Automated detection of a preseizure state based on a decrease in synchronization in intracranial...

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PHYSICAL REVIEW E 67, 021912 ~2003!

Automated detection of a preseizure state based on a decrease in synchronization in intracranielectroencephalogram recordings from epilepsy patients

Florian Mormann,1,2,* Ralph G. Andrzejak,3 Thomas Kreuz,1,3 Christoph Rieke,1,2 Peter David,2 Christian E. Elger,1

and Klaus Lehnertz11Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany

2Helmholtz-Institut fu¨r Strahlen- und Kernphysik, University of Bonn, Nußallee 14-16, 53115 Bonn, Germany3John-von-Neumann Institute for Computing, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany

~Received 30 August 2002; published 26 February 2003!

The question whether information extracted from the electroencephalogram~EEG! of epilepsy patients canbe used for the prediction of seizures has recently attracted much attention. Several studies have reportedevidence for the existence of a preseizure state that can be detected using different measures derived from thetheory of dynamical systems. Most of these studies, however, have neglected to sufficiently investigate thespecificity of the observed effects or suffer from other methodological shortcomings. In this paper we presentan automated technique for the detection of a preseizure state from EEG recordings using two differentmeasures for synchronization between recording sites, namely, the mean phase coherence as a measure forphase synchronization and the maximum linear cross correlation as a measure for lag synchronization. Basedon the observation of characteristic drops in synchronization prior to seizure onset, we used this phenomenonfor the characterization of a preseizure state and its distinction from the remaining seizure-free interval. Afteroptimizing our technique on a group of 10 patients with temporal lobe epilepsy we obtained a successfuldetection of a preseizure state prior to 12 out of 14 analyzed seizures for both measures at a very highspecificity as tested on recordings from the seizure-free interval. After checking for in-sample overtraining viacross validation, we applied a surrogate test to validate the observed predictability. Based on our results, wediscuss the differences of the two synchronization measures in terms of the dynamics underlying seizuregeneration in focal epilepsies.

DOI: 10.1103/PhysRevE.67.021912 PACS number~s!: 87.19.La, 05.45.Xt, 05.45.Tp, 05.10.2a

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I. INTRODUCTION

An important issue in epileptology is the question whethepileptic seizures can be anticipated prior to their occurrenMuch research has been done on this topic, and recent sies have shown that a number of characterizing measderived from the theory of dynamical systems are to soextent capable of extracting information from the electrocephalogram~EEG! that allow the definition of a preictastate, i.e., the state preceding a seizure~ictus!.

After some early work on the predictability of seizurdating back to the 1970s@1#, attempts to extract seizure precursors from the EEG were carried out by different grouusing mostly linear approaches@2,3# or analysis of spike oc-currence@4–7#. The earliest attempts to use nonlinear timseries analysis were started in the 1990s@8,9# using the larg-est Lyapunov exponent to describe changes in brain dynics. The first studies to describe characteristic chanshortly before an impending seizure in a larger group oftients @10–13# used the correlation dimension as a measfor neuronal complexity in the EEG or the correlation desity, respectively. These studies were followed by othersing measures such as dynamic similarity@14–17#. In a recentstudy, certain signal patterns~‘‘bursts’’ ! and changes in signal energy@18# were reported to be of predictive valuCommon to all of these analyses is the fact that they empunivariate measures. It is only recently that bivariate m

*Electronic address: [email protected]

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sures, namely, the difference between the largest Lyapuexponents of two channels@19#, and nonlinear interdependence measures@20#, as well a multivariate approach baseon simulated neuronal cell models@21#, have been applied tothe EEG of epilepsy patients.

A major problem with most of the studies presenteddate is that they do not sufficiently~or not at all! investigatethe specificity of the described precursors by analyzing inictal EEGs~i.e., EEGs recorded during the seizure-free intval! as control. Furthermore, many of these studies rely oaposteriori knowledge, e.g., by selecting the best channelof a large number of channels, or bear the risk of anin-sampleovertraining of parameters used to calculate measufor the extraction of predictive information.

