Brain Research, 591 (1992) 33-43 © 1992 Elsevier Science Publishers B.V. All rights reserved 0006-8993/92/$05.00

33

BRES 18079

Topographical analysis of epileptiform potentials in rat somatosensory cortex: the interictal to ictal transition D a n i e l S. B a r t h

a

a n d Shi Di

.~,b

a Department of Psychology, University of Colorado, Boulder, CO 80309-0345 (USA) and h Mental Heahh Institute, Beijing Medical Unicersity. Beijing (China) (Accepted 14 April 1992)

K~y words: Epilepsy; Interictal spike; Penicillin; Seizure; Topographical mapping

Large quantities of penicillin were applied to the face and forelimb region of rat somatosensor¥ cortex, producing an epileptic focus with both electrographic and behavioral signs of seizures that regularly repeated over a period of several minutes. Epicortical potentials were recorded simultaneously from a 64 channel micro-electrode array (8 x 8 platinum electrodes) with inter-electrode distances of 0.5 mm, covering a 3.5 × 3.5 mm 2 area centered on the penicillin injection site. Cluster analysis was used to classify successive epileptiform discharges into interictal, transitional, and ictal groups. Principal components analysis (PCA) was used to extract fundamental waveforms producing the spike complex in each group, and to estimate the locations and spatial extent of neuronal populations participating in epileptiform discharge. During all states of epileptic excitability, it was possible to account for over 90% of the variance in the epicortical potential waveforms using a model with only two spatially overlapping populations of cells. The location and spatial extent of the populations remained unchanged by the transition to seizures; the interictal and ictal states were distinguished only by changes in the timing and amplitude of potentials in the two putative neuronal populations. The present model, using only two stationary neuronal populations to reproduce all spatiotemporal patterns in the neocortical epileptogenic focus, is compared to models proposed by others in which epileptic discharge is thought to propagate sequentially through adjacent cortex, it is concluded that the initiation, maintenance, and termination of seizures in neocortex relies on mechanisms that are not necessarily reflected in changes in spatiotemporal interactions among epicortically recorded cell groups within the focus, These mechanisms may he distinguished from those responsible for the spread of seizures within neocortex.

INTRODUCTION Application of even very small amounts of penicillin 31'33 to rat neocortex results in frequent spontaneous electrical discharges or spikes that may be measured both extracranially in the electroencephalogram and with intracranial electrodes placed directly on the cortical surface. With application of larger amounts of penicillin, spontaneous spikes are often punctuated by distinct high-frequency repetitive discharges associated with the tonic and clonic phases of focal epileptic seizures 24'26'32. The alternation between interictal and ictal states in the penicillin focus usually requires several minutes to complete and may repeat regularly for hours 2'34. While this preparation is quite artificial compared to naturally occurring seizure phenomena in man, it does provide a stable model for studying inter-

actions in neural circuitry associated with the interictal to ictal transition. Much of our present knowledge about electrophysiological events accompanying the transition from normally responding cells to those producing interictal discharge, and the transition from interictal to ictal states, has been based on intracellular recordings of single cells in and about the epileptic focus. It is now well established that interictal spikes (llS), recorded as prominent surface negative field potentials near the center of the penicillin focus, are the extracellular reflection of large paroxysmal depolarization shifts (PDS t't3'14) in membrane potentials recorded intracellularly from individual neurons. A concurrent and longer lasting surface positive potential surrounding the focus has been associated with hyperpolarizing membrane currents, producing a surround inhibi-

Correspondence: D.S. Barth, Department of Psychology, Campus Box 345, University of Colorado at Boulder, Boulder, CO 80309-0345, USA. Fax: (1) (303) 492-2967.

34 tion -'°,-'-~,-'4'-'~'-~"that may possibly serve to contain the spread of interictal discharge and suppress the triggering a n d / o r spread of seizures "~°. Yet, the actual spatial and temporal pattern of surface potentials during both the IIS and during seizures often appears to be more complex than this simple two dimensional model would imply, suggesting the asynchronous participation of numerous adjacent cell groups in excitatory and inhibitory epileptic processes. Simultaneous measurements of the potential field at the cortical surface and measurements of intracellular currents at progressive distances from the center of the penicillin focus indicate an increased latency of PDS onset in relation to the central IIS with increased distance from the axis of the focus 14. These data suggest that the negative wave of the IIS may be due to the sequential onset of PDSs occurring progressively more distant from the center of the focus. Using a small array of 3 or 4 surface electrodes, Goldensohn et ai. ~4 demonstrated that the IIS at the center of the penicillin focus typically begins with a brief positive potential that is indistinguishable from a concurrent positivity in the surround. Only later is the prominent negative spike characteristic of the llS superimposed on this widespread positive component, suggesting the synchronous activation of cells first throughout much of the focus and only later more focally at the center. Similar results were reported by Vollmcr et al. "~' in a detailed spatiotemporal study of cortical seizure activities in the rabbit. Here, the surface positive wave beginning the IIS was seen to systematically propagate through the penicillin focus, whereas the surface negative spike appeared to remain stationary, Even more complex spatiotemporal patterns were noted for tonic and clonic seizure phases, where the surface positive field potential described almost circular propagation patterns across the cortical surface. Recent work in our laboratory concerned with numerical analysis of epicortical potentials evoked in rat sensory cortex .~,'~ has indicated, however, that even complex spatial and temporal patterns of field potentials at the cortical surface can often be attributed to only a few spatially overlapping cell groups. Thus, what might appear as a complex propagating potential across the cortical surface, suggesting the sequential activation of numerous cell groups, may in fact be the sum of asynchronously timed potentials from only two or three overlapping populations of cells, greatly altering and simplifying the interpretation of underlying electrophysiological events. The purpose of the present experiment was to apply these methods to the study of the penicillin focus with the objectives of (1) classifying and grouping the variety of interictal and ictal spike wave-

