Interictal spikes and sharp waves in human EEG are characteristic signatures
of epilepsy. These potentials originate as a result of synchronous,
pathological discharge of many neurons. The reliable detection of such
potentials has been the long standing problem in EEG analysis, especially after
long-term monitoring became common in investigation of epileptic patients. The
traditional definition of a spike is based on its amplitude, duration,
sharpness, and emergence from its background. However, spike detection systems
built solely around this definition are not reliable due to the presence of
numerous transients and artifacts. We use wavelet transform to analyze the
properties of EEG manifestations of epilepsy. We demonstrate that the behavior
of wavelet transform of epileptic spikes across scales can constitute the
foundation of a relatively simple yet effective detection algorithm.Comment: 4 pages, 3 figure

A. Babloyantz

Andrzej Kozik

Bruce J. West

C. Torrence

C.E. D’Attellis

C.J. Stam

F. Sartoretto

G. Widman

I. Clark

I.A. Rezek

J. Engel

J. Gotman

J. Gutiérrez

K. Lehnertz

L. Diambra

L. Ingber

L. Senhadji

M. Unser

M.C. Casdagli

M.J.A.M. van Putten

Miroslaw Latka

P. Jallon

P.L. Nunez

S. Blanco

W.S. Pritchard

Ziemowit Was

English

arXiv

Interictal spikes and sharp waves in human EEG are characteristic signatures of epilepsy. These potentials originate as a result of synchronous, pathological discharge of many neurons. The reliable detection of such potentials has been the long standing problem in EEG analysis, especially after long-term monitoring became common in investigation of epileptic patients. The traditional definition of a spike is based on its amplitude, duration, sharpness, and emergence from its background. However, spike detection systems built solely around this definition are not reliable due to the presence of numerous transients and artifacts. We use wavelet transform to analyze the properties of EEG manifestations of epilepsy. We demonstrate that the behavior of wavelet transform of epileptic spikes across scales can constitute the foundation of a relatively simple yet effective detection algorithm

