Extraction of spatio-temporal signatures from depth EEG seizure signals based on objective matching in warped vectorial observations

990 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 43, NO. 10, OCTOBER 1996

Fabrice Wendling,* Jean-Jacques Bellanger, Jean-Michel Badier, and Jean-Louis Coatrieux, Fellow, ZEEE

Abstruct- In the field of epilepsy, the analysis of slereoelec- troencephalographic (SEEG) signals recorded with depth electrodes provides major information on interactions between brain structures during seizures. A comprehensive methodology of comparing SEE6 seizure recordings is presented. It proceeds in three steps: 1) segmentation of SEEG signals; 2) characterization and labeling of segments; and 3) comparison of observations coded as sequences of symbol vectors. The third step reports a vectorial extension of the Wagner and Fischer’s algorithm to first, quantify similarities between observations and second, extract invariant sequences of events, referred to as spatio- temporal signatures. The study shows that two observations of nonequal duration can be matched by deforming the first one to optimally fit the second, under cost constraints. Results show that the methodology allows to exhibit signatures occurring during epileptic seizures and to point out different types of seizure patterns. The study brings objective results on reproducible interactions between brain structures during ictal periods and may help in the understanding of epileptogenic networks.

I. INTRODUCTION BOUT 0.5-1% of the population suffers from epilepsy, which is, next to strokes, the most common neurological

disease [ 11. Epilepsy is the result of abnormal synchronous discharges in large ensembles of neurons in brain structures. These discharges may be caused by many factors like trauma, tumors, and infections. However, in about half of the pa- tients no specific causative factors are found. The disease is characterized by epileptic seizures during which stereotyped and uncontrolled alterations occur in the behavior of the patient. These symptoms, also called “clinical signs,” vary strongly from one patient to another depending on the brain site affected by the original paroxystic discharge and its propagation through the brain.

Methods of investigation used in epilepsy are aimed at better defining and understanding the epileptogenic area [2] and can possibly lead to surgical treatment [3], [4]. These methods may be divided into three groups, depending on the type

Manuscript received June 5 , 1995; revised March 18, 1996. Asterisk indicates corresponding author.

*F. Wendling, is with the Laboratoire Traitement du Signal et de L’Image. INSERM CJF 93-04, Universitt de Rennes 1, Campus de Beaulieu, Bat. 22. 35042 Rennes Cedex, France (e-mail: [email protected] .fr).

J.-J. Bellanger and J.-L. Coatrieux are with the Laboratoire Traitement du Signal et de L’Image, INSERM CJF 93-04, Universitt de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France.

J.-M. Badier is with the Unitt d’Epileptologie Clinique, Service de Neu- rologie, CHR de Pontchaillou, 35033 Rennes Cedex, France.

Publisher Item Identifier S 0018-9294(96)07256-4.

of data they provide: anatomical, clinical, and physiological. Anatomical data are provided by imaging techniques [5]-[7] [magnetic resonance imaging (MRI), computed tomography (CT) scanning] that may localize brain disorders (like tumors, for instance) that produce epileptic discharges. The study of ictal signs and symptoms provides clinical data. The method consists of analyzing signs (gestural automatisms, tonic contractions, auditory hallucinations ...) occurring just at the beginning, during, and just after seizures in order to localize the brain site originally initiating the discharge and to identify the brain structures secondarily implied in the disease. Readers can refer to [SI and [9] for more detailed information on the classification of epilepsies based on symptoms and signs. Magnetoencephalography (MEG), elec- troencephalography (EEG), and stereoelectroencephalography (depth recording) provide physiological data in the form of time series signals which are, in fact, the only true time markers of brain activities.

Correlations between electrical (EEG, SEEG) and clinical data are of major importance in the understanding of the epileptic discharge propagation through brain structures [ 101. Usually, long-term monitoring systems [l 11, [12] are used to record the patient’s seizures with the corresponding EEG or SEEG signals on a same medium (videotape, for example). Detailed analysis of recordings of both seizure signs and electrophysiological signals not only allows the construction of hypotheses on possible paths of discharge propagation but also emphasizes reproducible phenomena which characterize epileptic processes. For a given patient, reproducible sequences of clinical signs may often be observed for different ictal periods [ 131. However, isolating precisely reproducible phenomena in EEG signals from different recordings remains a difficult task, especially in SEEG, where the signals are recorded from a hundred sensors located in the brain (Fig. 1 gives a schematic representation of the SEEG technique). Consequently, the following question still stands: is it possible, for a given patient, to find periods of time where signals recorded during seizures seem to conjointly reflect the same underlying neurophysiological mechanisms? A corollary to this question can also be: how can differences between seizure signals be interpreted?