I

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5mm Fig. 1. Potentials were measured from the surface of somatosensory cortex in the right hemisphere directly above the locus of penicillin injection with an 8 x 8 array of platinum electrodes covering a total area of 3.5 x 3.5 mm 2.

forms present in the penicillin focus according to least squares criteria, (2) applying multivariate statistical methods to identify putative cell populations giving rise to the topographical spike complex in each classified spike group, and (3) assessing possible changes i,l th~ spatial extent of putative cell populations, or changes in the timing of interactions between these populations, in the transition from interictal to ictal states. MATERIALS AND METHODS Animal preparation

Four adult male Sprague-Dawleyrats (280-300 g) were studied. General anesthesia was administered and maintained (by checking corneal and tail pinch reflex) usiug a combination of ketamine HCI (66 mg/kg) and xylazine(13 mg/kg) followedby atropine sulfate (0.6 mg/kg). A unilateral craniectomy exposed a region over the right hemisphere extending from bregma to lambda, and laterallyfrom the midlinc to 7 mm ventral to the temporal ridge. The dura mater was resected and the exposed cortex moistened with saline throughout the experiment, Seizure foci were created in the right hemisphere by microinjecting IO,O{X} IU of penicillin G potassium salt 0,5 mm below

the cortical surface in the approximate face and forelimb area of somatosensory cortex (3 mm caudal to bregma and 3 mm lateral to the midline). Recordo~g Epicorticai potentials were recorded simultaneously from a 64 channel micro-electrode array (8 x 8 platinum electrodes) with interelectrode distances of 0.5 ram, covering a 3.5 x 3.5 mm 2 area centered on the penicillin injection site (Fig. !). Recordings were referred to an Ag/AgCI ball electrode positioned at a burr hole in the frontal bone, amplified (Grass 12A5 amplifiers;,01-100 Hz bandpass) and stored in multiplexed form on video tape (Biomedical Monitoring Systems inc,) for subsequent analysis.

Analysis Segments of pre-recorded data were digitally sampled (200 sps) in sequential 10 s blocks that covered both interictal and ictal periods. Analysis was performed in 2 stages, The first stage was concerned with identifying and partitioning spikes into groups that characterized distinct states in the transition from interictal to ictal discharge. This was performed by converting visually identified spikes from the time domain to the frequency domain and using cluster analysis for spike classification, Blocks of data were plotted on a graphics screen and an electronic cursor used to time-mark the visually identified peaks of all spikes recorded at the center electrode of the epicortical array, 1,280 ms segments of data equally surrounding each marked spike were sampled across all channels, tapered with a cosine function at the first and last 10% of the sampling window, converted to power spectra over the frequency range of 1-50 Hz, and stored on disk, Power spectra provided an efficient description of each wave-

35 form with a minimum number of variables. Individual spikes were assigned to one of three groups according to similarities in their spatial distribution of power spectra, Classification was performed using a K-Means clustering algorithm that minimized the within groups variance and maximized the between groups variance. While there is no commonly agreed upon method for determining the number of groups to use in cluster analysis, in the present study three groups yielded the most parsimonious solution in all animals. When less then three groups were used, the members included spikes of clearly ictal and interictal origin. When more than three groups were used, the members in two of the groups were often difficult to visually distinguish. While spike classification was performed in the frequency domain, a representation of each spike group was subsequently computed by averaging all group members in the time domain. The second stage of analysis was concerned with identifying hypothetical populations of cells giving rise to temporally and spatially overlapping waveforms of the averaged spike complex in each group. Principal components analysis (PCA) was used to determine if the 64 spike waveforms within a given group (recorded at each of the 64 electrodes of the epicortical array) could be represented by a smaller number of fundamental waveforms (principal components). To perform PCA, the spike waveforms were first defined in a signal space of 64 dimensions, representing the epicortical recording sites. Each data sample represented a single point in this signal space. The task of PCA was to determine if the same data points could be adequately represented in a sub-space of fewer dimensions. The principal components are linear combinations of the original spike waveforms which explain successively a maximum amount of the system variance and are orthogonal to each other. The coefficients of the linear combinations are called component loads, and the values of the principal components calculated for each sample point of the original data are called component scores. The spatiotemporal pattern of each significant principal component can be reconstructed by multiplying the scores by the loads. These reconstructions were assumed to reflect potentials associated with distinct neuronal subpopulations involved in the spike complex. In this context, the two-dimensional spatial patterns of component loads were used to estimate the epicortical distribution of each subpopulation, and the temporal patterns of component scores were used to estimate the timing of surface potentials in each subpopulation. The coordinates of the principal components were also rotated to provide a solution

