 100, 10 kHz bandwidth), and intermedi-ate amplifiers (adjustable gain and 1 kHz bandwidth). A32 channel, 8 bit, 5 kHz/channel A/D converter was builtand interfaced to an AT&T 6300 PC for data acquisition,analysis, and display.

III. THEORYIn modeling the relationship between the significant un-

derlying neuroelectric event and the recorded potentials,the essential assumptions are that it is reasonable to modelevoked population responses as current sources and, untilbetter data are available, the medium as homogeneous andisotropic. Furthermore, the spatial variation of the currentsource density is such that the significant neural eventscan be localized with the available recording electrodes.The basis behind the current source assumption has been

reported [5]-[7]. Many stratified neural structures possesspopulations of cells which can be activated synchro-nously, acting as localized current sinks or sources atactive membrane areas coupled with more diffuse sourcesor sinks due to passive conduction along and through moredistant neural processes. The decline in the electrical var-iables with distance, even in highly branched dendritictrees, is scaled by the effective electrotonic space constant[17]. One can expect to see potentials reflecting the cur-rent source model within a distance of up to several spaceconstants, but at distances much greater, the potentials arethose of a dipole and attenuate more rapidly with dis-tance. In the CAl region of the guinea pig hippocampalslice the effective electrotonic lengths of the pyramidalcell dendritic trees have been reported to be on the orderof 200 ,im [18]. Larger values may be inferred for thelarger cells in the CA3 region [19]. The value of 260 ,tmhas been computed for a 1 ,um diameter cylindrical pro-cess with typical membrane and internal resistivities [5].The electrode array used here has separation on the orderof the electrotonic length and is likely to be able to reportcurrent source/sink information, not simply the presenceof a dipolar source.To simplify the modeling below we have assumed that

the hippocampal tissue is isotropic and locally homoge-neous. Inclusion of anisotropy and inhomogeneity will bejustified when better estimates of the conductivity areavailable for the structures from which the recordings aremade. A preliminary report [20] indicates their inclusionmay be necessary since, for the rat hippocampal slicepreparation, the extracellular conductivity has been esti-

mated at 1.7-2.8 mS/cm perpendicular to the cell layers,with local decreases by factors of 1.5 and 3.0 at the py-ramidal and granule cell body layers and at the hippocam-pal fissure. Rat hippocampal slice values appear approx-imately the same as for other preparations, but withsomewhat less anisotropy [20].For bioelectrical phenomena, the electric field may be

regarded as quasi-static and the medium as purely resis-tive [21]. For a point current source in an infinite, ho-mogeneous, isotropic medium, the potential at a distantpoint is inversely proportional to the distance between itand the source. Assuming that the point current source islocated a distance z directly above the origin of the x-yplane in which the electrodes are located, the potentialdue to a point current source of unit strength is

+(x, y, z) = -(1/47ru)/(X2 + y2 + z2)1/2. (1)

For homogeneous media the potential recorded at anyelectrode is the superposition of the potentials due to allof the point sources active within the slice. If it is as-sumed that all the sources lie in a plane at a fixed distancez from the surface, then the current source density acts asa source image, the potential distribution is a recordedimage, and +(x, y, z) can be taken as the point spreadfunction relating the two images. Fourier image recon-struction techniques are considered for estimation of thecurrent source image i(x, y) from the recorded potentialimage p(x, y). Let I(u, v), P(u, v), and c1(u, v) be thetwo-dimensional Fourier transforms of i(x, y), p(x, y), and+(x, y) (1), respectively. ¢(x, y) and 4(u, v) are the pointspread function (PSF) and the modulation transfer func-tion (MTF) which describe the image generation process.Let H(u, v) be a low-pass window filter. An estimate ofi(x, y) is defined by the frequency domain equation

I(u, v) = P(u, v)G(u, v)

= P(u, v)[H(u, v)l/4(u, v)]. (2)