In our earlier work@22#, we analyzed the degree of phasynchronization between EEG signals from different recoing sites and found a sensitivity to both physiological apathological synchronization in patients with temporal loepilepsy. In particular, we discovered the phenomenon odistinct drop in synchronization before seizures that was ually not found during the interictal state. This decreasesynchronization was found to occur well in advance, somtimes hours before a seizure, leading us to conclude thseizure may be seen as the mere ‘‘tip of the iceberg’’@54# inthe sense of it being the climax of successive changebrain dynamics that start long before the actual seizuThese findings have since then been confirmed by anostudy @23# qualitatively describing preictal drops in phassynchronization in patients with focal epilepsies of neococal origin.

©2003 The American Physical Society12-1

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MORMANN et al. PHYSICAL REVIEW E 67, 021912 ~2003!

In the present study, we characterize the degree of schronization between EEG signals recorded continuoufrom different locations within the brain and retrospectiveanalyze changes over time using the mean phase coheas a measure for phase synchronization and the maximlinear cross correlation as a measure for lag synchronizaOur specific aim is to design an automated technique fordetection of a preictal state and to test its performanceterms of both sensitivity and specificity on a group of tpatients with temporal lobe epilepsy. The parameters ofunderlying algorithm are optimized for the entire set of ptients and the apparent performance is checked for in-samovertraining via cross validation. A surrogate test for thetire set of recordings is carried out to serve as a teststatistical validity. Finally, the results obtained using the tdifferent synchronization measures are compared andcussed.

II. MATERIALS AND METHODS

A. Phase synchronization and mean phase coherence

One of the types of synchronization examined in tstudy, the so-called phase synchronization, is the oldestcept of synchronization in physics@24# and was originallyintroduced for the description of two coupled harmonic~lin-ear! oscillators@25#. Only recently has this concept been etended to nonlinear time series@26# and applied to biologicatime series such as the electrocardiogram and respiratorynals from healthy humans@27–30# as well as magnetoencephalograms and electromyograms from signals from Pkinsonian patients@31# and EEG signals from both epilepspatients@22# and animal models of epilepsy@32#. Tradition-ally, phase synchronization is defined as the locking ofphases of two oscillating systemsa andb:

fa~ t !2fb~ t !5const. ~1!

To quantify the degree of phase synchronization for two tiseriessa andsb we use themean phase coherencedefined as

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where 1/Dt is the sampling rate of the discrete time serof lengthN andVC denotes thecircular variance@33# of anangular distribution obtained by transforming the differencin phase onto the unit circle in the complex plane.~In theliterature,R is sometimes also referred to as the intensitythe first Fourier mode of the phase distribution@34#.! BydefinitionR is restricted to the interval@0,1# and reaches thevalue 1 if and only if the condition of phase lockingobeyed, whereas a uniform distribution of phases~whichwould be expected, on the average, for unsynchronizedseries! will result in R50.

Note that by definition the mean phase coherence isferent from other statistical measures for phase synchrontion described in the literature such as the index basedconditional probability and the index based on Shannontropy @31# but that all of them reflect the same properties

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the dynamics. Nevertheless, all analyses in this study wcarried out for the latter two measures as well. Since reswere almost identical for all three measures, in the followiwe only report on results obtained usingR as a measure fophase synchronization.

In order to determine the mean phase coherence ofsignalssa(t) and sb(t), it is first of all necessary to determine their phasesfa(t) and fb(t). For this purpose wefollow the analytic signalapproach@35,36# which renders anunambiguous definition of the so-called instantaneous phfor an arbitrary signals(t):

f~ t !5arctans~ t !

s~ t !, ~3!

where

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is the Hilbert transform of the signal~P denoting the Cauchyprincipal value!. Application of the convolution theoremturns the last equation into

s~ t !52 i •F 21$F @s~ t !#sign~v!%, ~5!

whereF denotes the Fourier transform andF 21 the in-verse Fourier transform. From this notation it becomes edent that the Hilbert transform performs a phase shift oforiginal signal byp/2 in the frequency domain while thpower spectrum remains unchanged. Note that anotherof defining the phase variable based on the wavelet transfhas been proposed@37#. Recently, it has been shown, however, that this definition is closely related to the definitibased on the Hilbert transform@32#.