Automatic seizure detection methods [ 141 as well as graphic representations of epileptic seizures [ 151 have already been described. However, the study of correspondences between recordings was not the intent of these papers. Methods of

0018-9294/96$05.00 0 1996 IEEE

WENDLING et al.: EXTRACTION OF SPATIO-TEMPORAL SIGNATURES FROM DEPTH EEG SEIZURE SIGNALS 99 1

1 I . \ - \ \

Fig. 1. The stereoelectroencephalographic technique (SEEG). Five to ten electrodes are implanted in a brain region. Ten to 15 sensors record signals from the different brain structures encountered along each electrode.

pattern recognition applied to seizure EEG have also been developed [16]. Still, the goal of these methods is more the identification of significant graphoelements in seizure signals than the comparison of signals from different seizures.

The present paper describes a comprehensive method of comparing SEEG recordings in order to: 1) quantify the degree of similarity between them and 2 ) extract reproducible sequences of events from them. These sequences are referred to as spatio-temporal signatures because they mark (or "sign") epileptic mechanisms in their spatial (the events occur in different brain structures) and temporal (the events occur in a given time order) dimension.

The paper is organized as follows. The first part gives the overview of the method: formalization of the problem, segmentation, characterization, and coding of seizure observations. The second part details the approach used to establish relationships between labeled data in order to extract signatures. The whole methodology is then exemplified through the analysis of five SEEG seizure recordings (from temporal lobe epilepsy). Results are described in the third part. The discussion deals with the potential use of the method to: 1) localize similar epileptic mechanisms reflected by similar signals; 2) define and evaluate a cost distance between recordings: and 3) point out general seizure patterns in certain types of epilepsies.

11. METHOD OVERVIEW SEEG is a clinical method of investigation used in epilepsy.

It consists in recording signals simultaneously from brain

structures by means of depth electrodes. For a given patient, this technique can provide a number of seizure signals recordings from 60-120 sensors located along the electrodes. Fig. 1 gives a schematic diagram of the SEEG technique through an example of two electrodes implanted in the temporal lobe of a left cerebral hemisphere.

Searching invariant information in multi-channel SEEG signals requires relating vectorial observations. This is the major difficulty of the problem. Signatures to be found are similar (and unknown) sequences of events occurring in different recordings, on the same sensors and according to a certain time order. In other words, the methodology must allow to establish relationships between observations of nonequal duration.

A. Problem Statement

A set of M observations O", e = l . . . M , is considered. Each observation 0" is chosen in SEEG recordings (performed during seizures) from sensors implanted in the patient's brain

where time periods [0, Te] may have different values from one observation to another. For given e and k , the signal o z ( t ) is regarded as the juxtaposition of periods of time for which the recorded ensemble of neurons acting on sensor k obeys a certain type of steady dynamics. In other words, the signals are assumed to be as piecewise stationary. These considerations allow the introduction of the following.

1) A segmentation of signals o z ( t ) on partitions {OZ( i ) , i = 1 .. 'n , ; } of time intervals [O, Tel. This leads to the following representation

A A where S;,(t) = o;( t ) if t E O; ( i ) , and Si,@) = 0 otherwise.

2) A grouping of all segments S;,(t) into a small number of classes arbitrarily marked a, b, c. . . Each of these classes, interpreted as a steady type of dynamics, can be considered as an element of a finite set D = {a, b, c. . .}. Assuming 2), it can be considered that at time t , the ensemble of neurons which acts locally on sensor k , generates a signal whose dynamics corresponds to an element of D. Thus, for each observation Oe, one can introduce a vectorial process Q"( t ) taking values into D N . Q e ( t ) represents on [0, T,] the evolution of a "global dynamical process" which takes into account all cerebral areas recorded by the N sensors.

