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Communications

Time-Frequency Matching of WarpedDepth-EEG Seizure Observations

F. Wendling,* M. B. Shamsollahi, J. M. Badier, and J. J. Bellanger

Abstract—A methodology of comparing depth-EEG seizure recordingsis presented. The approach is based on an extension of Wagner andFischer’s algorithm to N � 2-dimensionalsets, allowing a confrontationof nonequal duration observations characterized by their time-frequencydistributions. It proceeds by time and frequency warping on the firstobservation to match the second, under cost constraints. Preliminaryresults show that relevant signatures can be extracted from recordings.

Index Terms—Electroencephalography (EEG), epilepsy, matching, re-producibility, seizure, signal processing, time-frequency.

I. INTRODUCTION

Stereoelectroencephalography (SEEG) is a method of investigationused in epileptic patients candidate to a surgical treatment [1].It provides real-time markers of brain activities in the form oftime-series signals recorded from 70–120 sensors located on 5–10intracerebral electrodes. The presurgical evaluation, essentially basedon the recording of seizures, is usually performed during long-termmonitoring. Extracted from a large amount of data, ictal periodsmust be compared in order to extract and study the “habitual seizurepattern” of the patient. This analysis, correlated to clinical data, isof major importance in the understanding of the organization of theepileptogenic zone and may condition the surgical operation.

We recently proposed a comprehensive methodology of comparingSEEG observations [2], [3]. Although satisfying results are obtained,we try to improve the method by simplifying the steps dedicatedto the preprocessing of data: in the method presented here, thepreprocessing of SEEG signals only consists in the computation ofa time-frequency representation. The approach is exemplified on twotemporal lobe epilepsy seizures. Preliminary results are discussedthrough the potential use of this new approach to i) evaluate thedistance between seizure observations, ii) extract similar epilepticmechanisms in a same patient, and iii) point out general ictal patternsin patients suffering from a same type of epilepsy.

II. BACKGROUND AND PROBLEM STATEMENT

Searching invariant information in multichannel SEEG signalsrequires relating vectorial observations. This is the major difficultyof the problem. Signatures to be found are similar (anda prioriunknown) sequences of events occurring in different recordings, ac-

Manuscript received July 10, 1997; revised January 7, 1999. This work wassupported by INSERM N92/9/CNAMTS under contract CNAMTS.Asteriskindicates corresponding author.

*F. Wendling is with the Laboratoire Traitement du Signal et de L’Image,INSERM, Universite de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex,France (e-mail: wendling@next.univ-rennes1.fr).

M. B. Shamsollahi and J. J. Bellanger are with the Laboratoire Traitementdu Signal et de L’Image, INSERM, Universit´e de Rennes 1, Campus deBeaulieu, 35042 Rennes Cedex, France.

J. M. Badier is with the Laboratoire de Neurophysiologie et Neuropsy-chologie, INSERM, Universite de la Mediterranee, 13385 Marseille Cedex 5France.

Publisher Item Identifier S 0018-9294(99)03358-3.

Fig. 1. Method proposed to relate SEEG observations. (a) original SEEGobservations, (b) computation of the time-frequency distribution for eachsignal, and (c) Application of Wagner and Fischer’s algorithm, extended tothe computation of optimal correspondences between sets of time-frequencyplanes.

cording to a certain time order. In other words, the methodology mustallow to establish relationships between observations of nonequalduration.

A comprehensive methodology of comparing SEEG observationswas proposed by Wendlinget al. [2]. Applied in patients sufferingfrom temporal lobe epilepsy [3], the method allowed to 1) quantifythe degree of resemblance between seizure periods and 2) extractsimilarities, referred to as spatio-temporal signatures. Three stepswere involved in the method: i) segmentation of SEEG signals, ii)characterization, classification and labeling of SEEG segments, andiii) comparison of observations coded as sequences of symbol vectorsusing a vectorial extension of Wagner and Fischer’s algorithm [4].The approach may be improved, on at least two points. First, in thesegmentation step, signals are assumed to be piecewise stationary.This assumption is not always compatible with the nonstationaryintrinsic nature of SEEG signals. Second, in the labeling step, theclassification uses the expert’sa priori knowledge to group segmentsinto arbitrary chosen classes. This nonautomatic procedure, adaptedto each patient’s signals, is time consuming.