RESULTS T h e large quantities o f penicillin used in this study p r o d u c e d seizures in all a n i m a l s which cyclically rec u r r e d at intervals of 1 - 3 m i n TM.A typical cycle (shown for rat 1 in Fig. 2) b e g a n with interictal spikes of s i m p l e m o r p h o l o g y (usually a single spike and slow wave seq u e n c e ) a n d a 0 . 5 - 2 s i n t e r s p i k e interval (Fig. 2 A - C ) . T h e s e spikes were not a c c o m p a n i e d by detectable body m o v e m e n t . This p a t t e r n progressed to more r e g u l a r a n d f r e q u e n t spiking (Fig. 2 D - F ) , often in bursts o f two or m o r e spikes a n d always a c c o m p a n i e d by timelocked m o v e m e n t of the contralateral forelimb, face, a n d vibrissae. Seizures w e r e characterized by highf r e q u e n c y ( 1 0 - 3 0 Hz) spike trains (Fig. 2G,H) lasting 1 0 - 4 0 s. T h e y were a c c o m p a n i e d by bilateral rapid m o v e m e n t s o f the rostral body. However, even d u r i n g the most intense seizures recorded, no a n i m a l s disp l a y e d m o v e m e n t s s p r e a d i n g to more caudal regions of the body. T h e h i g h - f r e q u e n c y tonic seizure quickly evolved into lower f r e q u e n c y clonic bursts (Fig. 2H,I), the earliest of which were also associated with bilateral jerks o f the rostral body. Seizures t e r m i n a t e d with postictal suppression of all electrical activity a n d no m o v e m e n t (Fig. 21,J). Dots above each spike in Fig. 2 indicate the positions o f visually identified t i m e - m a r k s for s u b s e q u e n t cluster analysis. T h e width o f each dot identifies which of t h r e e groups the spike was subsequently assigned to by the clustering procedure, b a s e d on the spatial distrib u t i o n of its power s p e c t r u m at all 64 recording locations. In all animals, group assignments progressed through an orderly s e q u e n c e during the course of a given seizure cycle. In this example, the m e m b e r s of

that was most realistic according to physiological criteria. These criteria, and the process of rotation, are more easily understood in the context of a specific data set, and are thus described in greater detail in the results section,

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I Fig. 2. Raw potentials recorded in sequential 10 s blocks from an electrode near the center of the array in rat 1. Dots above each spike indicate visually identified time-marks used for subsequent cluster analysis and spike averaging. The thickness of each dot indicates the group to which its respective spike was assigned during cluster analysis. A typical ictal cycle repeated over a period of several minutes. The cycle shown here began with low frequency interictal spikes (Group 1, thick dots, A-C), progressed to higher frequency spikes (Group 2, medium dots, D-F), then to the highest frequency spikes associated with seizures (Group 3, thinnest dots, G and H), and terminated with postictal suppression of all activity (! and J) before repeating the cycle. Calibrations: horizontal = 1 s; vertical = 0.5 mY, negative up.

36 Group 1

Group 3

Group 2

Fig. 3. Averaged spike complex in each of the three cluster groups for rat 1. The complex appeared as a slow positive wave in the middle left region of the array (A) and a faster negative spike in the lower right region (B). The relative timing and morphology of these waveforms did not appear to change between groups. The main effect of increased excitability and ictus was a decrease in the amplitude and increase in frequency of the spike complex, with no apparent change in its spatial distribution. Calibrations: horizontal = 2.25 s (upper) and 321 ms (lower); vertical -- 1 mV (upper) and 0.5 mV (lower), negative up.

group 1 (widest dots) consisted of low frequency postictal (Fig. 2A,B,I,J) and interictal (Fig. 2C) spikes, spikes rarely associated with movement. Higher frequency spiking associated with contralateral movement (Fig. 2D-F) typically comprised the members of group 2 (medium dots). The highest frequency spikes of seizures, associated with bilateral movement (Fig. 2G,H), were almost exclusively assigned to group 3 (thinnest dots). Figure 3 depicts the spike complex of rat 1 as it appeared at all epicortical recording sites when averaged across the members of each cluster group, Visual inspection of the averaged spike complex for group 1 indicated two basic waveforms in different regions of the recording array. In the lower right region (Fig. 3B) the complex began with a focal biphasic sharp wave. The sharp wave, particularly its large negative phase,

appeared to overlap a second, more widespread waveform (Fig. 3A), consisting predominately of a slower positive component in the middle left region of the array. This pattern, consisting of a focal biphasic sharp wave overlapping with a more distributed and longer duration positivity, was also apparent in the averages of groups 2 and 3 in this animal, and appeared in similar form in the cluster groupings of the other animals. Thus, a qualitative assessment of the results suggested that the major difference between interictal and ictai groups was not in the relative spatial distribution of spike waveforms throughout the array, but was instead based almost completely on the spike frequency or interspike interval. PCA provides a more quantitative model of basic waveforms capable of producing the spike complex in each of the groups. Figure 4 shows reconstructions of

Data (group 2)

PCA (components 1+2)

PCA (component 1)

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r'-l--'r-'r-r-'r-,---

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Fig. 4. Result of principal components analysis (PCA) of the average group 2 spike complex in rat 1. Reconstruction of the first two principal components accounted for 94% of the original data variance. The first principal component accounted for 67% and the second for 27% of the variance. Reconstruction of the residual variance appeared as noise. The physiological interpretation of these unrotated results is that the first principal component was produced by two separate populations of ceils in the upper left and lower right region of the array, simultaneously producing surface potentials of the same waveshape but opposite polarity between these two regions. The second component reflected only a single cell group near the middle of the array. This solution and interpretation was not considered physiologically realistic. Calibrations: horizontal = 2.25 s; vertical = 1 mV, negative up.

