Nonlinear EEG Analysis in Epilepsy:

Its Possible Use for Interictal Focus Localization, Seizure Anticipation, andPrevention

*Klaus Lehnertz, *†Ralph G. Andrzejak, *‡Jochen Arnhold, *‡Thomas Kreuz,*†Florian Mormann, *†Christoph Rieke, *Guido Widman, and *Christian E. Elger

*Department of Epileptology and†Institute for Radiation and Nuclear Physics, University of Bonn; and the‡John-von-Neumann-Institute for Computing, Research Center Jülich, Germany

Summary: Several recent studies emphasize the high value of nonlinear EEG analysisparticularly for improved characterization of epileptic brain states. In this review theauthors report their work to increase insight into the spatial and temporal dynamics ofthe epileptogenic process. Specifically, they discuss possibilities for seizure anticipa-tion, which is one of the most challenging aspects of epileptology. Although there arenumerous studies exploring basic neuronal mechanisms that are likely to be associatedwith seizures, to date no definite information is available regarding how, when, or whya seizure occurs. Nonlinear EEG analysis now provides strong evidence that theinterictal–ictal state transition is not an abrupt phenomenon. Rather, findings indicatethat it is indeed possible to detect a preseizure phase. The unequivocal definition ofsuch a state with a sufficient length would enable investigations of basic mechanismsleading to seizure initiation in humans, and development of adequate seizure preven-tion strategies.Key Words: Epilepsy—Interictal state—Preictal state—Seizure antic-ipation—Seizure prevention—Focus localization—Nonlinear time series analysis—EEG.

With the advent of the physical–mathematical theoryof nonlinear deterministic dynamics (see Schuster [1989]and Ott [1993] for an overview, and Gleick [1987] for aneasy-to-read account), new concepts and powerful algo-rithms were developed to analyze apparently irregularbehavior—a distinctive feature of, for example, brainelectrical activity. During the last decade, a variety ofnonlinear time series analysis techniques (Kantz andSchreiber, 1997) have been applied repeatedly to EEGrecordings during physiologic and pathologic conditions.

Nonlinear measures like dimensions, Lyapunov expo-nents, entropies, or recent approaches that aim to char-acterize interdependencies, synchronization, or similari-ties were shown to offer new information about complexbrain dynamics (see Basar [1990], Duke and Pritchard[1991], Jansen and Brandt [1993], and Lehnertz et al.[2000c] for an overview). After an initial euphoric phase,it is now commonly accepted that the existence of adeterministic and even chaotic structure underlying neu-ronal dynamics is difficult or even impossible to prove.Moreover, the well-known nonlinear behavior of indi-vidual neurons, and with it the expectation of neuronalnetworks to behave in a similar way, is used as justifi-cation for applying these methods—an assumption thatstill is matter of debate (Schreiber, 2000a; Theiler andRapp, 1996). Nonetheless, there is converging evidence

Supported by the Deutsche Forschungsgemeinschaft (grant no.EL122/3-1–EL122/3-4).

Address correspondence and reprint requests to Dr. Klaus Lehnertz,Department of Epileptology, Medical Center, University of Bonn,Sigmund Freud Str. 25 53105 Bonn, Germany.

Journal of Clinical Neurophysiology18(3):209–222, Lippincott Williams & Wilkins, Inc., Philadelphia© 2001 American Clinical Neurophysiology Society

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that nonlinear approaches to the analysis of brain sys-tems are able to generate new clinical measures as wellas new ways of interpreting brain electrical function,particularly with regard to epileptic brain states.

In this review we report our work to increase insightinto the spatiotemporal dynamics of the epileptogenicprocess. Both linear and nonlinear analysis techniqueshave been applied to intracranial recordings (electrocor-ticograms [ECoG] and stereoelectroencephalograms[SEEG]) from more than 300 patients undergoing pre-surgical evaluation for resective therapy in differentcerebral regions. On this basis we show that nonlinearEEG analysis may become particularly important forboth clinical practice and basic science. Nonlinear EEGanalysis not only improves the presurgical evaluation butprovides strong evidence that the interictal–ictal transi-tion is not an abrupt phenomenon that occurs likea boltfrom the blue. Rather, this classic two-state model has tobe expanded to embed a third, preictal transitional phase.Recent findings indicate that it is indeed possible todetect such a state heralding a seizure (Elger and Leh-nertz, 1994, 1998; Iasemidis et al., 1990, 1997; Lehnertzand Elger, 1998; Lehnertz et al., 1999b; Le Van Quyen etal., 1999b, 2000, 2001; Martinerie et al., 1998; Moser etal., 1999; Sackellares et al., 2000) and, moreover, thatthis phase is long enough to allow investigation of basicmechanisms leading to seizure initiation in humans, thedevelopment of adequate seizure warning systems, oreven patient-specific prevention strategies.

