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Epilepsy is now conceptualized as a network disease. The epileptic brain network comprises structurally and functionally connected cortical and subcortical brain regions - spanning lobes and hemispheres -, whose connections and dynamics evolve in time. With this concept, focal and generalized seizures as well as other related pathophysiological phenomena are thought to emerge from, spread via, and be terminated by network vertices and edges that also generate and sustain normal, physiological brain dynamics. Research over the last years has advanced concepts and techniques to identify and characterize the evolving epileptic brain network and its constituents on various spatial and temporal scales. Network-based approaches further our understanding of how seizures emerge from the evolving epileptic brain network, and they provide both novel insights into pre-seizure dynamics and important clues for success or failure of measures for network-based seizure control and prevention. In this review, we summarize the current state of knowledge and address several important challenges that would need to be addressed to move network-based prediction and control of seizures closer to clinical translation., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law [Formula: see text] and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent [Formula: see text]. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them., (© 2022. The Author(s).)

Previous research has indicated that temporal changes of centrality of specific nodes in human evolving large-scale epileptic brain networks carry information predictive of impending seizures. Centrality is a fundamental network-theoretical concept that allows one to assess the role a node plays in a network. This concept allows for various interpretations, which is reflected in a number of centrality indices. Here we aim to achieve a more general understanding of local and global network reconfigurations during the pre-seizure period as indicated by changes of different node centrality indices. To this end, we investigate-in a time-resolved manner-evolving large-scale epileptic brain networks that we derived from multi-day, multi-electrode intracranial electroencephalograpic recordings from a large but inhomogeneous group of subjects with pharmacoresistant epilepsies with different anatomical origins. We estimate multiple centrality indices to assess the various roles the nodes play while the networks transit from the seizure-free to the pre-seizure period. Our findings allow us to formulate several major scenarios for the reconfiguration of an evolving epileptic brain network prior to seizures, which indicate that there is likely not a single network mechanism underlying seizure generation. Rather, local and global aspects of the pre-seizure network reconfiguration affect virtually all network constituents, from the various brain regions to the functional connections between them.

Cross-frequency phase-phase coupling (PPC) has been suggested to play a role in cognitive processing and, in particular, in memory consolidation during sleep. Controversial results have been reported regarding the existence of spontaneous phase-phase coupling in the hippocampus. Here, we investigated this phenomenon in intracranial EEG recordings from the human hippocampus acquired during waking state and different sleep stages. We estimated the strength of interactions between different pairs of frequency bands and evaluated the statistical significance of findings using surrogates that build on different null hypotheses. Indications for spontaneous phase-phase coupling were only observed when testing with less rigorous surrogates. When requiring that all four surrogate tests be passed, however, there were no significant indications for phase-phase coupling. In conclusion, we did not detect evidence for spontaneous cross-frequency phase-phase coupling in the human hippocampus., (© 2019 The Authors. European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.

Extreme events occur in a variety of natural, technical, and societal systems and often have catastrophic consequences. Their low-probability, high-impact nature has recently triggered research into improving our understanding of generating mechanisms, providing early warnings as well as developing control strategies. For the latter to be effective, knowledge about dynamical resistance of a system prior to an extreme event is of utmost importance. Here we introduce a novel time-series-based and non-perturbative approach to efficiently monitor dynamical resistance and apply it to high-resolution observations of brain activities from 43 subjects with uncontrollable epileptic seizures. We gain surprising insights into pre-seizure dynamical resistance of brains that also provide important clues for success or failure of measures for seizure prevention. The novel resistance monitoring perspective advances our understanding of precursor dynamics in complex spatio-temporal systems with potential applications in refining control strategies.

Epilepsy is a common disorder characterized by recurrent seizures. An overwhelming majority of people with epilepsy regard the unpredictability of seizures as a major issue. More than 30 years of international effort have been devoted to the prediction of seizures, aiming to remove the burden of unpredictability and to couple novel, time-specific treatment to seizure prediction technology. A highly influential review published in 2007 concluded that insufficient evidence indicated that seizures could be predicted. Since then, several advances have been made, including successful prospective seizure prediction using intracranial EEG in a small number of people in a trial of a real-time seizure prediction device. In this Review, we examine advances in the field, including EEG databases, seizure prediction competitions, the prospective trial mentioned and advances in our understanding of the mechanisms of seizures. We argue that these advances, together with statistical evaluations, set the stage for a resurgence in efforts towards the development of seizure prediction methodologies. We propose new avenues of investigation involving a synergy between mechanisms, models, data, devices and algorithms and refine the existing guidelines for the development of seizure prediction technology to instigate development of a solution that removes the burden of the unpredictability of seizures.

