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The application of non-linear signal analysis techniques to biomedical data is key to improve our knowledge about complex physiological and pathological processes. In particular, the use of non-linear techniques to study electroencephalographic (EEG) recordings can provide an advanced characterization of brain dynamics. In epilepsy these dynamics are altered at different spatial scales of neuronal organization. We therefore apply non-linear signal analysis to EEG recordings from epilepsy patients derived with intracranial hybrid electrodes, which are composed of classical macro contacts and micro wires. Thereby, these electrodes record EEG at two different spatial scales. Our aim is to test the degree to which the analysis of the EEG recorded at these different scales allows us to characterize the neuronal dynamics affected by epilepsy. For this purpose, we retrospectively analyzed long-term recordings performed during five nights in three patients during which no seizures took place. As a benchmark we used the accuracy with which this analysis allows determining the hemisphere that contains the seizure onset zone, which is the brain area where clinical seizures originate. We applied the surrogate-corrected non-linear predictability score (ψ), a non-linear signal analysis technique which was shown previously to be useful for the lateralization of the seizure onset zone from classical intracranial EEG macro contact recordings. Higher values of ψ were found predominantly for signals recorded from the hemisphere containing the seizure onset zone as compared to signals recorded from the opposite hemisphere. These differences were found not only for the EEG signals recorded with macro contacts, but also for those recorded with micro wires. In conclusion, the information obtained from the analysis of classical macro EEG contacts can be complemented by the one of micro wire EEG recordings. This combined approach may therefore help to further improve the degree to which quantitative EEG analysis can contribute to the diagnostics in epilepsy patients. The authors acknowledge funding from the Spanish Ministry of Economy and Competitiveness, Grant No. FIS2014-54177-R (CM and RA) and by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme, MDM-2015-0502 (CM), from the Volkswagen foundation (FM), from the German Research Council (DFG MO 930/8-1, DFG SFB 1089 to FM).

Objective To show that time-irreversible EEG signals recorded with intracranial electrodes during seizures can serve as markers of the epileptogenic zone. Methods We use the recently developed method of mapping time series into directed horizontal graphs (dHVG). Each node of the dHVG represents a time point in the original intracranial EEG (iEEG) signal. Statistically significant differences between the distributions of the nodes’ number of input and output connections are used to detect time-irreversible iEEG signals. Results In 31 of 32 seizure recordings we found time-irreversible iEEG signals. The maximally time-irreversible signals always occurred during seizures, with highest probability in the middle of the first seizure half. These signals spanned a large range of frequencies and amplitudes but were all characterized by saw-tooth like shaped components. Brain regions removed from patients who became post-surgically seizure-free generated significantly larger time-irreversibilities than regions removed from patients who still had seizures after surgery. Conclusions Our results corroborate that ictal time-irreversible iEEG signals can indeed serve as markers of the epileptogenic zone and can be efficiently detected and quantified in a time-resolved manner by dHVG based methods. Significance Ictal time-irreversible EEG signals can help to improve pre-surgical evaluation in patients suffering from pharmaco-resistant epilepsies.

International audience; In patients diagnosed with pharmaco-resistant epilepsy, cerebral areas responsible for seizure generation can be defined by performing implantation of intracranial electrodes. The identification of the epileptogenic zone (EZ) is based on visual inspection of the intracranial electroencephalogram (IEEG) performed by highly qualified neurophysiologists. New computer-based quantitative EEG analyses have been developed in collaboration with the signal analysis community to expedite EZ detection. The aim of the present report is to compare different signal analysis approaches developed in four different European laboratories working in close collaboration with four European Epilepsy Centers. Computer-based signal analysis methods were retrospectively applied to IEEG recordings performed in four patients undergoing pre-surgical exploration of pharmaco-resistant epilepsy. The four methods elaborated by the different teams to identify the EZ are based either on frequency analysis, on nonlinear signal analysis, on connectivity measures or on statistical parametric mapping of epileptogenicity indices. All methods converge on the identification of EZ in patients that present with fast activity at seizure onset. When traditional visual inspection was not successful in detecting EZ on IEEG, the different signal analysis methods produced highly discordant results. Quantitative analysis of IEEG recordings complement clinical evaluation by contributing to the study of epileptogenic networks during seizures. We demonstrate that the degree of sensitivity of different computer-based methods to detect the EZ in respect to visual EEG inspection depends on the specific seizure pattern