The search for thehidden informationpredictive of animpending seizure has a long history in EEG analysisinvolving autoregressive models (Rogowski et al., 1981)or coherence analyses (Duckrow and Spencer, 1992)from preictal EEG recordings. Although the former in-dicated that EEG changes characteristic for preictalstates may be detectable, at most, a few seconds beforethe actual seizure onset, the latter pointed to an increaseof inter- and intrahemispheric coupling that may occurminutes before a seizure. The relevance of brief bursts offocal pathologic neuronal activity leading to spikes in theEEG and occurring before seizure onset was investigatedin several clinical studies (Gotman et al., 1982; Katz etal., 1991; Lange et al., 1983; Wieser, 1989). Althoughsome of the aforementioned authors reported a decreaseor even total cessation of spikes before seizures, reex-amination did not confirm this phenomenon in a largersample. Attenuation or flattening of the backgroundactivity can be observed both as a concomitant EEGcorrelate of an aura and as a preictal EEG phenomenon.It may occur regionally or more generalized and is bestdetected using intracerebral electrodes. Duration of this

phenomenon, however, is often too short to allow timelydetection of a preictal state.

WHY NONLINEAR EEG ANALYSIS CAN BEATTRACTIVE

At first glance, the aforementioned inconsistent find-ings may appear discouraging because they limit theimportance of those aspects of brain electrical activitythat were presumed to be most relevant for a detection ofan increased probability of seizure occurrence. However,these findings also indicate that seizure occurrence maynot be regarded as a purely stochastic phenomenon(compare with Iasemidis et al. [1994]). Today, there isincreasing evidence that a number of key conceptualfeatures of nonlinear dynamic systems have particularrelevance to improve understanding of the spatiotempo-ral dynamics of the epileptogenic process:

First, the basic principle of almost all nonlinear timeseries analysis techniques is the reconstruction of theobserved system dynamics in a so-calledstate space.Although an unknown system may well be dependent ona large—and for the EEG often unknown—number ofvariables, the mathematical theorem of Takens (1981)states that the system’s behavior in state space can beapproximated using only asingleobserved variable (e.g.,the EEG).

Second, if the system is governed by nonlinearity, asimple cause–effect relationship cannot be expected.Rather, nonlinear systems are characterized by a richvariety of dynamics includingbifurcationsthat indicateabrupt state transition orintermittent behavior. EEGphenomena like spike–burst suppression patterns, epi-leptiform activity such as spikes, or the interictal–ictalstate transition point to nonlinearity. Abrupt state transi-tions from highly complex, irregular to less complex,almost periodic dynamics appear to be a characteristicfeature in many disorders and are one of the mostcompelling examples for the notion ofcomplexity loss.Such disorders have been termeddynamical diseases(Glass, 2001; Glass and Mackey, 1978; Goldberger,1997; Mackey and Glass, 1977; Reimann, 1963). “De-complexified” systems are less adaptable and less able tocope with the exigencies of a constantly changing envi-ronment (compare with Goldberger [1992]). Moreover, itis the very occurrence of periodicities and highly struc-tured patterns that allow identification and classificationof many pathologic phenomena.

Third, because of the sensitive dependence on initialconditions (thebutterfly effect) of a deterministic chaoticsystem, its long-term behavior can hardly be predicted.Conversely, a nonlinear system has an inherent ability to

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“self-organize” in the sense that it evolves toward anordered temporal and spatial structure called anattrac-tor. This mathematic concept may explain the well-organized, self-sustained oscillations in EEG recordingsthat occur during seizure activity (Fig. 1). This dualismof chaos and order is the key feature of nonlineardynamics.

And fourth, generally, the initial conditions and therules that govern a system like the epileptic brain areunknown. However, a variety of new concepts and mea-sures have been developed that allow one to characterizefully the dynamical behavior of an unknown system in atheoretic sense: Lyapunov exponents characterize thesystem’s stability under some small perturbation, andthus are a measure of how chaotic a system behaves;dimension estimates are closely related to the number ofdegrees of freedom of a system; and entropies measurethe degree of order/disorder. Dimensions and entropiescan thus be regarded as an estimate of the system’scomplexity. Recently, these univariate, nonlinear mea-sures have been supplemented by new approaches tocharacterize spatial- and time-invariant phenomena innonlinear systems.

These concepts allow one to describe sufficiently anonlinear dynamical system as shown for well-known

model systems that can be used to produce arbitrarilylong and stationary time series at almost infinite preci-sion. In contrast, a bulk of literature indicates an abatedimportance of nonlinear time series analysis techniqueswhen applied to short, noisy, and nonstationary timeseries like the EEG—generated from a system with analmost unknown structure. Despite these shortcomings, itis commonly accepted today that nonlinear EEG analysisis nonetheless able to provide new and relevant informa-tion as long as the limitations of the techniques are takeninto consideration and the results are interpreted care-fully (e.g., operationally defined or relative measures areused). Following this premise, we have investigated theapplicability of already established measures and havedeveloped new measures to characterize the spatiotem-poral dynamics of the epileptogenic process.

CHARACTERIZING THE INTERICTAL STATEBY NONLINEAR EEG ANALYSIS

Several lines of evidence originating from studies ofhuman epileptic brain tissue as well as of animal modelsof chronic seizure disorders indicate that the epilepticbrain, even between seizures, is different from normal.Based on the well-known fact that neurons involved in

FIG. 1. EEG signals in the time domain (upper) and the corresponding trajectories in a two-dimensional state space (lower). Here, the EEG timeseries x(t) is plotted versus itself; however, with an appropriately chosen time delayt on one axis. Left, normal EEG; middle, EEG with spikes; right,seizure EEG. Scale bars indicate 500mV and 1 second respectively.

