Journal of Clinical Neurophysiology 18(3):209 –222, Lippincott Williams & Wilkins, Inc., Philadelphia © 2001 American Clinical Neurophysiology Society

Nonlinear EEG Analysis in Epilepsy: Its Possible Use for Interictal Focus Localization, Seizure Anticipation, and Prevention *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-NeumannInstitute for Computing, Research Center Jülich, Germany

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

With the advent of the physical–mathematical theory of nonlinear deterministic dynamics (see Schuster [1989] and Ott [1993] for an overview, and Gleick [1987] for an easy-to-read account), new concepts and powerful algorithms were developed to analyze apparently irregular behavior—a distinctive feature of, for example, brain electrical activity. During the last decade, a variety of nonlinear time series analysis techniques (Kantz and Schreiber, 1997) have been applied repeatedly to EEG recordings during physiologic and pathologic conditions.

Nonlinear measures like dimensions, Lyapunov exponents, entropies, or recent approaches that aim to characterize interdependencies, synchronization, or similarities were shown to offer new information about complex brain 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 a deterministic and even chaotic structure underlying neuronal dynamics is difficult or even impossible to prove. Moreover, the well-known nonlinear behavior of individual neurons, and with it the expectation of neuronal networks to behave in a similar way, is used as justification for applying these methods—an assumption that still is matter of debate (Schreiber, 2000a; Theiler and Rapp, 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.

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that nonlinear approaches to the analysis of brain systems are able to generate new clinical measures as well as new ways of interpreting brain electrical function, particularly with regard to epileptic brain states. In this review we report our work to increase insight into the spatiotemporal dynamics of the epileptogenic process. Both linear and nonlinear analysis techniques have been applied to intracranial recordings (electrocorticograms [ECoG] and stereoelectroencephalograms [SEEG]) from more than 300 patients undergoing presurgical evaluation for resective therapy in different cerebral regions. On this basis we show that nonlinear EEG analysis may become particularly important for both clinical practice and basic science. Nonlinear EEG analysis not only improves the presurgical evaluation but provides strong evidence that the interictal–ictal transition is not an abrupt phenomenon that occurs like a bolt from the blue. Rather, this classic two-state model has to be expanded to embed a third, preictal transitional phase. Recent findings indicate that it is indeed possible to detect such a state heralding a seizure (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; Martinerie et al., 1998; Moser et al., 1999; Sackellares et al., 2000) and, moreover, that this phase is long enough to allow investigation of basic mechanisms leading to seizure initiation in humans, the development of adequate seizure warning systems, or even patient-specific prevention strategies. The search for the hidden information predictive of an impending seizure has a long history in EEG analysis involving autoregressive models (Rogowski et al., 1981) or coherence analyses (Duckrow and Spencer, 1992) from preictal EEG recordings. Although the former indicated that EEG changes characteristic for preictal states may be detectable, at most, a few seconds before the actual seizure onset, the latter pointed to an increase of inter- and intrahemispheric coupling that may occur minutes before a seizure. The relevance of brief bursts of focal pathologic neuronal activity leading to spikes in the EEG and occurring before seizure onset was investigated in several clinical studies (Gotman et al., 1982; Katz et al., 1991; Lange et al., 1983; Wieser, 1989). Although some of the aforementioned authors reported a decrease or even total cessation of spikes before seizures, reexamination did not confirm this phenomenon in a larger sample. Attenuation or flattening of the background activity can be observed both as a concomitant EEG correlate of an aura and as a preictal EEG phenomenon. It may occur regionally or more generalized and is best detected using intracerebral electrodes. Duration of this J Clin Neurophysiol, Vol. 18, No. 3, 2001