Latka, M

Was, Zbigniew

Kozik, A

West, B J

CERN Document Server

arXiv:physics/0301065 v1   27 Jan 2003WaveletanalysisofepilepticspikesMiroslawLatkaandZiemowitWasyInstituteofPhysics,WroclawUniversityofTechnology,WybrzezeWyspianskiego27,50-370Wroclaw,PolandAndrzejKozikzVideoEEGLab,DepartmentofChildNeurology,RegionalMedicalCenter,ul.Traugutta116,40-529Wroclaw,PolandzBruceJ.WestxMathematicsDivision,ArmyResearchOÆce,P.O.Box12211,ResearchTriangle,NC27709-2211,USA(Dated:January17,2003)InterictalspikesandsharpwavesinhumanEEGarecharacteristicsignaturesofepilepsy.Thesepotentialsoriginateasaresultofsynchronous,pathologicaldischargeofmanyneurons.ThereliabledetectionofsuchpotentialshasbeenthelongstandingprobleminEEGanalysis,especiallyafterlong-termmonitoringbecamecommonininvestigationofepilepticpatients.Thetraditionaldeni-tionofaspikeisbasedonitsamplitude,duration,sharpness,andemergencefromitsbackground.However,spikedetectionsystemsbuiltsolelyaroundthisdenitionarenotreliableduetothepres-enceofnumeroustransientsandartifacts.WeusewavelettransformtoanalyzethepropertiesofEEGmanifestationsofepilepsy.Wedemonstratethatthebehaviorofwavelettransformofepilep-ticspikesacrossscalescanconstitutethefoundationofarelativelysimpleyeteectivedetectionalgorithm.PACSnumbers:87.10.+e,05.45.-aRecordingsofhumanbrainelectricalactivity(EEG)havebeenthefundamentaltoolforstudyingthedynam-icsofcorticalneuronssince1929.Eventhoughthegistofthistechniquehasessentiallyremainedthesame,themethodsofEEGdataanalysishaveprofoundlyevolvedduringthelasttwodecades.In1985Babloyantzetal.demonstratedthatcertainnonlinearmeasures,rstin-troducedinthecontextofchaoticdynamicalsystems,changedduringslow-wavesleep[1].Theurryofre-searchworkthatfollowedthisdiscoveryfocusedontheapplicationofnonlineardynamicsinquantifyingbrainelectricalactivityduringdierentmentalstates,sleepstages,andundertheinuenceoftheepilepticprocess(forareviewseeforexample[2,3]).Itmustbeem-phasizedthatastraightforwardinterpretationofneu-raldynamicsintermsofsuchnonlinearmeasuresasthelargestLyapunovexponentorthecorrelationdimensionisnotpossiblesincemostbiologicaltimeseries,suchasEEG,arenonstationaryandconsequentlydonotsat-isfytheassumptionsoftheunderlyingtheory.Ontheotherhand,traditionalpowerspectralmethodsarealsobasedonquiterestrictiveassumptionsbutneverthelesshaveturnedouttobesuccessfulinsomeareasofEEGanalysis.DespitethesetechnicaldiÆculties,thenumberofapplicationsofnonlineartimeseriesanalysishasbeenElectronicaddress:mirek@if.pwr.wroc.plyElectronicaddress:zwas@wp.plzElectronicaddress:andrzejkozik1@wp.plxElectronicaddress:westb@aro-emh1.army.milgrowingsteadilyandnowincludesthecharacterizationofencephalopaties[4],monitoringofanesthesiadepth[5],characteristicsofseizureactivity[6],andpredictionofepilepticseizures[7].Severalotherapproachesarealsousedtoelucidatethenatureofelectricalactivityofthehumanbrainrangingfromcoherencemeasures[8,9]andmethodsofnonequilibriumstatisticalmechanics[10]tocomplexitymeasures[11,12].OneofthemostimportantchallengesofEEGanaly-sishasbeenthequanticationofthemanifestationsofepilepsy.Themaingoalistoestablishacorrelationbe-tweentheEEGandclinicalorpharmacologicalcondi-tions.OneofthepossibleapproachesisbasedonthepropertiesoftheinterictalEEG(electricalactivitymea-suredbetweenseizures)whichtypicallyconsistsoflin-earstochasticbackgrounductuationsinterspersedwithtransientnonlinearspikesorsharpwaves.Thesetran-sientpotentialsoriginateasaresultofasimultaneouspathologicaldischargeofneuronswithinavolumeofatleastseveralmm3.Thetraditionaldenitionofaspikeisbasedonitsamplitude,duration,sharpnessandemergencefromitsbackground[13,14].However,automaticepilepticspikedetectionsystemsbasedonthisdirectapproachsuerfromfalsedetectionsinthepresenceofnumeroustypesofartifactsandnon-epileptictransients.Thisshortcom-ingisparticularlyacuteforlong-termEEGmonitoringofepilepticpatientswhichbecamecommonin1980s.ToreducefalsedetectionsGotmanandWang[15]madetheprocessofspikeidenticationdependentuponthestateofEEG(activewakefulness,quietwakefulness,desyn-2chronized EEG, phasic EEG, and slow EEG). This modi-cation leads to signicant overall improvement providedthat state classication is correct.Diambra and Malta [16] adopted nonlinear predictionfor epileptic spike detection. They demonstrated thatwhen the model's parameters are adjusted during the\learning"phase to assure good predictive performancefor stochastic background uctuations, the