Epilepsy can be regarded as a network phenomenon with functionally and/or structurally aberrant connections in the brain. Over the past years, concepts and methods from network theory substantially contributed to improve the characterization of structure and function of these epileptic networks and thus to advance understanding of the dynamical disease epilepsy. We extend this promising line of research and assess-with high spatial and temporal resolution and using complementary analysis approaches that capture different characteristics of the complex dynamics-both strength and direction of interactions in evolving large-scale epileptic brain networks of 35 patients that suffered from drug-resistant focal seizures with different anatomical onset locations. Despite this heterogeneity, we find that even during the seizure-free interval the seizure onset zone is a brain region that, when averaged over time, exerts strongest directed influences over other brain regions being part of a large-scale network. This crucial role, however, manifested by averaging on the population-sample level only - in more than one third of patients, strongest directed interactions can be observed between brain regions far off the seizure onset zone. This may guide new developments for individualized diagnosis, treatment and control.

Drug-resistant, multifocal, non-resectable epilepsies are among the most difficult epileptic disorders to manage. An approach to control previously uncontrollable seizures in epilepsy patients would consist of identifying seizure precursors in critical brain areas combined with delivering a counteracting influence to prevent seizure generation. Predictability of seizures with acceptable levels of sensitivity and specificity, even in an ambulatory setting, has been repeatedly shown, however, in patients with a single seizure focus only. We did a study to assess feasibility of state-of-the-art, electroencephalogram-based seizure-prediction techniques in patients with uncontrollable multifocal seizures. We obtained significant predictive information about upcoming seizures in more than two thirds of patients. Unexpectedly, the emergence of seizure precursors was confined to non-affected brain areas. Our findings clearly indicate that epileptic networks, spanning lobes and hemispheres, underlie generation of seizures. Our proof-of-concept study is an important milestone towards new therapeutic strategies based on seizure-prediction techniques for clinical practice.

Objective: To investigate whether functional brain networks of epilepsy patients treated with antiepileptic medication differ from networks of healthy controls even during the seizure-free interval., Methods: We applied different rules to construct binary and weighted networks from EEG and MEG data recorded under a resting-state eyes-open and eyes-closed condition from 21 epilepsy patients and 23 healthy controls. The average shortest path length and the clustering coefficient served as global statistical network characteristics., Results: Independent on the behavioral condition, epileptic brains exhibited a more regular functional network structure. Similarly, the eyes-closed condition was characterized by a more regular functional network structure in both groups. The amount of network reorganization due to behavioral state changes was similar in both groups. Consistent findings could be achieved for networks derived from EEG but hardly from MEG recordings, and network construction rules had a rather strong impact on our findings., Conclusions: Despite the locality of the investigated processes epileptic brain networks differ in their global characteristics from non-epileptic brain networks. Further methodological developments are necessary to improve the characterization of disturbed and normal functional networks., Significance: An increased regularity and a diminished modulation capability appear characteristic of epileptic brain networks., (Copyright (c) 2009 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.)

Inferring directional interactions from biosignals is of crucial importance to improve understanding of dynamical interdependences underlying various physiological and pathophysiological conditions. We here present symbolic transfer entropy as a robust measure to infer the direction of interactions between multidimensional dynamical systems. We demonstrate its performance in quantifying driver-responder relationships in a network of coupled nonlinear oscillators and in the human epileptic brain.

We assess electrical brain dynamics before, during, and after 100 human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal evolution of characteristic path length and cluster coefficient indicative of a movement from a more random toward a more regular and then back toward a more random functional topology. Surprisingly, synchronizability was significantly decreased during the seizure state but increased already prior to seizure end. Our findings underline the high relevance of studying complex systems from the viewpoint of complex networks, which may help to gain deeper insights into the complicated dynamics underlying epileptic seizures., ((c) 2008 American Institute of Physics.)

We propose a data-driven approach to measure interdependences between dissipative dynamical systems under the influence of noise. We estimate drift and diffusion coefficients of a Fokker-Planck equation and derive measures that allow one to quantify the asymmetry in coupling in a fully automated and computationally inexpensive and simple way. Our approach makes it possible to discriminate between interdependences in the deterministic and stochastic parts of the dynamics. We report results of numerical studies of exemplary time series from coupled stochastic and deterministic model systems and of an application to electroencephalographic recordings from epilepsy patients.