Hence, the problem can be stated as follows: Given two observations O e ( t ) and Oe'( t ) with nonequal duration, the process of finding optimal correspondences between 0" ( t ) and

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 43, NO. 10, OCTOBER 1996

Oe’(t) , is equivalent to finding a sequence of pairs of time intervals on which the vectorial processes Q e ( t ) and Qe’(t) are close (in terms of a distance) on a maximal number of sensors.

B. Method As shown in Fig. 2, the proposed method proceeds in

three steps that consist in: 1) delimiting segments S,&(t) by segmentation of signals 0; ( t ) ; 2) characterizing and coding the dynamics of each segment using elements of set D; and 3) relating observation Oe( t ) to observation Oe’(t) , both coded as sequences of symbol vectors, in order to quantify possible similarities and extract invariant information.

1) Delimiting Segments Sg,(t): SEEG signals have dynamical features which depend on the brain structure they are recorded from [17]. Signals from intemal structures (nu- clei, hippocampus, for example) seem to present “nonlinear” characteristics when exhibiting patterns that cannot be easily synthesized by linear gaussian models. These patterns were not encountered in signals from external structures (lateral neocortex, for example) which generally resemble those recorded on the scalp with classical EEG. This is illustrated in Fig. 2(a) which shows SEEG signal recorded from internal brain structures (sensor 3: corpus amygdaloideum) and from external structures (sensor 1: lateral cortex of the temporal lobe).

Segmentation methods based on detection of changes in autoregressive (AR) models [18], [19] give good results on EEG signals [20], [21]. However, and for the above reasons, these methods cannot be easily applied to intemal SEEG signals. Parameters such as the window size, threshold or bias in cumulative sums are difficult to adjust and often lead to over-segmentation when used on the whole duration of the recording without any parameter re-adjustment. Consequently, we developed a simple adaptative segmentation method which gives satisfying results in all situations, with, of course, a loss of accuracy (compared to parametric methods) in the estimation of the change instant. The method is based on the detection of changes in the mean of a statistic that reflects the average rhythm of the signal. The detection of changes is ensured by a Page-Hinkley algorithm [22]. A major advantage of the method used is that the resulting instants of changes are essentially linked to frequency changes (a key parameter in EEG analysis) and are not linked to amplitude changes which are considered to have less interest for the clinical analysis. Results obtained with this method on SEEG signals are in agreement with the interactive delineation performed by EEG experts. A study of performances (according to the criterion False alarm rate versus Mean delay for detection) was also performed and showed that the method may be less accurate than the 2-model method proposed by Basseville et al. [18] but is more robust with respect to the type of change and easier to carry out. The segmentation method, which is not the main topic of this study, will not be detailed in this paper but, for illustration, Fig. 3 shows its behavior on a signal o i ( t ) along with the resulting segments Si, ( t ) .

2 ) Characterizing and Coding Segments S,& (t): a) Characterization: To assign a class (chosen in set 0)

to each segment, a data analysis (linear discriminant analysis

Sensor 1

Sensor 2

Sensor 3

I 76 78 80 82 84 86 88 90 e2 84 88 88 Iw 102 1 0 4

Segment characterization

1 I I I

I I Sensor 2

U Sensor 3

L (C)

Sensor

Sensor

Sensor

2

3

* t , 4; 45 4; . . ’ . . . 474, Sequence rliy

(d) Application of Wagner & Fisher’s algorithm to sequences of symbol vectors

Fig. 2. Method used to relate SEEG observations: (a) original SEEG ohser- vations, (b) segmentation of signals and classificatlon of segnients, (c) coding of the observations as sequences of symbol vectors, and (d) application of Wagner and Fischer’s algorithm to coded observations.

based on a generalization of the Mahalanobis distance) is achieved on the whole set of segments Sg,(t). It proceeds in two steps: first, a feature selection allows to choose the most discriminant noncorrelated parameters to describe the

WENDLING et al.: EXTRACTION OF SPATIO-TEMPORAL SIGNATURES FROM DEPTH EEG SEIZURE SIGNALS 993

TABLE I METHODS USED TO CHARACTERIZE SEEG SEGMENTS. AFTER DATA ANALYSIS, THE FINAL FEATURE VECTOR (USED FOR THE CLASSIFICATION) W A S REDUCED TO 12 PARAMETERS (THOSE WRITTEN IN BOLD ITALIC) FROM THE 18 LISTED IN THE TABLE

Example of SEEG segment Characterization methods Feature vector

Spectral features.