These considerations led us to develop a new approach. Asshown in Fig. 1(a)–(c), the proposed methodology now involves

0018–9294/99$10.00 1999 IEEE

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only two steps: i) a preprocessing of the observations in which atime-frequency representation is computed for each signal and ii)a comparison of the observations coded as sets of quantified time-frequency representations. This second step reports a new extensionof Wagner and Fischer’s algorithm that allows to find the optimalmatching between vectorial observations warped in time and infrequency. As in the previous work, this matching leads to i) quantifythe degree of resemblance between seizures and ii) extract timeintervals on which signals exhibit reproducible ictal mechanisms,referred to as spatio-temporal signatures.

In both methods, a set ofM observationsOe; e = 1; � � � ;M; isconsidered for each patient. Each observationOe is composed ofN SEEG signals recorded from relevant brain structures with depthelectrodes

fOe(t); t 2 [0; Te] for e = 1; � � � ;Mg

Oe(t) = o

e1(t)o

e2(t) � � � o

eN (t)

T; o

ek(t) 2 R

for k = 1; � � � ; N

where time intervals[0; Te] may be different from one observationto another. In the sequel, these intervals, as well as the variablet,will be considered as discrete.

In the previous method, for givene and k, signal oek(t) wasassumed to be piecewise stationary. This assumption allowed tosegment SEEG signals, considering that each segment results fromsteady neural dynamics. The method presented in this paper differsfrom the previous one on two major points.

• Each oek(t) is preprocessed to obtain a time-frequency repre-sentation (TFR)T e

k describing the energy distribution of thesignal in the time-frequency plane, such that each observationOe; e = 1; � � � ;M; can now be represented as a setT e of NTFR’s

f(T e(t; f); t 2 [0; Te]; f 2 [0; F ]) for e = 1; � � � ;M)g

T e(t; f) = [T e1 (t; f)T

e2 (t; f) � � � T

eN(t; f)]

T; T e

k (t; f) 2 R

for k = 1; � � �N:

• The setsT e andT e of TFR’s computed for two observationsOe andOe are matched without preliminary segmentation andclassification.

Hence, the problem may now be stated as follows: finding theoptimal correspondences between two observationsOe andOe ofnonequal duration is equivalent to finding a sequence of pairs of timeintervals, respectively, belonging toT e and T e , for which energyvalues are close in close frequency bands, on a “large” number oftime-frequency representations.

III. M ETHOD OVERVIEW

Signatures to be found are reproducible (and unknown) sequencesof “time-frequency patterns” occurring on the same sensors in dif-ferent recordings and according to a certain time order. Thus, themethod must establish relationships between vectorial observationsof nonequal duration in order to point out similar patterns. Two stepsare involved in the method: i) computation of time-frequency energydistributionsT e

k andT ek for signalsoek(t) andoek (t) of observations

Oe andOe and ii) confrontation of observationsOe andOe , bothcharacterized by sets of quantified time-frequency representationsT e

and T e .

A. Computation of the Time-Frequency Distribution

Time-frequency representations (TFR) are now well establishedand an intensive literature at both theoretical and applied levels is

available [5]. In the present study, the smoothed pseudo Wigner–Villedistribution (SPWVD), denoted byT e

k (t; f); has been chosen to char-acterize the time-frequency content of SEEG signaloek(t). Carryingout a separable smoothing in time and in frequency, the SPWVD wasshown to visualize the time-frequency content of SEEG signals witha good resolution [6], [7].

B. Finding the Optimal Matching Between ObservationsCharacterized in Time and in Frequency

Observations do not have the same duration and, moreover, se-quences to be extracted have elements (vectors) that i) do not appearat synchronous instants (time shifts and time elongations) and ii) donot have strictly identical energy levels in strictly identical frequencybands (frequency shifts). Hence, in the stated problem, the majorconstraint is the following: the method used to relate one set ofTFR’s to another cannot be a simple ‘time to time’ and ‘frequencyto frequency’ comparison but must allow conjoint deformations (orwarping) along the time axis and on the frequency axis. To find anoptimal matching between sets of TFR’s, we propose a method basedon a new vectorial extension of Wagner and Fischer’s algorithm.This algorithm was initially developed to compute the “edit distance”between two monodimensional strings of symbols. In the methodpresented here, this algorithm is used both in time and frequency,simultaneously onN channels, in order to find intervals for whichenergy values are similar in close frequency bands.

