Dynamical Diseases of Brain Systems: Different Routes to Epileptic Seizures

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1 540 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 5, MAY 2003 Dynamical Diseases of Brain Systems: Different Routes to Epileptic Seizures Fernando H. Lopes da Silva, Wouter Blanes, Stiliyan N. Kalitzin*, Jaime Parra, Piotr Suffczynski, and Demetrios N. Velis Invited Paper Abstract In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the system s attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the system s parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the system s response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed. Index Terms Biomedical signal analysis, brain modeling, dynamics, electroencephalography, epilepsy, magnetoencephalography, nonlinear systems. Manuscript received December 1, 2002; revised January 6, Asterisk indicates corresponding author. F. H. Lopes da Silva, W. Blanes, J. Parra and D. N. Velis are with the Dutch Epilepsy Clinics Foundation, Meer en Bosch, 2103 SW, Heemstede, The Netherlands (skalitzin@sein.nl). *S. N. Kalitzin is with the Dutch Epilepsy Clinics Foundation, Meer en Bosch, Achterweg 5, 2103 SW, Heemstede, The Netherlands (skalitzin@sein.nl). P. Suffczynski is with the Dutch Epilepsy Clinics Foundation, Meer en Bosch, 2103 SW, Heemstede, The Netherlands, and also with the Laboratory of Medical Physics, University of Warsaw, Warsaw, Poland. Digital Object Identifier /TBME I. THE CONCEPT OF EPILEPSY AS A DYNAMICAL DISEASE EPILEPSY is characterized by the sudden occurrence of synchronous activity within relatively large neuronal networks that disturb the normal working of the brain. Such an activity may lead simply to a brief impairment of consciousness but also to a more or less complex series of abnormal sensory and motor manifestations, what is usually called a seizure. The latter may be triggered by some changes in network s parameters and/or inputs not evident to an observer. The so-called reflex epilepsies may be good examples of the above hypotheses, since in these cases a seizure is precipitated by a characteristic influx of afferent impulses. Reflex epilepsies occur in a variety of animal species, including man, and may be induced by a diversity of precipitating factors such as visual stimuli of different kinds: intermittent photic stimulation, geometric patterns, and computer video games, among others. In a normal brain such stimuli would not cause more than a transient and harmless modification of brain activity; but in the epileptic brain, they can cause massive synchronous discharges suddenly occurring and eventually leading to a seizure. This is the essence of a paroxysmal disorder. Why and how paroxysmal episodes occur is difficult to apprehend based only on current knowledge of pathophysiology, due to the complexity of the factors that jointly are responsible for their occurrence. The main purpose of this paper is to show that in order to understand this kind of phenomena it is useful to apply concepts derived from the mathematics of nonlinear complex systems for the analysis of the workings of neuronal networks. Likewise, such concepts are relevant to understand similar complex natural phenomena in hydrodynamics, meteorology or the physics of plasmas [29]. In general, we assume that neuronal networks can display different kinds of stationary dynamical states corresponding to specific attractors. Such attractors can become deformed due to changes of the system s parameters. In addition, dynamical states can be created or annihilated. A deformation may be reflected in specific EEG patterns (preictal stages). However, a deformation may not be noticeable in the EEG by using passive methods of signal analysis. Then, active methods to probe the dynamical state of the neuronal networks may have to be used. In other words, neuronal networks may have bi(multi)-stable states. Transitions between such states may occur under defined conditions. We assume further that the epileptic brain differs from the normal brain in that some neuronal networks of the former have an abnormal set of control parameters, that /03$ IEEE