Division of P(u, v) by the MTF (4'(u, v)) alone wouldconstitute the ideal reconstruction filter. Since 4(u, v) de-creases rapidly with frequency, any errors in the estimateof the height z along with high frequency spatial noise arelikely to cause large errors in the estimate of the CSD.The practical reconstruction filter G(u, v) includes thelow-pass window function H(u, v), which eliminates orreduces high frequency components in P(u, v) which tendto be dominated by noise. In the simulations belowH(u, v) was trapezoidal.The traditional approach to CSD analysis has been to

use a finite difference estimate of the Laplacian. For thetwo-dimensional case

I/47ro = -V2p = -a2PaX2_a2p/a2Y2- (3)

where I, is the volume current source density. Using dis-crete functions the current source at x, y is approximated

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WHEELER AND NOVAK: CURRENT SOURCE DENSITY ESTIMATION USING MICROELECTRODE ARRAY DATA1

by

i(x, y) = -K[p(x + d, y) + p(x - d, Y)+ p(x, y + d) + p(x,y - d) -4p(x, y)]

(4)where K is a proportionality constant equal to 47rad, whered is the sample interval, or

i(x, y) = Kp(x, y) * I(x, y) (5)where * indicates two-dimensional convolution and I isthe pattern

-1 4 -1

This is one of a large class of image sharpening functions.Below we investigate the use of spatial convolution witha truncated version of the spatial domain equivalent of thefilter function given above.

-J

;7-zwI--0a.

.I

w

-

w

-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0RADIAL DISTANCE (mm)

Fig. 2. Relative point spread function describing the variation in potentialdue to a point current source. The PSF potentials are plotted on a linearscale for values of the distance from the source to recording plane equalto 100 (top curve), 200, 300, 400, and 500 Atm (bottom curve).

(x2 + y2)1/2 < p

elsewhere

where F-' indicates the inverse Fourier transform. If p issmall, then spatial domain convolution can be computedquickly.

IV. COMPUTER SIMULATIONSComputations were done in order to describe the signals

encountered in actual recording, to aid in understandingthe limits of the reconstruction algorithms, and to suggestbetter ways of computing the CSD with our 4 by 8 array.

Most of the calculations were done assuming a 64 by 64element array of sample points at 50 A.m intervals, a

greater sampling density than our actual array or any we

have planned. The results represent an upper limit on thepractically achievable signal resolution. The point source

was assumed to be at a height z, taken as a parameter over

the range from 50 ,tm, a minimal estimate of the thicknessof the dead cell layer, to 450 tm, the location- of the deadcell layer near the other surface. The source is above thecenter electrode. Since both the spatial and frequency do-main functions are radially symmetric, they are plotted as

functions of radius only in the discussion which follows.Fig. 2 describes the radial decline of the PSF with

source height as a parameter. It indicates that a casualinspection of the potentials is likely to lead one to con-

clude that a neural event is much broader that it really is.This figure illustrates that the difficulty of locating a pointsource increases with distance into the slice, partially be-cause of the decreased signal amplitude, but also becauseof the decreased curvature of the spatial function. The fig-ure implies that high spatial frequency components ofCSD distributions will be severely attenuated. A plot (notshown) of the MTF indicates that 40 dB attenuation, rel-ative to a spatially uniform source, occurs at 3.5 cycles/

0.41

(7)

0.3-

EE SNR= 10

0.2- R= 100

w

a.

0. I-

0.0-

0.0 0.1 0.2 0.3 0.4 0.5CURRENT SOURCE HEIGHT (mm)

Fig. 3. Reconstructed point current source width as a function of assuniedsource height. Each point represents the minimal pulse width (peak to

half maximum amplitude) achievable asguming that an inverse filter isused with appropriate focal length and low-pass cutoffs set at the spatialfrequency at which the, signal power equals the noise power for the twoassurned SNR's shown.

mm and 1.25 cycles/mm for current source heights of 50and 250 Am, respectively. The reconstruction prob-lem becomes more difficult as the high frequency com-

ponents necessary to localize a point source becomesmaller and more likely to be buried in noise. The inverseMTF filter (4Vl(u, v)) must be truncated by the low-passfilter H(u, v) in order that the noise components not dom-inate the reconstructed image.