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the epileptic process exhibit high-frequency dischargesthat are scarcely modulated by physiologic brain activity(Wyler and Ward, 1980), we hypothesized that thisneuronal behavior should be accompanied by an inter-mittent loss of complexity or an increase of nonlineardeterministic structure in the corresponding electro-graphic signal even during the interictal state (Lehnertzand Elger, 1995). Thus, to evaluate the efficacy ofanalysis techniques for characterizing the spatiotemporaldynamics of the epileptogenic process, we applied themto long-lasting interictal recordings covering differentstates of normal behavior and vigilance, as well asdifferent extents of epileptiform activity. Because thereare phases of dynamical changes during the interictalstate that point to abnormalities but are not followed bya seizure, we regarded this approach mandatory to eval-uate the specificity of possible seizure predictiontechniques.

In the following paragraphs we present findings thatwere obtained from retrospective analyses of interictalECoG/SEEG recordings in patients with mesial temporallobe epilepsy (MTLE) and/or neocortical lesional epi-lepsy (NLE) undergoing presurgical evaluation. We in-cluded data of patients for whom surgery led to completepostoperative seizure control (follow-up, at least 1 year)as well as data for patients who did not benefit fromsurgery. This allowed us to estimate sensitivity andspecificity of the different analysis techniques for theepileptogenic process as well as their possible impact onpredicting postoperative outcome.

Introducing the neuronal complexity loss L* (Fig. 2)as an integral measure for temporal changes of an esti-mate D* of an effective correlation dimension (Grass-berger et al., 1991), we obtained first evidence for a

decreased complexity of neuronal networks involved inthe epileptogenic process (Lehnertz and Elger, 1995).We extracted L* from interictal ECoG/SEEG recordingsof 20 MTLE patients and showed that this measurereflects temporal and spatial aspects of the epileptogenicprocess at a high sensitivity. Maximum L* values wereconfined to focal and adjacent recording sites, decreasinggradually with an increasing distance from the primaryepileptogenic area. In all patients, the spatial distributionof L* allowed us to lateralize clearly the primary epilep-togenic area regardless of whether obvious epileptiformactivity was present in the ECoG/SEEG recordings.

Applying the same analysis technique to semi-inva-sive recordings employing foramen ovale electrodes,Weber et al. (1998) replicated the discriminative powerof L* in 16 of 19 MTLE patients. Further evidence of themeasure’s sensitivity came from a study evaluating themodulating influence of antiepileptic drugs (Lehnertzand Elger, 1997). Here, we analyzed interictal ECoG/SSEG recordings from 10 MTLE patients sampled atsubsequent days during the presurgical evaluation withstrongly variant carbamazepine serum levels. We ob-served a close inverse relationship between L* and car-bamazepine serum level restricted spatially to the pri-mary epileptogenic area.

To prove applicability of nonlinear EEG analysis be-yond the well-defined MTLE syndrome (Gloor, 1991),we investigated interictal ECoG recordings from 10 NLEpatients with lesions in the frontal, parietal, or temporalneocortex (Widman et al., 2000). We observed a highconformity between maximum values of L* and the areaof resection, especially in those patients who becameseizure free after extended lesionectomy. This effect wascomplemented by a more widespread and diffuse spatial

FIG. 2. Computation of the neuronalcomplexity loss L*. Examples of tem-poral variations of dimension valuesD* (dimension profile) extracted fromelectrocorticograms/stereoelectroen-cephalograms at different sites. A re-duction of the complex informationcontent of dimension profiles isachieved by L*. This measure repre-sents the integral between the actualdimension profile and an upper reso-lution bound (here Du 5 10; comparewith Lehnertz and Elger [1995] fordetails).

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distribution of L* in those patients who had no benefitfrom the resection, indicating the existence of additionalfoci. We obtained similar findings in another studyestimating the possible extent of a hippocampal partici-pation in the epileptogenic process of NLE patients(preliminary findings in Widman et al. [1997]). Weincluded 20 patients with clinical hints for a hippocampalinvolvement but for whom presurgical evaluation led toan extended lesionectomy. In 10 patients we observedmaximum values of L* only at mesial temporal record-ing sites. From this group only one patient becameseizure free. For the remaining 10 patients, 9 of whombecame seizure free, maximum L* was found at neocor-tical recording sites. Because postoperative outcome ofneocortical epilepsy is still unsatisfying compared withMTLE (e.g., see Williamson et al. [2000]), we considernonlinear EEG analysis a valuable extension to otherdiagnostic approaches already established in this field(Elger et al., 2000a, b).

We have recently reexamined the merit of L* for theinterictal lateralizationand localization of the primaryepileptogenic area in a larger group comprising 75 pa-tients (preliminary findings in Lehnertz et al. [1999c]).Postoperative complete seizure control confirmed MTLEin 52 patients and lateral TLE in 23 patients respectively.The electrode contact exhibiting the maximum L* valueindexed correctly both the side and the site of theprimary epileptogenic area in 44 of 52 MTLE patientsand in 20 of 23 lateral TLE patients (Fig. 3). Failure ofcorrect localization could be attributed to either almostidentical ipsilateral and contralateral L* values or tovalues close to or at the theoretic resolution limit of theapplied method (compare with Ruelle [1990]).