2 LOPES DA SILVA et al.: DYNAMICAL DISEASES OF BRAIN SYSTEMS: DIFFERENT ROUTES TO EPILEPTIC SEIZURES 541 Fig. 1. (top) Computer-simulated EEG signals from a network that is in a state close to the separatrix between the normal ongoing EEG activity attractor and the seizure attractor, characterized by a relatively low amplitude predominantly alpha activity and a large-amplitude 3-Hz spike-and-wave oscillations, respectively. (bottom) Two epochs of real EEG signals recorded from a patient with absence-type of seizures. make those state transitions easier to occur. This means that in epileptic brains, the transition between the normal state and an abnormal one characterized by widespread synchronous activity can occur even with a precipitating factor that is harmless for a normal subject. In this case, the state transition depends on a set of critical parameters that define the operating regime of the system. A reflex epileptic seizure may then occur when some critical parameters of a neuronal network change in such a way that a bifurcation to a low-dimensional attractor occurs. This concept accounts for the two main characteristics of epilepsy: 1) that an epileptic brain can function apparently normally between seizures, i.e., during the interictal state; and 2) that the seizures occur in a paroxysmal way to impair brain function. In this sense, epileptic disorders may be considered as special cases of the large class of dynamical diseases, characterized by the occurrence of abnormal dynamics, a theoretical concept proposed by Glass and Mackey [13], that we and others have used in the context of epilepsy [2], [3], [26], [27]. In this overview, using computer model simulations and some experimental data, we concentrate, on three basic cases that are particularly illustrative of different routes to epileptic seizures: 1) an abrupt transition, of the bifurcation type, caused by a random perturbation (absence type of seizures); 2) a route where a deformation of the attractor is caused by an external perturbation (photosensitive epilepsy); and 3) a deformation of the attractor leading to a gradual evolution onto the ictal state [e.g., temporal lobe epilepsy (TLE)]. A. The Random Route: A Computer Model Showing how Bifurcations Between Distinct Oscillatory States can Take Place in a Thalamo-Cortical Network An interesting case that helps to illustrate the concept of the random route toward seizures is the epileptic syndrome characterized by paroxysmal spike-and-wave discharges in the EEG and nonconvulsive absence seizures [33]. A number of detailed, distributed models of thalamic and thalamocortical networks have been developed to account for this kind of seizure EEG activity [1], [11], [12], [14], [39]. These models can give insight into basic neuronal mechanisms [32]. The 3-Hz spike and wave (SW) absence-type seizures reflect the dynamical properties of neuronal populations at the macroscopic level. In order to elucidate the generation of SW complexes, we did not simulate the explicit behavior of individual neurons but rather modeled the populations of interacting neurons. [34]. Using this approach we were able to simulate distinct oscillatory modes of thalamo-cortical networks (Fig. 1) This can best be visualized by way of state-space plots as illustrated in Fig. 2. Separatrices between basins of attraction of the attractors in state space can then be defined. It can also be shown that such a dynamical system presents hysteresis and jump phenomena, i.e., the system s dynamics may jump abruptly from one oscillatory mode to another. One mode may correspond to the normal oscillatory state (e.g., the typical alpha rhythm), while the other correspond to the SW mode, characteristic of the absence-type seizure. According to our hypothesis, the basic difference between a normal brain and the one of an epileptic patient suffering from absence seizures is that in the former the basin of attraction of the ictal attractor (that corresponds to the 3-Hz SW oscillatory mode) is very distant from the separatrix, while in the latter this distance is very small (Fig. 2). This distance is likely determined by the existence of abnormal neuronal parameters [4] [6], [21], that may affect the low-threshold channels and/or and receptors, due to genetic and/or developmental defects as revealed in some experimental animal models [26]. Therefore, in this pathophysiological case, any small random fluctuation of parameters or inputs may flip the system s trajectory over the separatrix, thus entering the basin of attraction of the 3-Hz SW paroxysmal mode. If random

3 542 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 5, MAY 2003 (a) (b) Fig. 2. State-plane representation of the attractors obtained by way of computer simulations of the thalamo-cortical network using two sets of parameters. (a) Parameters from a normal brain, and (b) from an epileptic brain. In the normal brain, there is a larger distance between the normal attractor, with a concentrated basin of attraction, and the seizure attractor. A transition to the latter will practically never occur. On the contrary, the one on the right side shows a much smaller distance between the two attractors, such that any fluctuation in the critical parameters, or the initial conditions, can give rise to a transition to the seizure attractor. The separatrix between the two basins of attraction is represented by the thick line (adapted from Suffczynski et al. [35]). (a) (b) Fig. 