Computations were done in order to determine the rangeof heights at which reconstruction was feasible. For eachsource height z, the potential distribution p(x, y) was com-

puted and then inverse filtered (G(u, v)) using a low-pass

g(x, y, p) = F11[G(u, v)]= 0

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-33, NO. 12, DECEMBER 1986

1.00-

0.75-

0

z(0

2 0.50-

w

LL 2

0.25

SOURCEHEIGHT(m) .

.w

-a.s

-jJ

U.U)_-I.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0

DISTANCE (mm)Fig. 4. Estimated CSD's as a function of source height with a filter fixed

at a focal height of 150 jim. In constructing the filter a trapezoidal func-tion H( u, v) was used which was flat from 0 to 1.5 cycles/mm andtapered linearly to 0 at 2.5 cycles/mm. The simulated source heightswere 50, 100, 150, 200, and 250 ,^m.

filter (H(u, v)) with a cutoff equal to the frequency atwhich the noise and signal power are equal. It was as-sumed, arbitrarily, that the spatial noise was white andhad total power equal to either 1 percent or 10 percent ofthe signal power. The width of the reconstructed pulse,measured from the peak to the point of half maximumamplitude, was compared to estimates of the electrotoniclength. If the pulse is wider than this length, it is unlikelythat a neural point current source could be localized. Also,two point sources, separated by twice that distance, can-not be distinguished. Fig. 3 shows the resulting values.The computations indicate that the reconstruction can bedone to distances of approximately one-half the thicknessof a typical slice, or 250 ,.m, which is also approximatelyequal to estimates of the electrotonic length.A critical question in the design of future electrode ar-

rays is the determination of the interelectrode separationwhich is necessary and/or useful. This depends primarilyon the nature of the biological signals, but, in the casehere, the filtering due to the displacement of the neuralcurrent source from the recording potential plane impliesa lower bound on the minimum sampling distance.A conservative estimate of the minimum sampling dis-

tance was made with the following procedure. Assumethat the CSD is confined to the plane 50 Am above theelectrode array and that the CSD power spectrum, as atwo-dimensional spatial function, is white. Then the spec-trum of recorded signals is described by the MTF. Cal-culations of cumimulative signal energy over the two-di-mensional frequency space show that 95 percent of thespatially varying signal energy occurs at spatial frequen-cies of 3.125 cycles/mm or less, and that 99 percent oc-curs below 4.7 cycles/mm. Thus, if the minimum sam-pling distances are 160-.m (107 ELm) one can represent

0.4 -

0.3 -

E-I

2 0.2-

wU/) _-J

a.

0.1 -

0.00

0.05 0.10 0.15 0.20 0.ASSUMED SOURCE HEIGHT (mm)

(a)

FILTER FOCUS- 50pm

5 POINTLAPLACIAN

0.05 0.10 0.15 0.20ASSUMED SOURCE HEIGHT (mm)

(b)

0.25

Fig. 5. Reconstructed current source amplitude (a) and width (b) as func-tions of assumed source height for filters with focal distances of 50 and250 ym, and for the five point Laplacian. Simulations were for a 64 by64 grid with 50 tim separation. The amplitudes have been normalizedfor equal amplitudes for sources 50 itm from the array. Note the largeratio in amplitudes for sources originating 250 /Am into the slice.

all but 5 percent (1 percent) of the signal energy. Onlyslight improvement in signal representation is likely toresult from further reductions in the sampling interval.Recalculation with other assumed source to electrode ar-ray heights yields larger minimum sampling distances.

Computations were performed to better understand theeffects of assuming one focal distance z for the reconstruc-tion filter with the current source at a different height. Fig.4 shows a family of reconstructions using a filter in whichthe focal distance is 150 ,um, to estimate the CSD for sev-eral assumed current source locations. Although the filteris optimal for the reconstruction of the current source at150 t,m, the figure shows that the sharpest, strongest re-constructed CSD images occur when the source is closestto the electrode array despite the mismatch of the inverse

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WHEELER AND NOVAK: CURRENT SOURCE DENSITY ESTIMATION USING MICROELECTRODE ARRAY DATA

filter. Fig. 5 describes the variation of the maximum am-plitude and width of reconstructed point sources for fivevalues of source height, with the filter focus equal to twoof those source heights. It shows that with longer focaldistance filters one can expect reconstructed pulses whichare narrower and smaller (much smaller if the source'isfarther from the electrode plane). If one were to choose asingle filter to process all data from an experiment, somecompromise is necessary between signal strength and res-olution. Since the resolution is on the order of an electro-tonic space constant for most of the filters, the relativeamplification of distant events is more likely important,indicating that the choice would be a filter computed as-suming smaller source height z.