phenomenon, however, is often too short to allow timely detection of a preictal state. WHY NONLINEAR EEG ANALYSIS CAN BE ATTRACTIVE At first glance, the aforementioned inconsistent findings may appear discouraging because they limit the importance of those aspects of brain electrical activity that were presumed to be most relevant for a detection of an increased probability of seizure occurrence. However, these findings also indicate that seizure occurrence may not be regarded as a purely stochastic phenomenon (compare with Iasemidis et al. [1994]). Today, there is increasing evidence that a number of key conceptual features of nonlinear dynamic systems have particular relevance to improve understanding of the spatiotemporal dynamics of the epileptogenic process: First, the basic principle of almost all nonlinear time series analysis techniques is the reconstruction of the observed system dynamics in a so-called state space. Although an unknown system may well be dependent on a large—and for the EEG often unknown—number of variables, the mathematical theorem of Takens (1981) states that the system’s behavior in state space can be approximated using only a single observed variable (e.g., the EEG). Second, if the system is governed by nonlinearity, a simple cause– effect relationship cannot be expected. Rather, nonlinear systems are characterized by a rich variety of dynamics including bifurcations that indicate abrupt state transition or intermittent behavior. EEG phenomena like spike– burst suppression patterns, epileptiform activity such as spikes, or the interictal–ictal state transition point to nonlinearity. Abrupt state transitions from highly complex, irregular to less complex, almost periodic dynamics appear to be a characteristic feature in many disorders and are one of the most compelling examples for the notion of complexity loss. Such disorders have been termed dynamical diseases (Glass, 2001; Glass and Mackey, 1978; Goldberger, 1997; Mackey and Glass, 1977; Reimann, 1963). “Decomplexified” systems are less adaptable and less able to cope with the exigencies of a constantly changing environment (compare with Goldberger [1992]). Moreover, it is the very occurrence of periodicities and highly structured patterns that allow identification and classification of many pathologic phenomena. Third, because of the sensitive dependence on initial conditions (the butterfly effect) of a deterministic chaotic system, its long-term behavior can hardly be predicted. Conversely, a nonlinear system has an inherent ability to

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

“self-organize” in the sense that it evolves toward an ordered temporal and spatial structure called an attractor. This mathematic concept may explain the wellorganized, self-sustained oscillations in EEG recordings that occur during seizure activity (Fig. 1). This dualism of chaos and order is the key feature of nonlinear dynamics. And fourth, generally, the initial conditions and the rules that govern a system like the epileptic brain are unknown. However, a variety of new concepts and measures have been developed that allow one to characterize fully the dynamical behavior of an unknown system in a theoretic sense: Lyapunov exponents characterize the system’s stability under some small perturbation, and thus are a measure of how chaotic a system behaves; dimension estimates are closely related to the number of degrees of freedom of a system; and entropies measure the degree of order/disorder. Dimensions and entropies can thus be regarded as an estimate of the system’s complexity. Recently, these univariate, nonlinear measures have been supplemented by new approaches to characterize spatial- and time-invariant phenomena in nonlinear systems. These concepts allow one to describe sufficiently a nonlinear dynamical system as shown for well-known

model systems that can be used to produce arbitrarily long and stationary time series at almost infinite precision. In contrast, a bulk of literature indicates an abated importance of nonlinear time series analysis techniques when applied to short, noisy, and nonstationary time series like the EEG— generated from a system with an almost unknown structure. Despite these shortcomings, it is commonly accepted today that nonlinear EEG analysis is nonetheless able to provide new and relevant information as long as the limitations of the techniques are taken into consideration and the results are interpreted carefully (e.g., operationally defined or relative measures are used). Following this premise, we have investigated the applicability of already established measures and have developed new measures to characterize the spatiotemporal dynamics of the epileptogenic process. CHARACTERIZING THE INTERICTAL STATE BY NONLINEAR EEG ANALYSIS Several lines of evidence originating from studies of human epileptic brain tissue as well as of animal models of chronic seizure disorders indicate that the epileptic brain, even between seizures, is different from normal. Based on the well-known fact that neurons involved in J Clin Neurophysiol, Vol. 18, No. 3, 2001

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the epileptic process exhibit high-frequency discharges that are scarcely modulated by physiologic brain activity (Wyler and Ward, 1980), we hypothesized that this neuronal behavior should be accompanied by an intermittent loss of complexity or an increase of nonlinear deterministic structure in the corresponding electrographic signal even during the interictal state (Lehnertz and Elger, 1995). Thus, to evaluate the efficacy of analysis techniques for characterizing the spatiotemporal dynamics of the epileptogenic process, we applied them to long-lasting interictal recordings covering different states of normal behavior and vigilance, as well as different extents of epileptiform activity. Because there are phases of dynamical changes during the interictal state that point to abnormalities but are not followed by a seizure, we regarded this approach mandatory to evaluate the specificity of possible seizure prediction techniques. In the following paragraphs we present findings that were obtained from retrospective analyses of interictal ECoG/SEEG recordings in patients with mesial temporal lobe epilepsy (MTLE) and/or neocortical lesional epilepsy (NLE) undergoing presurgical evaluation. We included data of patients for whom surgery led to complete postoperative seizure control (follow-up, at least 1 year) as well as data for patients who did not benefit from surgery. This allowed us to estimate sensitivity and specificity of the different analysis techniques for the epileptogenic process as well as their possible impact on predicting postoperative outcome. Introducing the neuronal complexity loss L* (Fig. 2) as an integral measure for temporal changes of an estimate D* of an effective correlation dimension (Grassberger et al., 1991), we obtained first evidence for a