B. Lag synchronization and maximum linear cross correlation

A further type of synchronization is thelag synchroniza-tion @38# which is characterized by a condition in which thstate variablessa(t) andsb(t) of two systems are shifted ba time lagt but are otherwise identical:

sa~ t1t!5sb~ t !. ~6!

A common measure for the similarity of two signalssa(t)andsb(t) is the linear cross correlation functiondefined as

corr~sa ,sb!~t!5E2`

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This function yields high values for such time lagst forwhich the signalssa(t) andsb(t1t) have a similar course intime. It is therefore well suited as a quantitative measurelag synchronization. In order to keep this measure indepdent of the variance of the signalssa(t) andsb(t), we use anormalized cross correlation function

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AUTOMATED DETECTION OF A PRESEIZURE STATE . . . PHYSICAL REVIEW E 67, 021912 ~2003!

C~sa ,sb!~t!5U corr~sa ,sb!~t!

Acorr~sa ,sa!~0!•corr~sb ,sb!~0!U , ~8!

where corr(sa ,sa)(0) andcorr(sb ,sb)(0) are thevalues ofthe linear autocorrelation functions att50 limiting therange of the cross correlation function to the interval@0,1#.As an actual measure for the degree of lag synchronizawe use themaximum linear cross correlation

Cmax5maxt

$C~sa ,sb!~t!%, ~9!

whereCmax51 means that the two systems exactly fulfill thcriterion of lag synchronization while unsynchronized sytems will result inCmax values close to zero. Note thatCmaxresembles the similarity function used in@38#.

C. Patient characteristics and data acquisition

The analyzed EEG signals were recorded from ten elepsy patients with medically intractable focal epilepsiesthe mesial temporal lobe undergoing invasive presurgicaagnostics at the Department of Epileptology of the Univsity of Bonn, Germany. Focal epilepsies are characterizedthe fact that seizures do not instantly affect the entire brbut rather begin in a circumscribed region of the brain, calthe epileptic focus. Since the localization of the epileptifocus could not be accomplished by means of noninvasEEG recordings, intracranial electrodes were implantedthe purpose of identifying the focal seizure origin as a prequisite for possible epilepsy surgery. All patients achievcomplete seizure freedom after surgery so the epileptic focan be assumed to be contained within the resected are

EEG recordings were performed under video controling stereotactically implanted elastic intrahippocampal deelectrodes~Fig. 1!, each equipped with ten cylindrical contacts of a nickel-chromium alloy~length 2.5 mm; intercon-

FIG. 1. Schematic view of intrahippocampal depth electrod

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tact distance 4 mm!. EEG signals were recorded using128-channel amplifier system with bandpass filter setting0.5 – 85 Hz~12 dB/octave! using a common average refeence. The sampling rate was 173.61 Hz, and analog-digconversion was performed at 12-bit resolution.

Data sets for each patient included one or two seizuwith a minimum of 10 min recording time before seizuonset and at least one interictal recording of at least 15length to serve as control. The total number of seizures alyzed in this study was 14. During interictal and preictrecordings, patients were awake and at rest. All recordepochs were free from artifacts. In two of the 14 seizurecordings patients were asked to hyperventilate prior tozure onset to provoke the onset of the seizure. Epochs wselected by EEG technicians prior to and independently frthe design of this study.

Since opinions differ as to how long before a seizuremechanisms leading to this event actually begin, any recoings within 4 h prior to seizure onset were excluded from tinterictal controls and instead regarded as preictal recordiIn order to neglect the postictal period, which is charactized by an altered appearance of the EEG, recordings wi1 h after a seizure were discarded from the analysis. Difent interictal data sets were usually recorded on differdays. The average length of the 35 analyzed interictal Erecordings was 25 min. The total amount of data analyzincluding seizure recordings, was 31 h. The average interirecording time per patient was 90 min~range 15 – 192 min!.The average preictal recording time was 50 min per seiz~range 10 – 105 min!.