Based on the key conceptual features of nonlineardynamical systems mentioned earlier, we hypothesizedfurther that the epileptogenic process induces or en-hances nonlinear deterministic structures in the other-wise linear stochastic appearance of brain electrical ac-tivity (compare with Pijn et al. [1991, 1997], Casdagli etal. [1997], and van der Heyden et al. [1999]). To verifythis assumption, we introduced a new measure, x, (An-drzejak et al., 1999, 2000b, 2001), that combines tests fordeterminism (Kaplan and Glass, 1992) and for nonlin-earity (Schreiber and Schmitz, 1996). Previous researchhad failed to identify nonlinear determinism in scalpEEG recordings of healthy subjects (e.g., Palus [1996]and Jeong et al. [1999]). However, extraction of x, for atotal of 82 interictal ECoG/SEEG recordings (averageduration per patient, 84 minutes) from 25 MTLE pa-tients, provided strong evidence for nonlinear determin-ism in recordings from within the primary epileptogenicarea, whereas signals from other sites mainly resembled

linear stochastic dynamics. Preliminary findings in eightNLE patients indicated a discriminative power similar tothe neuronal complexity loss L*; in other words, highconformity between maximum values of x and area ofresection in postoperatively seizure-free patients, and amore widespread and diffuse spatial distribution of x inthose patients who did not benefit from the resection(Andrzejak et al., 1999) (Fig. 4).

Univariate nonlinear EEG analysis techniques allowclassification of temporal aspects and, when applied tomultichannel recordings, allow classification of the rel-ative spatial distribution of the epileptogenic process.However, they do not provide information about spatial

FIG. 3. Interictal lateralization and localization of the primary epilep-togenic area. (A) Group means and standard deviations of maximumipsilateral and contralateral L* values (L*max) and results of post hocWilcoxon’s signed rank test. Preceding analysis of variance indicated ahighly significant effect of the side of the primary epileptogenic area onL* max values for each group (lateral temporal lobe epilepsy [LTLE]group: F[2,20]5 7.754, P , 0.005; mesial temporal lobe epilepsy[MTLE] group: F[2,49] 5 6.972,P , 0.005; total group: F[2,72]514.738,P , 0.001). (B) Lateralization: efficiency indicates correspon-dence between side of L*max and side of primary epileptogenic area.Localization: correspondence between recording site exhibiting earliestsigns of seizure activity and site of L*max.

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interactions or spatial synchronization phenomena,which are considered to play a crucial role in epilepto-genesis and ictogenesis. Discerning the synchronizationof spatially and temporally distributed processes andevents in the brain may offer the possibility of gatheringdeeper insight into pathologic, interictal phenomena aswell as seizure development. We approached this prob-lem by developing and evaluating a variety of bivariateanalysis techniques, two of which turned out to be wellsuited. The nonlinear interdependence measureS (seeArnhold [2000] and Arnhold et al. [1999, 2000], andreferences therein) attempts to characterizestatisticalrelationships between two time series (see also Le VanQuyen et al. [1999a], Pereda et al. [2001], and Schiff etal. [1996]). By construction, it does not treat phaseinformation (discussed later) differently from amplitudeinformation. In contrast to commonly used techniqueslike cross-correlations, coherence, or mutual informa-tion, S is nonsymmetric and thus provides additional

information about the direction of interdependence. Ap-plication of this technique to interictal SEEG recordings(duration, 10 minutes) from 13 MTLE patients revealedmaximum values ofS to be confined to the primaryepileptogenic area in 10 patients. Analysis of the direc-tion of interdependence provided strong evidence for ahigher contralateral-to-ipsilateral similarity in SEEG re-cordings from 11 patients than vice versa. The interpre-tation of this finding as an indication for a causal driver–responder relationship deserves further investigation.

The other approach characterizing spatial interactionsor synchronization phenomena is based on the statisticaldistribution of the relative instantaneous phases of twotime series using the Hilbert transform (compare withPanter [1965] and Mardia [1972]). Because no unifieddefinition for synchronization has been established sofar, we introduced the mean phase coherenceR as astatistical measure for phase synchronization (Mormannet al., 1999, 2000b). We analyzed 40 interictal SEEG

FIG. 4. Examples of spatial distribution of neuronal complexity loss L* and fraction of nonlinear determinism x; in two patients with neocorticallesional epilepsy. The thick black line indicates the area of resection. (Extended lesionectomy of glioneuronal hamartia in Patient A and indicatesthearea of cortical dysplasia in Patient B. There has been complete postoperative seizure control in both patients for more than 2 years.) Distributionsof both measures exhibit a high congruence with the area of resection (notice, however, the more circumscribed spot that is gained from the fractionof nonlinear determinism, x). Side length of voxels, 1.5 cm.

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segments (mean duration, 34 minutes) recorded from 17MTLE patients and observed higher values ofR on thefocal side in 14 patients.

