al. 1993), in a number of instances the seizure onset cannot be appreciated or localized by scalp recordings alone. Seizures originating from deep mes

Transcription

1 Analysis of mesial temporal seizure onset and propagation using the directed transfer function method Piotr J. Franaszczuk a b Maciej J. Kaminski b Gregory K. Bergey a c 1 a Maryland Epilepsy Center, Department of Neurology, University of Maryland School of Medicine and Medical Center, 22 South Greene Street,Baltimore, MD (USA) b Laboratory of Medical Physics, Institute of Experimental Physics, Warsaw University, Warsaw (Poland) c G. K. Bergey is with Department of Physiology, University of Maryland School of Medicine, Baltimore, MD (USA) The directed transfer function (DTF) method, a multichannel parametric method of analysis based on an autoregressive model, is a newly developed tool that permits determination of patterns of ow of activity. The DTF method of analysis was applied to seizures originating from mesial temporal lobe structures in three patients recorded by combined subdural grid and depth electrode arrays. These rst applications to human intracranial recordings, demonstrated that the DTF method can accurately determine patterns of seizure onset and propagation. In addition the DTF method can provide evidence regarding patterns of ow of seizure activity that are not readily apparent from visual inspection of the EEG recordings. Important considerations for appropriate application of the DTF method for the analysis of intracranial ictal recordings are discussed. Key words: Seizure propagation, EEG, autoregressive, directed transfer function, temporal lobe, depth electrodes Understanding the characteristics of seizure onset and propagation is important for localization of seizure foci in patients being considered for seizure surgery. Continuous monitoring of patients with medically intractable seizures is now common in epilepsy centers. While scalp recordings of ictal events can often provide clues as to seizure localization (Risinger et al Wieser et 1 Corresponding author. Tel.: Fax: gbergey@umabnet.ab.umd.edu Preprint submitted to Elsevier Preprint September 1994

2 al. 1993), in a number of instances the seizure onset cannot be appreciated or localized by scalp recordings alone. Seizures originating from deep mesial temporal structures may on occasion not be apparent on scalp recordings until the seizures have spread to the lateral neocortex at times lateralization or localization may be dicult (Sammaritano et al. 1987). Seizures originating from lateral temporal lobe structures are being more frequently recognized (Spencer et al Pacia and Ebersole 1993). These lateral temporal onset seizures as well as other seizures, particularly those originating from parietal or frontal cortex may be dicult to localize from scalp ictal recordings because of rapid regional spread (Williamson 1992 Williamson et al Quesney et al. 1992). Invasive monitoring of seizures with depth electrode arrays or subdural grids can assist in seizure localization, but even with these methods seizure onsets cannot always be fully appreciated by visual analysis of intracranial EEG (ICEEG) recordings (Matsuoka and Spencer 1993). Recently Kaminski and Blinowska (1991) developed and described the directed transfer function (DTF) method of EEG analysis. This is a multichannel parametric method formulated in the framework of an autoregressive (AR) model. The DTF method oers distinct advantages over previously described methods of computer analysis (review, Gotman et al. 1993) in that patterns of ow of electrical activity can be more directly determined. In this initial description of the DTF method by Kaminski and Blinowska there were preliminary limited applications to experimental animals, simulated epileptiform EEG, and one human epileptic scalp EEG recording. Here we report the rst application of this method to intracranial recordings with combined depth electrode and subdural grid recordings of seizures in three patients with refractory complex partial seizures originating from mesial temporal lobe structures. The purpose of this initial report is to describe the characteristics of the DTF method and the important considerations regarding its application. This report illustrates that this DTF method can be a valuable supplement to the visual analysis of these records and suggests additional potential applications. A preliminary report of this data has been presented in abstract form (Franaszczuk et al. 1993). 1 Methods 1.1 Data acquisition Data from three patients with complex partial seizures originating from mesial structures of the left temporal lobe were retrospectively analyzed. All three patients had seizures refractory to medical therapy with standard antiepileptic medications. Wada testing had revealed the left temporal lobe to be dominant 2

3 for language in each of these right handed patients. Prior to anterior temporal lobe resection an MRI compatible (platinum contacts) 32 contact subdural grid array (PMT Corp.) was placed over the lateral temporal lobe to allow functional mapping of language areas during the week prior to surgery, to minimize the risk of language decits following resection. At the time of grid Fig. 1. T1-weighted axial MRI image (second patient) revealing two depth electrode arrays passing through 32-contact subdural grid array (arrow). The subdural grid array overlies the lateral temporal surface. The deepest contacts of the depth electrode array are in the amygdala and hippocampus respectively. placement one or two eight contact depth electrode arrays were placed freehand to record from the mesial temporal structures. This combined depth and grid approach has been described previously (Barry et al. 1992). Fig. 1 is an MRI illustrating the depth and grid locations after surgical placement. Three to six seizures were recorded with these arrays from each patient during the week prior to anterior temporal lobe resection. Visual ICEEG review demonstrated seizures originating from the mesial structures with variable subsequent regional or generalized spread. Each patient underwent a standard dominant anterior temporal lobe resection which included the amygdala, the anterior cm of hippocampus and cm of lateral temporal neocortex, sparing the superior temporal gyrus. Pathological examination of the surgical specimens revealed a low grade astrocytoma in one patient the other two patients had gliosis. All three patients are seizure free following surgery 3