1) The Original Algorithm [4]: The algorithm determines a dis-tance (called “edit distance”) between two stringsu andv of symbolstaken in a common given setS. This distance is defined as the costof the minimum cost sequence of “edit operations” (i.e. deletions,insertions and substitutions) needed to change one string into theother.

A cost is associated to each sequenceE = e1; � � � ; en thattransformu in E(u) = v. This cost is the sumC(E) = �

n

i=1 g(ei)of elementary costsg associated to elementary operationsei. Amongall possible sequencesE (nE bounded or not), those referred to as“traces” are of particular interest. A traceTu;v for a pair (u; v) isa sequence ofL links (i1 with j1; j2 with j2; � � � ; iL with jL) thatbijectively relates a substring ofu to a substring ofv, preserving theorder: ik >ik ! jk >jk.

If ET denotes the sequence of edit operations associated with traceT; the cost of is defined as follows:

C(ET ) =(i;j)2T

g(ui; vj) +i2I

g(ui; �) +j2J

g(�; vj)

where g(ui; vj); g(ui; �) and g(�; vj) are the respective costs forsubstituting elementu)i with vj , for deleting elementui in u and forinserting elementvj in v: � is the null sequence(j�j = 0). I andJare the sets of indexes inu andv which are not related throughT .

The cost functiong on S [ ��S [ �, is a distance onS [ �

(this implies thatg(ui; vj) � g(ui; �)+g(�; vj), i.e., the cost of onedeletion plus the cost of one insertion must never be strictly lowerthan the cost of the equivalent substitution). An important result of[4] relates the edit distance� to the trace: “the edit distance fromuto v is equal to the cost of a least cost trace fromu to v”

�(u; v) = minfcost(T )jT is a trace fromu to vg: (1)

Moreover, the least cost trace can be extracted by an algorithm(dynamic programming) based on the recursive relation

�(ui; vj) = min�(ui�1; vj�1) + g(ui; vj)�(ui�1; vj) + g(ui; �)�(ui; vj�1) + g(�; vj):

(2)

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whereui andvi; respectively denote substrings(u1; u2; � � � ; ui) and(v1; v2; � � � ; vj).

It may be easily verified that� is a distance on the set of finitelength strings of symbols taken inS. Wagner and Fischer’s algorithmwas originally developed withS defined as a finite set of symbols(alphabetical, for example). In [2], the algorithm was extended to thecomparison of sequences of symbol vectors taking values inSN . Inthe work presented here, the algorithm will be generalized to sets ofsequences of symbol vectors taking values inSF�N . In both cases,the extension is based on an appropriate choice for distanceg. In thesequel, the edit distance, obtained from distanceg, will always bedenoted as�(u; v), independently of the nature ofS.2) Finding the Optimal Matching Between Time-Frequency Repre-

sentations: The problem is to find the optimal matching between twoseizure observations in order to extract invariant information. Eachsignal in a given observationOe is characterized by a time-frequencyrepresentationT e

k . Thus, a way to find the optimal matching betweentwo seizure signalsoek(t) and oek (t), respectively, taken from thesame sensork in two different observationsOe and Oe , is tosearch the associated TFR’sT e

k andT ek for vectorsT e;t

k andT e ;t

k

exhibiting close energy values in close frequency bands. To performthis matching, the algorithm presented in Section III-B1) may beextended to the vectorial case, as follows.

Each time-frequency representationT ek may be seen as a sequence

of vectorsT e;t

k ; t 2 [0; Te]; taking values into F . However, inpractice, theT e

k (t; f) are normalized and quantified such that valuesare not taken in but in a finite setSQ = f0; 1; � � � ; QMg:Consequently, in the following, will be restricted toSQ. Giventwo sets of TFR’sT e(t; f) andT e (t; f); f 2 [0; F ], respectively,defined on[0; Te] and [0; Te ]:

1) we can equivalently consider the corresponding matrices forthe same sensork in recordingsl = e and l = e0

T lk =

T lk (t1; 0) T l

k (t2; 0) � � � T lk (tl; 0)