(0-ZHZ, 2 3 . 5 H Z . 3.5-5.5HZ, SS-~SHZ, 7.5-10H~. 10-12.5H~, 12.5-1 ~ H z , 16-24H~. 24-1 OOHZ)

Linear approximation of the segment

Morphological features.

- Mean number of zero-crossings - Mean number of extrema - Mean duration of monotonies - Mean duration of phases - Mean amplitude of monotonies

1 0 1 5 2 0 2 5 30 36 4 0 4 5 5 0 Time

Higher order spectral moments Features based on spectral moments (Hjorth descriptom).

-activny= a0 I ExDresslon of the sDectral moment of order n :

spectral and morphological content of each segment (as shown in Table I) and second, a supervised (with help of the expert) classification of feature vectors allows to group segments into a small number of classes. Fig. 2(b) shows examples of classified SEEG segments (recorded from internal and external structures) and presents the corresponding classes. Letters assigned to each cluster were arbitrarily chosen.

b) Coding: Seizure periods [0, Te] are partitioned into intervals S;, z E 1.. .1, , of equal length 6 (assumed to be small when compared to the actual duration of transitions between segments). Then, a sequence q:, i E 1. . .1 , , of vectors taking values into D N , is associated to each vectorial process Qe( t ) : for i E 1 . . . l e , 4: = Q e ( t ) if t E 6: (a round off procedure is applied in the rare cases where Q e ( t ) is not constant on SF). By doing so, each observation O e ( t ) becomes a matrix of symbols whose lines correspond to original SEEG segments coded as sequences of symbols and whose columns correspond to process Q e ( t ) sampled as a sequence 4: of vectors of symbols. Fig. 2(a)-(c) summarizes the operations through which each observation O e ( t ) is transformed into a sequence 4: of symbol vectors.

3) Confronting Coded Observations: Observations do not necessarily have the same duration and, moreover, sequences to be extracted (signatures) have elements (vectors) that do not appear at synchronous instants. This is the major constraint. Indeed, the method used to relate one observation to another cannot be a simple time to time comparison and must allow deformations (or warping) along the time axis (seizures of a given patient do not necessarily have the same duration). The method we propose to achieve this goal is described in details in the next section.

111. FINDING OPTIMAL MATCHING BETWEEN CODED OBSERVATIONS

The approach used to establish relationships between observations belongs to the set of syntactic methods. Applications of syntactic analysis technique to EEG signal have been reported [23], [24]. Usually, a syntactic grammar is derived from primitive sequences and used to parse normal and abnormal EEG’s [25]. In this paper, the problem we address is different: given two seizure SEEG observations coded as sequences of symbol vectors, the objective is to automatically: 1) estimate the degree of resemblance between two observations; and 2) extract from these two observations an optimal common sequence of vectors ordered in time and exhibiting a maximal number of identical coordinates. A solution to this problem is based on the computation of the edit distance between matrices of symbols. To perform this computation, a vectorial extension of the algorithm proposed by Wagner and Fischer [26] was developed.

A. The Original Algorithm

The algorithm determines the “distance between two strings of symbols as measured by the minimum cost sequence of ‘edit operations’ needed to change one string into the other” [26]. Considered edit operations include deletions, insertions, and substitutions of symbols in the first string to match the second one.

An edit distance can be defined and computed [26] from “traces” where a trace, TA, B , from sequence A to B, is a sequence of ordered pairs of integers ( i , j ) satisfying the following.


- L N O

Fig. 3. Segmentation of SEEG signals with respect to variations of rhythm.

1) i = l...IA/; j = l...IBI . 2) For any two pairs ( i , j) and (2, j') in TA,B, i < i' +

j < j', the progression in traces is always from left to right and lines of traces never cross.

The cost of trace TA.B is defined as follows:

cost (T) =

where y(A, i B3) is the cost for substituting symbol A, for B,, ?(A, i A) is the cost for deleting symbol A, and y(X i B,) is the cost for inserting symbol B,.