appearanceof an interictal spike is marked by a very large forecast-ing error. This novel approach is appealing because itmakes use of changes in EEG dynamics. One expectsgood nonlinear predictive performance when the dynam-ics of the EEG interval used for building up the model issimilar to the dynamics of the interval used for testing.However, it is uncertain at this point whether it is possi-ble to develop a robust spike detection algorithm basedsolely on this idea.As Clark et al. put it succinctly, automatic EEG anal-ysis is a formidable task because of the lack of \...featuresthat reect the relevant information "[17]. Another dif-culty is the nonstationary nature of the spikes and thebackground in which they are embedded. One techniquedeveloped for the treatment of such nonstationary timeseries is wavelet analysis [18, 19]. The goal of this paperis to characterize the epileptic spikes and sharp waves interms of the properties of their wavelet transforms. Inparticular, we search for features which could be impor-tant in the detection of epileptic events.The wavelet transform is an integral transform forwhich the set of basis functions, known as wavelets, arewell localized both in time and frequency. Moreover, thewavelet basis can be constructed from a single function (t) by means of translation and dilation: a;t0=  t  t0a: (1) (t) is commonly referred to as the mother function oranalyzing wavelet. The wavelet transform of functionh(t) is dened asW (a; t0) =1paZ1 1h(t) a;t0dt; (2)where  (t) denotes the complex conjugate of  (t). Thecontinuous wavelet transform of a discrete time seriesfhigN 1i=0of length N and equal spacing Æt is dened asWn(a) =rÆtaN 1Xn0=0hn0 (n0  n)Æta: (3)The above convolution can be evaluated for any of Nvalues of the time index n. However, by choosing all Nsuccessive time index values, the convolution theorem al-lows us to calculate all N convolutions simultaneously inFourier space using a discrete Fourier transform (DFT).The DFT of fhigN 1i=0is^hk=1NN 1Xn=0hne 2ikn=N; (4)where k = 0; :::; N   1 is the frequency index. If onenotes that the Fourier transform of a function  (t=a) isjaj^ (af) then by the convolution theoremWn(a) =paÆtN 1Xk=0^hn (afk)e2ifknÆt; (5)frequencies fkare dened in the conventional way. Us-ing (5) and a standard fast Fourier transform (FFT) rou-tine it is possible to eÆciently calculate the continuouswavelet transform (for a given scale a) at all n simul-taneously [20]. It should be emphasized that formallyequation (5) does not yield the discrete linear convolu-tion corresponding to (3) but rather a discrete circularconvolution in which the shift n0  n is taken moduloN . However, in the context of this work, this problemdoes not give rise to any numerical diÆculties. This isbecause, for purely practical reasons, the beginning andthe end of the analyzed part of data stream are not takeninto account during the EEG spike detection.From a plethora of available mother wavelets, we em-ploy the Mexican hat (t) =2p3 1=4(1  t2)e t2=2(6)which is particularly suitable for studying epilepticevents.In the top panel of Fig. 1 we present two pieces ofthe EEG recording joined at approximately t = 1s. Thedigital 19 channel recording sampled at 240 Hz was ob-tained from a juvenile epileptic patient according to theinternational 10-20 standard with the reference averageelectrode. The epileptic spike in this gure (marked bythe arrow) is followed by two artifacts. The bottom panelof Fig. 1 displays the contour map of the absolute valueof Mexican hat wavelet coeÆcients W (a; t0). It is ap-parent that the red prominent ridges correspond to theposition of either spike or the motion artifacts. Whatis most important, for small scales, a, the values of thewavelet coeÆcients for the spike's ridge are much largerthan those for the artifacts. The peak value along thespike ridge corresponds to a = 7. In sharp contrast, forthe range of scales used in Fig. 1 the absolute value ofcoeÆcients W (a; t0) for the artifacts grow monotonicallywith a.The question arises as to whether the behavior of thewavelet transform as a function of scale can be used todevelop a reliable detection algorithm. The rst step inthis direction is to use the normalized wavelet powerw(a; t0) =W2(a; t0)=2(7)instead of the wavelet coeÆcients to reduce the depen-dence on the amplitude of the EEG recording. In theabove formula 2is the variance of