D. Data analysis

The recorded data were analyzed using a moving-windtechnique@39#: EEG signals were divided into segments4096 sampling points each, corresponding to a windlength of 23.6 s at the given sampling rate, and windooverlapped by 20% so the distance in time between the sing points of two consecutive windows was 18.9 s. This wdow length can be regarded as a compromise betweenrequired statistical accuracy for the calculation of the degof synchronization and approximate stationarity withinwindow’s length@40,41#.

Prior to the calculation of the mean phase coherenthree steps of data preprocessing were carried out for edata window. First, the data in each window were demeanwhich corresponds to setting the dc Fourier coefficientv50) to zero. Next, to avoid edge effects, each window wtapered using a cosine half wave~Hanning window! beforeperforming the Fourier transform. Finally, since the calcution of the Hilbert transform in principle requires integratioover infinite time, which cannot be performed for a windoof finite length, 10% of the calculated instantaneous phvalues were discarded on each end of every window.

Given the symmetry of both synchronization measurthe number of possible combinations of different electrocontacts~ten in each hemisphere! amounts to 190. Takinginto account that the statistical significance of the time pfiles increases with the mean values of the respective s

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chronization measure, which in turn decrease with increasdistance between EEG contacts@22#, we restricted the fol-lowing analysis to neighboring channel combinationthereby reducing the number of combinations to 18. Ththe mean phase coherenceR and the maximum linear croscorrelation Cmax were computed for all combinations oneighboring contacts and for every consecutive windowsulting in 18 different time profiles for every recording anfor each synchronization measure. Since the algorithmbe implemented employing the fast Fourier transform@42#, itis possible to process even a large number of channels intime on a conventional computer.

E. Detection of a preseizure state

One aim of this study was to design an automated arithm to detect a preictal state based on a decrease in psynchronization described in our earlier work@22# and todistinguish it from the interictal state. In order to obtainbaseline in terms of a reference level for the interictal stawe calculated the mean valuemi j and standard deviations i jfor bothR andCmax ~in the following both denoted byX) byprocessing the synchronization profiles from all interictalcordings of a particular patient for every combinationneighboring channelsi and j.

In relation to any given baseline, a local drop cancharacterized by two independent parameters: its depthduration. The depth of such a drop can be measured in uof the standard deviation of the baseline epoch, whereaduration can be quantified by the time during which tmean value of a profile drops below a certain threshold.

For a practical implementation, we first applied a bacward moving-average filter of widthd to smooth the timeprofiles of Xi j (t) and then declared a preictal state if tsmoothed profilesXi j

d (t) dropped below the interictal meami j by more thanr standard deviationss i j :

PSD5H positive if Xi jd ~ t !,mi j 2rs i j ,

negative otherwise,~10!

where PSD stands for preseizure state detection.Note that this technique is equivalent to using a movin

window technique, measuring the area between the interreference level and the course of the original~unsmoothed!profile within a window of lengthd, and comparing this areto a rectangular reference area of widthd and a height ofrinterictal standard deviations.

Hence, we obtain two parametersr andd that govern themean depth of a drop over a certain time to be used athreshold for preictal state detection. In order to estimboth the sensitivity and specificity of the designed algorithwe applied it to all preictal and all interictal recordings, rspectively.

F. Parameter optimization

In order to determine suitable values for the two paraetersr and d, we carried out an in-sample optimization fothe entire group of patients by maximizing the performanP of our method defined as

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where f se is the sensitivity, defined as the fraction of sezures for which a preseizure state could be detected, anf spis the specificity rate, defined as 1 minus the average numof false positive detections per hour of interictal EEG for tentire group of patients~for more than 1 false positive pehour, f sp was set to zero for the particular combination ofrandd). For the calculation of the specificity rate, the durtion of each interictal recording was reduced by the lengtdof the moving-average window, keeping it thereby proptional to the specificity~the ratio of true negatives to thnumber of points in the smoothed profile!. Note that there areother ways of defining a performance, e.g., by normalizthe specificity to the duration of the preictal recordings avaable for each patient, and that they always represent a ceweighting of sensitivity and specificity. For our purpose whave deliberately chosen a performance measure that phigh emphasis on specificity.