X is the null sequence, 1x1 = 0, I and J are the sets of positions of symbols A, and B,, respectively, which are not related through T .

An important result of [26] relates the edit distance to the trace: the edit distance from A to B is equal to the cost of a least cost trace from A to B.

Wagner and Fischer also showed that longest common subsequences may be derived from traces if insertion, deletion, and substitution costs verify the following relations.

1) $A, i B,) = 0 if A, = B,. 2 ) $A, + B3) = $A, + A) + r ( X 4 B,) if A, # B,. Fig. 4 illustrates the application of this algorithm on two

sequences A and B.

B. Extension to the Computation of the Edit Distance Between Matrices

In our case, observations are coded as sequences of vectors and are, in fact, matrices with identical number of lines. The edit distance will be used to quantify the degree of correspondence between matrices. A small distance will denote a small transformation cost from a matrix to another. This also means strong similarities between the two.

To find the edit distance between matrices M ( p , m) and M'(p, m'), edit operations with respective costs are intro- duced as follows:

* given the two matrices

M =

and

all a21

a P 1

b l l b2l

1$1

i I . . .

9 . . . apm U 2

995 WENDLING et al.: EXTRACTION OF SPATIO-TEMPORAL SIGNATURES FROM DEPTH EEG SEIZURE SIGNALS

(4 A:[aI [bl c [dl d (b)

I \ I T B : [a] c (bI [d] e e

T = l - I , 3 -2 , 4 - 3 , 5 - 4

A = abcdd * B = acbdee a - + a h + c b + b c - + h d + d d - + ) i k - + e h + e

(4

Fig. 4. Wagner and Fischer’s algorithm: (a) editing path between sequences A and B, (b) a least cost trace from A to B, and (c) the corresponding sequence of edit operations. Diagonal, horizontal, and vertical paths segments in (a) correspond to substitution, insertion, and deletion operations, respectively. Symbols between brackets compose the longest common sequence between A and B.

I

Fig. 5. Extension of Wagner and Fischer’s algorithm to the vectorial case: (a) the editing path on which (b) a trace from matrix M to matrix M’ along with (c) the corresponding sequence of edit operations on symbol vectors. Diagonal, horizontal, and vertical paths segments in (a) correspond to substitution, insertion, and deletion operations, respectively.

Given U‘, a column vector of M and v j , a column vector of MI, we define the following operations on vectors:

P

substitution, with cost q u e , u J ) = y(uk, U;) (1)

insertion, with costr(A, wJ) = y(A, v i ) (2)

k = l P

k = l P

deletion, with costII(z2, A) = y ( u i , A) (3) k = l

where A is the null vector, X is the null vector coordinate, and y defines the elementary cost for changing symbol

U ; into symbol .U:, inserting symbol u: or deleting symbol U;.

The cost of a trace from matrix M to matrix M’ is now defined as cost(T) =

quz + U J ) + r (uZ + A) + r(n + .7)

( 2 , J )€T e E U 3 E V

where uz and v3 are the ith and the j th column vectors of matrices M and M‘, respectively, and where U U V is the set of positions of vectors which are not related through T .

If the triangle inequality holds for cost function I?, the result obtained in the original algorithm is still valid for the edit

distance A between matrices M and M’

A(M, MI) = min{cost(T)ITis a trace fromMtoM’}. (4)

The above result, and the recursive relation due to Wagner and Fischer

~ ( ~ % - l , + r(d, u ~ ) A(i, j ) = min A(ua-l, u J ) + F(u’, A) { A(u’, U”-’) + r ( A , w J )

. . .m , j = l . . . ”

leads directly, through dynamic programming, to iterative procedures for computing A(M, MI). Again, by choosing appropriate function r, the sequence of vectors exhibiting a maximal number of common coordinates may be derived from traces, using algorithm “Y” in [26]. Fig. 5 describes the results obtained with the extended algorithm when applied to two 3 line matrices. In this simple case, Fig. 6 shows two possibilities of vectorial sequences common to matrices M and M’ and explains how the optimal sequence is chosen by the algorithm.