37 the results of PCA performed on group 2 spikes of rat 1. In this example, the first two principal components explained 94% of the variance in the data. Thus, PCA indicated that each of the 64 waveforms of the original data could be reconstructed by the weighted combination of only two fundamental waveforms (principal components). Reconstructions of the principal components in Fig. 4 graphically depict the contribution each fundamental waveform makes t o the data recorded at each position in the electrode array. The spatial distribution of component 1 suggested a waveform of opposite polarity between the lower right and upper left region of the recording array. The second component was of the same polarity at all recording sites and concentrated in the lower central region of the array. Each of these reconstructions was computed by multiplying the spatial distribution of component loads (weights) by the temporal waveform represented by the component scores (Fig. 5). While mathematically correct, these are purely statistical results and are not necessarily related to underlying physiology. As depicted in Fig. 4, if the hypothetical waveforms of principal components one and two are summed, they will accurately model the waveforms of the original data. However, this does not mean that the component reconstructions accurately reflect actual activity in underlying populations of cortical cells. PCA is computed so that the first component accounts for most of the variance, the second component, a maximum amount of residual variance, and so on until all of the variance is explained. This strategy is not governed by any physiological constraints, but simply by the method by which the principal components are extracted, in fact there are no a priori reasons to expect that activity in one population of cells should account for more of the data variance than another. In this light, PCA must be viewed as a method for forming quantitative models about activity in underlying populations of cells, but is not in itself conclusive. It is incumbent upon the investigator to decide if the results of PCA are physiologically realistic. An advantage of PCA in the present application is that most of the variance of the original data set was successfully accounted for in a space of only two dimensions (principal components). Once this has been accomplished, the coordinates of the original data points in this two-dimensional space may be transformed (rigid axis rotation) without affecting the total amount of variance accounted for by the model TM. The effect of axis rotation is to redistribute the variance accounted for by each component, necessarily changing the patterns of both their respective loads and scores. We performed rotations with the single criteria that

Loads

Scores

Component 1 (unrotatezl)

Component 2

(unrotat ) i~ "",. ",./I Component I ~" A..'JJ (rotated) ~

Component 2 (rotated) I

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Fig. 5. Axis rotations performed on PCA results from group 2 of rat 1. Each principal component consists of a spatial pattern of component loads (which represent the weighted contribution of that component to the waveforms at each electrode in the recording array) and a temporal pattern of component scores (representing the fundamental waveform characteristicof each component). Reconstruction of the principal components in Fig. 4 were performed by multiplying the component scores by their loads. Once the data had been reduced to two dimensions by PCA, the coordinates of the original data points in this space were linearly transformed by the procedure of rigid axis rotation. Axis rotation has no effect on the total system variance accounted for by the two components, but does change the relative variance accounted for by each component, necessarily changing the pattern of both scores and loads. While all angles of rotation produce mathematically correct results, a simple physiological criterion was applied to determine the best angle. This criterion stated that the pattern of component loads should be primarily of the same polarity across the recordingarray. A rotation of 40° produced a substantial improvement in the physiological realism of loads f{Jr component 1, transforming them from two regions of equal hu~topposite polarity in the upper left and lower right region of the array to mainly one region of a single polarity in the lower right region. In contrast to the unrotated results, the scores for both of the rotated components closely approximated actual spike waveforms taken from the original data in the regions of the array were the loads indicated the component was of maximum amplitude (light traces, scaled from traces for group 2 in Fig. 3A and B). Calibrations: horizontal = 562 ms.

the loads conform to a physiologically realistic pattern. Here, it was assumed that a distinct population of synchronously activated neocortical cells will produce epicortical potentials of the same polarity throughout the recording array, and not potentials of differing polarity at adjacent locations on the cortical surface. By this criterion, the unrotated results shown in Fig. 5 were not considered physiologically realistic. The spatial distribution of loads for component 1 suggested a synchronously active population of cells, distributed in the lower right and upper left region of the array, producing potentials of exactly the same waveform but opposite polarity. Furthermore, the score waveforms of

38 Group I

Group 2

Group 3

Average

Component 1

Component2

Fig. 6. Rotated loads for both principal components computed separately for each of the cluster groups in rat 1. While the degree of rotation differed slightly between groups, the final loading patterns were nearly identical, justifying the use of an average loading pattern for subsequent analysis.

both components were dissimilar to the actual spike complex recorded in any region of the array. Figure 5 (bottom) shows the results of rotating the coordinate axes by 40° in this example, producing the most realistic loads by our criteria. The rotated loads of component 1 suggested a population of cells concentrated in the lower right region of the array with scores reflecting primarily a biphasic sharp wave. The rotated loads of component 2 were centered on the middle left region of the array and overlapped those of component 1, with scores reflecting a slow wave. in contrast to the unrotated results, the scores for both rotated components closely approximated to actual spike waveforms taken from the original data in the regions of the array where the loads indicated the component was of maximum amplitude (light traces in Fig. 5, scaled from traces for group 2 in Fig. 3A and B), Thus, the rotated