T lk (t1; f1) T l

k (t2; f1) � � � T lk (Tl; f1)

� � � � � �T lk (t1; F ) T l

k (t2; F ) � � � T lk (Tl; F )

= [T l;1

k T l;2

k � � � T l;T

k ] (3)

where T l;i

k in SFQ corresponds to theith column vector ofmatrix T l

k :2) we can also simultaneously consider the set ofN TFR’s

computed from theN seizure signals in recordingsl = e andl = e0

T l =

T l;11

T l;21

� � � Tl;T1

T l;12

T l;22

� � � Tl;T2

� � � � � �T l;1N T l;2

N � � � Tl;T

N

= T l;1 T l;2 � � � T l;T (4)

whereT l;i; i = 1; � � � ; Tl is a sequence ofTl column vectorsin SF�NQ , each one obtained from the concatenation of theN

columnsT l;i; T l;i2

; � � � ; T l;iN :

The optimal correspondences between two seizure signals (from achannelk) or between two seizure observations (N channels) may beobtained by confronting (or “matching”) the associated TFR’s or theassociated sets ofN TFR’s. Hence, two matching problems (M.P.)have to be solved.

M.P.1: Finding the matching between two sequencesT ek =

[T e;1

k T e;2

k � � � T e;T

k ] and T ek = [T e ;1

k T e ;2

k � � � Te ;T

k ] of vectorsin SFQ (3).

M.P.2: Finding the matching between two sequencesT e =

[T e;1T e;2 � � � T e;T ] and T e = [T e ;1T e ;2 � � � T e ;T ] of vectorsin SF�NQ (4).

To resolveM.P.1 andM.P.2, the method presented in Section III-B1) may be extended. This extension consists in defining adapteddistances and �, corresponding tog, respectively, onS1 =SFQ [ �F and S2 = SF�NQ [ �F�N , where�F and �F�N

denote the null sequences, respectively, inSFQ andSF�NQ . Distance will be first described,� being a generalization of to N signals.

Solution toM.P.1—Definition of Distance : Distance must bea distance onS1: In particular, this implies that

(x1; x2) � x1; �F + �F ; x2 :

A solution to M.P.1 is to consider vectorsx1 and x2 of SFQ astwo strings, of same lengthF , taking values intoSQ and to define (x1; x2) as being equal�(x1; x2) such that possible frequencyshifts will be taken into account, in addition to time deformations.This solution relies on the definition of a distance (corresponding todistanceg in Section III-B1) on the setSQ [ �.

Our choice is to defineg as

g(s1; s2) = js1 � s2j for s1 2 SQ ands2 2 SQ

g(s; �) = g(�; s) =QM

2for s 2 SQ

such thatg is a distance onSQ [ � sinceg(s1; �) + g(�; s2) =(QM=2) + (QM=2) � js1 � s2j = g(s1; s2).

Consequently, , obtained from� computed itself from this dis-tanceg, is a distance onS1. Finally, M.P.1 can be solved with

(T e;i

k ; T e ;j

k ) = �(T e;i

k ; T e ;j

k ) (substitution of vectorT e;i

k

with vectorT e ;j

k )

(T e;i

k ; �F ) =F �QM

2(deletion of vectorT e;i

k )

(�F ; T e ;j

k ) =F �QM

2(insertion of vectorT e ;j

k ):

Used in the recursive relation of (2), this definition of leads tothe extraction of the optimal trace and to the computation of the edit

distance� T ek ; T

ek between sequencesT e

k andT ek .

Solution toM.P.2—Definition of Distance�: Here,x1 andx2 re-fer to T e;i andT e ;j , elements ofSF�NQ . We must define

�(x1; x2) = �(T e;i; T e ;i) = �

T e;i1

...T e;iN

;

T e ;j1

...T e ;jN

on S2 taking into account that sequenceT ek of vectorsT e;i

k ; i =1; � � � ; Te; corresponding to signaloek(t) in Oe should not be com-pared to sequenceT e

k of vectorsT e ;j

k ; j = 1; � � � ; Te ; k0 6= k;

corresponding to signaloek (t) in Oe , since both signalsoek(t)and oek (t) are recorded in two different brain structures. Thisconsideration led us to propose the following solution for� on S2to solve M.P.2:

�(T e;i; T e ;j) =

N

k=1

(T e;i

k ; T e ;j

k )

(substitution of vectorT e;j with vectorT e ;j)

�(T e;i; �F�N) =

N

k=1

(T e;i

k ; �F )

=N � F �QM

2(deletion of vectorT e;i)

604 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 46, NO. 5, MAY 1999

�(�F�N ; T e ;j) =

N

k=1

(�F ; T e ;j

k )

=N � F �QM

2(insertion of vectorT e ;j): (5)

As above, the optimal trace, as well as the edit distance�(T e; T e )

between sequencesT e and T e , is obtained from�; using (2).Algorithms are given in the Appendix.