3. Distributions of durations of (a) ictal epochs and (b) seizure free (interictal) intervals obtained with the model of Suffczynski et al. [35]. Note that both distributions are exponential, indicating the random nature of the underlying process. fluctuations in a bistable network are responsible for the sudden onset of the absence seizures in idiopathic (primary) generalized epilepsy, it seems reasonable to assume that the occurrence of those seizures cannot be predicted, as fluctuations are by definition unpredictable. Recently, a more elaborated model was constructed [35] in order to obtain insight in the long-term dynamics of SW seizures. This model showed that a random process governs the occurrence of paroxysmal activity, i.e., both the onset and cessation of paroxysms occur randomly over time with certain probabilities. The distribution of the duration of paroxysms, as well as of the periods with normal ongoing activity is exponential (Fig. 3). This prediction of the model was verified in a rat genetic model with EEG paroxysmal activity that resembles that of typical absence seizures in humans (WAG/Rij model [8]). B. The Mixed Route (Attractor Deformation and Bifurcation): Experimental Evidence for the Existence of Specific Features of EEG/magnetoencephalogram (MEG) Signals Preceding the Transition to SW Discharges in Photo-Sensitive Epilepsy Reflex epilepsies offer a natural model to investigate the dynamics of the process of transition from normal to paroxysmal activity. Indeed, in photosensitive epilepsies, the intermittent light, at a given frequency and after a number of repetitions, can elicit the transition to paroxysmal SW oscillations characteristic of absence-type seizures. We assume that the stimulus leads to a dynamical change of the underlying attractor (deformation component) that facilitates the transition to the ictal phase (bifurcation component). This means that, in these cases, a mixed scenario could account for the route to the seizure. According to these assumptions, we searched for features of the EEG activity that would indicate the change in network s parameters and

4 LOPES DA SILVA et al.: DYNAMICAL DISEASES OF BRAIN SYSTEMS: DIFFERENT ROUTES TO EPILEPTIC SEIZURES 543 Fig. 4. Analysis of 151 MEG signals recorded from one patient who developed an absence seizure after intermittent light stimulation at 10 Hz. The signals analyzed were recorded during the light stimulation but before a paroxysm occurred (adapted from Parra [30]). The analysis was performed with Gabor based wavelets. (upper plot) The value of the phase clustering index computed according to the method of Kalitzin et al. [20] is shown in a color scale. Each of 151 magnetic sensors is depicted in the x-axis. (lower plot) The amplitude of each frequency component is presented (in Teslas). The plots on the left of each graph represents the average phase clustering index (above) and amplitude (below) for all 151 magnetic sensors. Note that a clear yellow line, indicating large phase clustering index, appears mainly at 40 and 80 Hz with a widespread distribution at different magnetic sensors. However no significant amplitude increases appear at these frequencies. would reveal the process of attractor s deformation. Without entering here into methodological details that are published elsewhere [20], we were able to find features in the MEG/EEG signals of patients before the transition to paroxysmal epileptiform activity mode occurs, that appear to be significantly associated with the probability of such a transition taking place a few seconds later. The most significant feature in this respect is a decrease of the phase dispersion, or increase of the phase clustering index, of components in the gamma frequency range that are harmonically related to the fundamental frequency of the intermittent light stimulation. It should be noted that in the normal functioning of the brain the formation of dynamic links mediated by synchrony over multiple frequency bands has been proposed [36] as the mechanism responsible for a large-scale integration of distributed anatomical and functional domains of brain activity that may enable the emergence of coherent behavior and cognition. We hypothesize that the mechanisms involved in this large-scale synchronization may be disturbed in some brains such that they become unstable and, eventually, undergo a transition to another, pathophysiological, oscillatory state resulting in a seizure. The finding of the enhancement of phase clustering index within the gamma frequency range in the photosensitive epileptic patients [30], [31] may be interpreted as evidence for such an entrainment. The observation that this increased phase clustering is much enhanced in the cases where intermittent light stimulation leads to the transition