PCA results conformed well with both physiological criteria and with qualitative assessment of the data. The degree of rotation required to meet our physiological criteria differed slightly between the three cluster groups in this animal. However, the final rotated loads were nearly identical (Fig. 6), and permitted the computation of an average pattern that accurately reflected all three groups in this animal. Similar averaged loading patterns were also computed across cluster groups for the other animals. While a weighted combination of the average loading patterns for the first two principal components was capable of explaining 95% of the variance across cluster groups in rat 1 (Table 1), the question remained as to whether these patterns could also be used to model the original unclustered data. Figure 7 depicts linear regression weights, indicating the relative contribution

Crop. 1 Group 1

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Group 3

Fig. 7. Linear regression weights reflecting the relative contribution of average loading patterns for components 1 and 2 in modeling 10 s blocks of raw data in rat I, The raw data blocks were chosen to be representative of spikes characterizing the three cluster groups. The top trace in each group reflects the weighted contribution of the loading pattern for component 1 (Crop. 1; patative population of cells in the lower right region of the recording matrix) and the bottom trace, the contribution of loading patterns for component 2 (Crop. 2; putative population of cells in the upper left region of the recording matrix), In all cases, the linear combination of the two component loading patterns was capable of accounting for over 90% of the variance of the raw data. Furthermore, the waveforms for each component indicated by the regression weights applied to the raw data approximated the scores computed for each of the averaged groups (dark trace). These are superimposed on the raw regression weights for comparison. Calibrations: horizontal = 1 s.

39 TABLE I Percent variance accounted for across cluster groups for the first two principal components in each animal Rat I

Rat 2

Rat 3

Rat 4

Component 1 Component 2

65 30

70 24

80 14

75 15

Total

95

94

94

90

of loading patterns for components 1 and 2, computed over 10 s blocks of raw data containing spikes representative of the three different cluster groups. In all blocks, the regression model accounted for over 90% of the variance in the raw data. Furthermore, the morphology of regression weights computed for the raw data closely approximated the PCA scores for the respective averaged cluster groups (Fig. 7, dark traces). DISCUSSION

Principal components analysis In all animals, PCA was able to account for 90-95% of the system variance with only two principal components. These results indicate that the dimensionality of the data, the number of sources of independent variance, is quite low and remains constant regardless of epileptic excitability. The number of asynchronously activated cell populations within the penicillin focus is invariant throughout each seizure cycle. However, these are purely statistical results and more direct physiological interpretation must be performed cautiously. We assumed that the unrotated loading patterns (reflecting the spatial or topographical distribution of putative cell populations producing that component) were not physiologically realistic. This was concluded because reconstruction of most principal components indicated synchronously active populations of cells separated by only 1-2 mm that had identical waveforms but produced epicortical potentials of equal but opposite polarity. This possibility was considered unlikely given the synaptic arrangement and geometry of neocortical cells. It could be argued that two epicortical potential maxima of equal but opposite polarity, indicated by the unrotated loads of a given principal component, might be created if the underlying cellular generator approximated a current dipole oriented tangential to the cortical surface. Indeed in gyrated neocortex, such an arrangement is a distinct and likely possibility. However, in the present study, this is not considered a realistic interpretation for two reasons. First, the most likely

generators of epicortical potentials are the apical dendrites of pyramidal ceils6-s,19.21.22. This conclusion is based on the parallel arrangement of the apical dendrites, providing an open field 22 geometry, where the potentials of many thousands of synchronously active processes may sum coherently to produce a net potential at the cortical surface. The basilar dendrites of pyramidal cells, and the processes of other cells such as the glia and stellate cells, are of a more radially symmetric configuration that would be expected to produce self canceling or closed fields when measured at the cortical surface with respect to a distant reference electrode. While the apical dendrites of the cortical pyramids typically produce a dipolar field when activated, in lissencephalic cortex such as the rats, this field is consistently oriented perpendicular to the cortical surface and the measurement array and not tangentially, as suggested by the unrotated loads. A second related reason for rejecting the possibility of a tangentially oriented dipole to explain the component loads is that the epicortical electrodes of our array are assumed to be dominated by post-synaptic potentials of cells directly beneath or closely adjacent to the electrodes. This is because the field amplitude of an equivalent current dipole in a volume conductor falls off with the inverse square of the distance between the source and the measurement site. Detection of a purely tangential dipole pattern (from a necessarily distant source since the source must lie miowa) between the field extrema) with epicorticai electrodes is therefore unlikely since it would require electrical silence of most cells directly beneath the recording array. In all animals it was possible to rotate the coordinates of the principal component axes to achieve loading patterns for both components that remained primarily of one polarity throughout the recording array, and thus were considered more physiologically realistic. Interestingly, this also resulted in component scores (reflecting the temporal pattern of membrane potentials specific to each putative neuronal group) that closely matched potential waveforms recorded from cortical regions were the putative neuronal groups were located. The loading patterns of the rotated principal components were almost identical across interictai and ictal spike groups within a given animal. An averaged pattern across groups was equally capable of modeling the data within each group. Thus, not only did the dimensionality of the data remain invariant throughout a seizure cycle, but the spatial extent and location of participating neuronal populations was not changed during ictus. This result could have been artificially