the portion of the sig-nal being analyzed (typically we use pieces of length 1024for EEG tracings sampled at 240 Hz). In actual numeri-cal calculations we prefer to use the square of w(a; t0) to3merely increase the range of values analyzed during thespike detection process. In Fig. 2 w2for the signal usedin Fig. 1 is plotted for three scales A = 3, B = 7 andC = 20.In the most straightforward approach, we identify anEEG transient potential as a simple or isolated epilepticspike if and only if: the value of w2at a = 7 is greater than a predeter-mined threshold value T1, the square of normalized wavelet power decreasesfrom scale a = 7 to a = 20, the value of w2at a = 3 is greater than a predeter-mined threshold value T2.The threshold values T1and T2may be considered asthe model's parameters which can be adjusted to achievethe desired sensitivity (the ratio of detected epilepticevents to the total number of epileptic events presentin the analyzed EEG tracing) and selectivity (the ratioof epileptic events to the total number of events markedby the algorithm as epileptic spikes).While this simple algorithm is quite eective for simplespikes such as one shown in Fig. 1 it fails for the com-mon case of an epileptic spike accompanied by a slowwave with comparable amplitude. The example of suchcomplex is given in Fig. 3(a). The overlap of the neg-ative tail of the Mexican hat with the slow wave yieldsthe inherently low values of w2at scale A (panel (b)) andscale B (panel (c)) as compared to those characteristic ofthe \isolated"spike. Nevertheless, the normalizedwaveletpower does decrease from scale B to C. Consequently,in the same vein as the argument we presented above,we can develop an algorithm which detects the epilepticspike in the vicinity of a slow wave by calculating thefollowing linear combination of wavelet transforms:~W (a; t0) = c1W (a; t0) + c2W (as; t0+  ) (8)and checking whether the square of corresponding nor-malized power ~w(a; t0) =~W2(a; t0)=2at scales a = 3and a = 7 exceeds the threshold value~T1and~T2, respec-tively. The second term in (8) allows us to detect theslow wave which follows the spike. The parameters asand  are chosen to maximize the overlap of the waveletwith the slow wave. For the Mexican hat we use as= 28and  = 0:125s. By varying the values of coeÆcients c1and c2, it is possible to control the relative contributionof the spike and the slow wave to the linear combination(8).For testing purposes, we built up the database of arti-facts and spikes. We made available some of these EEGtracings at [21] along with the examples of the numeri-cal calculations. While the analysis of the pieces of EEGrecordings such as those shown in Fig. 2 and 3 is essentialin determining the generic properties of epileptic events,it can hardly reect the diÆculties one can encounterin interpretation of clinical EEG. Therefore we selectedfour challenging EEG tracings with 340 epileptic events.The algorithm described in this work marked 356 eventsout of which 239 turned out to be the epileptic events.Thus the sensitivity of the algorithm was 70% and its se-lectivity was equal to 67%. We then analyzed the sametracings with the leading commercial spike detector de-veloped by the Persyst Development Corporation (In-sight 2001.07.12). This software marked 654 events outof which 268 were epileptic events. Thus slightly bettersensitivity of 79% was achieved at the expense of the low41% selectivity. The performance of preliminary numeri-cal implementation of the detection algorithm presentedin this work is excellent and allows to process 24 hourEEG recording (19 channels sampled at 240 Hz) in amatter of minutes on the average personal computer.The goal of wavelet analysis of the two types of spikes,presented in this paper, was to elucidate the approachto epileptic events detection which explicitly hinges onthe behavior of wavelet power spectrum of EEG signalacross scales and not merely on its values. Thus, thisapproach is distinct not only from the detection algo-rithms based upon discrete multiresolution representa-tions of EEG recordings [22, 23, 24, 25, 26] but also fromthe method developed by Senhadji and Wendling whichemploys continuous wavelet transform [27].Epilepsy is a common disease which aects 1-2% ofthe population and about 4% of children [28]. In someepilepsy syndromes interictal paroxysmal discharges ofcerebral neurons reect the severity of the epileptic dis-order and themselves are believed to contribute to theprogressive disturbances in cerebral functions (eg. speechimpairment, behavioral disturbances) [29]. In such casesprecise quantitative spike analysis would be extremelyimportant. The epileptic event detector described in thispaper was developed with this particular goal in mindand its application to the studies of the Landau-Klenersyndrome will be presented elsewhere.