Fig.' 5 also shows pulse amplitude and width values forreconstruction with the Laplacian operator (4). The ap-plication of the Laplacian to data sampled at 50 ,um inter-vals is likely to severely attenuate signals originating fur-ther into the slice.We briefly investigated spatial domain reconstruction

techniques which use a small convolution kernel functionas described by (7). The results for p = 8 showed re-sponses which appeared approximately as useful as thefrequency domain techniques. When p is much smaller,the reconstructions tend toward narrower and attenuatedpeaks. The Laplacian is a special case in which p = 1.Further investigation is warranted should one have a 64by 64 element array.

For application to our electrode array we redid the sim-ulations as if we had an 8 by 8 grid with 200 Am separa-tion. The results are very similar to those for the 64 by 64element' computations, including the trends evident inFigs. 4 and 5. Also, when the convolution kernels weretruncated'to five or nine points, the reconstructions wereof nearly equivalent quality. The five point versions of theLaplacian operator and the 100 ,lm focal length filter havenearly equal coefficients and perform equivalently. It ap-pears that we will be able to use these reduced convolu-tion kernels in our experiments where it is important tocalculate the CSD function quickly to provide feedbackto the experimenter.

V. APPLICATION TO EXPERIMENTAL DATA

The artificial current source described above was usedwith a slice on top of the array. The decline in amplitudeof the signal with distance along the array and with theheight of the source is plotted in Fig. 6. This figure in-dicates rough agreement with theoretical values. Fig. 7shows an example of the improvement in the sharpness ofthe image when one of the inverse filters is applied.To evaluate the ability of several reconstruction filters

to restore the point current source, the following calcu-lations were made. The potential image was consideredto consist of a signal equal to the d'ata value at the centerelectrode, plus noise equal to the rms average amplitudeof the potentials at the remaining electrodes. The ratio ofthese values is the SNR before filtering. A similar com-

wz-J

w

i-

a.

cr-J-CL I.

a

-0.2 0 0.2

DISTANCE (mm)

0.4 0.6

0.4 0.6

Fig. 6. Relative signal strength of test current source versus position onthe array and source height. Source heights: 50 ,um squares; 100 ,^mcircles; 150 ym triangles. The predicted curves are plotted continuously,whereas points only are given for the actual data values. The predictedvalues are proportional to the inverse of the source to electrode distanceand normalized to the center value at 50 Hm source height. The centerelectrode data value for 100 i.m is within experimental error, includingnormalization, predicted by a ±10 Am uncertainty in the positions of thecurrent source.

1.00-

0.75-wD

a.

0.50 - POTENTIALw

>IDATAF-

w

0.25-CSD

0.00-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

DISTANCE (mm)

Fig. 7. Reconstructed CSD and recorded potential data with artificial cur-rent source, using a filter with 50 ,um focal height to sharpen data takenfor a source height.of 100 ,um.

putation was made after the application of the filters listedin Table I. The ratio of the SNR's measures the improve-ment in the sharpness of the image as a result of the filter.The improvement is better for smaller source heights andfor smaller filter focal lengths. The Laplacian is a superiorfilter function. Results were similar using the frequencydomain inverse filter described by (2).

Fig. 8 shows an evoked epileptiform potential from the

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-33, NO. 12, DECEMBER 1986

TABLE IIMPROVEMENT IN POINT SOURCE ESTIMATION WITH FILTERING

Filter Focal Height (/Am) Source Height (,um) SNR Improvement

50 50 3.8100 3.8150 2.9

100 50 5.0100 5.2150 3.4

150 50 1.2100 1.1150 0.7

5 point Laplacian 50 5.1100 5.2150 3.7

Different filter kernels were used to estimate the CSD from recordedpotential data from an artificial current source. The convolutions were donewith 3 by 3 kernel functions [see (8)] corresponding to filters with the givenfocal heights, or with the S point Laplacian. SNR was defined as the ratioof the data value at the electrode immediately below the current source tothe rms average of the values at the other electrodes. The improvement isthe ratio of the SNR after filtering to the SNR before filtering.