4 with follow-up periods of 22 to 24 months. Data for seizure analysis was collected using a 64 channel video-eeg recording system, the Telefactor MODAC 64-BSS, with a bandpass lter of Hz. The multichannel EEG signals were digitized at a rate of 200 samples/second and stored with the corresponding video patient image on VHS video tape. Data for analysis was transferred from the video tape to hard disc storage on a Telefactor Beekeeper Digital EEG Review Workstation. Data was then transferred for analysis to a MHz microcomputer with 16 MB RAM and 500 MB hard disc storage. Ten minutes of 64 channels of EEG require about 10 MB of hard disc storage. Data used for analysis utilized a common reference. Additional low-pass digital zero-phase ltering (50 Hz) was used for the records from the rst patient. 1.2 Multichannel analysis of data A multichannel autoregressive model is a parametric time series representation that best describes the signal in each channel as a linear combination of its own past activity and the past activity of all other channels plus an additional uncorrelated noise, px j=0 A j x t;j = e t (1) where A j are matrices of model coecients,x t is the vector of EEG multichannel signal, e t is the vector of multivariate zero mean uncorrelated white noise, and p is the model order. Multichannel AR spectral analysis of the EEG data was performed using the algorithm described by Franaszczuk et al. (1985). The unknown matrices of model coecients A j dened in Eqn. 1 were obtained by solving the system of m p linear equations: px j=0 A j R(j ; k) =;R(;k) for k =1 ::: m (2) were m is the number of channels, p is the estimated order of the AR model and R(k) are biased estimates of the multichannel covariance matrix (Marple 1987) computed from short (1-5 second) intervals of EEG data. The duration of the appropriate interval for analysis was determined by examination of the EEG records. When the EEG record changed rapidly (e.g. during seizure onset) one second intervals were used for analysis. The system from Eqn. 2 was solved by the Cholesky numerical method (Dahlquist and Bjorck 1969). 4

5 Model order was estimated using multichannel Akaike criterion dened by the equation (Marple 1987, Kaminski and Blinowska 1991): AIC(p) =ln(det(v e )) + 2pm 2 =N (3) where V e is the covariance matrix of the assumed white noise input, and N is the number of data points per channel. It has been suggested that an upper limit for the order is 3 p N=m (Marple 1987). Therefore the upper limit of the model order increases with the number of data points. In multichannel analyses when the channels are highly correlated, the optimal model order decreases as the number of channels increases. With rapidly changing EEG patterns, one second intervals were utilized and up to 16 channels were analyzed simultaneously. With more stable patterns (ictal or interictal) longer intervals (typically two to ve seconds) could be appropriately sampled and more channels could be analyzed simultaneously. Examples of ictal patterns where the longer intervals may be most appropriate include early periodic or pseudoperiodic discharges at seizure onset or regular rhythmic regional discharges later in seizure evolution. In each instance calculations of the Akaike criterium (Eqn. 3) were made to conrm the appropriateness of the model order. The criterium function almost always has a clear minimum for model order of 5 for most 8 channel analyses of one second (200 data point) intervals. For 16 channel analyses the model order is closer to 3 for the same intervals. After computing model coecients the spectral analysis was performed. Matrix spectral density function S(f) is computed according to the formula (Franaszczuk et al Marple 1987): S(f) =H(f)V e H(f) (4) where asterisk denotes matrix transposition and complex conjugation. H(f) is the Matrix Transfer Function dened by: H(f) = X 1 p ;1 A j e A ;2ijft j=0 (5) wheref is frequency and t is sampling interval. Multichannel analysis of spread was performed using the directed transfer function (DTF) method developed by Kaminski and Blinowska (1991). The DTF function 2 ij describing ow from channel j to channel i is dened as the square of the absolute value of the complex transfer function of the AR model, 5

6 divided by the sum of these values for row i of matrix H. 2 ij(f) = jh ij (f)j P 2 m (6) k=1 jh ik (f)j 2 Therefore the sum of DTF from all channels contributing to any given channel is equal to 1: mx k=1 2 ik(f) =1 for i =1 ::: m (7) The variabilityof 2 ij is governed by the same factors that aect the variability of ordinary coherence. At present the program allows for analysis 2-16 channels of multichannel AR spectral analysis. The DTF derivation is presented in greater detail elsewhere (Kaminski and Blinowska, 1991). The integrated directed transfer function (IDTF) is computed by numerical integration of the DTF over a selected frequency band. The digitized data recorded by the Telefactor unit has a maximum bandwidth of 0.5 to 70 Hz and all patient data was stored in this format. With the DTF program any range of frequencies can be examined and analyzed. Visual analyses of the full ( Hz) power spectra and directed transfer functions for each analysis was performed prior to any selection to determine the appropriate frequency range for further analyses power spectra diminished dramatically above 25 Hz. In previous analyses of coherence during seizures, frequency bands of 1-25 Hz were found to be appropriate (Gotman 1983 Duckrow and Spencer 1992). 2 Results The DTF method measures ow of activity from one point to another. Obviously the DTF analysis reects only those points where data has in fact been sampled. For instance, if subdural grid contacts alone are sampled then the patterns of ow are relative to those surface contacts only no information is provided regarding deep sources. When recordings are made from combinations of subdural grids and depth electrode arrays, this allows for analysis of seizure propagation from the deep mesial temporal regions to the lateral temporal neocortex as well as spread over the grid surface. Fig. 2 illustrates some potential patterns of ow from selected contacts of the arrays. Fig. 3 illustrates an ictal recording from one patient as recorded from the combination of a 32 contact subdural grid array and two multicontact depth 6