decreased complexity of neuronal networks involved in the epileptogenic process (Lehnertz and Elger, 1995). We extracted L* from interictal ECoG/SEEG recordings of 20 MTLE patients and showed that this measure reflects temporal and spatial aspects of the epileptogenic process at a high sensitivity. Maximum L* values were confined to focal and adjacent recording sites, decreasing gradually with an increasing distance from the primary epileptogenic area. In all patients, the spatial distribution of L* allowed us to lateralize clearly the primary epileptogenic area regardless of whether obvious epileptiform activity was present in the ECoG/SEEG recordings. Applying the same analysis technique to semi-invasive recordings employing foramen ovale electrodes, Weber et al. (1998) replicated the discriminative power of L* in 16 of 19 MTLE patients. Further evidence of the measure’s sensitivity came from a study evaluating the modulating influence of antiepileptic drugs (Lehnertz and Elger, 1997). Here, we analyzed interictal ECoG/ SSEG recordings from 10 MTLE patients sampled at subsequent days during the presurgical evaluation with strongly variant carbamazepine serum levels. We observed a close inverse relationship between L* and carbamazepine serum level restricted spatially to the primary epileptogenic area. To prove applicability of nonlinear EEG analysis beyond the well-defined MTLE syndrome (Gloor, 1991), we investigated interictal ECoG recordings from 10 NLE patients with lesions in the frontal, parietal, or temporal neocortex (Widman et al., 2000). We observed a high conformity between maximum values of L* and the area of resection, especially in those patients who became seizure free after extended lesionectomy. This effect was complemented by a more widespread and diffuse spatial

FIG. 2. Computation of the neuronal complexity loss L*. Examples of temporal variations of dimension values D* (dimension profile) extracted from electrocorticograms/stereoelectroencephalograms at different sites. A reduction of the complex information content of dimension profiles is achieved by L*. This measure represents the integral between the actual dimension profile and an upper resolution bound (here Du ⫽ 10; compare with Lehnertz and Elger [1995] for details).

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NONLINEAR EEG ANALYSIS IN EPILEPSY distribution of L* in those patients who had no benefit from the resection, indicating the existence of additional foci. We obtained similar findings in another study estimating the possible extent of a hippocampal participation in the epileptogenic process of NLE patients (preliminary findings in Widman et al. [1997]). We included 20 patients with clinical hints for a hippocampal involvement but for whom presurgical evaluation led to an extended lesionectomy. In 10 patients we observed maximum values of L* only at mesial temporal recording sites. From this group only one patient became seizure free. For the remaining 10 patients, 9 of whom became seizure free, maximum L* was found at neocortical recording sites. Because postoperative outcome of neocortical epilepsy is still unsatisfying compared with MTLE (e.g., see Williamson et al. [2000]), we consider nonlinear EEG analysis a valuable extension to other diagnostic approaches already established in this field (Elger et al., 2000a, b). We have recently reexamined the merit of L* for the interictal lateralization and localization of the primary epileptogenic area in a larger group comprising 75 patients (preliminary findings in Lehnertz et al. [1999c]). Postoperative complete seizure control confirmed MTLE in 52 patients and lateral TLE in 23 patients respectively. The electrode contact exhibiting the maximum L* value indexed correctly both the side and the site of the primary epileptogenic area in 44 of 52 MTLE patients and in 20 of 23 lateral TLE patients (Fig. 3). Failure of correct localization could be attributed to either almost identical ipsilateral and contralateral L* values or to values close to or at the theoretic resolution limit of the applied method (compare with Ruelle [1990]). Based on the key conceptual features of nonlinear dynamical systems mentioned earlier, we hypothesized further that the epileptogenic process induces or enhances nonlinear deterministic structures in the otherwise linear stochastic appearance of brain electrical activity (compare with Pijn et al. [1991, 1997], Casdagli et al. [1997], and van der Heyden et al. [1999]). To verify this assumption, we introduced a new measure, x, (Andrzejak et al., 1999, 2000b, 2001), that combines tests for determinism (Kaplan and Glass, 1992) and for nonlinearity (Schreiber and Schmitz, 1996). Previous research had failed to identify nonlinear determinism in scalp EEG recordings of healthy subjects (e.g., Palus [1996] and Jeong et al. [1999]). However, extraction of x, for a total of 82 interictal ECoG/SEEG recordings (average duration per patient, 84 minutes) from 25 MTLE patients, provided strong evidence for nonlinear determinism in recordings from within the primary epileptogenic area, whereas signals from other sites mainly resembled