IV. PRELIMINARY RESULTS AND DISCUSSION

The method was applied to the analysis of two seizure record-ings obtained in a patient suffering from temporal lobe epilepsy(M.P.2 problem). From these two recordings, two observations,denoted byO1 and O2, were built. Both included three signals(k = 1; 2; 3) recorded from internal brain structures of the limbicsystem(o11(t); o

2

1(t): posterior cornu amonis,o12(t); o2

2(t): anteriorcornu amonis,o13(t); o

2

3(t): amygdala), clinically recognized to havea strong implication in the patient’s epilepsy. The edit distance�(T 1; T 2), equal to the cost of the least cost trace between setsof TFR’s T 1 and T 2 associated to observationsO1 and O2, wascomputed from (2) using the definition of� given by (5). Time-frequency representations, computed from each signal of confrontedobservations, were normalized and quantified. The least cost trace waspositioned on setsT 1 andT 2 as shown in Fig. 2. One can notice thatsubsequences of pairs of matched vectors, automatically extracted bythe algorithm, reflect similar ictal mechanisms. Of special interest arethose pointed out by thick line rectangles (visually selected).

1) At the beginning of both seizure periods (pairs #1 and #2), theanterior cornu amonis is concerned by a clonic discharge ofspikes (as seen in signalso12(t) and o22(t)) occupying a widefrequency band [as seen in TFR’sT 1

2 (t; f) andT 2

2 (t; f)]. Si-multaneously, during this same period, a rapid tonic discharge,of decreasing frequency (as seen in TFR’sT

1

1 andT 2

1 ), appearsin the amygdala.

2) At the end of both periods, strong correspondences are alsopointed out (pair #3): the three recorded structures of the limbiccortex are simultaneously concerned by a discharge of spikes ofsimilar frequency content. This signature (increase in frequencyfollowed by a decrease), reproduced during both seizures, couldbe interpreted as a synchronization of neural populations indistant structures from which signals are recorded. It must alsobe emphasized that both signatures correspond to the time forwhich ictal signs may be visually observed in the patient.

From the theoretical point of view, the proposed solution is wellsuited to the problem of confronting observations with nonequalduration. The method involves only two steps. In the second step, anew extension of Wagner and Fischer’s algorithm is proposed: now,the algorithm proceeds by elastic deformations not only on the timeaxis but also on the frequency axis for the first set of time-frequencyplanes to optimally match the second one, under cost constraints.Here, it should also be emphasized that these time deformationsand frequency shifts would lead to poor performances of classiccorrelation-based methods. If the problem of distances and matchingbetween sequences of symbols has been studied in depth [8]–[10],the search of optimal correspondences betweenN � 2-dimensionalsets has received no attention, to our knowledge. An original solutionis presented in this paper. As in the previous method, the resultingdistance quantifies the degree of similarity between observations andthe second part of the algorithm allows to extract signatures with noneed to makea priori assumptions on the “pattern” to be searched for.The new presented method has the significant advantage to avoid thesegmentation/classification steps in which some problems, essentially

Fig. 2. An example of result obtained from the application of the method ontwo sets of time-frequency planes corresponding to two seizure observationsin a same patient. Stronger correspondences, automatically extracted by thealgorithm, are underlined by thick line rectangles. For these time periods,signals (boxes 1, 2, and 3) seem to reflect similar underlying mechanisms.

due to the nonstationarity of SEEG signals, remained. However, thiscomes with an increase of the algorithm complexity whose order wasO(Te � Te � N) in the previous version and whose order is nowO(Te � Te �N � F 2). This also shows that the complexity couldbe decreased by decreasingF , i.e., in modifying parameters in thequantification of TFR’s.