40 focus) increases with distance from the center of the focus, suggesting a sequential onset of FDS directed peripherally at a rate of approximately 0.25 m/s. We created a model of a propagating field potential waveform to determine how our analysis, based on stationary neural populations, would perform. The model field potential was a biphasic sine wave of 10 Tns duration, approximating the morphology and duration of evoked paroxysomal field potentials reported in the neocortical slice 4. The latency of the wave was increased by 1 ms with each 0.1 mm increment in recording distance across the cortical surface and away from the site of origin. The field potential pattern for a linear array of 20 recording sites, covering a total of 2 mm on the cortical surface, is shown in Fig. 8A. These model data were then subjected to the same PCA used in the present study. In this situation, where potentials change progressively in both time and space, PCA does a poor job in reducing the dimensionality of the data. The sum of the first five principal components could account for only 87% of the data variance (Fig. 8B). The separate variance accounted for by the five components was 24, 23, 17, 14 and 9%, respectively. The number of components required, the large fraction of variance accounted for even by the fifth component, and the spatiotemporal patterns of the reconstructed components (Fig. 8C-O), suggest that our analysis would not perform well if applied to field potentials propagating uniformly through the epileptic focus. In all animals in all states of epileptic excitability measured in the present study, PCA is capable of explaining from 90-95% of the data variance with only two principal components. These results do not rule out

produced by the grouping and averaging of spikes. If the averaged spike complex of each group actually contained a mixture of spikes from both interictal and ictal states, this would obscure ~.iifferences between states. However, this explanation is unlikely for two reasons. First, the results of cluster analysis were closely monitored in all animals prior to averaging. The choice of three cluster groups resulted in very little classification error. Second, within a given animal, the averaged loading patterns were capable of modeling over 90% of the variance of the raw data during intcrict~l, ictal, and transitional states.

Stationary t:~. propagating potentials The present model, using only two stationary cell populations to explain all excitability states in the penicillin focus, departs from that suggested by others 4's'~4-L~'''5.27'2s'36, where the interictal and ictal spike complex is seen to result from the progressive propagation of activity throughout the focus. Based on field potential measurements of interictal spikes produced by bicucuiline methiodide in the neocortical slice 5, paroxysmal discharge has been estimated to propagate horizontally (tangential to the cortical surface) at a speed of approximately 0.06-0.09 m/s. In a similar preparation, but with less bicuculline and therefore greater GABA-mediated inhibition left intact, the direction and extent of propagating potentials becomes more variable 4. Further support for the concept of propagating spikes in the epileptic focus comes from intracellular recordings of the PDS in and about the focus L4, The latency of PDS oqset (in relation to a reference field potential recording at the center of the

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Fig. 8. A model of a propagating waveform in neocortex was created to test the applicability of the principal components analysis (PCA) in circumstances where potentials change in both time and space, A: the model field potential was a biphasic sine wave of ]0 ms duration. The latency of the wave was increased by I ms with each 0.I mm increment in recording distance across the cortical surface and away from the site of origination (top trace). The field potential pattern for a linear array of 20 recording sites, covering a total of 2 mm on the cortical surface, is shown. B: the sum of the first five principal components accounted for only 8"/% of the data variance. C-G: reconstructions of the five principal components accounted for 24, 23, I'/, 14 and 9 % of the data variance, respectively. Calibrations: horizontal = ]0 ms.

41 the possibility that potentials also propagate throughout the epileptic focus. As demonstrated in vitro 'us, the presence and pattern of propagation depends on the quantity and distribution of epileptic agent. However, in the present study, where large quantities of penicillin were applied in a single bolus (as opposed to other in vivo and in vitro studies where penicillin was permitted to diffuse over wide cortical areas), the data suggest that the dominate influence on epicortical field potentials was that of two stationary cellular populations with asynchronously timed postsynaptic potentials. Figure 9 depicts an averaged IIS complex from the present study, subjected to a different method of topographical field potential analysis similar to that used by Petsche and co-workers 2s'27`2s'36. This method differs from the present analysis in that epicortical potentials are considered to move continuously across the cortical surface during the elaboration of the spike complex. The equipotential maps of Fig. 9A read from left to right and top to bottom and represent the topographical distribution of potentials in 5 ms increments from 10 ms before to 45 ms following the negative peak of the IIS complex. In this type of analysis, the locations of the peaks of both negative and positive potentials are tracked over time. Prior to the appearance of the negative spike, potentials throughout the array are weakly positive, with a maximum near the center of the array (first map). As the negative peak of the IIS

forms, the peak positivity appears to shift up and to the left. With the decline of negativity, the movement of the positive peak reverses direction, heading diagonally acros~ the matrix toward the lower right corner. Figure 9B summarizes the movement of both the positive and negative maxima during the IIS. The positive maxima describes a double loop and appears to move a total distance of 2 ram. The movement of the negative maxima is less (approximately 1 ram) and remains confined to the lower right region of the matrix. The results of topographical analysis shown here for the IIS are quite similar to previous reports, and suggest that the generation of IIS involves the propagation of both positive and negative potentials across wide cortical areas. Yet, these are data that may be satisfactorily modeled with two stationary neural sources. This example demonstrates that the movement of field potential peaks across the cortical surface does not necessarily indicate a continuous propagation of activity. Indeed, the simplest explanation is provided by a fixed source model. CONCLUSION

These data suggest a physiological model in which the complex topography of epicortical field potentials associated with interictal, ictal, and transitional states in the rat neocortical penicillin focus, may be produced by only two asynchronously active populations of uells

A)

~ 1 ~~.~,.. ~.::r-::~ (;.~.......CO~:-/I~ (,(,(~".@.....~.;;~...ql .,;,,..~"-.-.'::::,..'r

-".°~.-oo,'"

~

ii i

B)

Fig. 9. Topographical field potential analysis of an averaged IIS complex. A: equipotentiai maps read from left to right and top to bottom and represent the topographical distribution of potentials in 5 ms increments from 10 ms before to 45 ms following the negative peak of the IIS complex (solid lines = positive; dotted lines = negative). B: the peak of positive potential during this period appears to move over a distance of approximately 2 ram, describing a double loop pattern. The peak of the negative potential also appears to move, but only over a 1 mm distance.