Purpose: To assess whether EEG synchronization changes during short-term low-frequency electrical stimulation of the seizure onset zone., Methods: In 10 patients (34+/-11 years) with pharmaco-resistant epilepsy the seizure onset zone (9 temporal lobe, 1 frontal lobe) was electrically stimulated at 1Hz for 5min via intracranial electrodes. Bipolar stimuli were applied and four pulse widths (0.05, 0.1, 0.5, and 1.0ms) were tested. Stimulation amplitudes were held fixed at 1mA for strip electrodes and at 2mA for depth electrodes. Changes of EEG synchronization were assessed by the eigenvalue dynamics of the cross-correlation matrix computed from a 2.5s sliding window., Results: 37 stimulations were performed. We observed EEG desynchronization in 49% (18/37), an increase of EEG synchronization in 27% (10/37) and an EEG pattern with no significant change of synchronization in 24% (9/37). EEG synchronization most frequently occurred when stimulating with a pulse width of 0.5ms. In a patient with bilateral independent seizure onsets stimulation effects on EEG synchronization were different for each side. In the patient with the shortest duration of temporal lobe epilepsy, stimulation triggered periodic epileptic spikes phase-locked to stimulation. One patient experienced an aura during stimulation, which did not evolve into a seizure, and in one patient a sub-clincial seizure occurred., Discussion: Low-frequency stimulation of the seizure onset zone is associated with different changes of EEG synchronization and its effects depend on the widths of the stimulation pulses. It may be an appropriate stimulation technique for long-term studies assessing whether synchronized or desynchronized brain dynamics prevent seizure occurrence.

We propose a method for estimating nonlinear interdependences between time series using cellular nonlinear networks. Our approach is based on the nonlinear dynamics of interacting nonlinear elements. We apply it to time series of coupled nonlinear model systems and to electroencephalographic time series from an epilepsy patient, and we show that an accurate approximation of symmetric and asymmetric realizations of a nonlinear interdependence measure can be achieved, thus allowing one to detect the strength and direction of couplings.

Measuring the directionality of coupling between dynamical systems is one of the challenging problems in nonlinear time series analysis. We investigate the relative merit of two approaches to assess directionality, one based on phase dynamics modeling and one based on state space topography. We analyze unidirectionally coupled model systems to investigate the ability of the two approaches to detect driver-responder relationships and discuss certain problems and pitfalls. In addition we apply both approaches to the intracranial electroencephalogram (EEG) recorded from one epilepsy patient during the seizure-free interval to demonstrate the general suitability of directionality measures to reflect the pathological interaction of the epileptic focus with other brain areas.

We evaluate the capability of reconstructing Fokker-Planck equations for an improved characterization of electroencephalographic (EEG) recordings from epilepsy patients. We derive stochastic qualifiers of brain dynamics that are based on specific characteristics of the Kramers-Moyal coefficients estimated from the EEG. Analyzing long-lasting multichannel EEG recordings from eight patients suffering from focal epilepsies we show that particularly the stochastic part of the dynamics can yield valuable information for diagnostic purposes.

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.

Epileptic seizures are commonly characterized as 'hypersynchronous states'. This habit is doubly misleading, because seizures are not necessarily synchronous and are not unchanging 'states' but dynamic processes. Here the temporal evolution of the correlation structure in the course of 100 focal onset seizures of 60 patients recorded by intracranial multichannel EEG was assessed. To this end a multivariate method was applied that at its core consists of computing the eigenvalue spectrum of the zero-lag correlation matrix of a short sliding window. Our results show that there are clearly observable and statistically significant changes of the correlation structure of focal onset seizures. Specifically, these changes indicate that the zero-lag correlation of multi-channel EEG either remains approximately unchanged or-especially in the case of secondary generalization-decreases during the first half of the seizures. Then correlation gradually increases again before the seizures terminate. This development was qualitatively independent of the anatomical location of the seizure onset zone and therefore seems to be a generic property of focal onset seizures. We suggest that the decorrelation of EEG activity is due to the different propagation times of locally synchronous ictal discharges from the seizure onset zone to other brain areas. Furthermore we speculate that the increase of correlation during the second half of the seizures may be causally related to seizure termination.

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.

The detection of patterns embedded within a complex, nonstationary, and noisy background activity is a crucial and important task in EEG analysis. The authors present a biologically inspired, analog approach to EEG analysis that is conceptually different from a variety of statistical approaches currently used. A nonlinear, excitable, spatially extended medium that is composed of diffusively coupled model neurons is considered. When EEG recordings are applied as local perturbations to such an excitable neural tissue, the induced transient changes in the dynamics of the perturbed system can be regarded as an instantaneous characterization of transient processes in the brain reflected by the EEG, e.g., in the form of a sequence of correlated dynamical events (patterns). Nonlinear excitable media can be implemented in form of an array of locally coupled integrated analog nonlinear electrical circuits called cellular neural networks, which represent a next evolutionary step in the parallel analog computer architecture. Using cellular neural networks, the authors show that the concept of signal-induced pattern generation allows an almost instantaneous and unsupervised detection of seizure onsets in EEG recordings. In addition, they show that a cellular neural network can be trained in a supervised way to approximate the degree of synchronization in EEG recordings. The resulting pattern-recognition device may be suitable for the prediction of epileptic seizures.