The sudden and apparently unpredictable nature of seizures is one of the most disabling aspects of the disease epilepsy. A method capable of predicting the occurrence of seizures from the electroencephalogram (EEG) of epilepsy patients would open new therapeutic possibilities. Since the 1970s investigations on the predictability of seizures have advanced from preliminary descriptions of seizure precursors to controlled studies applying prediction algorithms to continuous multi-day EEG recordings. While most of the studies published in the 1990s and around the turn of the millennium yielded rather promising results, more recent evaluations could not reproduce these optimistic findings, thus raising a debate about the validity and reliability of previous investigations. In this review, we will critically discuss the literature on seizure prediction and address some of the problems and pitfalls involved in the designing and testing of seizure-prediction algorithms. We will give an account of the current state of this research field, point towards possible future developments and propose methodological guidelines for future studies on seizure prediction.

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena.A recent and not yet fully understood example is the collapse of coexisting synchronous and synchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications. The authors are grateful to Ernest Montbrió and Arkady Pikovsky for useful discussion. R.G.A. and F.M. acknowledge funding from the Volkswagen foundation. R.G.A was supported by the Spanish Ministry of Economy and Competitiveness (Grant FIS2014-54177-R). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642563 (R.G.A.). F.M. acknowledges support from the German Research Council (DFG, MO 930/4-1 and SFB 1089) and the European Commission (FP7 602102 EPITARGET). K.S. and C.R. are grateful for support by the Swiss National Science Foundation (Projects No. SNF 320030_122010, No. 33CM30-140332, No. 32003B_155950).

BACKGROUND/nEpilepsy surgery is a potentially curative treatment option for pharmacoresistent patients. If non-invasive methods alone do not allow to delineate the epileptogenic brain areas the surgical candidates undergo long-term monitoring with intracranial EEG. Visual EEG analysis is then used to identify the seizure onset zone for targeted resection as a standard procedure./n/nMETHODS/nDespite of its great potential to assess the epileptogenicty of brain tissue, quantitative EEG analysis has not yet found its way into routine clinical practice. To demonstrate that quantitative EEG may yield clinically highly relevant information we retrospectively investigated how post-operative seizure control is associated with four selected EEG measures evaluated in the resected brain tissue and the seizure onset zone. Importantly, the exact spatial location of the intracranial electrodes was determined by coregistration of pre-operative MRI and post-implantation CT and coregistration with post-resection MRI was used to delineate the extent of tissue resection. Using data-driven thresholding, quantitative EEG results were separated into normally contributing and salient channels./n/nRESULTS/nIn patients with favorable post-surgical seizure control a significantly larger fraction of salient channels in three of the four quantitative EEG measures was resected than in patients with unfavorable outcome in terms of seizure control (median over the whole peri-ictal recordings). The same statistics revealed no association with post-operative seizure control when EEG channels contributing to the seizure onset zone were studied./n/nCONCLUSIONS/nWe conclude that quantitative EEG measures provide clinically relevant and objective markers of target tissue, which may be used to optimize epilepsy surgery. The finding that differentiation between favorable and unfavorable outcome was better for the fraction of salient values in the resected brain tissue than in the seizure onset zone is consistent with growing evidence that spatially extended networks might be more relevant for seizure generation, evolution and termination than a single highly localized brain region (i.e. a “focus”) where seizures start. This study was supported by the Swiss National Science Foundation (SNF) via the projects 122010, 124089, 140332 and 155950. R.G. Andrzejak was supported by grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science and funding from the Volkswagen Foundation. M. Müller acknowledges the Consejo Nacionál de Ciencia y Technología, Mexico, project 156667. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Objective: An important issue in epileptology is the question whether information extracted from the EEG of epilepsy patients can be used for the prediction of seizures. Several studies have claimed evidence for the existence of a pre-seizure state that can be detected using different characterizing measures. In this paper, we evaluate the predictability of seizures by comparing the predictive performance of a variety of univariate and bivariate measures comprising both linear and non-linear approaches. Methods: We compared 30 measures in terms of their ability to distinguish between the interictal period and the pre-seizure period. After completely analyzing continuous inctracranial multi-channel recordings from five patients lasting over days, we used ROC curves to distinguish between the amplitude distributions of interictal and preictal time profiles calculated for the respective measures. We compared different evaluation schemes including channelwise and seizurewise analysis plus constant and adaptive reference levels. Particular emphasis was placed on statistical validity and significance. Results: Univariate measures showed statistically significant performance only in a channelwise, seizurewise analysis using an adaptive baseline. Preictal changes for these measures occurred 5‐30 min before seizures. Bivariate measures exhibited high performance values reaching statistical significance for a channelwise analysis using a constant baseline. Preictal changes were found at least 240 min before seizures. Linear measures were found to perform similar or better than non-linear measures. Conclusions: Results provide statistically significant evidence for the existence of a preictal state. Based on our findings, the most promising approach for prospective seizure anticipation could be a combination of bivariate and univariate measures. Significance: Many measures reported capable of seizure prediction in earlier studies are found to be insignificant in performance, which underlines the need for statistical validation in this field. q 2004 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