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FIG. 3. Interictal lateralization and localization of the primary epileptogenic area. (A) Group means and standard deviations of maximum ipsilateral and contralateral L* values (L*max) and results of post hoc Wilcoxon’s signed rank test. Preceding analysis of variance indicated a highly significant effect of the side of the primary epileptogenic area on L*max values for each group (lateral temporal lobe epilepsy [LTLE] group: F[2,20] ⫽ 7.754, P ⬍ 0.005; mesial temporal lobe epilepsy [MTLE] group: F[2,49] ⫽ 6.972, P ⬍ 0.005; total group: F[2,72] ⫽ 14.738, P ⬍ 0.001). (B) Lateralization: efficiency indicates correspondence between side of L*max and side of primary epileptogenic area. Localization: correspondence between recording site exhibiting earliest signs of seizure activity and site of L*max.

linear stochastic dynamics. Preliminary findings in eight NLE patients indicated a discriminative power similar to the neuronal complexity loss L*; in other words, high conformity between maximum values of x and area of resection in postoperatively seizure-free patients, and a more widespread and diffuse spatial distribution of x in those patients who did not benefit from the resection (Andrzejak et al., 1999) (Fig. 4). Univariate nonlinear EEG analysis techniques allow classification of temporal aspects and, when applied to multichannel recordings, allow classification of the relative spatial distribution of the epileptogenic process. However, they do not provide information about spatial J Clin Neurophysiol, Vol. 18, No. 3, 2001

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

interactions or spatial synchronization phenomena, which are considered to play a crucial role in epileptogenesis and ictogenesis. Discerning the synchronization of spatially and temporally distributed processes and events in the brain may offer the possibility of gathering deeper insight into pathologic, interictal phenomena as well as seizure development. We approached this problem by developing and evaluating a variety of bivariate analysis techniques, two of which turned out to be well suited. The nonlinear interdependence measure S (see Arnhold [2000] and Arnhold et al. [1999, 2000], and references therein) attempts to characterize statistical relationships between two time series (see also Le Van Quyen et al. [1999a], Pereda et al. [2001], and Schiff et al. [1996]). By construction, it does not treat phase information (discussed later) differently from amplitude information. In contrast to commonly used techniques like cross-correlations, coherence, or mutual information, S is nonsymmetric and thus provides additional J Clin Neurophysiol, Vol. 18, No. 3, 2001

information about the direction of interdependence. Application of this technique to interictal SEEG recordings (duration, 10 minutes) from 13 MTLE patients revealed maximum values of S to be confined to the primary epileptogenic area in 10 patients. Analysis of the direction of interdependence provided strong evidence for a higher contralateral-to-ipsilateral similarity in SEEG recordings from 11 patients than vice versa. The interpretation of this finding as an indication for a causal driver– responder relationship deserves further investigation. The other approach characterizing spatial interactions or synchronization phenomena is based on the statistical distribution of the relative instantaneous phases of two time series using the Hilbert transform (compare with Panter [1965] and Mardia [1972]). Because no unified definition for synchronization has been established so far, we introduced the mean phase coherence R as a statistical measure for phase synchronization (Mormann et al., 1999, 2000b). We analyzed 40 interictal SEEG

NONLINEAR EEG ANALYSIS IN EPILEPSY segments (mean duration, 34 minutes) recorded from 17 MTLE patients and observed higher values of R on the focal side in 14 patients. Results obtained from our bivariate measures indicate that the epileptogenic focus is characterized by a pathologically increased level of interdependence or synchronization even during the interictal state. Our univariate and bivariate measures thus share the ability to detect dynamical changes related to the epileptic condition. Moreover, the ability of bivariate measures to reflect anatomic boundaries of brain structures because of their enhanced intrinsic synchronization allows functional analysis of specific brain functions such as memory formation (Lehnertz et al., 1999a, 1997a, b). Although the high intrinsic synchronization in several anatomic structures makes it difficult to separate clearly physiologic from pathologic synchronization, bivariate measures have the important advantage of allowing examination of long-range effects such as entrainment of adjacent or remote brain areas into the epileptogenic process (discussed later). Summarizing this section, we conclude that our EEG analysis techniques approach the problem of characterizing the epileptogenic process from different points of view, and they indicate the potential relevance of nonlinear EEG analysis to improve understanding of intermittent dysfunctioning of the dynamical brain system between seizures. Moreover, our results also stress the high relevance of nonlinear EEG analyses in clinical practice because they provide potentially useful diagnostic information and thus contribute to an improvement of the presurgical evaluation (Elger et al., 1999, 2000b; Lehnertz et al., 2000a). DETECTING PREICTAL STATES BY NONLINEAR EEG ANALYSIS A preictal state may be defined as a condition of the epileptic brain and its functioning that inevitably evolve into a seizure unless some kind of intervention takes place. Given the a posteriori knowledge of a seizure occurrence, it appears rather trivial to postulate the existence of such a state. However, its unequivocal a priori definition, and with it the possibility to anticipate an impending seizure, is obviously far from being trivial. Nevertheless, a variety of clinical observations support the notion that at least certain seizures can be anticipated. First, several seizure-facilitating factors are known. In the context of his “reservoir theory,” Lennox (1946) has defined seizure facilitation as the input of sensory, metabolic, emotional, or other yet unknown factors that fill up some reservoir until it overflows, which in turn results