Results obtained from our bivariate measures indicatethat the epileptogenic focus is characterized by a patho-logically increased level of interdependence or synchro-nization even during the interictal state. Our univariateand bivariate measures thus share the ability to detectdynamical changes related to the epileptic condition.Moreover, the ability of bivariate measures to reflectanatomic boundaries of brain structures because of theirenhanced intrinsic synchronization allows functionalanalysis of specific brain functions such as memoryformation (Lehnertz et al., 1999a, 1997a, b). Althoughthe high intrinsic synchronization in several anatomicstructures makes it difficult to separate clearly physio-logic from pathologic synchronization, bivariate mea-sures have the important advantage of allowing exami-nation of long-range effects such as entrainment ofadjacent or remote brain areas into the epileptogenicprocess (discussed later).

Summarizing this section, we conclude that our EEGanalysis techniques approach the problem of character-izing the epileptogenic process from different points ofview, and they indicate the potential relevance of non-linear EEG analysis to improve understanding of inter-mittent dysfunctioning of the dynamical brain systembetween seizures. Moreover, our results also stress thehigh relevance of nonlinear EEG analyses in clinicalpractice because they provide potentially useful diagnos-tic information and thus contribute to an improvement ofthe presurgical evaluation (Elger et al., 1999, 2000b;Lehnertz et al., 2000a).

DETECTING PREICTAL STATES BYNONLINEAR EEG ANALYSIS

A preictal state may be defined as a condition of theepileptic brain and its functioning that inevitably evolveinto a seizure unless some kind of intervention takesplace. Given thea posteriori knowledge of a seizureoccurrence, it appears rather trivial to postulate the ex-istence of such a state. However, its unequivocala prioridefinition, and with it the possibility to anticipate animpending seizure, is obviously far from being trivial.Nevertheless, a variety of clinical observations supportthe notion that at least certain seizures can be anticipated.First, several seizure-facilitating factors are known. Inthe context of his “reservoir theory,” Lennox (1946) hasdefined seizure facilitation as the input of sensory, met-abolic, emotional, or other yet unknown factors that fillup some reservoir until it overflows, which in turn results

in a seizure. Among others, levels of consciousness,sleep deprivation, tension states, disturbances of waterand acid–base balance, and sensory and drug stimulationare regarded as potential influencing factors (Aird,1983). However, apart from the rare exception of senso-ry-evoked or reflex epilepsies, these factors are obvi-ously unspecific and highly variant because they dependon habits and daily activities of the patient. Moreover, itis clinically undisputed from many descriptions of closerelatives that long-lasting behavioral and/or prodromalchanges of the autonomous nervous system exist incertain patients. These alterations include depressivemood changes, irritability, sleep problems, nausea, andheadache. Finally, few reports indicate the possibility ofseizure self-abatement (e.g., see Efron [1956] and Pri-chard et al. [1985]). Moreover, when asked more thor-oughly, certain patients declared that they had developedtheir own seizure prevention strategies that are used at avarying degree of success. Although these strategiesoften appear extremely complicated, they can neverthe-less be considered specific in the sense that these patientsattempt to prevent neuronal networks from being re-cruited into the epileptogenic process by forcing theminto some physiologic processing.

During the past few years a variety of potential icto-genic mechanisms have been identified in experimentalmodels of focal epilepsy, including synaptic and cellularplasticity and changes in the extracellular milieu. How-ever, it is still a matter of debate whether these mecha-nisms can indeed be regarded as purely ictogenic, con-sidering their critical role for and involvement in normalbrain activities. In addition, it remains to be provedwhether findings obtained from experimental models arefully transformable to human epilepsies.

On the level of neuronal networks, focal seizures areassumed to be initiated by abnormally discharging neu-rons (so-calledbursters; compare with Calvin [1971],Calvin et al. [1973], Colder et al. [1996], Sanabria et al.[2001], and Traub and Wong [1982]) that recruit andentrain neighboring neurons into a “critical mass.” Thisbuildup may be mediated by an increasing synchroniza-tion of neuronal activity that is accompanied by a loss ofinhibition, or by facilitating processes, as mentionedearlier, that permit seizure emergence by lowering athreshold. In this context, the termcritical massmay bemisleading in the sense that it just implies an increasingnumber of neuronsthat are entrained into an abnormaldischarging process. Thismassphenomenon would beeasily accessible for conventional EEG analyses that,however, failed to detect it. Rather, the seizure-initiatingprocess can probably be regarded as an unfolding of anincreasing number of critical, possibly nonlineardynam-

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ical interferencesbetween neurons within the focal areaas well as with neurons surrounding this area. Indeed,there is now converging evidence from different labora-tories that nonlinear analysis is capable of characterizingthis collective behavior of neurons from the gross brainelectrical activity and hence allows one to define apreictal transition state, at least for a high percentage ofcases (Elger and Lehnertz, 1994, 1998; Iasemidis et al.,1990, 1997; Lehnertz and Elger, 1998; Lehnertz et al.,1999b; Le Van Quyen et al., 1999b, 2000, 2001; Mar-tinerie et al., 1998; Mormann et al., 2000a; Moser et al.,1999; Sackellares et al., 2000).