7 Fig. 2. The directed transfer method is designed to measure ow of activity from each contact to other contacts. Diagram A shows potential patterns of ow from the deepest contact of a depth electrode array to other more supercial contacts as well as contacts of the subdural grid array overlying the lateral temporal cortex. Diagram B shows a potential pattern of ow of activity from two surface contacts (solid and dotted lines) to the other contacts of the subdural grid. electrode arrays. This combination of recording electrodes clearly shows the mesial temporal onset seen most prominently in the deepest contacts of the depth arrays. During the rst four seconds shown, there is some spread to the lateral temporal surface as recorded by the subdural grid array. After four seconds there is an abrupt transition to rhythmic regional activity. In applying the DTF method, it is important that the data segments selected for analysis be quasistationary. Care was taken to adjust time epochs so that such abrupt transitions of activity did not occur during the segments to be analyzed. For instance in Fig. 3A any of the rst four seconds provided suitably quasistationary data, but it would have been inappropriate to analyze the entire ve second interval as a single segment because of the abrupt transition. In Fig. 3B one, two orve second epochs could be selected for analysis because the rhythmic pseudoperiodic activity is suitably quasistationary for appropriate application of the DTF method. Fig. 4 illustrates the plots of Asymptotic Information Criterion (AIC see Eqn. 3 in methods) as a function of model order for multiple one second epochs from multichannel depth electrode recordings of the seizure illustrated in Fig. 3. The ability to determine a clear minimum provides for selection of the model order in the DTF method. The model order is a whole number in the two families of curves shown in Fig. 4 a model order of 4 or 5 is appropriate. With sixteen channels 7

8 Fig. 3. Ictal recordings from a 32 contact subdural grid over lateral temporal lobe cortex (T1- T22 not all contacts shown) in combination with two depth arrays, oneneartheamygdala (A1-A6 A1 deepest, A6 most supercial) and the other just posterior in the anterior hippocampus (HI-H6 H1 deepest). The two most supercial contacts of eacharray (A7, A8, H7, H8) are not included because of artifact. The ve second epoch shown in A is shortly after the onset of the seizure as seen in deepest depth contacts (A1, H1, H2 arrow). Spread to the lateral temporal cortex (e.g. T17, T25) is seen after one second. After four seconds there is spread of the seizure throughout the recording arrays. The horizontal bar is one second and marks the second of data analyzed by the directed transfer function in Fig. 6. The vertical bar in A is 1000 V. The next ve seconds (B) are continuous with panel A and show a continued regional seizure discharge involving both depth electrodes and the lateral temporal cortex. Clinically the patient experienced and aura of "strangeness" during the localized hippocampal activity, evolving to a motionless stare with unawareness and automatisms after temporal lobe spread. Data from the entire seizure were analyzed the horizontal bar in B marks the second of activity analyzed for Fig. 8. The vertical calibration bar in B is 2000 V. 8

9 Fig. 4. Asymptotic Information Criteria (AIC) as a function of model order. The nine plots in the upper portion of the graph are from nine consecutive seconds including the rst four seconds of the seizure illustrated in Fig. 3A, plus the ve one second epochs of EEG before the onset of the seizure (eight channel multichannel analysis). Appropriate model orders as determined from these estimates are 3 to 5 and each curve is relatively consistent. The lower family of plots is from six one second epochs after the seizure has spread regionally (includes the last second shown in Fig. 3A plus the ve seconds shown in Fig. 3B). (not shown) the model order is closer to 3. These model orders are consistent with previously reported model orders of between 3-10 for single channel EEG data and other signals up to four channels (Lopes da Silva and Mars 1987). As the number of channels increases, the model order typically decreases for a given time segment. As illustrated in Fig. 4 the model order is consistent from sample interval to sample interval. Samples from before and during the seizure do not reveal a major change in model order. Lower (more negative) values mean that the residual variance is smaller and the model is better suited to the data. The ability to choose a model order from the graphs of the AIC provides verication that the data is suitable for this autoregressive analysis. If epochs are inappropriately selected then the TIC graph may not have a clear minimum, continuing downward with increasing model order or having multiple minima. The lack of a clear minimum of the AIC may result from insuciently stationary data. In other instances even when data appears suciently stationary a lack of a clear minimum may suggest that additional data is necessary to best t the AR model. When no clear model order was apparent this data was not used for analysis. Fig. 5A illustrates a plot of AIC values as a function of model order for the second patient discussed below. After an apparent minimum at low model 9