to the SW dynamical state, implies that in these cases there is a stronger tendency for the occurrence of the entrainment of beta/gamma oscillators (Fig. 4). There are experimental data [15] showing that human subjects stimulated with flickering light at frequencies from 1 to 100 Hz exhibit event-related potentials with steady-state oscillations at all frequencies up to at least 90 Hz. Interestingly, the steady-state potentials exhibited clear resonance phenomena around 10, 20, 40, and 80 Hz. How these physiological properties relate to the pathophysiological enhancement that we found in patients, as described above, is discussed elsewhere in more detail [30], [31]. C. The Attractor Deformation Route: A Computer Model of how a Gradual Change in Network Parameters and EEG Dynamics may Precede Limbic Epileptic Seizures We may assume that in a class of epileptic seizures (e.g., temporal lobe epilepsies) the pathophysiology of the epileptogenic network is characterized by a set of cellular/molecular changes rendering certain control parameters, essential in maintaining stability of the neuronal networks, extremely vulnerable to the influence of exogenous and/or endogenous factors. In these cases, the distance between the basins of attraction of the

5 544 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 5, MAY 2003 Fig. 5. Model simulations of EEG signals by changing values of two parameters: the slow (parameter B) and the fast (parameter G) types of GABAergic inhibition. Top left: the trajectory of the changes in the two-dimensional parameter space (B 2 G). First trace: the time evolution of the changes in both parameters. Middle trace: the resulting EEG signals. Low trace: the corresponding power spectra. Note the appearance of a series of interictal spikes in epoch b2, of gamma activity in epoch b3 and of a seizure in epoch b4. (With permission adapted from Wendling et al. [40]). normal steady-state oscillatory behavior of the interictal state and the one of the ictal oscillations is large enough such that random fluctuations do not lead to a seizure. However this distance may gradually become smaller due to changes of some critical parameters, i.e., the attractor may suffer a deformation in such a way that it becomes ictal, and a seizure eventually appears. This route to a seizure can be well illustrated by way of simulations of EEG signals in Wendling s model of hippocampal neuronal networks [40]. The model consists, essentially, of a population of neurons containing four interacting subsets. The first subset is composed of the main cells (i.e., pyramidal cells in the hippocampus or neocortex). It receives feedback from three other subsets composed of local interneurons, one excitatory, another inhibitory GABAergic with slow kinetics and a third one also GABAergic but with fast kinetics. More recently Banks et al. [7] showed that both classes of inhibitory interneurons interact: GABA-slow interneurons inhibit not only pyramidal cells but also the GABA-fast interneurons. Using this model, it is possible to reconstruct EEG signals that appear in the interictal state and at different states of a limbic epileptic seizure. In this way, Wendling et al. [40] were able to find a pathway of successive changes in a number of parameters that can reproduce the temporal dynamics of the real EEG signals recorded from the human hippocampus at the beginning of a seizure as illustrated in Fig. 5. Following the normal ongoing state, and by influence of some not well-specified endogenous factors, some critical parameters change in a more or less gradual way. In one exemplary case, we may assume that there are two consecutive reductions of dendritic inhibition (b-1 b-2 and b-2 b-3 in Fig. 5) whereas the somatic inhibition initially remains constant. When the dendritic inhibition increases again (b-3 b-4), the somatic inhibition decreases. The first decrease of the slow inhibition leads the model to generate discharges of spikes (phase b-2), comparable to those often observed during the transition from interictal to ictal activity. The second decrease, that causes activation (disinhibition) of the fast inhibitory interneurons, leads the model to generate a low-voltage rapid (gamma frequency band) discharge (phase b-3) similar to that often observed at seizure onset in real EEG signals. Finally, the slower quasisinusoidal activity (phase b-4) is observed when fast inhibition weakens and slow inhibition re-increases. These results, of course, are just model simulations. Nevertheless, they reveal what may happen in reality if some basic parameters of neuronal networks within an epileptogenic zone, are unstable. In other words, these parameters may shift away from the normal range of values under the influence of some endogenous factors (e.g., metabolic or hormonal ones).