Iv. RESULTS AND DISCUSSION

A. Results This methodology was exemplified through the analysis of

five observations obtained in a patient suffering from temporal lobe epilepsy. Seizure recordings included signals from 75 sensors located on five depth electrodes. Nine of them were


I I I

Fig. 6. Two possible sequences of vectors, exhibiting at least one common coordinate, and present in both matrices M and M'. The algorithm keeps only sequence 2 in which the third vector exhibits 2 common coordinates, one more than in sequence 1, which is not retained. Circles indicate the number of common coordinates (symbols between brackets) in vectors in correspondence.

chosen to constitute input matrices to the analysis. These TABLE I1

nine channels, Clinically relevant, were also used by the EEG NORMALIZED EDIT DISTANCES BETWEEN FIVE SEEG SEIZURE OBSERVATIONS (RECORDED IN A PATIENT SUFFERING FROM TEMPORAL LOBE EPILEPSY)

experts to study the patient's seizures. Thus, each observation I was coded in a reduced form of nine lines x 150 columns (6 was chosen to be 1 s, and the average seizure duration was approximately 2.5 min). For clarity, chosen electrodes are denoted by letters A, B, and C and their respective considered sensors are numbered 1, 2, and 3. Internal sensors (Al, B1, and C1) record signals from internal brain structures (corpus amygdaloideum, anterior comu ammonis, and posterior cornu ammonis, respectively) whereas extemal sensors A3, B3, and C3 record signals from the temporal neocortex. The edit distance, equal to the cost of a least cost trace, was computed from (4) and using the following elementary costs in (1)-(3):

0 In the substitution operation, y(uk, U ; ) = 2 if u i # U;

In the insertion operation, y(X, U ; ) = 1. 0 In the deletion operation, y ( u i , A) = 1. The edit distance was normalized by dividing each value

by the maximum distance p . (m + m') between observations, obtained assuming the two matrices do not have any vector having at least one common coordinate: the maximum distance corresponds to the resulting cost of deleting all vectors in the first matnx ( p . m) and inserting all vectors of the second matrix ( p . m').

Table I1 gives the normalized distances between the five observations. This table displays small distances between pairs (O', 04), (02, 03), and (O', 05). On the opposite, pairs (O', 03) and (O' , 05) are separated by greater distances. This result will be further discussed.

A search for common sequences was performed. Fig. 7(a) provides an example of the results obtained by application of algorithm on observations 0' and 04, coded as sequences of vectors. Symbols between brackets are those automatically found by the algorithm. They correspond to the vectors matched by the trace in observations 0' and 04. The figure may sequentially be analyzed as follows: signals are approximately the same at the beginning of the seizure. Then, during 10 s, observation O4 does not have any correspondence in observation 0'. After this time, once more, strong similarities appear in both observations for a new period of about 15 s. This representation is interesting because it reveals that seizure 4 is longer in time than seizure 1. However, in both observations, a same mechanism is pointed out, after

and y ( u i , U ; ) = 0 if = U;.

i 05

0 10.164 I O . 1 9 9 1 a 0.233) I I I I I

0.148 1 0.156 1 0.165 I 0 1 0.161 I I I I I

0.2331 0.1291 0.1701 0.161 1 0 I

the beginning of the seizure. It is transcribed by notable modifications of signals recorded on the nine selected sensors, as shown by the coding which is different, at this point, from the beginning of the seizure. This signature, which identifies a same spatio-temporal process between brain structures, is shown in Fig. 7(b).

Another spatio-temporal signature, shown in Fig. 8, was also extracted from observations 02, 03, and 05. Again, a same epileptic mechanism, present in the three seizure recordings and lasting approximately 20 s, is underlined by the algorithm. However, noticeable differences may be seen from the comparison of this signature with that extracted from 0' and 04. Interactions between brain structures recorded by sensors B1 and C1 are not similar in the two cases, although the five seizures were recorded in the same patient. Discus- sion with experts in neurophysiology led to the following comments.

0 First, the signature extracted from 02, 03, and O5 is es- sential and shows exactly the phenomenon they observed for this patient: the origin of the paroxystic discharge is always in the corpus amygdaloideum (Al) and its propagation first affects the anterior cornu ammonis (B 1) and second the posterior comu ammonis (Cl). For this patient, there is no secondary propagation to the lateral cortex (A3, B3, and C3). Signals from the lateral cortex (C3) exhibit slow waves in the five signatures. This significant modification in the

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rhythm is caused by the internal interactions occurring approximately at the same time. This decrease in frequency was also observed in other cases.