We propose a method for estimating phase synchronization between time series using the parallel computing architecture of cellular nonlinear networks (CNN's). Applying this method to time series of coupled nonlinear model systems and to electroencephalographic time series from epilepsy patients, we show that an accurate approximation of the mean phase coherence R--a bivariate measure for phase synchronization--can be achieved with CNN's using polynomial-type templates.

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.

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 H0 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.

A number of recent studies indicate that nonlinear electroencephalogram (EEG) analyses allow 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.

Transcutaneous auricular vagus nerve stimulation (taVNS) is a novel non-invasive brain stimulation technique considered as a potential supplementary treatment option for subjects with refractory epilepsy. Its exact mechanism of action is not yet fully understood. We developed an examination schedule to probe for immediate taVNS-induced modifications of large-scale epileptic brain networks and accompanying changes of cognition and behaviour. In this prospective trial, we applied short-term (1 h) taVNS to 14 subjects with epilepsy during a continuous 3-h EEG recording which was embedded in two standardized neuropsychological assessments. From these EEG, we derived evolving epileptic brain networks and tracked important topological, robustness, and stability properties of networks over time. In the majority of investigated subjects, taVNS induced measurable and persisting modifications in network properties that point to a more resilient epileptic brain network without negatively impacting cognition, behaviour, or mood. The stimulation was well tolerated and the usability of the device was rated good. Short-term taVNS has a topology-modifying, robustness- and stability-enhancing immediate effect on large-scale epileptic brain networks. It has no detrimental effects on cognition and behaviour. Translation into clinical practice requires further studies to detail knowledge about the exact mechanisms by which taVNS prevents or inhibits seizures. [ABSTRACT FROM AUTHOR]

Pharmaco-electroencephalography (pharmaco-EEG) has never gained great popularity in epilepsy research. Nevertheless, the electroencephalogram (EEG) is the most important neurological examination technique in this patient population. Development and investigation of antiepileptic drugs (AEDs) involves EEG for diagnosis and outcome evaluation. In contrast to the common use of the EEG for documenting the effect of AEDs on the presence of interictal epileptiform activities or seizures, quantitative analysis of drug responses in the EEG are not yet standard in pharmacological studies. We provide an overview of dedicated pharmaco-EEG studies with AEDs in humans. A systematic search in PubMed yielded 43 articles, which were reviewed for their relevance. After excluding studies according to our exclusion criteria, nine studies remained. These studies plus the retrieved references from the bibliographies of the identified studies yielded 37 studies to be included in the review. The most prominent method in pharmaco-EEG research for AEDs was analysis of the frequency content in response to drug intake, often with quantitative methods such as spectral analysis. Despite documenting the effect of the drug on brain activity, some studies were conducted in order to document treatment response, detect neurotoxic effects, and measure reversibility of AED-induced changes. There were some attempts to predict treatment response or side effects. We suggest that pharmaco-EEG deserves more attention in AED research, specifically because the newest drugs and techniques have not yet been subject to investigation. [ABSTRACT FROM AUTHOR]

We investigate the temporal and spatial variability of the importance of brain regions in evolving epileptic brain networks. We construct these networks from multiday, multichannel electroencephalographic data recorded from 17 epilepsy patients and use centrality indices to assess the importance of brain regions. Time-resolved indications of highest importance fluctuate over time to a greater or lesser extent, however, with some periodic temporal structure that can mostly be attributed to phenomena unrelated to the disease. In contrast, relevant aspects of the epileptic process contribute only marginally. Indications of highest importance also exhibit pronounced alternations between various brain regions that are of relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches. Nonetheless, these findings may guide new developments for individualized diagnosis, treatment, and control. [ABSTRACT FROM AUTHOR]