10 Fig. 5. Asymptotic Information Criteria (AIC) as a function of model order. The fteen plots in A are from fteen consecutive seconds beginning with the ve seconds shown in Fig. 9A. This plot illustrates one pattern of the function with an early minimum and a later second minimum at higher model orders. The six plots in B are analyses using consecutive ve second intervals beginning with the panel shown in Fig. 9B. Here a single minimum is seen with model order about 3 to 4. orders the graph then continues downward. Although it has been suggested (Broersen and Wensink 1993) that selecting the early minimum yields an appropriate model order, in instances when AIC plots like these were obtained, these epochs (one second) were not analyzed using the DTF method. Fig. 5B illustrates the AIC values for the same data (and additional segments) analyzed in ve second epochs. These plots yielded a clearer minimum and these data (ve second epochs) were used for the DTF analyses. Fig. 6 shows a matrix of graphs of DTF functions. This is the typical format for display. In this instance the analyses were limited to the six contacts of the hippocampal depth electrode for purposes of illustration. In the groups of graphs shown, the diagonal DTF ( 2 ii) are not illustrated to allowdisplayofthe power spectra and because they do not reveal ow between channels. In this instance the rhythmic seizure activity early in the seizure is seen in peaks on the power spectra at 18 Hz. This activity is best seen in the power spectra of the deepest contacts (H1, H2) but also is present to a lesser degree in the other contacts. Each graph is the DTF for a pair of contacts, reecting patterns of ow of activity from the contact on the origin axis to the respective contact on the destination axis. Examination of the columns above each contact on the origin axis reveals patterns of ow from a given contact to other contacts. The column of graphs above H2 on the origin axis reveals that the 18 Hz activity ows from H2 to all other contacts. The most prominent peaks in the DTF graphs are seen in H2! H1 and H2! H3. To determine the most likely source the patterns of ow to immediately adjacent contacts should be 10

11 Fig. 6. Directed transfer function for the seizure activity recorded from the hippocampal depth electrode during the third second of the seizure shown in Fig. 3A. The power spectra for each depth electrode contact are on the diagonal. The peak on the power spectra at 18 Hz, is best seen in the deepest contacts (H1, H2 solid arrows) but also seen in the intermediate contacts (H3, H4). The open arrows identify prominent peaks in the DTF graphs corresponding to this peak in the power spectra (column H2). The most important peaks in the DTF graphs are these that have corresponding peaks in the power spectra. Peaks can be identied in the H5 column (open arrowheads) but there is no prominent peak at this frequency in the power spectrum for H5 only a small peak is seen (closed arrowhead). Each individual DTF is labeled to reect the pattern of ow shown (e.g. H1 H2). The model order was 5. The horizontal scale for each box is Hz. The vertical scale for the DTF is 0-1 (full scale). The power spectra are normalized to unit power. examined. In Fig. 6, the peaks seen in H1! H2 do not correlate as closely with the peak in the H1 power spectra as does H2! H1, supporting H2 as the predominant source of activity. At greater distances (e.g. H5 and H6), ow appears to be originating from both H2 and H1 sources. Following a row horizontally for a given contact on the destination axis reveals the relative contribution of activity from other contacts to that one selected contact. For instance for the 18 Hz band of activity most of the ow is from H2. The activity at each frequency is normalized according to the formula (Eqn. 3) for all DTF graphs in a given row. This allows for comparisons of relative contributions of 11

12 dierent channels at a given frequency. In examining peaks seen in various graphs it is important to also examine whether the peak in a given DTF graph corresponds to a peak in the respective power spectrum. This is illustrated in Fig. 6 for two instances. Because of normalization of the rows there can frequently be prominent peaks seen in the DTF graphs that do not correspond to the most prominent peaks in the power spectra (Fig. 6, open arrowheads). At other times the peaks seen in the DTF graphs may be close to but not correspond exactly to the peaks seen on the power spectra. As noted above (for column H1) this suggests that these contacts are not the primary source of the major activityidentied in the power spectra. When correlating the DTF graphs with the EEG, generally the prominent peaks in the power spectra identify the signals of greatest interest. While artifacts are generally much less common in intracranial recordings than in scalp recordings, these can occur due to contacts that may not be stable (e.g. over cerebral sulci, veins. etc.) If visual inspection of the ICEEG reveals channels that are frequently contaminated by artifact, these channels are not included in the analyses. The DTF method itself, however, can provide for discrimination of artifact even if not detected prior to analysis. When an isolated channel demonstrates prominent activity,yet the DTF analysis reveals no ow, then this activity is typically artifactual. Therefore an artifact might produce a prominent peak in the power spectrum of a given channel, but no ow of activity would be evident in the DTF analyses. The partial coherence functions for the same second of data analyzed for Fig. 6 are shown in Fig. 7. These are computed from the AR model according to previously published formulas (Franaszczuk et al. 1985). As such it is directly comparable to coherence measurements made from fast Fourier transforms (FFT). This analysis reveals high coherence between all contacts, particularly between adjacent electrodes. Because the pattern of graphs is symmetrical, however, no information about patterns of ow of activity can be determined. Expanding the analysis to 16 channels (the present limit of the program) permits the incorporation of more contacts into the patterns of ow and allows the illustration of patterns of ow between various contacts on the depth arrays and the subdural grid. Including subdural contacts into such expanded analyses (not shown) for the seizure epoch analyzed in Fig. 6 reveals that the deepest contacts of the depth arrays continue to be the source of the 18 Hz rhythmic activity. Later in the seizure (Fig. 3B) such expanded analyses can provide information about ow of activity that is not apparent from visual inspection. Fig. 8 illustrates the results of such an analysis. The predominant activity seen on the EEG is now a fairly regular, rhythmic 3-4 Hz activity. Visual examination of the EEG reveals a regional discharge localization of the origin of activity is dicult. Application of the DTF method, however, reveals that even at this time of regional activity, the mesial temporal region (H1, H3) 12