A number of recent studies indicate that nonlinear electroencephalogram (EEG) analyses allow one to define a state predictive of an impending epileptic seizure. In this paper, we combine a method for detecting nonlinear determinism with a novel test for stationarity to characterize EEG recordings from both the seizure-free interval and the preseizure phase. We discuss differences between these periods, particularly an increased occurrence of stationary, nonlinear segments prior to seizures. These differences seem most prominent for recording sites within the seizure-generating area and for EEG segments less than one minute's length.

The exact mechanisms leading to the occurrence of epileptic seizures in humans are still poorly understood. It is widely accepted, however, that the process of seizure generation is closely associated with an abnormal synchronization of neurons. In order to investigate this process, we here measure phase synchronization between different regions of the brain using intracranial EEG recordings. Based on our preliminary finding of a preictal drop in synchronization, we investigate whether this phenomenon can be used as a sensitive and specific criterion to characterize a preseizure state and to distinguish this state from the interictal interval. Applying an automated technique for detecting decreased synchronization to EEG recordings from a group of 18 patients with focal epilepsy comprising a total of 117 h, we observe a characteristic decrease in synchronization prior to 26 out of 32 analyzed seizures at a very high specificity as tested on interictal recordings. The duration of this preictal state is found to range from several minutes up to a few hours. Investigation of the spatial distribution of preictal desynchronization indicates that the process of seizure generation in focal epilepsy is not necessarily confined to the focus itself but may instead involve more distant, even contralateral areas of the brain. Finally, we demonstrate an intrahemispheric asymmetry in the spatial dynamics of preictal desynchronization that is found in the majority of seizures and appears to be an immanent part of the mechanisms underlying the initiation of seizures in humans.

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals). R.G.A. acknowledges Grant No. FIS-2010-18204 of the Spanish Ministry of Education and Science and funding from the Volkswagen Foundation. K.S. and C.R. are grateful for support by the Swiss National Science Foundation (Projects No. SNF 320030-122010 and No. 33CM30-124089).

The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure ξ , designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, ξ was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.