It is important to point out that noa posterioriknowledgein the sense of a ‘‘best channel selection’’ was used, whwould require an appropriate statistical correction for mtiple testing. For a positive detectionat least oneof the chan-nel combinations analyzed needed to have a positive Pand, accordingly, for a negative detectionall combinationsneeded to have negative PSDs. The depth parameterr wasvaried from 0 to 6 interictal standard deviations while tduration parameterd was varied from 0 to 30 windows~cor-responding to;10 min!.

G. Cross validation

As always with in-sample parameter optimization, therea risk of overtraining an algorithm in the sense that paraeters are optimized on a given sample to yield a performafor this sample~estimated performance! that may not beachieved in an out-of-sample trial~true performance!. To re-duce the risk of an overestimation of our method’s perfmance due to in-sample optimization, we performed a crvalidation analysis. For the given sample of patients, a tfold cross validation was carried out using the ‘‘leaving-onout’’ method @43,44#, i.e., each of the ten patients was susequently used as a test sample while the remainingpatients served as training samples, i.e., for parameter omization. The overall performance of the individual tesamples was then compared to the performance of the egroup as defined in the previous section. Similar valuesboth performance estimates indicate that the parametersnot been overtrained. The standard error of the sensitivitgiven by

E5Af se~12 f se!

n~12!

wheren is the number of test cases~i.e.,n510 in this study!.The standard error for the specificity is calculated accoingly, and the resulting error of the performance can be cculated using Gaussian error propagation.

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FIG. 2. Examples of EEG segments from neighboring channels of one patient during the interictal, preictal, and ictal state avalues for the mean phase coherenceR and the maximum linear cross correlationCmax calculated from these segments.

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H. Test for statistical validity

Time series such as the profilesXi j (t) that were obtainedfrom measured data usually contain fluctuations and thfore in principle have a nonzero probability of crossing athreshold within their range of definition. This has to be kein mind whenever a threshold criterion is applied to real daConcerning our analysis, this means that there is no guatee that the observed effects are indeed due to different cacteristics of the interictal and preictal state but instead cobe caused, at least in part, by these fluctuations. Givenrespective duration of the interictal and preictal recordinthere is a nonzero probability of finding a ‘‘preictal’’ drop iat least one of the 18 possible combinations of neighbochannels just by chance. Therefore, the null hypothesis ttested is that the observed performance values are mecaused by fluctuations in synchronization that are not relato the existence of a preictal state.

With this aim, we designed a surrogate of the analyzedof recordings@45#. For each patient and every recording swe replaced any preictal interval~i.e., any recording within 4h before seizure onset! by randomly selected interictal oneand vice versa, applying constraints to keep the ratio of pictal and interictal time constant for the entire group andmaximize the overall amount of data contained in the sugate set. The same process of preictal state detectionoptimization was then applied to this surrogate set of recoings. To test the null hypothesis, the maximum performafound for the original set of recordings was compared to tfor the surrogate set.

III. RESULTS

Examples of the raw data analyzed in this study are giin Fig. 2. Displayed are original EEG segments recordsimultaneously from two neighboring recording sites ofpatient during the seizure-free interval, during the period pceding a seizure, and during the seizure itself, along withcorresponding values for each of the two synchronizatmeasuresR andCmax.

Figure 3 shows an illustration of the detection techniq

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described above for an interictal EEG recording and acording containing a seizure from one patient. It is easynote that preictal synchronization values are lower thanterictal values. A remarkable aspect is the similarity of tprofiles for the two different measures for synchronizatioTo quantify this similarity the linear correlation coefficient2

between the two synchronization measures was calculfor all possible channel combinations for all profiles of eapatient. Correlation coefficients were found to range fro0.32 to 0.69 for different patients, indicating a medium dgree of linear correlation between the two measures.