13 Fig. 7. Partial coherence for the third second of Fig. 3A as recorded from the hippocampal depth electrode, the same time period analyzed by the DTF method and shown in Fig. 6. Power spectra (PS) for each channel are on the diagonal. The horizontal scale for each box is Hz. The vertical scale is 0-1 (full scale). continues to be the most important source of the predominant frequency (now 3-4 Hz instead of 18 Hz). Even though the rhythmic activity is prominent over the lateral temporal cortex (subdural grid contacts), the DTF graphs in the columns above the selected subdural grid contacts are almost empty illustrating that there is little activity originating from these lateral contacts. Although the 16 channel limit of the current program prevents simultaneous inclusion of all subdural grid contacts, various combinations were examined (ultimately including all contacts) to ascertain that no subdural grid contact was a signicant source of activity. The DTF graphs for column H5 reveal peaks, but these occur in domains where there are no corresponding peaks in the power spectrum, therefore H5 is not a signicant source of predominant EEG frequencies (see also Fig. 6 and text). Indeed at the 3-4 Hz region the DTF graphs in column H5 show a relative dip, further supporting the origin of these frequencies from contacts other than H5. An ICEEG of a seizure from the second of three patients analyzed is shown in Fig. 9. A combination of depth and subdural grid arrays similar to the rst illustration was utilized. Again visual inspection of the seizure onset reveals a clear mesial temporal onset as reected by the initiation of the seizure in the deepest contacts of the depth arrays. This example was selected because of the coexistence of two predominant frequencies as the seizure evolved. Even thirty seconds into the seizure (not shown) the two frequencies persisted in contrast to the rst example (Fig. 3) when the seizure evolved to a regional discharge of 13

14 Fig. 8. Directed transfer functions for 16 channels (6 from hippocampal depth electrode and 10 selected from subdural grid array) for a one second period (Fig. 3B) eleven seconds into the seizure illustrated in Fig. 3. The power spectra for each contact is shown on the diagonal. The predominant peak seen on the ICEEG is now alow frequency peak this is seen in the power spectra of all channels. Examination of the columns illustrates that, although there is considerable activity in this band in all channels, it originates almost exclusively from the depth electrode contacts (most prominently H1, arrow). Indeed the DTF columns for the subdural grid contacts are almost empty. This indicates that, although there is considerable activity recorded from the lateral temporal cortex, it is still owing from the deeper regions of the temporal lobe monitored by the depth electrodes. The model order was 3. The horizonal scale for each box is Hz. The vertical scale is normalized for each row. a predominant frequency domain. The following DTF analysis illustrates the ability of this method to determine the origins of ow of concurrent activity of dierent frequencies. The 16 channel DTF analysis for a one second epoch near the onset of the seizure is illustrated in Fig. 8. The characteristics of this matrix of DTF graphs are similar to those of Figs. 6 and 8. The power spectra for the respective channels are again on the diagonal. The predominant peak of activity at Hz originates from the deeper depth contacts, particularly H2 and H4. The contacts from the other, more anterior depth array were not incorporated in 14

15 Fig. 9. Ictal recordings from 32 contact subdural grid over the lateral temporal lobe cortex (T1-T31 T32 was artifact), and two depth electrodes placed through the grid. The most anterior depth electrode (A) had its deepest contacts near the amygdala, the posterior electrode (H) was in the anterior hippocampus. About 7 mm separated the tips of the two depth electrodes. Panel A illustrated show the seizure several seconds after onset from a mesial temporal focus with a predominant (12-14 Hz discharge). Panel B, continuous with panel A reveals further evolution of the seizure with a lower frequency (4-5 Hz) discharge seen on the subdural grid contacts. The horizonal bar marks the one second of the seizure utilized for the DTF analysis in Fig. 10. this display. Other DTF analyses (not shown) revealed similar patterns of activity and spread from each depth array. By incorporating only one depth array in the 16 channel analysis, more surface contacts could be included. An analysis of this seizure several seconds later is shown in Fig. 11. The

16 Fig. 10. Directed transfer functions for 16 channels (8 from hippocampal depth electrodes and 8 selected from subdural grid array for a one second period (Fig. 9A) near the onset of the seizure illustrated in Fig. 9. The power spectra for each contact is shown on the diagonal. The predominant peak seen on the ICEEG is the Hz peak this is most prominent in the power spectra from deep hippocampal contacts. The predominant source of this activity can be found on the origin axis, where H2 and H4 are the greatest contributors (solid arrows). The model order is 3. The horizonal scale for each box is Hz. The vertical scale for DTF is 0-1 the power spectra are normalized to unit power. Hz activity is now fairly restricted to the deepest hippocampal contacts H1- H3. The low frequency activity seen on the surface, recorded by the subdural grid array has the H5 contact, an intermediate depth contact, as the most prominent source. This source is more supercial than the source of the higher frequency activity. Whether H5 represents a focus in a deep cortical layer or a sulcus cannot be determined. Some lesser surface contributions can be seen, particularly from contact T19. Although the 16 channel analysis limited the number of lateral temporal contacts that could be analyzed and displayed, multiple DTF analyses were performed to incorporate all subdural contacts. No other lateral temporal contacts were a predominant source of the low frequency activity. A ve second epoch was used for analysis of the seizure activity shown in Fig. 9B. When only one second epochs were utilized the AIC minimum was less clear (Fig. 5A) than ve second analyses which produced a 16