To derive tests for randomness, nonlinear-independence, and stationarity, we combine surrogates with a nonlinear prediction error, a nonlinear interdependence measure, and linear variability measures, respectively. We apply these tests to intracranial electroencephalographic recordings (EEG) from patients suffering from pharmacoresistant focal-onset epilepsy. These recordings had been performed prior to and independent from our study as part of the epilepsy diagnostics. The clinical purpose of these recordings was to delineate the brain areas to be surgically removed in each individual patient in order to achieve seizure control. This allowed us to define two distinct sets of signals: One set of signals recorded from brain areas where the first ictal EEG signal changes were detected as judged by expert visual inspection (“focal signals”) and one set of signals recorded from brain areas that were not involved at seizure onset (“nonfocal signals”). We find more rejections for both the randomness and the nonlinear-independence test for focal versus nonfocal signals. In contrast more rejections of the stationarity test are found for nonfocal signals. Furthermore, while for nonfocal signals the rejection of the stationarity test increases the rejection probability of the randomness and nonlinear-independence test substantially, we find a much weaker influence for the focal signals. In consequence, the contrast between the focal and nonfocal signals obtained from the randomness and nonlinear-independence test is further enhanced when we exclude signals for which the stationarity test is rejected. To study the dependence between the randomness and nonlinear-independence test we include only focal signals for which the stationarity test is not rejected. We show that the rejection of these two tests correlates across signals. The rejection of either test is, however, neither necessary nor sufficient for the rejection of the other test. Thus, our results suggest that EEG signals from epileptogenic brain areas are less random, more nonlinear-dependent, and more stationary compared to signals recorded from nonepileptogenic brain areas. We provide the data, source code, and detailed results in the public domain. R.G.A. acknowledges grant FIS-2010-18204 of the Spanish Ministry of Education and Science. K.S. and C.R. are grateful for support by the Swiss National Science Foundation (projects nos. SNF 320030-122010 and 33CM30- 124089).