From the clinical point of view, these first results seem promising.Indeed, the edit distance will certainly gives a criterion to quantify theglobal degree of resemblance between ictal periods while extractedsignatures will help in the understanding of reproducible sequencesof mechanisms—leading to—and—occurring during—seizures. Thevalidation must now be extended to other cases and could lead tothe study of interpatients correlations. Indeed, through large scaleexperiments, the presented method may bring some hints to questionsthat have not been answered yet: “for a given type of epilepsy (forinstance, temporal lobe epilepsy), is it possible to point out similarseizure patterns among several patients?”

V. CONCLUSION

A methodology for objectively comparing vectorial SEEG seizurerecordings has been presented. The approach is well suited to theproblem of confronting observations of nonequal duration character-ized by their time-frequency distribution: it proceeds by horizontal(along the time axis) and vertical (along the frequency axis) warpingon the first observation to optimally match the second, under cost con-straints. Preliminary results are encouraging since relevant sequencesof similar time-frequency patterns (or signatures) are automatically

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TABLE IALGORITHM 1—COMPUTATION OF THE EDIT DISTANCE

BETWEEN TWO VECTORSu AND v OF RESPECTIVE LENGTHS

juj AND jvj. SEE THE TEXT FOR DEFINITION OF DISTANCE

TABLE IIALGORITHM 2—COMPUTATION OF THE EDIT DISTANCE BETWEEN TWO

SETS OFN SEQUENCES OFVECTORS, U AND V OF RESPECTIVE

LENGTHSLU AND LV . IS COMPUTED USING ALGORITHM 1

extracted. Both theoretical and clinical fields will take benefit offuture improvements.

APPENDIX

See Tables I–III.

ACKNOWLEDGMENT

The authors wish to thank Prof. P. Chauvel for his fruitfulcomments on the clinical results presented in this paper. They would

TABLE IIIALGORITHM 3—EXTRACTION OF THE LEAST COST TRACE

FROM MATRIX D COMPUTED WITH ALGORITHM 2

also like to thank Dr. L. Senhadji and Dr. R. Le Bouquin for theirhelpful advice on time-frequency characterization methods.

REFERENCES

[1] J. Talairach and J. Bancaud, “Stereotaxic exploration and therapy inepilepsy,”Handbook of Clinical Neurology, The Epilepsies, vol. 15, P.J. Vinken and G. W. Bruyer, Eds. Amsterdam, The Netherlands: NorthHolland, 1974, pp. 758–782.

[2] F. Wendling, J. J. Bellanger, J. M. Badier, and J. L. Coatrieux,“Extraction of spatio-temporal signatures from depth EEG seizuressignals based on objective matching in warped vectorial observations,”IEEE Trans. Biomed. Eng., vol. 43, no. 10, pp. 990–1000, 1996.

[3] F. Wendling, J. M. Badier, P. Chauvel, and J. L. Coatrieux, “A methodto quantify invariant information in depth-recorded epileptic seizures,”Electroencephalogr. Clin. Neurophysiol., 1997, in press.

[4] R. A. Wagner and M. J. Fischer, “The string-to-string correctionproblem,”J. Assoc. Computing Machinery, vol. 21, no. 1, pp. 168–173,1974.

[5] L. Cohen,Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995, p. 299.

[6] M. B. Shamsollahi, L. Senhadji, and R. Le Bouquin-Jeannes, “Time-Frequency analysis: A comparison of approaches for complex EEGpatterns in epileptic seizures,” presented at17th Ann. Int. Conf.IEEE/EMBS, 1995.

[7] M. B. Shamsollahi, J. L. Coatrieux, L. Senhadji, F. Wendling, and J. M.Badier, “On some time-frequency representation signatures in SEEG,”presented at18th Ann. Int. Conf. IEEE/EMBS, 1996.

[8] A. V. Aho and M. J. Corasick, “Efficient string matching: An aid tobibliographic search,”Commun. ACM, vol. 18, no. 6, pp. 333–340, 1975.

[9] E. Ukkonen, “Finding approximate matching in strings,”J. Algorithms,no. 6, pp. 132–137, 1985.

[10] K. Abrahamson, “Generalized string matching,”SIAM J. Computing,vol. 16, no. 6, pp. 1039–1051, 1987.