42 within somatosensory cortex. The relative locations of these populations vary between animals and are not directly correlated with the site of penicillin injection, possibly due to diffusion of penicillin over time. Within a given animal, however, the location and spatial distribution of the cell populations does not appear to be changed by seizure onset. Thus, the transition from interictal to ictai states is associated almost exclusively with alterations in the amplitude and frequency of epileptiform discharge, and not in the spatial distribution of participating cells. These conclusions hold only for epicortical potentials, which do not directly reflect demonstrated changes in the participation of lamina specific cell populations during the transition to ictus2a ~.~2. These results emphasize the distinction between seizure initiation and seizure propagation in neocortex. The first sign of ictus was twitching of face and forelimb contralateral to the epileptic focus. This behavior then spread ipsilaterally during the most intense electrographic ictal discharge. Since all penicillin foci were situated in the face and forelimb area of somatosensory cortex, behavioral signs were probably effected through established cortico-cortical connections between somatosensory and motor cortex in the rat |°,l~.xs. While seizures propagated easily between cerebral hemispheres, in no animals was there behavioral evidence that the seizure discharge had spread to cortex associated with more caudal body regions. This apparent containment of seizure discharge within a given hemisphere is closely reflected in the immobility of the electrographic discharge through the interictal-ictal transition. While the present data demonstrate that seizures may be triggered and maintained in neocortex without any change in the spatial characteristics of involved neuronal populations, it will be of interest in future studies to compare these results to those obtained from loci in which the behavioral signs of seizure clearly spread to other body regions. In this way, spatiotemporal electrographic changes uniquely associated with seizure propagation might be distinguished from those responsible for the interictal-ictal transition. Acknowk, dgments. This research was supported by United States Public Health Service Grant I-R01-NS22575, National Science Foundation Grant BNS-86-57764, Whitaker Foundation Grant $880620, and a Grant in Aid from the Graduate School Council on Research and Creative Work at the University of Colorado at Boulder. REFERENCES ! Ayala, G.F., Matsumoto, H. and Gumnit, R.J., Inhibitory mechanisms during tonic clonic seizures, Eiectroenceph. Clin. Neurophysiol., 28 (! 970) 96.