17 Fig. 11. Directed transfer functions for 16 channels (8 hippocampal depth and 8 subdural grid) for the ve second epoch illustrated in Fig. 9B. The power spectra (PS) for each contact is shown on the diagonal. The solid arrow illustrates the greatest contributor (H5) to the most prominent low frequency peak of the power spectra. The model order is 4. The horizonal scale for each box is Hz. The vertical scale for DTF is the power spectra are normalized to unit power. clear AIC minimum for determination of model order (Fig. 5B). Another method of data display is the integrated directed transfer function (IDTF). These analyses numerically integrate activity over a selected bandwidth providing a relative contribution from each contact on the origin axis. The IDTF for the ve second seizure epoch in Fig. 9B is shown in Fig. 12. The IDTF provides conrmation that H5 is the most prominent source of the low frequency activity. Of the subdural grid contacts, T19 is the most important contributor, but still less than H5. Selection of the appropriate bandwidth for integration is critical. When multiple frequencies are prominent in the ICEEG, as in this second patient, a broad band analysis for the IDTF may give misleading information and a narrower band should be selected. The band selected was Hz because the predominant activity was at 3-4 Hz. Although at times providing a clearer graphic display of overall activity the IDTF does not allow for determinations of origins of specic frequencies. The DTF typically provides more detailed information than does the IDTF because origins of 17

18 Fig. 12. Integrated directed transfer function (IDTF) for the ve second epoch shown in Fig. 9B and analyzed by the DTF method in Fig. 11. Frequencies from Hz are shown as the band integrated directed transfer function. The diagonal bins are set to zero. The vertical axis shows the average DTF for the frequency band. multiple frequencies can be seen and correlated with the power spectra. Data from one seizure from each of two patients are illustrated above the other recorded seizures in each patient were similar in their patterns of origin and propagation. A third patient with combined depth electrode and subdural grid recordings of complex partial seizures originating from mesial temporal structures was analyzed. Again the DTF analysis revealed patterns of ow of activity similar to the two illustrated patients. 3 Discussion The ability to localize seizure foci is an important criteria for the successful application of seizure surgery for control of medically refractory seizures. While a number of seizures can be identied and localized with some combination of EEG recording methods, some seizures can be dicult to localize even with intracranial electrodes. Indeed a recent report (Matsuoka and Spencer 1993) found that in patients with partial seizures originating from lateral temporal and extratemporal regions only 15of the patients had lesions demonstrated 18

19 on MRI. Presumably these seizures are spreading regionally so rapidly that visual analysis of these records cannot yield localizing information. Additional methods for localization would clearly be of benet. Although a number of parametric methods have been applied to ictal EEG analysis (Gotman et al. 1993), most of these have been used for spike and seizure detection rather than localization since these methods do not permit detection of patterns of ow of activity. Utilization of autoregressive models for EEG analysis is becoming increasingly popular with the availability of appropriate programs and computational ability. From coecients of the AR model, power spectra, coherence and phase spectra can be computed. Neuronal synchronization between dierent regions of the brain during seizures can be analyzed by coherence analysis of multichannel data however, this method does not demonstrate patterns of spread. The analytic methods of multilag crosscovariance functions of Gevins (1989), coherence/phase analysis (Gotman 1983), and coherence comparisons provide information regarding neuronal synchronization these methods do not directly yield information regarding ow of activity. Phase measurements, when resulting in linear phase spectra, can provide information regarding time delays between contacts (Gotman 1983). Directed coherence methods (Saito and Harashima 1981 Wang and Takigawa 1992), also based on an AR model, reveals some information about ow of activity but are limited to analysis of ow between two channels. Coherence/phase analysis is also limited to simultaneous analysis of only two channels and requires longer epochs of quasistationary data (Gotman et al. 1993). Inferences about spread of activity are based on sequential analysis of channel pairs over a broad range of frequencies. Nonlinear measures of correlation (Pijn et al. 1989) have been also applied to measure delays between two channels to infer patterns of spread of activity. With methods limited to analysis of only two channels, it is necessary to compare all possible pairs of channels to determine potential patterns of spread (Lieb et al. 1987). The DTF method provides for a determinations of patterns of ow of activity from simultaneous measurements from multiple channels. This method not only greatly facilitates multichannel analysis, but avoids the potential misleading information regarding ow that could result from sequential pair analyses. The autoregressive model used in the studies reported here is based on a linear correlation analysis. While patterns of brain activity are frequently nonlinear, it is not yet established whether linear or nonlinear methods are best for EEG and seizure analysis. Even, however, if one assumes that the brain is nonlinear or chaotic, much of the output from the brain can be analyzed using linear stochastic methods, providing certain basic considerations are applied. Signals such asinterictal spikes are clearly not appropriately analyzed using linear methods. Nonlinear methods are required for analysis when the adjacent channels are not highly correlated. When high correlation exists, the more readily applied linear analyses are sucient (Allen et al. 1992). In 19