[1] A. Babloyantz, J. M. Salazar, and C. Nicolis, PhysicsLetters A 111, 152 (1985).[2] B. J. West, M. N. Novaes, and V. Kovcic, in Fractal Ge-ometry in Biological Systems, edited by P. M. Iannocconeand M. Khokha (CRC Press, Boca Raton, FL, 1995), pp.267{316.[3] W. S. Pritchard and D. W. Duke, Intern. J. Neuroscience67, 31 (1992).[4] C. J. Stam, E. M. H. van der Leij R. W. M. Keunen, andD. L. J. Tavy, Theory Biosci. 118, 209 (1999).[5] G. Widman, T. Schreiber, B. Rehberg, A. Hoeft, andC. E. Elger, Phys. Rev. E 62, 4898 (2000).[6] M. C. Casdagli, L. D. Iasemidis, R. S. Savit, R. L.Gilmore, S. N. Roper, and J. C. Sackellares, Electroen-cephalogr. Clin. Neurophysiol. 102, 98 (1997).[7] K. Lehnertz and C. E. Elger, Phys. Rev. Lett. 80, 50194(1998).[8] P. L. Nunez, R. Srinivasan, A. F. Westdorp, R. S. Wi-jesinghe, D. M. Tucker, R. B. Silberstein, and P. J.Cadusch, Electroencephalogr. Clin. Neurophysiol. 103,499 (1997).[9] P. L. Nunez, R. B. Silberstein, Z. P. Shi, M. R. Car-penter, R. Srinivasan, D. M. Tucker, S. M. Doran, P. J.Cadusch, and R. S. Wijesinghe, Clin. Neurophysiol. 110,469 (1999).[10] L. Ingber, Physica D 5, 83 (1982).[11] I. A. Rezek and S. J. Roberts, IEEE Trans. Biomed. Eng.45, 1186 (1998).[12] M. J. A. M. van Putten and C. J. Stam, Phys. Letters A281, 131 (2001).[13] J. Gotman and P. Gloor, Electroencephalogr. Clin. Neu-rophysiol. 41, 513 (1976).[14] J. Gotman and L. Y. Wang, Electroencephalogr. Clin.Neurophysiol. 54, 530 (1982).[15] J. Gotman and L. Y. Wang, Electroencephalogr. Clin.Neurophysiol. 79, 11 (1991).[16] L. Diambra and C. P. Malta, Phys. Rev. E 59, 929 (1999).[17] I. Clark, R. Biscay, M. Echeverria, and T. Virues, Com-put. Biol. Med. 25, 373 (1995).[18] S. Mallat, A Wavelet Tour of Signal Processing (Aca-demic Press, San Diego, 1998).[19] M. Unser and A. Aldroubi, Proc. IEEE 84, 626 (1996).[20] C. Torrence and G. P. Compo, Bull. Amer. Meteor. Soc.79, 61 (1998).[21] URL http://republika.pl/eegspike/.[22] S. Blanco, C. E. D'Attellis, S. I. Isaacson, O. A. Rosso,and R. O. Sirne, PRE 54, 6661 (1996).[23] C. E. D'Attellis, S. Isaacson, and R. O. Sirne, Ann.Biomed. Eng. 25, 286 (1997).[24] F. Sartoretto and M. Ermani, Clin. Neurophysiol. 110,239 (1999).[25] M. Calvagno, M. Ermani, R. Rinaldo, and F. Sartoretto,in Proceedings of the 2000 IEEE International Confer-ence on Acoustics, Speech, and Signal Processing (2000),vol. 6.[26] J. Gutierrez, R. Alcantara, and V. Medina, Medical En-gineering & Physics 23, 623 (2001).[27] L. Senhadji and F. Wendling, Neurophysiol. Clin. 32, 175(2002).[28] P. Jallon, Epileptic Disord. 4, 1 (2002).[29] J. Engel, Epilepsia 42, 796 (2001).50 0.5 1 1.5 2−1012EEG [mV]time [s]← S20 40 60 80 100 120  a102030FIG. 1: Top panel: simple epileptic spike (marked by S) fol-lowed by two artifacts. Bottom panel: contour map of theabsolute value of the Mexican hat wavelet coeÆcients (arbi-trary units) calculated for the EEG signal shown above. Theshades of blue correspond to low values and the shades of redto high values.0 0.5 1 1.5 2−1012EEG [mV] (a)0 0.5 1 1.5 205001000scale A (b)0 0.5 1 1.5 20500010000scale BSquare of normalized wavelet power(c)0 0.5 1 1.5 20500010000scale CTime [s](d)FIG. 2: Square of normalized wavelet power for three dierentscales A < B < C (Panels (b)-(d)). The EEG signal shownin panel (a) is the same as the one used in Fig. 160 0.5 1 1.5 2−101EEG [mV] (a)0 0.5 1 1.5 202550scale A (b)0 0.5 1 1.5 205001000scale B (c)0 0.5 1 1.5 2050001000015000scale CTime [s]                Square of normalized wavelet power(d)FIG. 3: (a) Epileptic spike - slow wave complex. The ampli-tude of the slow wave is comparable to that of the spike. Thesquare of normalized wavelet power for this signal is shown inpanels (b)-(d) for three dierent scales A < B < C.

Wavelet analysis of epileptic spikes

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Wavelet analysis of epileptic spikes

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