Determining how distinct neurons or brain regions are connected and communicate with each other is a crucial point in neuroscience, as it allows to investigate how the functional integration of specialized neural populations enables the emergence of coherent cognitive and behavioral states. The general concept of brain connectivity encompasses different aspects: structural connectivity is related to the description of anatomical pathways and synaptic connections; functional connectivity investigates statistical dependencies between spatially separated brain regions; effective connectivity refers to models aimed at elucidating driver-response relationships. The study of these different modes of brain connectivity is fundamental both for the investigation of the neurophysiological processes engaged in cognitive and perceptive processing and for the assessment of a variety of neurological disorders. Over the last past few decades, the continuous advancement of multichannel data acquisition technologies has made it possible to collect neuroscience data at multiple levels of description, ranging from neural spikes to local field potentials and electroencephalography (EEG)-magnetoencephalography (MEG). This increasing data availability and the contemporaneous improvement of signal processing capabilities have contributed in placing increasing demands on methods for the quantitative assessment of neural interactions. Accordingly, a variety of methodological approaches have emerged for the estimation of brain connectivity from multivariate neurophysiological time series. These approaches build on different analysis frameworks which point out specific aspects of connectivity: linear parametric models are explicitly related to the frequency domain representation of multivariate data, thus favoring the assessment of connectivity for specific brain rhythms; information theory provides tools that describe both linear and nonlinear interactions and are free from the shortcomings of model specification; phase synchronization analysis characterizes the relation between the phases of different brain units seen as coupled oscillators, allowing detection of synchronization regardless of the relation between signal amplitudes. All these frameworks provide measures able to reflect the various aspects of brain connectivity, such as undirected measures of association (e.g., coherence, mutual information, phase synchronization index) and directed measures of Granger causality (e.g., partial directed coherence, transfer entropy). To get new and deeper insights into the complex dynamics of interacting brain regions, the existing brain connectivity measures need to be refined, extended, and complemented with other tools. Common issues to be addressed are estimation problems arising in the presence of noise contamination and nonstationarity, significance assessment, distinguishing direct from indirect causal effects, and aspects related to the difficulty of performing full multivariate analyses over short data sets. An important problem of EEG/MEG recordings is that the connectivity patterns estimated at the sensor level may strongly differ from those really existing between the underlying neural sources, as a consequence of a mixing effect known as volume conduction. While a common approach to deal with this issue is to estimate connectivity after application of an inverse method for source localization, methodological advances are needed to improve the localization accuracy of ill-posed inverse problems. Moreover, once brain connectivity measures are computed, the formal representation of connectivity patterns in graph or matrix format leads to employ concepts of network analysis to interpret these patterns. Accordingly, the study of topological properties like clustering degree, modularity, and presence of network motifs is becoming increasingly popular for the investigation of the organizational principles of brain processes. The papers of this special issue reflect the variety in the approaches for the estimation of brain connectivity described above, as well as the need to improve and adapt these approaches to the more and more demanding qualitative requirements and challenges of modern neurophysiological applications. J. Sun et al. offer a review of phase synchronization analysis methods for the inference of functional brain connectivity, describing definitions, estimation, and significance assessment, presenting some extensions, and discussing the issues that affect the detection of phase synchronization from neural data. C. Alvarado-Rojas and M. Le Van Quyen exploit phase synchronization analysis and clustering techniques to identify, from intracranial EEG recordings acquired in epileptic patients during seizure-free periods, dynamic modes of brain synchrony which are characteristic for the wake-sleep cycle. L. Faes et al. introduce a common framework for the unified description of the most popular frequency domain connectivity measures based on linear parametric modeling of multiple time series, discussing their relations, theoretical interpretation, advantages and limitations, and practical estimation. A. Brovelli assesses the reliability of frequency domain Granger causality analysis performed on a single-trial basis, showing that, when combined with parametric statistical tests, Granger causality spectra successfully recover causal interactions in both synthetic and neurophysiological data. Y. Liu and S. Aviyente illustrate the advantages over linear parametric Granger causality of an information theoretic tool, the directed information, as regards the assessment of directional connectivity in both simulated time series and EEG data. D. Marinazzo et al. face the important problem of estimating causality in complex brain networks through fully multivariate approaches; working in the frame of information theory, they provide a novel approach for partial conditioning to a subset of informative variables, showing that this approach can help to overcome computational and numerical problems otherwise arising with traditional full conditioning schemes. P. Belardinelli et al. investigate in a realistic MEG environment the known localization bias due to correlation between source time series occurring for the popular beamformer inverse method, showing that this bias is relevant only for extremely high degrees of source correlation. F. Avarvand et al. combine subspace and beamformer source localization methods with estimation of the imaginary part of the coherence in simulated and real EEG data, implementing an approach that is sensitive to connectivity rather than to activity and, as such, improves localization accuracy and detection of source interactions. C. Micheli and C. Braun deal with the problem of characterizing connectivity between neural source activity and muscular activity after the localization of multiple correlated sources; when applied to MEG and electromyographic signals during a pinch grip task, their approach highlights patterns of corticomuscular coherence otherwise not obtainable with the use of standard methods. C. Schmidt et al. propose a new analytical approach to the detection of topological motifs in EEG connectivity networks estimated in patients with major depression during painful stimulation, suggesting that specific motifs may help explaining the relationship between pain and depression. A. Alvarellos-Gonzalez et al. study structural brain connectivity at the synaptic level, presenting enhanced computational models of neural networks which evidence the potentiation of synaptic connectivity that takes place in the brain when glial cells are considered in addition to artificial neurons. Luca Faes Ralph G. Andrzejak Mingzhou Ding Dimitris Kugiumtzis

Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However, its original definition led to spuriously high instantaneous values for event-like firing patterns. Here we present a substantial improvement of this measure which eliminates this shortcoming. The reliability gained allows us to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. Additional new features include selective and triggered temporal averaging as well as the instantaneous comparison of spike train groups. In a second step, a causal SPIKE-distance is defined such that the instantaneous values of dissimilarity rely on past information only so that time-resolved spike train synchrony can be estimated in real-time. We demonstrate that these methods are capable of extracting valuable information from field data by monitoring the synchrony between neuronal spike trains during an epileptic seizure. Finally, the applicability of both the regular and the real-time SPIKE-distance to continuous data is illustrated on model electroencephalographic (EEG) recordings., Comment: 16 pages, 10 figures, 35 references; 1 supplementary figure, 1 supplementary movie (see author's webpage http://www.fi.isc.cnr.it/users/thomas.kreuz/sourcecode.html)