20 the recordings presented here for DTF analysis, the high coherence between channels (Fig. 7) indicates high correlation. The ability to use linear models instead of nonlinear models for analysis allows one to draw upon considerable previous theoretical and applied research and also has the practical benet of greatly facilitating computation. As described above, segmenting the ictal EEG into quasistationary segments and avoiding abrupt transitions during the sampling interval permits autoregressive analyses. Although automatic segmenting algorithms exist (Kitagawa and Akaike 1978), visual selection was sucient here. The calculation of the AIC and its plot relative to model order provides further validation of the appropriateness of the analyses. Signals that are not appropriately analyzed with the autoregressive method will not have a readily apparent minimum and model order. Changes in model order during seizures have been reported for single channel EEG analysis (Hilker and Egli 1992), but this is because the AR model is not the best model for analysis of single channel data and requires relatively large model orders. The multichannel autoregressive model has autospectra with more degrees of freedom than single channel autoregressive autospectra and thus is appropriate for ictal analysis. The ability to choose a model order from the graphs of the AIC plots provides for verication that the data is being appropriately selected for this autoregressive analysis. As shown (Fig. 4), the model order during DTF analysis remains stable during ictal transition. The purpose of this initial report is to provide validation of the appropriateness of the directed transfer function method to human intracranial ictal recordings and to illustrate the important considerations and characteristics of application. Therefore examples were selected where the visual analysis of the ictal recordings clearly illustrated a mesial temporal onset of the seizures with subsequent spread. In patients like these the DTF method is able to clearly demonstrate that the deep mesial structures are the source of seizure activity. More importantly, even these initial applications of the DTF method have demonstrated that the DTF method can provide information regarding ow that are not readily apparent from visual inspection. As the seizure activity spreads regionally, the DTF method can determine whether the initial focus continues to be the source ofagiven frequency (as illustrated by the rst patient) or whether other more remote areas become secondary generators (as in the second patient illustrated). Whether such secondary generators could at a later time become independent seizure foci is an important question in patients with longstanding seizure disorders. The ultimate goal is for applications of the DTF method or similar autoregressive analyses to provide insights into sources of seizure activity in seizure originating from lateral temporal, frontal and parietal regions where presumed rapid regional spread often precludes accurate localization by visual analysis. 20

21 These seizures often begin with broad regional low voltage fast activity, a pattern that should be suitably quasistationary to allow appropriate application of the DTF method for analysis. The frequently associated regional electrodecremental responses seen at the onset of these seizures should not be problematic since the DTF method does not rely upon or utilize amplitude criteria. The current limitations of 16 channels of simultaneous analysis are being addressed (Franaszczuk and Bergey, unpublished data). However, some expansions of these multichannel analyses may be restricted by the required length of quasistationary data needed to achieve appropriate model order. Clinical applications of the DTF method could be facilitated by the development of modied displays. The IDTF histograms may, however, sacri- ce some frequency information to achieve this more readily visualized format. The DTF method could conceivably be extended to analyses of nonlinear phenomena by incorporating nonlinear correlation functions (Pijn et al. 1989) or applying nonlinear autoregressive modeling (Victor and Canel 1992), although this latter application is more complicated for multichannel data. Acknowledgement The authors wish to thank Drs. E. Barry, A. Krumholz, and A. Wolf for their participation in the clinical management of these patients and C. P. Fleming, R.EEGT. and E. Frear, R.EEGT. for their helpful assistance in the initial processing of the ICEEG data. We would like to recognize the contributions of Prof. K. J. Blinowska to the development of the directed transfer function method. References [1] P. J. Allen, S. J. M. Smith, and C. A. Scott, Measurement of interhemispheric time dierences in generalized spike-and-wave, Electroenceph. clin. Neurophysiol., 82 (1992) 81{84. [2] E. Barry, A. L. Wolf, S. L. Huhn, G. K. Bergey, and A. Krumholtz, Presurgical evaluation of patients with refractory complex partial seizures using simultaneous subdural grid and depth electrodes, J. Epilepsy, 5 (1992) 111{118. [3] P. M. T. Broersen and E. Wensink, On nite sample theory for autoregressive model order selection, IEEE Trans. Signal Process., 41 (1993) 194{204. [4] G. Dahlquist and A. Bjorck, Numerical Methods, (Prentice-Hall, Englewood Clis, NJ, 1969). 21