The dependence of the performance of the algorithmthe parametersr andd in terms of both sensitivity and specficity is illustrated by Fig. 4. Optimum performance for thmean phase coherenceR could be obtained, e.g., for valuer 54 andd'2.5 min ~eight windows!, and amounted toP50.93 for the entire group. For the maximum linear crocorrelationCmax, parameter values of, e.g.,r 53.8 andd'3.5 min ~11 windows! led to the same maximum performance. Using these parameters for the ten patients analin this study, we found positive PSDs in 12 out of 14 seizurecordings corresponding to eight out of ten patients. Forgiven parameters there was not a single false positive detion during the entire 15 h of interictal recordings for eithmeasure, corresponding to a specificity of 1 for the whgroup of patients. Concerning the variability of optimum prameters among the different patients, we found that for eof the eight patients for whom a preseizure state coulddetected, there was a large contiguous region of paramcombinations rendering a performance of 1, while for tremaining patients there was no such region. These twotients were the same for both synchronization measures

The number of channel combinations with positive PSfor the remaining patients ranged from 1 to 7~mean 3! for Rand from 1 to 8~mean 3! for Cmax for the different seizuresFor all but one seizure with positive PSD, there was at leone channel combination exhibiting positive PSD for bomeasures. Furthermore, this combination was usually thethat exhibited the most prominent drops in synchronizatfor both measures.

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FIG. 3. ~Color online! Interictal and preictal synchronization profiles from one patient. Displayed are both the original and the smprofiles of one channel combination for both the mean phase coherenceR ~upper row! and the maximum linear cross correlationCmax ~lowerrow! along with the mean value and standard deviation~horizontal gray bars! calculated from the interictal recordings as well as the detecthreshold~horizontal thick black line! calculated from these values using optimized parameters. The seizure is marked by a gray vertNote that the preictal state has already started at the beginning of the recording containing the seizure.

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The duration of the detected preictal state could notactly be determined in most cases since the preictal statealready started at the beginning of the preictal recordinThe anticipation time for a seizure was defined as the tinterval between the first positive PSD found in any of tcombinations of neighboring channels during the preictalriod of 4 h before the seizure and the seizure onsetranged, as determined from the data available, from 4 minto more than 219 min~mean 86 min! for the mean phasecoherence and from 7 min up to more than 218 min~mean102 min! for the maximum linear cross correlation. Anticpation times exceeding the preictal recording time are dugaps in these recordings. The difference in anticipation timfound for the two measures did not exceed 10 min excepttwo seizures where anticipation times forCmax were signifi-cantly longer than forR.

Analyses of the preictal drops revealed that in 9 out of12 detected preictal states, at least for one combinationpreictal drop lasted until the onset of the seizure whereathe remaining cases the preictal synchronization level rabove the PSD threshold before~although usually very closeto! seizure onset. During the actual seizure activity, the usfinding was a steep increase in synchronization reachineven surpassing the interictal mean value. As for the postperiod, we found that in 7 out of the 12 seizures with posit

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PSD, the degree of synchronization remained above the Pthreshold while in the remaining cases it started decreashortly after the seizure.

Results of the cross validation yielded a corrected permance ofP50.91 for the mean phase coherence that diddeviate from the in-sample performance given abovemore than the standard error ofE50.11. For the maximumlinear cross correlation, the corrected performance wasactly the same as the original performance.

As a check for statistical validity of the observed effecthe surrogate test was carried out as described above. Reof the parameter optimization for the surrogate set of recoings are displayed in Fig. 5. Note that for both synchronition measures the maximum the performance is obtainedparameters yielding either a high sensitivity or a high speficity, but no parameter values could be found for which bosensitivity and specificity rate simultaneously exceed a vaof 0.54.