6 LOPES DA SILVA et al.: DYNAMICAL DISEASES OF BRAIN SYSTEMS: DIFFERENT ROUTES TO EPILEPTIC SEIZURES 545 D. Search for Analytical Methods That may Anticipate Ictal Transitions The changes of parameter values described above, that affect the dynamics of the neuronal networks and can lead to a seizure, may not be easily detectable by visual inspection of the EEG. Therefore, the search is on for powerful analytical methods that may be used to detect this kind of evolution of the dynamics from the EEG signals. Should such changes be detectable using the mathematical tools derived from the theory of nonlinear dynamical systems, one would be able to anticipate the occurrence of an epileptic seizure. In practice, to assess the performance of such analytical methods in seizure prediction, it is important to recognize a sequence of changes leading to an electrographic seizure event, that the EEGer would normally fail to identify by classical visual inspection of the record. Epileptic seizures, particularly if they are recorded intracranially, are characterized by a sequence of events in time, starting with the earliest EEG change associated with the seizure, that may precede the unequivocal EEG seizure onset, followed by the earliest clinical signs and finally, by the unequivocal clinical seizure onset [25]. The main question is, therefore, whether it is possible to anticipate the detection of a seizure some time before the occurrence of the earliest EEG change. The underlying assumption is that the dynamical properties of the preseizure EEG state should be distinguishable from those of the ongoing interictal state, and they should likely differ from those of the ictal state too. This is an assumption of potential clinical significance. Already in the seventies, Viglione and Walsh [41] developed and patented a method for an epileptic seizure warning system. However this system was never applied in a clinical setting mainly due to the large number of false positives. In the 1990s, with the emergence of analytical methods derived from the theory of complex nonlinear systems, a number of studies appeared with the same purpose. One of the first to report a method able to detect specific changes in the intracranial EEG preceding a seizure was the group of Iasemidis, Sackellares, and collaborators [16] [19], who showed evidence for the convergence (entrainment) of phases and values of the maximum rate of generation of information (maximum Lyapunov exponent) from multichannel intracranial and scalp EEG recordings several minutes prior to a seizure. Also, an important contribution in this context was given in a number of studies showing decreased values of correlation dimension in interictal EEGs preceding epileptic seizures recorded intracranially [22]. In yet other studies, a method based on the correlation dimension and surrogate signals was reported to anticipate seizures several minutes before seizure onset in intracranial EEG studies of epileptic patients [28]. In a follow-up study [23], the same group were able to anticipate epileptic seizures on both scalp and intracerebrally recorded EEG signals using a measure of nonlinear similarity. These and other contributions [24] have been reviewed recently [25]. In our experience, using a modified method of computing the correlation dimension, we also found that changes of this statistic may sometimes precede seizures by a few minutes [37]. However these methods appear to have a rather weak specificity, i.e., similar changes may be detected while no seizure occurs within a reasonable interval of time. Nevertheless, we cannot simply consider such changes as false positives since they may correspond to changes in the dynamical state of neuronal networks en route to seizures. Recent reports in the literature indicate that use of more traditional signal analysis methods may identify changes in interictal intracranial EEG recordings preceding seizure occurrence in TLE patients [24]. This raises the following intriguing question: which of all these measurable dynamical changes in the state of neuronal networks do actually lead to an epileptic seizure? Could this be related to the duration and magnitude of the dynamical change, and/or the extent of the neuronal networks that participate in the ictal attractor? In this context, we have been exploring the possibility of using intracranial electrostimulation protocols to evoke neuronal activity that may reveal the dynamical state of the underlying networks over time, instead of the cumbersome long term monitoring. Some