0 The clonic discharge of spikes and spike-waves (Bl) of the first signature is morphologically different from the rapid tonic discharge (Bl) of the second one. Visibly, the involved mechanisms are dissimilar in the two cases.

In the five seizures, clinical signs were considered identical and occurred in a same order. However, the very first sign occurs approximately 20 seconds after the paroxystic discharge recorded on Al . Consequently, a first and simple hypothesis on the epileptogenic network may be proposed: the brain structures implied in the disease may be those recorded by sensors A1 and B1. Their abnormal and reproducible interactions (either tonic or clonic) may be at the origin of this temporal lobe epilepsy. Neurophysiological modifications in the other recorded structures appear later and are probably a consequence of the initial interactions between A1 and B1.

B. Discussion

From the clinical point of view, the presented methodology leads to promising results. The edit distance gives a criterion to objectively quantify similarities between seizures. The algorithm allows to clearly distinguishes two groups in the five observations: (O' , 04) and (02, 03, 05). These two groups also correspond to two types of abnormal mechanisms. The validation must now be extended to other cases. As far as future work is concerned, interpatients correlations will be analyzed. Indeed, the question of specific seizure patterns for given types of epilepsy (for instance, temporal lobe epilepsy) still remains. The presented method may bring some answers, through large scale experiments.

From the theoretical point of view, the proposed solution is well suited to the problem of confronting observations with nonequal duration. Three steps are involved in the methodology: 1) segmentation: 2) characterization and labeling using a finite set of symbols; and 3) comparison of coded observations.

The segmentation was based on a simple adaptative method rather than on the more usual procedure of sectioning the EEG signal into short segments of fixed length. Thus, the resulting quasistationary EEG segments better describe the underlying mechanisms of neural activatiodde-activation. Al- though vectorial methods were proposed for segmenting EEG signals [27], the method used in this study proceeds channel by channel, and thus, enables the detection of nonnecessarily synchronous rupture instants on multiple channels. This type of rupture is often observed in SEEG where different brain structures are directly recorded.

The characterization of SEEG segments is performed through standard methods which describe spectral as well as morphological features of each segment. Data analysis used to classify segments before labeling is also based on a standard method of hard clustering (Mahalanobis distance [28]). At present, segments are coded as mono-dimensional sequences. However, signal mixtures can often be observed in SEEG and may usually be separated on different decomposition levels using signal processing techniques such as wavelets or time-

c3

c2

c1

B2

B1

A3

c3

c2

23

22

21 I 83 I

Fig. 8. A spatio-temporal signature extracted from observations 02, 03, and 05. Again, mechanisms pointed out seem to be similar in these three seizures. However, significant differences (on sensors E1 and C1) may be observed when compared to the second signature extracted from 0' and 04. Arrows show some particularly reproducible aspects. [A1 : corpus amygdaloideum, B1: anterior cornu ammonis, C1: posterior cornu ammonis, A2-B2-C2: white matter, A3-B3: temporal neocortex (gyrus T2, anterior part), C3: temporal neocortex (gyrus T2, posterior part).].

frequency decomposition. A multi-symbol coding of each SEEG segment could lead to a more accurate representation of seizures. Moreover, a study of correspondences on chosen levels could be performed and would certainly lead to better localize specific cellular mechanisms through signals (for example, paroxystic discharges would be pointed out by similarities on the level corresponding to high frequencies).

The method proposes a vectorial extension of Wagner and Fischer's algorithm to put observations coded as matrices

WENDLING et al.: EXTRACTION OF SPATIO-TEMPORAL SIGNATURES FROM DEPTH EEG SEIZURE SIGNALS 999

of symbols in relationship. The problem of distances and matching between sequences of symbols has been studied in depth [29]-[3 11. However, the problem of finding optimal correspondences between two-dimensional (2-D) matrices has received less attention. Methods like those used by UNIX commands [32] to compute a delta file from two 2-D text files usually treats each line as a single entity and are, in fact, the application of n times the scalar method. Other studies, developed in the field of genetics [33], allow to find matching in 2-D matrices, but corresponding only to nondeformable patterns. In the present study, the approach is different. The method enables elastic deformations (on time) of the first matrix to optimally match the second one, under cost constraints. The resulting distance quantifies the degree of correspondences between observations. The second part of the algorithm allows to extract signatures which provide objective results on reproducible phenomena occurring during seizures. The algorithm complexity is of order (m. m’. p ) and few seconds are needed to process matrices such as those presented here.