2 Barth, D.S., Baumgartner, C. and Di, S., Laminar interactions in rat motor cortex during cyclically occurring seizure bursts, Soc. Neurosci. Abstr., 15 (1989) 339. 3 Barth, D.S. and Di, S., Three-dimensional analysis of auditory evoked potentials in rat neocortex, J. Neurophysiol., 64 (1990) 1527-1536. 4 Chagnac-Amitai, Y. and Conners, B.W., Horizontal spread of synchronized activity in neocortex and its control by GABAmediated inhibition, J. Neurophysiol., 61 (1989)747-758. 5 Chervin, R.D., Pierce, P.A. and Conners, B.W., Periodicity and directionality in the propagation of epileptiform discharges across neocortex, J. Neurophysiol., 60 (1988) 1695-1713. 6 Creutzfeldt, O.D., Neuronal mechanisms underlying the EEG. in H.H. Jasper, A.A. Ward and A. Pope (Eds.), Basic Mechanisms of the Epilepsies, Little, Brown and Co., Boston, 1969, pp. 397-420. 7 Creutzfeldt, O.D. and Houchin, J., Neuronal basis of EEG-waves. in A. Remond (Eds.), Handbook of Electroencephalography and Clinical Neurophysioiogy, 2C Elsevier, Amsterdam, 1974, pp. 5-55. 8 Creutzfeldt, O.D., Watanabe, S. and Lux, H.D., Relations between EEG phenomena and potentials of single cortical cells. I. Evoked responses after thalamic and epicortical stimulation, Electroenceph. Ciin. Neurophysiol., 20 (1966) 1-18. 9 Di, S. and Barth, D.S., Topographic analysis of field potentials in rat vibrissa/barrel cortex, Brain Res., 546 (1991) 106-112. 10 Donoghue, J.P., Kerman, K.L. and Ebner, F.F., Evidence for two organizational plans within the somatic sensory-motor cortex of the rat, J. Comp. Neuroi., 183 (1979)647-664. 11 Ebersole, J.S. and Chatt, A.B., Laminar interactions during neecortical epileptogenesis, Brain Res., 298 (1984) 253-271. 12 Ebersole, J.S. and Chart, A.B., Spread and arrest of seizures: the importance of layer 4 in laminar interactions during neocortical epileptogenesis. In A.V. Delgado-Escueta, A.A.J. Ward, D.M. Woodbury and RJ. Porter (Eds.), Advances in Neurology, Vol. 44 Raven Press, New York, 1986, pp. 515-558. 13 Goldensohn, E.S. and Purpura, D.P., lntracellular potentials of cortical neurons during focal epileptogenic discharges, Science, 139 (1963) 840-842. 14 Goldensohn, E.S, and Salazar, A,M,, Temporal and spatial distribution of intraccllular potentials during generation and spread of ¢pil0plogcnic discharges, In A,V. Delgado,Escucta, A,A,W, Jr., D.M. Woodbury and R J, Porter (Eds,), Advanc~:~"ha Neurolo~, VoL 44 Raven Press, New York, 1986, pp. 559-582, 15 Goldensohn, E.S,, Zablow, L. and Salazar, A,, The penicillin focus. I. Distribution of potential at the cortical surface, Elec. troenceph. Clin. Neurophysiol., 42 (1977)480-492. 16 Gumnit, RJ. and Takahashi, T., Changes in direct current activity during experimental focal seizures, Electroenceph. Clin, Neurophysiol., 19 (1965) 63-74. 17 Hall, R.D. and Lindholm, E.P., Organization of motor and somate-sensory neocortex in the albino rat, Brain Res,, 66 (1974) 23-28. 18 Harman, H.H., Modern Factor Analysis, University of Chicago Press, Chicago, 1967. 19 Humphrey, D.R., Re-analysis of the antidromic cortical response. II, On the contribution of cell discharge and PSPs to the evoked potentials, Electroenceph. Clin. Neurophysiol., 25 (1968) 421-442. 20 Jordan, .I.E., Changes in the inhibitory surround associated with penicillin spike, Electroenceph. Clin. Neurophysiol., 56 (1983) 5P. 21 Lopes da Silva, F, and Van Rotterdam, A., Biophysical aspects of EEG and MEG generation. In E. Niedermeyer and F. Lopes da Silva (Eds,), Electroencephalography, Basic Principles, Clinical Applications and Related Fields, Urban Schwarzenberg, Baltimore, Munich, 1982, pp. 15-26. 22 Lorente de N6, R., A Study of Nerve Physiology, Part 2, Rockefeller Institute, 1947. 23 Matsumoto, H. and Ajmone Marsan, C., Cortical cellular phenomena in experimental epilepsy: interictal manifestations, Exp. Neurol., 9 (1964) 286-304. 24 Matsumoto, H. and Ajmone-Marsan, C., Cortical cellular phenomena in experimental epilepsy: ictal manifestations, Exp. Neutel., 9 (1964) 305-326. 25 Petsche, H., Nagypal, T., Prohaska, O., Rappelsberger, P. and

43

26

27

28 29 30

Vollmer, R., Approaches to the spatio-lemporal analysis of seizure patterns. In G. Dolce and H. Kiinkel (Eds.), CEAN-Computerized EEG Analysis, Gustav Fischer, Stuttgart, 1975. Petsche, H., Pockberger, H. and Rappelsberger, P., Mechanisms leading to the propagation of self-sustained seizure activities, in H.G. Wieser, E.J. Speckmann and J. Engel (Eds.), Current Problems in Epilepsy: The Epileptic Focus, Libbey, London, 1987, pp. 59-81. Petsche, H., Prohaska, O., Rappelsberger, P., Vollmer, R. and Kaiser, A., Cortical seizure patterns in multi-dimensional view: the information content of equipotential maps, Epilepsia, 15 (1974) 439-463. Petsche, H., Rappelsberger, P. and Trappl, R., Properties of cortical seizure potential fields, Electroenceph. Clin. Neurophysiol., 29 (1972) 567-578. Prince, D.A., The depolarization shift in 'epileptic' neurons, Exp. Neurol., 2 ! (1968) 467-485. Prince, D.A. and Wilder, B.J., Control mechanisms in cortical epileptogenic foci: 'surround' inhibition, Arch. Neurol., 16 (1967) 194-202.

31 Purpura, D.P., Penry, J.K., Tower, D.M., Woodbury, D.M. and Walter, R., Experimental Models of Epilepsy - A Manual for the Laboratory Worker Raben Press, New York, 1972. 32 Ralston, B.L., The mechanism of transition of interictal spiking loci into ictal seizure discharges, Electroenceph. Clin. Neurophys. iol., 10 (1958) 2"7-232. 33 Reichenthal, E. and Hocherman, S., A critical epileptic area in the cat's cortex and its relation to the cortical columns, Electroetlceph. Clin. Neurophysiol., 47 (1979) 147-152. 34 Rekhtman, M.B., Samsonova, N.A. and Kryzhanovskii, G.N., Effect of diazepam on cyclic change of excitability in a cortical epileptic focus, Neurophysiology, 12 (1980) 365-371. 35 Sanderson, K.J., Welker, W. and Shambes, M., Re-evaluation of motor cortex and sensorimotor overlap in cerebral cortex of albino rats, Brain Res., 292 (1984) 251-260. 36 Vollmer, R., Petsche, H., Pockberger, H., Prohaska, O. and Rappelsberger, P., Spatiotemporal analysis of seizure activities in a homogeneous cytoarchitectonic region. In M.A.B. Brazier and H. Petsche (Eds.), Architectonics of the C,,rebral Cortex, Raven Press: New York, 1978, pp. 281-305.