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in a seizure. Among others, levels of consciousness, sleep deprivation, tension states, disturbances of water and acid– base balance, and sensory and drug stimulation are regarded as potential influencing factors (Aird, 1983). However, apart from the rare exception of sensory-evoked or reflex epilepsies, these factors are obviously unspecific and highly variant because they depend on habits and daily activities of the patient. Moreover, it is clinically undisputed from many descriptions of close relatives that long-lasting behavioral and/or prodromal changes of the autonomous nervous system exist in certain patients. These alterations include depressive mood changes, irritability, sleep problems, nausea, and headache. Finally, few reports indicate the possibility of seizure self-abatement (e.g., see Efron [1956] and Prichard et al. [1985]). Moreover, when asked more thoroughly, certain patients declared that they had developed their own seizure prevention strategies that are used at a varying degree of success. Although these strategies often appear extremely complicated, they can nevertheless be considered specific in the sense that these patients attempt to prevent neuronal networks from being recruited into the epileptogenic process by forcing them into some physiologic processing. During the past few years a variety of potential ictogenic mechanisms have been identified in experimental models of focal epilepsy, including synaptic and cellular plasticity and changes in the extracellular milieu. However, it is still a matter of debate whether these mechanisms can indeed be regarded as purely ictogenic, considering their critical role for and involvement in normal brain activities. In addition, it remains to be proved whether findings obtained from experimental models are fully transformable to human epilepsies. On the level of neuronal networks, focal seizures are assumed to be initiated by abnormally discharging neurons (so-called bursters; compare with Calvin [1971], Calvin et al. [1973], Colder et al. [1996], Sanabria et al. [2001], and Traub and Wong [1982]) that recruit and entrain neighboring neurons into a “critical mass.” This buildup may be mediated by an increasing synchronization of neuronal activity that is accompanied by a loss of inhibition, or by facilitating processes, as mentioned earlier, that permit seizure emergence by lowering a threshold. In this context, the term critical mass may be misleading in the sense that it just implies an increasing number of neurons that are entrained into an abnormal discharging process. This mass phenomenon would be easily accessible for conventional EEG analyses that, however, failed to detect it. Rather, the seizure-initiating process can probably be regarded as an unfolding of an increasing number of critical, possibly nonlinear dynamJ Clin Neurophysiol, Vol. 18, No. 3, 2001

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FIG. 5. Results of seizure anticipation in 95 preictal recordings of 59 patients with either mesial temporal lobe epilepsy (MTLE) or neocortical lesional epilepsy (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, t is 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 the maximum deflection of D*(T) within these intervals. Preictal dimension drops are assumed predictive when they are confined to the primary epileptogenic area, when they directly precede a seizure, and when preictal dimension drop parameters exceed maximum values of interictal dimension drops (compare with Elger and Lehnertz [1998] and Lehnertz and Elger [1998] for details). The gray area denotes the ictal state.

ical interferences between neurons within the focal area as well as with neurons surrounding this area. Indeed, there is now converging evidence from different laboratories that nonlinear analysis is capable of characterizing this collective behavior of neurons from the gross brain electrical activity and hence allows one to define a preictal transition state, at least for a high percentage of cases (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; Martinerie 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 spontaneously occurring complex partial seizures in seven MTLE patients. Particularly at recording sites exhibiting earliest signs of seizure activity we observed long-lasting (10 to 15 minutes) changes toward less complex system states (dimension drops) preceding seizures. We argued that a decreasing complexity of neuronal activity within the primary epileptogenic area might reflect the hypothesized increasing spatial and temporal synchronization of the activity of abnormally bursting neurons and thus might be indicative for an impending seizure (Elger and Lehnertz, 1994). However, as discussed previously and shown in the previous section, phases of subcritical dynamic changes exist even during the interictal state. Thus, we evaluated whether the observed preictal deJ Clin Neurophysiol, Vol. 18, No. 3, 2001