IV. DISCUSSION

A. Preseizure state detection

Results show that the period preceding a seizure cancharacterized by a decrease in synchronization between

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FIG. 4. ~Color! Optimization of parameters~see text!. Color-coded values for sensitivity, specificity rate, and performance are displin dependence on the parametersd ~filter width in minutes! andr ~average depth of drops in units of the interictal standard deviation! for bothR ~upper row! andCmax ~lower row!. Parameter combinations yielding maximum performance are marked by bold frames.

FIG. 5. ~Color! Same as Fig. 4, but for the surrogate set of recordings.

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ferent EEG recording sites. This decrease in synchronizacan be detected using the automated technique introducethis study. The overall performance of the method basedthe given data indicates that it works well for most patiealthough it fails in some cases. The optimization of therameters used in the detection algorithm was carried outthe entire group of patients and can be regarded as formost part free from overtraining as confirmed by cross vdation.~To actually prove this point, validation in an out-osample trial would be necessary, which, however, goesyond the scope of this study.! The results of the surrogate tefor statistical validity indicate that our findings are indecaused by different characteristics of the interictal and prtal periods and cannot be explained by merely random fltuations of the synchronization profiles.

B. Comparison of the synchronization measures

When comparing the mean phase coherence as a mefor phase synchronization and the maximum linear crossrelation as a measure for lag synchronization it shouldkept in mind that the latter depends on both amplitudesphases of the time series while the former depends solelthe phases, i.e., in the case of phase synchronization amtudes may be completely uncorrelated or even chaotic.

As for the duration of the detected state it is possibledistinguish between the anticipation horizon~the time be-tween detection and seizure onset! and the actual duration othe preictal state~from the beginning of a significant drop tseizure onset! where the difference between the two is givby the above defined parameterd. For both of the differentsynchronization measures, the duration of the anticipatimes is mostly of the order of several tens of minutes. Tstands in contrast to earlier studies@11–17# where mean an-ticipation times from 2 to 11 min have been reported. Tdifferent range of anticipation times implies that changesdynamics tracked by synchronization measures are diffefrom those tracked by other, mostly univariate nonlinemeasures. It should not be omitted that in some recent sies @18,19,21# similar anticipation times have been reportas found in this study. Whether these findings reflectsame dynamical aspects, remains to be investigatedshould be pointed out that with the extended anticipathorizons found in this study, there is little information abowhen exactly the seizure will occur. We therefore avoidterm ‘‘prediction’’ and rather speak of ‘‘anticipation’’ of seizures, implying that we may know that a seizure has a cerprobability to occur within a certain time frame but we dnot know exactly when. An anticipation horizon of thlength could on the other hand enable patients to responthe threat of an impending seizure.

Concerning the location of the observed preictal dropssynchronization, it turned out that for half of the patienwith positive PSDs~four out of eight!, the most prominentpreictal drops in synchronization were found in the nonfohemisphere, while for the remaining patients they wfound in the focal hemisphere, although not necessawithin the focus~as determined by electrographical seizuonset! itself. This effect was found for both synchronizatio

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measures and stands in agreement with earlier studies~e.g.,@15,19#! while in other studies seizure precursors wemostly found within or near the focal area~e.g., @11,18#!.This finding indicates that the process of seizure generain focal epilepsy may not necessarily be confined to the foarea but may instead involve more distant areas of btissue, even in the nonfocal hemisphere.

Evaluation of the postictal period shows that in the mjority of cases the interictal level is retained after the seizregardless of which measure was evaluated. This effectresponds well to the hypothesis of a seizure acting as asetting mechanism from unstable dynamics to a more stone @46#. Such a resetting phenomenon, however, wasfound in all cases, which could be interpreted in the sethat the resetting attempt is not always successful, partlarly as there was no apparent correlation of a ‘‘futile resting’’ with an increased occurrence of subsequent seizure

The results of this study generally show a similar perfmance for both synchronization measures. In particular,outcome of the patients in terms of positive or negative Pwas the same for both measures. Furthermore, anticipatimes were found to be in the same range, and combinatwith positive PSD matched for both measures in the majoof patients. This indicates that the preictal changes in dynics analyzed in this study can be sufficiently characterizusing a linear measure. If these changes in synchronizahad been nonlinear in nature, we would have expectesuperior performance of the mean phase coherence as alinear measure. A way to further investigate this issue wobe the use of bivariate surrogates@47# to discern linear as-pects of synchronization from nonlinear ones which, hoever, goes beyond the scope of this study.