preliminary data from our group appear to be encouraging in this context. We have shown that, in at least some cases, changes in the excitatory/inhibitory balance within neuronal networks of the hippocampal formation, minutes before a limbic epileptic seizure, can be detected by monitoring the response (evoked field potentials) of the neuronal networks to low-amplitude, subthreshold, paired-pulse stimulation applied to intracerebral electrodes. This is the case in an experimental animal model of epilepsy and in TLE patients undergoing invasive EEG recordings in the course of presurgical evaluation. Nevertheless, it is unclear at this moment whether failure to obtain results of such changes in some cases investigated thus far was due to an inherent weakness of the scheme, or to individual variability in the positioning of the implanted stimulating and/or recording electrodes. In this respect, certain parallels may be drawn to the reports by others about the difficulty to obtain consistent responses from paired pulse paradigm studies in experimental animal models of TLE [9] or in implanted patients [10]. Another protocol that we are exploring consists of delivering 5-s-long trains of biphasic pulses at frequencies between 2 and 50 Hz (low-amplitude, subthreshold) to pairs of intracerebral electrode contacts in patients. This stimulus evokes local activity that can be analyzed using time-frequency maps. In this way, it is possible to compute the phase clustering index for each electrode site, a concept that was recently introduced by our group [20] as a measure of phase synchrony. Preliminary results [38] indicate that the relative phase clustering index (rpci), appears to be able to perform reliable long-term seizure forecasting using intracranial EEG signals in addition to correctly lateralizing and localizing the site of ictal onset (Fig. 6). In fact, it appears that rpci is a robust indicator of changes associated with the prodromal phase of ictal clustering, which usually precedes the actual occurrence of seizures by several hours and, thus, may afford early warning of impeding changes in a neuronal system s state of ictability, rather than of anticipating, or truly predicting, a seizure. It is important to note that this methodology consists of active probing in contrast to other methods of analysis that, of course, are applied in a passive way. It appears that the computation of phase clustering index, combined with active probing, yields more robust results than the classic methods, but this needs further confirmation in a larger set of clinical cases. If it is proven

7 546 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 5, MAY 2003 Fig. 6. A: Distribution of relative PCI values of depth electrode contacts H7 (trigger zone in the hippocampus, red stars) and H4 (1.5 cm proximal to trigger zone, same temporal lobe, blue stars) in a patient suffering from mesial TLE (MTLE). Each star represents the value obtained after 20-Hz trains of biphasic stimuli (carrier signal) administered at adjacent contacts H5 and H6, located in-between H7 and H4 (stimulus intensity 750 ua, stimulus length 10 s/phase, train duration 5 s, administered every 4 min for more than one week). The rpci values show a marked, statistically high significant increase in the 48 hrs preceding the seizure cluster (seizures denoted by vertical green lines) and a decline to baseline values afterwards. Note that the prodromal phase shows an increase in rpci values for both contacts, initially more pronounced in H7, but also spreading to H4 in the period closely preceding seizures. This suggests that the extent of the actual trigger zone may be important in the route toward a seizure. B: Carrier signal amplitude demodulation versus rpci in interictal trials in a patient suffering from MTLE. Identical stimulation protocol as in A. Values in magenta and red are derived from electrode contacts in the trigger zone (hippocampus), whereas those in green and blue are from homologous contacts in the contralateral hippocampus. Note that the distribution of the individual responses measured in the interictal state is markedly different for the two hippocampi. High rpci values correctly lateralize the trigger zone. These high values combined with the relative low values of the amplitude demodulated carrier signal indicate that the contacts in the trigger zone may exhibit an enhanced potential to an ictal transition, markedly different from homologous contacts in the contralateral hemisphere. (Both figures presented at the 2002 