In an early study we calculated time profiles of D*from peri-ictal SEEG/ECoG recordings of spontaneouslyoccurring complex partial seizures in seven MTLE pa-tients. Particularly at recording sites exhibiting earliestsigns of seizure activity we observed long-lasting (10 to15 minutes) changes toward less complex system states(dimension drops) preceding seizures. We argued that adecreasingcomplexityof neuronal activity within theprimary epileptogenic area might reflect the hypothe-sized increasing spatial and temporal synchronization ofthe activity of abnormally bursting neurons and thusmight be indicative for an impending seizure (Elger andLehnertz, 1994). However, as discussed previously andshown in the previous section, phases of subcriticaldynamic changes exist even during the interictal state.Thus, we evaluated whether the observed preictal de-

crease in complexity is indeed specific for a preseizurestate. For this purpose we analyzed ECoG/SEEG datasetsfrom another 16 MTLE patients recorded before sponta-neously occurring complex partial seizures and com-pared the results with those obtained from interictalrecordings during the awake state. In all but one patient,changes toward long-lasting (as long as 25 minutes)dimension drops directly preceding seizures were morepronounced thanmaximumdimension drops occurringduring interictal states (Elger and Lehnertz, 1994, 1998;Lehnertz and Elger, 1998) (Fig. 5). Again the mostprominent findings were restricted to recording siteswithin the focal area, although in the majority of caseswe observed similar but less pronounced transition phe-nomena also at recording sites adjacent to the focal area.

To validate further our observations on a larger groupof patients and to evaluate whether similar findings canalso be obtained from seizures originating in the neocor-tex, we carried out a study including intracranial, mul-tichannel recordings from another 59 patients (prelimi-nary findings in Lehnertz et al. [1998]). Postoperativecomplete seizure control had confirmed NLE in 28 pa-tients and MTLE in 31 patients. We analyzed 95 peri-ictal recordings (50 seizures of neocortical origin and 45seizures of mesial temporal origin) and contrasted preic-tal dimension drops to maximum changes occurringduring 230 interictal recordings (duration,.30 minutes),which we selected to cover different states of vigilance

FIG. 5. Results of seizure anticipation in 95 preictal recordings of 59 patients with either mesial temporal lobe epilepsy (MTLE) or neocortical lesionalepilepsy (NLE). Upper left inset describes parameterization of dimension drops. For interictal recordings,t is the longest time interval, with D*(T)below the mean interictal level (determined individually for each recording site from all interictal data sets;dashed line). For preictal recordings,tis the time interval defined to reach from electrical seizure onset back to the previous intersection of D*(T) with the mean interictal level.d is themaximum deflection of D*(T) within these intervals. Preictal dimension drops are assumed predictive when they are confined to the primaryepileptogenic area, when they directly precede a seizure, and when preictal dimension drop parameters exceed maximum values of interictal dimensiondrops (compare with Elger and Lehnertz [1998] and Lehnertz and Elger [1998] for details). The gray area denotes the ictal state.

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and sleep. Although dimension estimates are known todecrease with increasing depth of sleep (e.g., Achermannet al. [1994] and Fell et al. [1993, 1996, 2000]) in healthysubjects, possible interactions between pathologicallyand sleep-induced types of synchronization as well astheir impact on nonlinear measures are not yet fullyunderstood (preliminary findings in Widman et al.[1998a]). Nevertheless, we expected a diminished per-formance of our method. Indeed, preictal dimensiondrops only exceeded the corresponding maximum inter-ictal values in 30 of 45 seizures (67%) in the MTLEgroup and in 15 of 50 seizures (29%) in the NLE group.The observed mean duration of preictal dimension dropsamounted to 19 minutes in both groups (Fig. 5).

Based on our finding that the epileptogenic processinduces or enhances nonlinear deterministic structures inthe otherwise linear stochastic appearance of interictalbrain electrical activity, we hypothesized further that apreictal state might be characterized as anadditionalenhancement of nonlinear deterministic structures. Weanalyzed ECoG/SEEG recordings of 32 spontaneouslyoccurring complex partial seizures of different cerebralorigins (neocortical, 23 seizures; mesial temporal, 9seizures) and contrasted findings to those obtained fromrecordings during the interictal state (30 to 120 minutesper patient; preliminary findings in Andrzejak et al.[2000a]). We observed increased values of x; before 25seizures, however, interictal values exceeded preictalones in 18 seizures. This finding indicates that thepreictal transition may often be too complex or too highdimensional to be detected with the time series analysistechniques currently available. In these cases we expectrefined methods for stochastic and possibly nonlineardynamics (Siegert et al., in preparation) to improvecharacterization of preictal transition phenomena.

In the studies described so far, we tracked the temporalevolution of nonlinear measures at different recordingsites, thus considering no spatial interactions during thetransition to the ictal state. Although preliminary, appli-cation of our bivariate measures (nonlinear interdepen-denceSand mean phase coherenceR) revealed interest-ing insights into the spatiotemporal characteristics of apreictal state. Fig. 6 depicts representative examples ofthe temporal evolution ofS before a spontaneouslyoccurring complex partial seizure characterizing interac-tions between different brain areas: within the primaryepileptogenic area, between the primary epileptogenicarea and its surrounding, and between the primary epi-leptogenic area and remote brain areas.