C. Future perspectives

For the four patients with more than one seizure wpositive PSD, we found that although the PSD was usurestricted to a few channel combinations, in three cases twas at least one combination for which the PSD was posifor all seizures of a particular patient. Also, it was usuathis combination that exhibited the most prominent dropssynchronization. This finding stands in contrast to earstudies @14,19# where electrode sites exhibiting predictivfeatures were reported to change from seizure to seizurethe same patient. The described stability over seizures cbe used to further improve the specificity of the methodonly considering channel combinations for a particular ptient that have proven to be sensitive for preictal state detion, and thus omitting possible false positive detectionsthe remaining channel combinations.~As expected for pa-tients analyzed in this study, such a ‘‘best channel selectiyielded an even better performance but also a lower statcal validity as determined by the corresponding surrogtest.! Another way to improve the method’s performancelong-term evaluations could be an individual parameterjustment for each patient to obtain the best possible discrnation between interictal and preictal states. It shouldpointed out, however, that both of these improvements wo

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require a great deal of preanalysis and additional traindata for each patient in order to obtain the necessary inmation.

In this context it is important to once again emphasize tthe results described above were obtained from a retrostive study on selected data samples in the sense thatinstance, any sleep recordings were excluded from the sinterictal data. The sensitivity and specificity obtained in tstudy might therefore significantly differ from what onwould find in a prospective study. The aim of this study wmerely to examine whether a statistically valid discrimintion between preictal states and selected interictal statesprinciple possible with the method introduced. From our pliminary experience with long-term recordings we wouconjecture that including unselected interictal data suchdifferent states of vigilance could decrease the predicperformance, whereas best channel selection and patspecific parameters will on the other hand be likely to resin an increase in performance. The extended anticipationrizons found in this study would leave enough time fortervention strategies such as automated on-demand metion @48,49#, electrical stimulation@50–52#, or local cooling@53#, provided that a sufficient performance of the methintroduced can be obtained in a prospective setting.

In order to adapt this method to such a prospective stdesign for continuous recordings, it is necessary to reathat the definition of a baseline becomes a nontrivial prlem. To avoid false detections due to trends or shifts in baline we would recommend the use of an adaptive baselinsimple realization of such an adaptive baseline could,instance, be given by defining the adaptive meanmt as

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wheret is the time index of the continuous time series of tmeasureXt5X(t), w is the time interval between two consecutive analysis windows~i.e., two consecutive valuesXt),T is the duration of the baseline epoch, andL is the time lagbetween the~moving! baseline and the time of~prospective!analysis. The standard deviation for the adaptive baseshould, of course, be determined accordingly. From our pliminary experience with long-term recordings, we woupropose to use, for instance, a time lag ofL524 h to adapt tocircadian fluctuations and a baseline lengthT of a few hours.

V. CONCLUSION

Based on the findings of a preictal loss in synchronizatbetween EEG signals recorded simultaneously from differlocations in the brain, we have investigated the suitabilitythis phenomenon for characterization of the preseizure sBy evaluating both sensitivity and specificity, by checkinfor in-sample overtraining via cross validation, and by apping a surrogate test for statistical validity, we have demostrated that our method for preictal state detection in pciple allows us to discriminate the preictal from the intericstate, thus satisfying a necessary condition for prospecseizure anticipation. The similar performance of the two dferent measures for synchronization, one linear and one nlinear, indicates that the changes in dynamics before seizthat were found in this study are not necessarily causednonlinear features of the dynamics.

ACKNOWLEDGMENTS

We are grateful to Martin Kurthen for useful discussioand valuable comments. This work was supported byDeutsche Forschungsgemeinschaft.

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