Annual Meeting of the American Epilepsy Society, Velis et al. [38]). true, an increase of rpci computed from EEG signals recorded at the site of seizure onset and nearby sites, might indicate the degree of elasticity of the interictal attractor along the deformation route ultimately leading to a seizure. II. CONCLUSION In this paper, we present our view of what we may call the basic mechanisms of three possible routes to epileptic seizures. To understand these mechanisms it is necessary to combine concepts of the neurophysiology of neuronal networks with those of the mathematics of nonlinear systems. The reason is that neuronal networks, in general, behave as nonlinear systems with complex dynamics. This is an essential feature that has to be taken into account in order to understand how neuronal networks can have bi (multi)-stable states and display bifurcations between such states. We herein presented a theoretical framework to account for different routes of a neuronal network from its normal mode of activity to a seizure mode. We propose three basic routes to epileptic seizures that help to understand under which circumstances the transition from the ongoing (interictal) activity mode to the ictal (seizure) mode may, or may not, be anticipated [27]. We draw the conclusion that any of the three routes is possible, depending on the type of the underlying epilepsy. Seizures may be essentially unpredictable, as most often in absence-type seizures of idiopathic (primary) generalized epilepsy, or predictable, preceded by a gradual change in dynamics, detectable some time before the manifestation of a seizure, as in TLE. The latter has been already demonstrated in a number of studies, by mostly employing analytical methods derived from the theory of nonlinear dynamics. 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Lopes da Silva was born in He received the M.D. degree from the University of Lisbon, Lisbon, Portugal, in In 1960, he joined the Psychiatry Department of the Medical Faculty, University of Lisbon, where he worked in setting up an experimental neurophysiological laboratory. He did a post-graduate course on engineering and physics for physiologists, Imperial College of the University of London, London, U.K. He worked at the Department of Physiology and Pharmacology of the National Institute of Medical Research (Mill Hill). Thereafter, he went to Utrecht, The Netherlands, to become a member of the research staff of the Institute of Medical Physics (TNO) where he worked towards the Ph.D. degree. His thesis was on system analysis of visual evoked potentials. He received the Ph.D. degree from the University of Utrecht in In 1997, he received the degree of Doctor Honoris Causa from the University of Lisbon. He has been a Full Professor in General Animal Physiology at the Faculty of Sciences at the University of Amsterdam, Amsterdam, The Netherlands, since He taught Neurophysiology (from 1975 to 1985) as a Visiting Professor at the Twente University (THT), Enschede, The Netherlands, as part of the biomedical engineering program. In 1985, he was elected member of the Netherlands Royal Academy of Arts and Sciences. In 1993, he was appointed Scientific Director of the newly created Institute of Neurobiology, and member of the Scientific Directorate of the Graduate School of Neurosciences, Amsterdam. Since 1995, he is Scientific Director of the Institute for Epilepsy Meer en Bosch in Heemstede. In March 2000, he was elected Invited Professor of the Faculty of Medicine of the University of Lisbon. In September 2000, he became Emeritus Professor of the University of Amsterdam due to reaching the official retirement age. His research interests are mainly the study of the basic electrophysiology of the brain, in particular of the limbic system, and the origin of epileptic phenomena. Furthermore, he studies the functional organization of neuronal networks in relation to memory, attention and consciousness. Dr. Lopes da Silva received a Gulbenkian Scholarship ( ). He was selected by the American Clinical Neurophysiology Society as the recipient of the 1999 Herbert H. Jasper Award. In 2000, he was awarded the degree of grand-officer of the Order of Santiago da Espada by the President of the Republic of Portugal, that is given for distinction in the fields of science, art and literature. He is Honorary Member of the Dutch and British Societies of Clinical Neurophysiology. In March 2001, he was awarded by the Queen of the Netherlands the degree of knight of the order of the Nederlandse Leeuw.