crease in complexity is indeed specific for a preseizure state. For this purpose we analyzed ECoG/SEEG datasets from another 16 MTLE patients recorded before spontaneously occurring complex partial seizures and compared the results with those obtained from interictal recordings during the awake state. In all but one patient, changes toward long-lasting (as long as 25 minutes) dimension drops directly preceding seizures were more pronounced than maximum dimension drops occurring during interictal states (Elger and Lehnertz, 1994, 1998; Lehnertz and Elger, 1998) (Fig. 5). Again the most prominent findings were restricted to recording sites within the focal area, although in the majority of cases we observed similar but less pronounced transition phenomena also at recording sites adjacent to the focal area. To validate further our observations on a larger group of patients and to evaluate whether similar findings can also be obtained from seizures originating in the neocortex, we carried out a study including intracranial, multichannel recordings from another 59 patients (preliminary findings in Lehnertz et al. [1998]). Postoperative complete seizure control had confirmed NLE in 28 patients and MTLE in 31 patients. We analyzed 95 periictal recordings (50 seizures of neocortical origin and 45 seizures of mesial temporal origin) and contrasted preictal dimension drops to maximum changes occurring during 230 interictal recordings (duration, ⬎30 minutes), which we selected to cover different states of vigilance

NONLINEAR EEG ANALYSIS IN EPILEPSY and sleep. Although dimension estimates are known to decrease with increasing depth of sleep (e.g., Achermann et al. [1994] and Fell et al. [1993, 1996, 2000]) in healthy subjects, possible interactions between pathologically and sleep-induced types of synchronization as well as their impact on nonlinear measures are not yet fully understood (preliminary findings in Widman et al. [1998a]). Nevertheless, we expected a diminished performance of our method. Indeed, preictal dimension drops only exceeded the corresponding maximum interictal values in 30 of 45 seizures (67%) in the MTLE group and in 15 of 50 seizures (29%) in the NLE group. The observed mean duration of preictal dimension drops amounted to 19 minutes in both groups (Fig. 5). Based on our finding that the epileptogenic process induces or enhances nonlinear deterministic structures in the otherwise linear stochastic appearance of interictal brain electrical activity, we hypothesized further that a preictal state might be characterized as an additional enhancement of nonlinear deterministic structures. We analyzed ECoG/SEEG recordings of 32 spontaneously occurring complex partial seizures of different cerebral origins (neocortical, 23 seizures; mesial temporal, 9 seizures) and contrasted findings to those obtained from recordings during the interictal state (30 to 120 minutes per patient; preliminary findings in Andrzejak et al. [2000a]). We observed increased values of x; before 25 seizures, however, interictal values exceeded preictal ones in 18 seizures. This finding indicates that the preictal transition may often be too complex or too high dimensional to be detected with the time series analysis techniques currently available. In these cases we expect refined methods for stochastic and possibly nonlinear dynamics (Siegert et al., in preparation) to improve characterization of preictal transition phenomena. In the studies described so far, we tracked the temporal evolution of nonlinear measures at different recording sites, thus considering no spatial interactions during the transition to the ictal state. Although preliminary, application of our bivariate measures (nonlinear interdependence S and mean phase coherence R) revealed interesting insights into the spatiotemporal characteristics of a preictal state. Fig. 6 depicts representative examples of the temporal evolution of S before a spontaneously occurring complex partial seizure characterizing interactions between different brain areas: within the primary epileptogenic area, between the primary epileptogenic area and its surrounding, and between the primary epileptogenic area and remote brain areas. When compared with long-range interactions, we observed a higher level of interdependencies within the primary epileptogenic area, which increased further as

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FIG. 6. Time-dependent changes of nonlinear interdependencies S calculated from pairs of peri-ictal electrocorticograms/stereoelectroencephalograms at different recording sites in a patient with mesial temporal lobe epilepsy. (Top to bottom) Both recording sites within the primary epileptogenic area, recording sites within and adjacent to the primary epileptogenic area, and recording site within the primary epileptogenic area and the remote recording site. The gray area denotes the ictal state. The horizontal dashed lines indicate the mean value of all interictal recordings for a given pair of recording sites. The vertical dashed lines indicate the beginning of the preictal phase.