When compared with long-range interactions, we ob-served a higher level of interdependencies within theprimary epileptogenic area, which increased further as

the seizure approached. This may coincide with ourprevious observations of a preictally decreasing com-plexity as measured by D*. During the same period oftime (several minutes), long-range dynamic interactionsremained almost constant. We did, however, observe adistinct decrease of interaction between the primaryepileptogenic area and its surroundings. At first sight, apreictal decrease in interaction may seem to be a para-dox. One hypothesis to explain this phenomenon is thatthe decrease in interaction is the result of the fact thatdifferent recording sites are located within different areasof synchronization. If, for instance, one site was locatedwithin neuronal tissue already involved in the pathologicsynchronization progressing from the epileptogenic fo-cus while the other was located in a region still belongingto some process of physiologic synchronization, thedegree of interactions between these sites would beexpected to be low. Another hypothesis is that neuronsnot involved in any synchronized physiologic process

FIG. 6. Time-dependent changes of nonlinear interdependenciesScalculated from pairs of peri-ictal electrocorticograms/stereoelectroen-cephalograms at different recording sites in a patient with mesialtemporal lobe epilepsy. (Top to bottom) Both recording sites withinthe primary epileptogenic area, recording sites within and adjacent tothe primary epileptogenic area, and recording site within the primaryepileptogenic area and the remote recording site. The gray area denotesthe ictal state. The horizontal dashed lines indicate the mean value ofall interictal recordings for a given pair of recording sites. The verticaldashed lines indicate the beginning of the preictal phase.

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may be recruited more easily into a critical mass. Thus,the state of decreased preictal interaction could be re-garded as a state of increased susceptibility for patho-logic synchronization, thereby possibly representing alowered threshold for seizure activity.

Analyzing phase relationships, we obtained similarresults. As already mentioned, during the interictal statethe epileptogenic process can be characterized by apathologically increased and almost constant level ofsynchronization as measured by the mean phase coher-enceR. Preictally, however, the temporal evolution ofRshowed a significantlylower level as well as a highervariance in the majority of patients analyzed so far(Mormann et al., 2000b) (Fig. 7).

In fact, the effect was so distinct that it offered a basisfor a preseizure state detection (Mormann et al., 2000a;Mormann et al., in preparation). In comparison with theunivariate measures described so far, it appears that theobserved changes in synchronization occur on a largertime scale, sometimes hours before an actual seizure.This indicates that the observed changes in brain dynam-ics may be different from those traced by other measures,possibly yielding complementary information. In thecontext of such a long preictal phase, an epileptic seizuremay be interpreted as the “tip of the iceberg” in the sensethat it is just the climax of a process of changes in braindynamics that start long before the seizure.

Summarizing this section, we conclude that our non-linear EEG analysis techniques allow one to define apreictal phase, at least for a high percentage of seizures,and to characterize different temporal and spatial aspectsof this phase. The time scales observed so far range fromseveral minutes to hours. Although the existence of suchlong preictal transition states has sometimes been

doubted and simply regarded as a random event (e.g.,Thomasson et al. [2001]), our findings indicate thatcorrelates of the different ictogenic mechanisms men-tioned earlier can indeed be detected by nonlinear EEGanalysis. Long-lasting preictal states probably reflectnonspecific, widespread changes that increase suscepti-bility for seizure activity. On the other hand, short-lasting states probably indicate critical recruitment phe-nomena within the primary epileptogenic area and itssurroundings, with hypersynchronous behavior that isintensified gradually by the aforementioned generalizedchanges. Interestingly, other physiologic indices likeregional cerebral blood flow (Baumgartner et al., 1998;Weinand et al., 1997) or cerebral oxygenation (Adelsonet al., 1999) were shown to exhibit preictal changes onsimilar time scales. Whatever the pathophysiologic basisof preictal states may be, the observed duration is suffi-cient to enable investigations of basic mechanisms lead-ing to seizure initiation in humans and to develop ade-quate seizure prevention strategies.

THE NEXT STEPS

Nonlinear EEG analysis is still at its beginning. Nev-ertheless, the results obtained so far are promising andemphasize the high value of nonlinear EEG analysistechniques for both clinical practice and basic science.However, up until now, findings were mainly obtainedfrom retrospective studies in well-elaborated cases andusing invasive recording techniques. Thus, on the onehand, evaluation of more complicated cases as well asprospective studies on a larger population of patients arenecessary. On the other hand, only a few studies havereported nonlinear analyses of noninvasive recordings

FIG. 7. Time-dependent changes of themean phase coherenceR in interictal andperi-ictal stereoelectroencephalogramsfrom two patients with mesial temporallobe epilepsy. Recording sites: withinand adjacent to the primary epilepto-genic area. The gray area denotes theictal state. The horizontal dashed linesindicate the mean value of all interictalrecordings for a given pair of recordingsites.

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from epilepsy patients for clinical applications like, forexample, focus localization (Feucht et al., 1999; Silva etal., 1999). So far, lack of practicability of nonlinear EEGanalysis mainly had its reason in the assumption thatnonlinear deterministic structures in noninvasive record-ings may be too high dimensional to be detected withtoday’s methods. This may be related to the differentconductivities of the brain, cerebrospinal fluid, skull, andscalp all acting like a low-pass filter. In addition, theimportance of nonlinear EEG measures is influencedstrongly by artifacts that are hard to avoid using nonin-vasive recording techniques. This indicates that bothsensitivity and specificity of analysis techniques are notyet sufficient to allow broader clinical application.Clearly, nonlinear EEG analysis requires new develop-ments to improve further our understanding of the spa-tiotemporal dynamics of the epileptogenic process. Inthis context, new techniques are needed that allow abetter characterization of nonstationarity and high di-mensionality in brain dynamics, techniques disentan-gling even subtle dynamic interactions between patho-logic disturbances and surrounding brain tissue as well asrefined artifact detection and elimination techniques.We expect that recent developments in the field ofnonlinear time series analysis (e.g., Rieke et al. [2000]and Schreiber [2000b]) will help to overcome thesedifficulties.