22 [5] R. B. Ducrow and S. S. Spencer, Regional coherence and the transfer of ictal activity during seizure onset in the medial temporal lobe, Electroenceph. clin. Neurophysiol., 82 (1992) 415{422. [6] P. J. Franaszczuk, G. K. Bergey, and M. Kaminski, Multichannel autoregressive analysis of mesial temporal seizures using the method of directed transfer functions, Epilepsia, 34(Suppl. 6) (1993) 125. [7] P. J. Franaszczuk, K. J. Blinowska, and M. Kowalczyk, The application of parametric multichannel spectral estimates in the study of electrical brain activity, Biol. Cybern., 51 (1985) 239{247. [8] A. S. Gevins, Signs of model making by the human brain, in: E. Basar and T. Bullock, eds., Springer Series in Brain Dynamics, vol. 4ofSpringer Series in Brain Dynamics, (Springer, Berlin, 1989) 408{415. [9] J. Gotman, Measurements of small time dierences between EEG channels: method and application to epileptic seizure propagation, Electroenceph. clin. Neurophysiol., 56 (1983) 501{514. [10] J. Gotman, R. C. Burgess, T. M. Darcey, R. N. Harner, J. R. Ives, R. P. Lesser, J. P. M.Pijn,andD.Velis, Computer applications, in: J. Engel Jr., ed., Surgical treatment of the epilepsies, (Raven Press, New York, 1993) 429{439. [11] P. Hilker and M. Egli, Detection and evolution of rhythmic components in ictal EEG using short segment spectra and discriminant analysis, Electroenceph. clin. Neurophysiol., 82 (1992) 255{265. [12] M. Kaminski and K. J. Blinowska, A new method of the description of the information ow in the brain structures, Biol. Cybern., 65 (1991) 203{210. [13] G. Kitagawa and H. A. Akaike, A procedure for the modeling of non-stationary time series, Ann. Inst. Statist. Math., 30 (1978) 351{363. [14] J. P. Lieb, K. Hoque, C. E. Skomer, and X. W. Song, Inter-hemispheric propagation of human mesial temporal lobe seizures: a coherence/phase analysis, Electroenceph. clin. Neurophysiol., 67 (1987) 101{119. [15] F. H. Lopes da Silva and N. J. I. Mars, Parametric methods in EEG analysis, in: A. S. Gevins and A. Remond, eds., Methods of analysis of brain electrical and magnetic signals. EEG Handbook, vol. 1 of revised series, (Elsevier, Amsterdam, 1987) 243{260. [16] S. L. Marple, Digital Spectral Analysis with Applications, (Prentice-Hall, Englewood Clis, N.J., 1987). [17] L. K. Matsuoka and S. S. Spencer, Seizure localization using subdural grid electrodes, Epilepsia, 34(Suppl. 6) (1993) 8. [18] S. V. Pacia and J. S. Ebersole, Temporal neocortical epilepsy syndrome: intracranial EEG identication, Epilepsia, 34(Suppl. 6) (1993) 26{27. 22

23 [19] J. P. M. Pijn, P. C. M. Vijn, F. H. Lopes da Silva, W. Van Emde Boas, and W. Blanes, The use of signal analysis for the localization of an epileptogenic focus: a new approach, in: J. Manelis, E. Bental, J.N. Loeber, and F.E. Dreifuss, eds., Advances in Epileptology, XVIIth Epilepsy Int. Symp., (Raven Press, New York, 1989). [20] L. F. Quesney, M. Constain, and T. Rasmussen, Seizures from the dorsolateral frontal lobe, in: P. Chauvel, A.V. Delgado-Escueta, E. Halgren, and J. Bancaud, eds., Frontal Lobe Seizures and Epilepsies, vol. 57 of Advances in Neurology, (Raven Press, New York, 1992) 233{244. [21] M. W. Risinger, J. Engel Jr., P. C.Van Ness, T. R. Henry, and P. H. Crandall, Ictal localization of temporal lobe seizures with scalp/sphenoidal recordings, Neurology, 39 (1989) 1288{1293. [22] Y. Saito and H. Harashima, Tracking of information within multichannel EEG record- casual analysis in EEG, in: N. Yamaguchi and K. Fujisava, eds., Recent Advances in EEG and EMG data processing, (Elsevier, Amsterdam, 1981) 133{ 146. [23] M. Sammaritano, A. De Lotbiniere, F. Andermann, A. Olivier, and P. Gloor amd L. F. Quesney, False lateralization by surface EEG of seizure onset in patients with temporal lobe epilepsy and gross focal cerebral lesions, Ann. of Neurol., 21 (1987) 361{369. [24] S. S. Spencer, P. D. Williamson, D. D. Spencer, and R. H. Mattson, Combined depth and subdural electrode investigation in uncontrolled epilepsy, Neurology, 46 (1990) 74{79. [25] J. D. Victor and A. Canel, A relation between akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG, Ann. Biomed. Eng., 20 (1992) 167{180. [26] G. Wang and M. Takigawa, Directed coherence as a measure of interhemispheric correlation of EEG, Int. J. Psychophysiol., 13 (1992) 119{128. [27] H. G. Wieser, J. Engel Jr., P. D. Williamson, T. L. Babb, and P. Gloor, Surgically remediable temporal lobe syndromes, in: J. Engel Jr., ed., Surgical treatment of the epilepsies, (Raven Press, New York, 1993) 49{63. [28] P. D. Williamson, Frontal lobe seizures: problems of diagnosis ans classication, in: P. Chaauvel, A. V. Delgado-Escueta, E. Halgren, and J. Bancaud, eds., Frontal lobe seizures and epilepsy, vol. 57 of Advances in Neurology, (Raven Press, New York, 1992) 289{309. [29] P. D. Williamson, P. Boon, V. M. Thadani, T. M. Darcey, D. D. Spencer, S. S. Spencer, R. A. Novelly, and R. H. Mattson, Parietal lobe epilepsy: diagnostic considerations and results of surgery, Ann. Neurol., 31 (1992) 193{