the seizure approached. This may coincide with our previous observations of a preictally decreasing complexity as measured by D*. During the same period of time (several minutes), long-range dynamic interactions remained almost constant. We did, however, observe a distinct decrease of interaction between the primary epileptogenic area and its surroundings. At first sight, a preictal decrease in interaction may seem to be a paradox. One hypothesis to explain this phenomenon is that the decrease in interaction is the result of the fact that different recording sites are located within different areas of synchronization. If, for instance, one site was located within neuronal tissue already involved in the pathologic synchronization progressing from the epileptogenic focus while the other was located in a region still belonging to some process of physiologic synchronization, the degree of interactions between these sites would be expected to be low. Another hypothesis is that neurons not involved in any synchronized physiologic process J Clin Neurophysiol, Vol. 18, No. 3, 2001

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may be recruited more easily into a critical mass. Thus, the state of decreased preictal interaction could be regarded as a state of increased susceptibility for pathologic synchronization, thereby possibly representing a lowered threshold for seizure activity. Analyzing phase relationships, we obtained similar results. As already mentioned, during the interictal state the epileptogenic process can be characterized by a pathologically increased and almost constant level of synchronization as measured by the mean phase coherence R. Preictally, however, the temporal evolution of R showed a significantly lower level as well as a higher variance 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 basis for a preseizure state detection (Mormann et al., 2000a; Mormann et al., in preparation). In comparison with the univariate measures described so far, it appears that the observed changes in synchronization occur on a larger time scale, sometimes hours before an actual seizure. This indicates that the observed changes in brain dynamics may be different from those traced by other measures, possibly yielding complementary information. In the context of such a long preictal phase, an epileptic seizure may be interpreted as the “tip of the iceberg” in the sense that it is just the climax of a process of changes in brain dynamics that start long before the seizure. Summarizing this section, we conclude that our nonlinear EEG analysis techniques allow one to define a preictal phase, at least for a high percentage of seizures, and to characterize different temporal and spatial aspects of this phase. The time scales observed so far range from several minutes to hours. Although the existence of such long preictal transition states has sometimes been

doubted and simply regarded as a random event (e.g., Thomasson et al. [2001]), our findings indicate that correlates of the different ictogenic mechanisms mentioned earlier can indeed be detected by nonlinear EEG analysis. Long-lasting preictal states probably reflect nonspecific, widespread changes that increase susceptibility for seizure activity. On the other hand, shortlasting states probably indicate critical recruitment phenomena within the primary epileptogenic area and its surroundings, with hypersynchronous behavior that is intensified gradually by the aforementioned generalized changes. Interestingly, other physiologic indices like regional cerebral blood flow (Baumgartner et al., 1998; Weinand et al., 1997) or cerebral oxygenation (Adelson et al., 1999) were shown to exhibit preictal changes on similar time scales. Whatever the pathophysiologic basis of preictal states may be, the observed duration is sufficient to enable investigations of basic mechanisms leading to seizure initiation in humans and to develop adequate seizure prevention strategies. THE NEXT STEPS Nonlinear EEG analysis is still at its beginning. Nevertheless, the results obtained so far are promising and emphasize the high value of nonlinear EEG analysis techniques for both clinical practice and basic science. However, up until now, findings were mainly obtained from retrospective studies in well-elaborated cases and using invasive recording techniques. Thus, on the one hand, evaluation of more complicated cases as well as prospective studies on a larger population of patients are necessary. On the other hand, only a few studies have reported nonlinear analyses of noninvasive recordings

FIG. 7. Time-dependent changes of the mean phase coherence R in interictal and peri-ictal stereoelectroencephalograms from two patients with mesial temporal lobe epilepsy. Recording sites: within and adjacent to the primary epileptogenic area. The gray area denotes the ictal state. The horizontal dashed lines indicate the mean value of all interictal recordings for a given pair of recording sites.