In line with other reported findings, we regard thepossibility of defining a preictal state the most prominentcontribution of nonlinear EEG analysis to advanceknowledge about ictogenesis. This possibility has re-cently been expanded by studies indicating accessibilityof preictal changes from noninvasive EEG recordings(Iasemidis et al., 1997; Le Van Quyen et al. 2001). Therelevance of these studies for a broader clinical applica-tion is clearly undoubted. Nevertheless, the reportedfindings have to be interpreted with care because thesestudies lack the comparison with phases of abnormaldynamical changes during the interictal state. Thus, toachieve an unequivocal definition of a preictal state fromeither invasive or noninvasive recordings, a variety ofinfluencing factors has to be evaluated beforehand. De-spite considerable effort in characterizing the spatiotem-poral, interictal dynamics of the epileptogenic process, avariety of pathologically or physiologically induced dy-namical interactions are not yet fully understood. Amongothers, these include different sleep stages, differentcognitive states, as well as daily activities that clearlyvary from patient to patient. Moreover, the influence ofantiepileptic drugs other than carbamazapine, either assingle or as combined medication remains to be investi-gated. Along with these studies, nonlinear EEG analysis

techniques have to be further improved. Because thetechniques currently available allow a differentiatedcharacterization of the epileptogenic process, we regardthe combined use of these techniques (Lehnertz et al.,1999c, 2000b) along with appropriate classificationschemes (e.g., Petrosian et al. [2000] and Tetzlaff et al.[1999]) as a promising venture.

Once given an improved sensitivity and specificity ofnonlinear EEG analysis techniques, broader clinical ap-plications on a larger population of patients, either athome or in a clinical setting, can be envisaged. As afuture perspective, one may also consider implantableseizure anticipation and prevention devices similar todevices already in use in patients with Parkinson’s dis-ease. Although optimization of algorithms underlying thecomputation of specific nonlinear measures (Le VanQuyen et al.,1999b; Widman et al., 1998b) already al-lows one to track continuously the temporal behavior ofnonlinear measures in real time, currently these applica-tions still require the use of powerful computer systems,depending on the number of recording channels neces-sary to allow unequivocal characterization of the epilep-togenic process. Thus, further optimization and develop-ment of a miniaturized analyzing system are definitelynecessary. However, taking into account the technolo-gies currently available, we expect realization of suchsystems within the next few years.

Whatever the technological developments may be, thepossibility to anticipate epileptic seizures would dramat-ically change therapeutic possibilities. In a first step, onemight envisage a simple warning system that eventuallydecreases both the risk of injury and the feeling ofhelplessness resulting from the unpredictable occurrenceof seizures. If the analyzing system is powerful enough,one may also consider control of established presurgicalevaluation techniques, such as timely injection of asuitable single photon emission computed tomographictracer or control of recent seizure prevention techniqueslike vagal nerve stimulators. Moreover, control of pa-tient-specific prevention strategies can be regarded as aparticular alternative for those patients in whom presur-gical evaluation indicates surgical intervention as notfeasible. Long-term treatment with antiepileptic drugsthat might cause cognitive or other neurologic deficitscould be diminished to an on-time and local applicationof a short-demand, powerful drug (compare with Eder etal. [1997] and Stein et al. [2000]). Moreover, besideselectrical interventions (Gluckman et al., 2001; Schiff etal., 1994b; Velasco et al., 2000), we consider biofeed-back operant conditioning (e.g., Sterman [2000]) byapplying neuropsychological or behavioral tools, such as

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sensory processing, or motor task or memory processing(Lehnertz, 1999).

Last but not least, basic mechanisms leading to seizureinitiation in humans could be investigated. Clearly, thisresearch has to be accompanied by studies in animalmodels of epilepsy. Different lines of evidence alreadyindicate that when using nonlinear analysis techniques,similar transition phenomena can be observed before theonset of induced epileptiform activity (Aitken et al.,1995; Hajashi and Ishizuka, 1995; Koutsoukos et al.,1994; Lian et al., 2001; Schiff et al., 1994a; Widman etal., 1999). Moreover, the increasing number of surgicalinterventions along with the development of adequateexperimental techniques allows investigation of livingspecimens from epilepsy patients (Brooks–Kayal et al.,1999; Köhling et al., 1998; Nagerl et al., 2000). Thisopens the unique possibility to compare directly findingsobtained from human and animal studies, and eventuallyto identify basic mechanisms underlying the preictaltransition phase in humans.

Acknowledgment: The authors thank Wieland Burr, PeterDavid, Peter Grassberger, Christoph Helmstaedter, ThomasSchreiber, Ronald Tetzlaff, Bruno Weber, and Heinz GregorWieser for their valuable discussions.

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