PAM 2

6AAv1/ 9 1 0IM°IAA111rtIMU-VA1 Anv

,~~~~~= T:

n, 14 1 A/\1s

26

v^Va3

30/ ,\Aco t,\ AVTwvv-

3 4

7 ~~~~8

, 11-\ ' AA

vv-\v -12

/n t_fa.CSV' -

VV-

20

24

281 _n\ _

32

23

'An A A a2

1 V- V V

Fig. 8. Epileptiform activity recorded from the hippocampal slice with thearray. See Figs. 1 and 9 for the location of the array. Data for nonfunc-tioning electrodes 3 and 18 have been interpolated. Each trace lasts 30ms and has a vertical scale spanning -2 to +2 mV.

CAl region of the rat hippocampal slice shown in Fig. 9.The plots indicate the nature of the signals recordable withthe surface electrode array and the difficulty in localizingthe source of the.activity.

S. pyr

Xr1d s.rd

7.~~~~~~~~~~4

Fig. 9. Schematic diagram of the rat hippocampal slice indicating the lo-cations of the array and stimulating electrodes. Stimulation of the Schaf-fer collateral fibers antidromically activated the CAl region. The pyra-midal cell body layer (stippled, s.pyr.) and the adjoining dendritic region(s. rad.) are indicated as lying over the center two columns of the elec-trode array.

The signals of Fig. 8 were filtered.with the five pointLaplacian, with the results shown in Fig. 10. The resultclearly shows that the strata radiatum and pyramidale, thedendritic and cell body regions, respectively, are actingas source/sink pairs (positions 6 versus 7, and 10 versus11). The high frequency oscillations are propagating awayfrom the antidromic stimulus at approximately 1/4 m/s.In contrast the large slow potentials upon which much ofthe high frequency oscillations ride are effectively can-celled by the CSD algorithm, indicating that they are notdue to local current generators.

Fig. 8 data were also filtered with nine point convolu-tion kernels with focal heights of 50 and 150 ,um. The.resulting plots were qualitatively quite similar to thoseshown in Fig. 10. The amplitudes of the high frequencyoscillations were increased (50 .tm focus) or decreased(150 ,um focus) on average by 12 percent compared tothose filtered with the Laplacian, which approximates the100 , 4m focus filter quite well. These changes are inagreement with the trends in Fig. 5(b).

VI. SUMMARY AND DISCUSSIONThe goal of the simulations was to describe the char-

acteristics of the potentials recordable from the electrodearray under the assumption that the appropriate model isone of neural current sources and sinks. Using the 64 by64 element computations, the signals and several Fourier

IU ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I/<,~~~~~~~~~~~~~~~~~~~~

13

17

21

25

29

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1210

ic;d

/-\ ^ cin- -N.Iv

-

I

WHEELER AND NOVAK: CURRENT SOURCE DENSITY ESTIMATION USING MICROELECTRODE ARRAY DATA

Fig. 10. CSD analysis of the epileptiform activity. Computations weredone with the five point Laplacian kernel function as described in thetext. Each of the two diagonal lines indicates propagation of an event ata velocity of approximately X m/s away from the stimulus and parallel tothe long axis of the array. The lines intersect the time axes of horizon-tally adjacent traces at the same time, allowing easy recognition thatthere is a 1800 phase difference between the oscillations in traces 6 and7. The width of the time axis is 30 ms. The vertical scale is arbitrary butoriented so that current sources are above zero. Since the CSD at eachedge electrode was computed assuming that the potential at an adjacentsite beyond the array had the same potential as that of the edge electrode,the CSD at the edges is incompletely estimated.