9 548 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 5, MAY 2003 Wouter Blanes was born in Amsterdam, The Netherlands, in He received the HBS-B degree in 1967 and began his study of physics at the University of Amsterdam. He complemented his interest to include electronics and computer science. Since 1967, he is an Electronics Designer and Scientific Programmer with the Dutch Epilepsy Clinics Foundation (SEIN), Heemstede, The Netherlands, mainly working in the field of data conversion, data acquisition, and system software. Jaime Parra was born in Madrid, Spain, in He received the M.D. degree from the Complutense University, Madrid. After completing his residence in neurology in Madrid, he completed a fellowship in epilepsy, clinical neurophysiology and sleep disorders at Rush Presbyterian St. Luke s Medical Center, Chicago, IL. He joined the staff at SEIN in His current research interests lie in the study of the genesis of human photosensitive epilepsy, and in the development of preventive measures that could be implemented in the audio visual media. Dr. Parra is board certified in neurology and clinical neurophysiology in the Netherlands and he is a member of the Dutch Collaborative Epilepsy Surgery Program. Stiliyan Kalitzin received the M.S. degree in nuclear and high-energy physics from the University of Sofia, Bulgaria, in He worked on the foundations of the harmonic superspace approach to extended supersymmetry and received the Ph.D. degree in theoretical physics from the Bulgarian Academy of Sciences, in In 1990, he joined the University of Utrecht, Institute of Theoretical Physics, Utrecht, The Netherlands, where he continued his work on supersymmetry and supergravity and get involved in research on cellular automata, neural networks and biological modeling. In 1992, he was a Researcher in the Visual Systems Analysis group, the Academic Medical Centre University Hospital, Amsterdam, The Netherlands, where he contributed to the development and analysis of biological neural network models of the human vision. From 1996 until 1999, he worked in the Image Sciences Institute at University Medical Center in Utrecht in the area of multiscale image analysis, topological structure analysis of images, and perceptual grouping. Since 1999, he is with the Dutch Epilepsy Clinics Foundation (SEIN), Heemstede, The Netherlands, as Head of the Medical Physics Department. His current research interests are in the fields of nonlinear system dynamics, signal and image processing, seizure prediction, closed-loop epileptic seizure control, and large-scale neural network modeling of normal and epileptic brain activity. Piotr Suffczynski was born in 1970 in Warsaw, Poland. He received the masters degree in 1995 and the Ph.D. degree in Medical Physics from the Warsaw University in Thereafter, he was appointed as an Assistant Professor in the group of Prof. Blinowska at the Laboratory of Medical Physics, Warsaw University. At present, he is a Research Fellow with the Medical Physics Department at the Dutch Epilepsy Clinics Foundation (SEIN), Heemstede, The Netherlands. He develops realistic neuronal network models that provide, among others, methodological support for clinically founded research programs. Demetrios N. Velis received the M.D. degree from Northwestern University Medical School, Evanston, IL, in He completed postgraduate training in neurology and clinical neurophysiology at the Academic Hospital of the University of Amsterdam, Amsterdam, The Netherlands. He holds the position of acting chairman at the Department of Clinical Neurophysiology and the Epilepsy Monitoring Unit at the Dutch Epilepsy Clinics Foundation in Heemstede, The Netherlands. His current research interests lie in the field of intracranial electrical stimulation and its role in elucidating events leading to the occurrence of epileptic seizures in man in addition to identifying complementary signal analysis techniques that may be of use in advance warning of an impeding seizure. Dr. Velis is board certified in neurology and clinical neurophysiology in the Netherlands. He is a member of the Dutch Collaborative Epilepsy Surgery Program and of the International League against Epilepsy s Subcommission on Clinical Neurophysiology.