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NONLINEAR EEG ANALYSIS IN EPILEPSY from epilepsy patients for clinical applications like, for example, focus localization (Feucht et al., 1999; Silva et al., 1999). So far, lack of practicability of nonlinear EEG analysis mainly had its reason in the assumption that nonlinear deterministic structures in noninvasive recordings may be too high dimensional to be detected with today’s methods. This may be related to the different conductivities of the brain, cerebrospinal fluid, skull, and scalp all acting like a low-pass filter. In addition, the importance of nonlinear EEG measures is influenced strongly by artifacts that are hard to avoid using noninvasive recording techniques. This indicates that both sensitivity and specificity of analysis techniques are not yet sufficient to allow broader clinical application. Clearly, nonlinear EEG analysis requires new developments to improve further our understanding of the spatiotemporal dynamics of the epileptogenic process. In this context, new techniques are needed that allow a better characterization of nonstationarity and high dimensionality in brain dynamics, techniques disentangling even subtle dynamic interactions between pathologic disturbances and surrounding brain tissue as well as refined artifact detection and elimination techniques. We expect that recent developments in the field of nonlinear time series analysis (e.g., Rieke et al. [2000] and Schreiber [2000b]) will help to overcome these difficulties. In line with other reported findings, we regard the possibility of defining a preictal state the most prominent contribution of nonlinear EEG analysis to advance knowledge about ictogenesis. This possibility has recently been expanded by studies indicating accessibility of preictal changes from noninvasive EEG recordings (Iasemidis et al., 1997; Le Van Quyen et al. 2001). The relevance of these studies for a broader clinical application is clearly undoubted. Nevertheless, the reported findings have to be interpreted with care because these studies lack the comparison with phases of abnormal dynamical changes during the interictal state. Thus, to achieve an unequivocal definition of a preictal state from either invasive or noninvasive recordings, a variety of influencing factors has to be evaluated beforehand. Despite considerable effort in characterizing the spatiotemporal, interictal dynamics of the epileptogenic process, a variety of pathologically or physiologically induced dynamical interactions are not yet fully understood. Among others, these include different sleep stages, different cognitive states, as well as daily activities that clearly vary from patient to patient. Moreover, the influence of antiepileptic drugs other than carbamazapine, either as single or as combined medication remains to be investigated. Along with these studies, nonlinear EEG analysis

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techniques have to be further improved. Because the techniques currently available allow a differentiated characterization of the epileptogenic process, we regard the combined use of these techniques (Lehnertz et al., 1999c, 2000b) along with appropriate classification schemes (e.g., Petrosian et al. [2000] and Tetzlaff et al. [1999]) as a promising venture. Once given an improved sensitivity and specificity of nonlinear EEG analysis techniques, broader clinical applications on a larger population of patients, either at home or in a clinical setting, can be envisaged. As a future perspective, one may also consider implantable seizure anticipation and prevention devices similar to devices already in use in patients with Parkinson’s disease. Although optimization of algorithms underlying the computation of specific nonlinear measures (Le Van Quyen et al.,1999b; Widman et al., 1998b) already allows one to track continuously the temporal behavior of nonlinear measures in real time, currently these applications still require the use of powerful computer systems, depending on the number of recording channels necessary to allow unequivocal characterization of the epileptogenic process. Thus, further optimization and development of a miniaturized analyzing system are definitely necessary. However, taking into account the technologies currently available, we expect realization of such systems within the next few years. Whatever the technological developments may be, the possibility to anticipate epileptic seizures would dramatically change therapeutic possibilities. In a first step, one might envisage a simple warning system that eventually decreases both the risk of injury and the feeling of helplessness resulting from the unpredictable occurrence of seizures. If the analyzing system is powerful enough, one may also consider control of established presurgical evaluation techniques, such as timely injection of a suitable single photon emission computed tomographic tracer or control of recent seizure prevention techniques like vagal nerve stimulators. Moreover, control of patient-specific prevention strategies can be regarded as a particular alternative for those patients in whom presurgical evaluation indicates surgical intervention as not feasible. Long-term treatment with antiepileptic drugs that might cause cognitive or other neurologic deficits could be diminished to an on-time and local application of a short-demand, powerful drug (compare with Eder et al. [1997] and Stein et al. [2000]). Moreover, besides electrical interventions (Gluckman et al., 2001; Schiff et al., 1994b; Velasco et al., 2000), we consider biofeedback operant conditioning (e.g., Sterman [2000]) by applying neuropsychological or behavioral tools, such as J Clin Neurophysiol, Vol. 18, No. 3, 2001

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sensory processing, or motor task or memory processing (Lehnertz, 1999). Last but not least, basic mechanisms leading to seizure initiation in humans could be investigated. Clearly, this research has to be accompanied by studies in animal models of epilepsy. Different lines of evidence already indicate that when using nonlinear analysis techniques, similar transition phenomena can be observed before the onset 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 et al., 1999). Moreover, the increasing number of surgical interventions along with the development of adequate experimental techniques allows investigation of living specimens from epilepsy patients (Brooks–Kayal et al., 1999; Köhling et al., 1998; Nagerl et al., 2000). This opens the unique possibility to compare directly findings obtained from human and animal studies, and eventually to identify basic mechanisms underlying the preictal transition phase in humans. Acknowledgment: The authors thank Wieland Burr, Peter David, Peter Grassberger, Christoph Helmstaedter, Thomas Schreiber, Ronald Tetzlaff, Bruno Weber, and Heinz Gregor Wieser for their valuable discussions.

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