based methods of inverse filtering have been described.These calculations took into account the uncertainty inknowledge of the height of the current source above therecording plane. We have calculated likely bounds on theminimum necessary sampling interval and on the maxi-mum source height for which we are likely to detectmonopolar sources. We observed that one should use in-verse filters with relatively short focal distances to avoidunnecessary attenuation of signals from more distantsources. Also, it was acceptable to perform spatial do-main convolution with a smaller filter kernel.The calculations were repeated for the 8 by 8 element

case which approximates our array, leading to the same

conclusions regarding the focal height of the filter and theuse of a small spatial domain convolution function. Theseconclusions were reinforced by the relative sharpening ef-fects of the filters on data acquired using the artificial cur-

rent source. In particular, the five point Laplacian tech-

nique was quite effective, and was used to filter dataacquired during evoked epileptiform activity. The result-ing CSD estimate suggests new interpretations of the re-corded data.The estimation of the minimum required sampling in-

terval was undertaken to aid the design of new arrays.Additional electrodes are very expensive, both in terms ofthe instrumentation required as well as in terms of thedifficulty in laying out the wiring pattern. Smaller sepa-ration and more electrodes imply smaller line widths andreduced yield in the fabrication process. Additionally, itis easier to do near real-time processing with fewer elec-trodes. Oversampling may be a more serious problem thanundersampling.The 100 gm minimum sample interval is a conservative

estimate based on a minimal estimate of the dead celllayer. Freeman and Nicholson [7], in reporting the spec-trum of field potentials evoked in the toad cerebellum,estimated that 95 percent of the signal energy in the cur-rent source plane lay at frequencies below 10 cycles/mm,requiring sampling intervals no greater than 50 ,tm. Sincewe have assumed a 50 ,tm dead cell layer which greatlyattenuates the high spatial frequency components of thisspectrum, it is reasonable to expect a larger estimate forthe minimum sample interval. The attenuation of the vol-ume conductor makes it unlikely that higher spatial fre-quency signals, which may be present in the tissue, willbe recordable with a surface electrode array.The investigation of the use of small kernel functions

was prompted by the need to do efficient processing andthe hope for future near real-time processing, where it isimportant to use no more few coefficients than necessary.The five point Laplacian, which was effective for sepa-rations of 200 ym but not 50 ,um, can be implemented ona computer with simple additions and looping control. Theuse of arbitrary coefficients, even for small kernels, maybe more expensive in computer time.

It is possible that more effective modeling could be doneassuming dipolar sources, probably oriented parallel tothe recording plane. The only way to answer the questionas to which is a better model is to see which model ex-plains more of the biological data which is soon to comewith this new recording technology.

This report is one of the first to deal with the signalprocessing needs for a new generation of arrays of micro-sensors. For many of these devices, it will be necessaryto incorporate models of the tissue activity taking into ac-count the dimensions of the cells in the tissue, such as inthe current source model, and the essentially dispersivespread of the signals, whether they be electrical, chemi-cal, or thermal. The signal processing techniques re-quired, including the solution of inverse problems, willhave much in common.

REFERENCES[1] R. Dingledine, J. Dodd, and J. S. Kelly, "The in vitro brain slice as

a useful neurophysiological preparation for intracellular recording,"J. Neurosci. Meth., vol. 2, pp. 323-362, 1980.

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[2] D. T. Jobling, J. G. Smith, and H. V. Wheal, "Active microelec-trode array to record from the mammalian central nervous system invitro," Med. Biol. Eng. Comput., vol. 19, pp. 553-560, 1981.

[3] J. L. Novak and B. C. Wheeler, "Multi-site stimulation and record-ing from rat hippocampal slices using a microelectrode array," inProc. 7th IEEE Biomed. Eng. Conf., Chicago, IL, 1985, p. 1275.

[4] T. J. Teyler, "Brian slice preparation: Hippocampus," Brain Res.Bull., vol. 5, pp. 391-403, 1980.

[5] C. Nicholson, "Theoretical analysis of field potentials in anisotropicensembles of neuronal elements," IEEE Trans. Biomed. Eng., vol.BME-20, pp. 278-288, 1973.

[6] C. Nicholson and J. A. Freeman, "Theory of current source-densityanalysis and determination of conductivity tensor for anuran cerebel-lum," J. Neurophysiol., vol. 38, pp. 356-368, 1975.