Theta oscillations in the medial temporal lobe (MTL) of mammals are involved in various functions such as spatial navigation, sensorimotor integration, and cognitive processing. While the theta rhythm was originally assumed to originate in the medial septum, more recent studies suggest autonomous theta generation in the MTL. Although coherence between entorhinal and hippocampal theta activity has been found to infl uence memory formation, it remains unclear whether these two structures can generate theta independently. In this study we analyzed intracranial electroencephalographic (EEG) recordings from 22 patients with unilateral hippocampal sclerosis undergoing presurgical evaluation prior to resection of the epileptic focus. Using a wavelet-based, frequency-band-specifi c measure of phase synchronization, we quantifi ed synchrony between 10 different recording sites along the longitudinal axis of the hippocampal formation in the non-epileptic brain hemisphere. We compared EEG synchrony between adjacent recording sites (i) within the entorhinal cortex, (ii) within the hippocampus, and (iii) between the hippocampus and entorhinal cortex. We observed a signifi cant interregional gap in synchrony for the delta and theta band, indicating the existence of independent delta/theta rhythms in different subregions of the human MTL. The interaction of these rhythms could represent the temporal basis for the information processing required for mnemonic encoding and retrieval. This work was supported by the Intramural Research Fund BONFOR of the University of Bonn and the 6th Framework Programme of the European Commission (Marie Curie OIF 040445).

An advanced characterization of the complicated dynamical system brain is one of science's biggest challenges. Nonlinear time series analysis allows characterizing nonlinear dynamical systems in which low-dimensional nonlinearity gives rise to complex and irregular behavior. While several studies indicate that nonlinear methods can extract valuable information from neuronal dynamics, others doubt their necessity and conjecture that the same information can be obtained using classical linear techniques. To address this issue, we compared these two concepts, but included furthermore a combination of nonlinear measures with surrogates, an approach that has been designed to specifically focus on nonlinearity. As a benchmark we used the discriminative power to detect the seizure-generating hemisphere in medically intractable mesial temporal lobe epilepsy. We analyzed intracranial electroencephalographic recordings from the seizure-free interval of 29 patients. While the performance of both linear and nonlinear measures was weak, if not insignificant, a very high performance was obtained by the use of surrogate-corrected measures. Focusing on nonlinearity by using a combination of nonlinear measures with surrogates appears as the key to a successful characterization of the spatial distribution of the epileptic process.

In a growing number of publications it is claimed that epileptic seizures can be predicted by analyzing the electroencephalogram (EEG) with different characterizing measures. However, many of these studies suffer from a severe lack of statistical validation. Only rarely are results passed to a statistical test and verified against some null hypothesis H 0 in order to quantify their significance. In this paper we propose a method to statistically validate the performance of measures used to predict epileptic seizures. From measure profiles rendered by applying a moving-window technique to the electroencephalogram we first generate an ensemble of surrogates by a constrained randomization using simulated annealing. Subsequently the seizure prediction algorithm is applied to the original measure profile and to the surrogates. If detectable changes before seizure onset exist, highest performance values should be obtained for the original measure profiles and the null hypothesis. “The measure is not suited for seizure prediction” can be rejected. We demonstrate our method by applying two measures of synchronization to a quasicontinuous EEG recording and by evaluating their predictive performance using a straightforward seizure prediction statistics. We would like to stress that the proposed method is rather universal and can be applied to many other prediction and detection problems. This work was supported by the Deutsche Forschungsgemeinschaft (Grant No. SFB TR3).

In this overview we present our work investigating the spatio-temporal dynamics of the epileptogenic process using time series analysis techniques derived from the theory of nonlinear dynamics. Apart from a localization of epileptic foci in different anatomical locations during the seizure-free interval we discuss possibilities for seizure prediction, a field that represents one of the greatest challenges in epileptology. The unequivocal definition of a pre-seizure state of a sufficient length would enable investigation of basic mechanisms leading to seizure initiation in humans and provide a basis for the development of adequate seizure prevention strategies.