At the present time, the method uses constant elementary costs in edit operations. Future work will study another definition of the cost function (and thus, of the edit distance) by making elementary costs context-dependent. For instance, distances between classes of segments could be used in function I?. This new definition should make the edit distance more precise in modulating substitution costs in function of distances between classes of neural dynamics.

V. CONCLUSION

In this paper, a comprehensive methodology for objectively comparing SEEG seizure recordings has been presented. The approach is well suited to the problem of confronting recordings of nonequal duration: it proceeds by horizontal deformations of the first observation to optimally match the second, under cost constraints. Promising clinical results were obtained: similar processes were found in SEEG signals and two types of epileptic patterns were pointed out. The study brings objective results on reproducible mechanisms of neural activation during ictal periods and may help in the understanding of epileptogenic networks. Future work will enable to compare observations whose channels are coded as multi- symbol sequences to take into account the mixtures often observed in SEEG signals, and will make the interobservation distance context-dependent to improve the quantification of similarities.

ACKNOWLEDGMENT The authors wish to thank Prof. Chauvel and Dr. Vignal for

their fruitful comments on the clinical results presented in this paper. Dr. Carrault is also thanked for his helpful advice on this work.

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Jean-Michel Badier was born in France in 1962 He received the Biomedical Engineering degree and the Ph D. degree from the University of Technology of Compiegne (UTC), France, in 1985 and 1991, respectively

He is currently teaching Computer Sciences at the University of Rennes 1 and doing his research at the Clinical Epileptology Unit in Rennes Uni- versity Hospital. His main research interests include source localization of evoked and spontaneous bram activities

Fabrice Wendling was born in France in 1967. He received the Biomedical Engineering degree from the University of Technology of Compiegne, France, in 1990 and the master’s degree from the Georgia Institute of Technology, Atlanta, in 1991. He is currently workng toward the PhD. degree at the University of Rennes 1, France. His research interests include biomedical signal processing, pattern recognition, and modeling of brain activities.

Jean-Jacques Bellanger received the electrical engineering degree in 1971 from the Ecole Nationale d’ingenieur de Brest, France and the MSc. from the University of Rennes 1, France, in 1973.

He is currently Assistant Professor in Signal Processing and Probabilities at the University of Rennes 1. His research interests are focused on adaptive detection, estimation and representation methods, and statistical validation of algorithms with application to biomedical signals

Jean Louis Coatrieux (M185-SM’91-F’95) received the electrical engineering degree from the Polytechnic Institute of Grenoble in 1970; the Ph.D. in 1973, and the State Doctorate in Sciences in 1983, from the University of Rennes 1.

He was Assistant Professor (1970-1975) and Associate Professor (1976-1986) at the Institute of Technology of Rennes. Since 1986, he has been Director of Research at the National Institute for Health and Medical Research, France (INSERM) and Adjunct Professor at the New Jersey Institute of

Technology (1993-). He is also Piofessor at Telecom Bretagne (Biest, France). He is the head of the Laboratoire Traitement du Signal et de 1’Image.

Dr. Coatrieaux is Vice President for Publications and Technical Activities for IEEE-EMBS (1993-1994); he is also member of Scientific Boards of national (INSERM, CNRS, Foreign Office Ministry) and international institutions (USA, Canada, Spain, UK, and Europe). He has been Co- Chair of the 1992 IEEE-EMBS Conference held in Paris, and he founded the First International Summer School of IEEE-EMBS, held in Brittanny (France) in July 1994. His experience is related to three dimensional image, signal processing, pattern recognition, and knowledge-based systems with applications in Medicine. He has published more than 100 papers in journals and conferences and has given more than 50 lectures at the international level.

Documents

Extraction of spatio-temporal signatures from depth EEG seizure signals based on objective matching in warped vectorial observations