[7] J. A. Freeman and C. Nicholson, "Experimental optimization of cur-rent source-density technique for anuran cerebellum," J. Neurophys-iol., vol. 38, pp. 369-382, 1975.

[8] R. Llinas and C. Nicholson, "Analysis of field potentials in the cen-tral nervous system," in Handbook of Electroencephalography andClinical Neurophysiology, Part B, Vol. 2, C. F. Stevens, Ed. Am-sterdam, The Netherlands: Elsevier, 1974.

[9] J. A. Freeman and J. Stone, "A technique for current density analysisof field potentials and its application to the frog cerebellum," in Neu-robiology of Cerebellar Evolution and Development, R. Llinas, Ed.Chicago, IL: Amer. Medical Ass., 1969, pp. 421-430.

[10] J. Breckow, K. Kalmring, and R. Eckhorn, "Multichannel-record-ings and real-time current source density (CSD) analysis in the cen-tral nervous system of insects," Biol. Cybern., vol. 45, pp. 115-121,1982.

[11] J. S. Taupe and P. A. Schwartzkroin, "A current-source density anal-ysis of hippocampal CAl region following LTP," Soc. Neurosci.Abstr., p. 778, 1985.

[12] J. W. Swann, R. J. Brady, R. J. Friedman, and E. J. Smith, "Peni-cillin-induced epileptiform discharges in CA3 hippocampal pyramidalcells: A current source density analysis," Soc. Neurosci. Abstr., p.395, 1983.

[13] P. L. Nunez, Electric Fields ofthe Brain. New York: Oxford Univ.Press, 1981.

[14] W. J. Freeman, "Use of spatial deconvolution to compensate for dis-tortion of EEG by volume conduction," IEEE Trans. Biomed. Eng.,vol. BME-27, pp. 421-429, 1980.

[15] H. L. Haas, B. Schaerer, and M. Vomansky, "A simple perfusionfor the study of nervous tissue slices in vitro," J. Neurosci. Meth.,vol. 1, pp. 323-325, 1979.

[16] J. L. Novak and B. C. Wheeler, "Recording from the Aplysia ab-dominal ganglion with a planar microelectrode array," IEEE Trans.Biomed. Eng., vol. BME-33, pp. 196-202, 1986.

[17] W. Rall, "Time constants and electrotonic length of membrane cyl-inders and neurons," Biophys. J., vol. 13, pp. 648-688, 1973.

[18] D. A. Turner and P. A. Schwartzkroin, "Steady-state electrotonicanalysis of intracellularly stained hippocampal neurons," J. Neuro-physiol., vol. 44, pp. 184-199, 1980.

[19] R. D. Traub, "Simulations of intrinsic bursting in CA3 hippocampalneurons," Neuroscience, vol. 7, pp. 1233-1242, 1982.

[20] J. G. R. Jefferys, "Current flow through hippocampal slices," Soc.Neurosci. Abstr., p. 1074, 1984.

[21] R. Plonsey, Bioelectric Phenomena. New York: McGraw-Hill,1969.

Bruce C. Wheeler (S'75-M'80) was born inSchenectady, NY, in 1948. He received the S.B.degree from the Massachusetts Institute of Tech-nology, Cambridge, in 1971, and the M.S. andPh.D. degrees in electrical engineering from Cor-nell University, Ithaca, NY, in 1977 and 1981,respectively.

Since 1980 he has been with the University ofIllinois at Urbana-Champaign, where he is Assis-tant Professor of Electrical and Computer Engi-neering and of Bioengineering. His research in-

terests include the fabrication and use of microminiature sensors forneurobiological and other applications.

Dr. Wheeler is a member of Phi Beta Kappa.

James L. Novak (S'80) was born in Berwyn, IL,in 1961. He received the B.S. and M.S. degreesin electrical engineering from the University of Il-linois at Urbana-Champaign in 1983 and 1985, re-

spectively.Since 1983 he has been a Research Assistant in

the Department of Electrical and Computer En-gineering at the University of Illinois. Includedamong his research interests are the acquisitionand analysis of multiple-channel neurobiologicalsignals.

Mr. Novak is a member of Tau Beta Pi and Eta Kappa Nu.

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