Attempting to increase insight into the spatio-temporal dynamics of the epileptogenic process to address one of the greatest challenges in epileptology. In the field of EEG analysis the search for the hidden information predictive of an impending seizure has a long history. The nonlinear EEG analysis techniques we have used in principle allow one to define a pre-ictal state and to characterize different temporal and spatial aspects of this state. The results obtained so far emphasize the high value of nonlinear EEG analysis techniques for the detection of a long-lasting pre-ictal state. Once given a sufficient sensitivity and specificity of seizure prediction techniques, more extensive clinical studies on a larger population of patients, either at home or in a clinical setting, can be envisaged.

A rapidly growing number of studies deals with the prediction of epileptic seizures. For this purpose, various techniques derived from linear and nonlinear time series analysis have been applied to the electroencephalogram of epilepsy patients. In none of these works, however, the performance of the seizure prediction statistics is tested against a null hypothesis, an otherwise ubiquitous concept in science. In consequence, the evaluation of the reported performance values is problematic. Here, we propose the technique of seizure time surrogates based on a Monte Carlo simulation to remedy this deficit. C.E.E., T.K., K.L., F.M., and C.R. acknowledge support from the Deutsche Forschungsgemeinschaft.

Deterministic chaos offers a striking explanation for apparently irregular behavior of the brain that is evidenced in the EEG. Recent developments in the physical-mathematical framework of the theory of nonlinear dynamics (colloquially often termed chaos theory) provide new concepts and powerful algorithms to analyze such time series. Because of its high versatility, nonlinear time series analysis has already gone beyond the physical sciences and, at present, is being successfully applied in a variety of disciplines, including cardiology, neurology, psychiatry, and epileptology. However, it is well known that different influencing factors limit the use of nonlinear measures to characterize EEG dynamics in a strict sense. Nevertheless, when interpreted with care, relative estimates of, e.g., the correlation dimension or the Lyapunov exponents, can reliably characterize different states of normal and pathologic brain function. In epileptology, extraction of nonlinear measures from the intracranially recorded EEG promises to be important for clinical practice. In addition to an immense reduction of information content of long-lasting EEG recordings, previous studies have shown that these measures enable (a) localization of the primary epileptogenic area in different cerebral regions during the interictal state, (b) investigations of antiepileptic drug effects, (c) analyses of spatio-temporal interactions between the epileptogenic zone and other brain areas, and (d) detection of features predictive of imminent seizure activity. Nonlinear time series analysis provides new and supplementary information about the epileptogenic process and thus contributes to an improvement in presurgical evaluation.

The question whether information extracted from the electroencephalogram ~EEG! of epilepsy patients can be used for the prediction of seizures has recently attracted much attention. Several studies have reported evidence for the existence of a preseizure state that can be detected using different measures derived from the theory of dynamical systems. Most of these studies, however, have neglected to sufficiently investigate the specificity of the observed effects or suffer from other methodological shortcomings. In this paper we present an automated technique for the detection of a preseizure state from EEG recordings using two different measures for synchronization between recording sites, namely, the mean phase coherence as a measure for phase synchronization and the maximum linear cross correlation as a measure for lag synchronization. Based on the observation of characteristic drops in synchronization prior to seizure onset, we used this phenomenon for the characterization of a preseizure state and its distinction from the remaining seizure-free interval. After optimizing our technique on a group of 10 patients with temporal lobe epilepsy we obtained a successful detection of a preseizure state prior to 12 out of 14 analyzed seizures for both measures at a very high specificity as tested on recordings from the seizure-free interval. After checking for in-sample overtraining via cross validation, we applied a surrogate test to validate the observed predictability. Based on our results, we discuss the differences of the two synchronization measures in terms of the dynamics underlying seizure generation in focal epilepsies. This work was supported by the Deutsche Forschungsgemeinschaft.