Nodes in large-scale epileptic networks that are crucial for seizure facilitation and termination can be regarded as potential targets for individualized focal therapies. Graph-theoretical approaches based on centrality concepts can help to identify such important nodes, however, they may be influenced by the way networks are derived from empirical data. Here we investigate evolving functional epileptic brain networks during 82 focal seizures with different anatomical onset locations that we derive from multichannel intracranial electroencephalographic recordings from 51 patients. We demonstrate how the various methodological steps (from the recording montage via node and link inference to the assessment of node centralities) affect importance estimation and discuss their impact on the interpretability of findings in the context of pathophysiological aspects of seizure dynamics. [ABSTRACT FROM AUTHOR]

We investigate the relative merit of phase-based methods for inferring directional couplings in complex networks of weakly interacting dynamical systems from multivariate time-series data. We compare the evolution map approach and its partialized extension to each other with respect to their ability to correctly infer the network topology in the presence of indirect directional couplings for various simulated experimental situations using coupled model systems. In addition, we investigate whether the partialized approach allows for additional or complementary indications of directional interactions in evolving epileptic brain networks using intracranial electroencephalographic recordings from an epilepsy patient. For such networks, both direct and indirect directional couplings can be expected, given the brain's connection structure and effects that may arise from limitations inherent to the recording technique. Our findings indicate that particularly in larger networks (number of nodes ≫ 10), the partialized approach does not provide information about directional couplings extending the information gained with the evolution map approach. [ABSTRACT FROM AUTHOR]

We investigate the long-term evolution of degree-degree correlations (assortativity) in functional brain networks from epilepsy patients. Functional networks are derived from continuous multi-day, multi-channel electroencephalographic data, which capture a wide range of physiological and pathophysiological activities. In contrast to previous studies which all reported functional brain networks to be assortative on average, even in case of various neurological and neurodegenerative disorders, we observe large fluctuations in time-resolved degree-degree correlations ranging from assortative to dissortative mixing. Moreover, in some patients these fluctuations exhibit some periodic temporal structure which can be attributed, to a large extent, to daily rhythms. Relevant aspects of the epileptic process, particularly possible pre-seizure alterations, contribute marginally to the observed long-term fluctuations. Our findings suggest that physiological and pathophysiological activity may modify functional brain networks in a different and process-specific way. We evaluate factors that possibly influence the long-term evolution of degree-degree correlations. [ABSTRACT FROM AUTHOR]

We investigate the relative merit of phase-based methods--mean phase coherence, unweighted and weighted phase lag index--for estimating the strength of interactions between dynamical systems from empirical time series which are affected by common sources and noise. By numerically analyzing the interaction dynamics of coupled model systems, we compare these methods to each other with respect to their ability to distinguish between different levels of coupling for various simulated experimental situations. We complement our numerical studies by investigating consistency and temporal variations of the strength of interactions within and between brain regions using intracranial electroencephalographic recordings from an epilepsy patient. Our findings indicate that the unweighted and weighted phase lag index are less prone to the influence of common sources but that this advantage may lead to constrictions limiting the applicability of these methods. [ABSTRACT FROM AUTHOR]

Abstract: Graph-theoretical analyses of complex brain networks is a rapidly evolving field with a strong impact for neuroscientific and related clinical research. Due to a number of confounding variables, however, a reliable and meaningful characterization of particularly functional brain networks is a major challenge. Addressing this problem, we present an analysis approach for weighted networks that makes use of surrogate networks with preserved edge weights or vertex strengths. We first investigate whether characteristics of weighted networks are influenced by trivial properties of the edge weights or vertex strengths (e.g., their standard deviations). If so, these influences are then effectively segregated with an appropriate surrogate normalization of the respective network characteristic. We demonstrate this approach by re-examining, in a time-resolved manner, weighted functional brain networks of epilepsy patients and control subjects derived from simultaneous EEG/MEG recordings during different behavioral states. We show that this surrogate-assisted analysis approach reveals complementary information about these networks, can aid with their interpretation, and thus can prevent deriving inappropriate conclusions. [Copyright &y& Elsevier]

We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures - known for their complex spatial and temporal dynamics - we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis. [ABSTRACT FROM AUTHOR]

We investigate the influence of various pathophysiologic and physiologic processes on global statistical properties of epileptic brain networks. We construct binary functional networks from long-term, multichannel electroencephalographic data recorded from 13 epilepsy patients, and the average shortest path length and the clustering coefficient serve as global statistical network characteristics. For time-resolved estimates of these characteristics we observe large fluctuations over time, however, with some periodic temporal structure. These fluctuations can-to a large extent-be attributed to daily rhythms while relevant aspects of the epileptic process contribute only marginally. Particularly, we could not observe clear cut changes in network states that can be regarded as predictive of an impending seizure. Our findings are of particular relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches. [ABSTRACT FROM AUTHOR]

Abstract: To improve the estimation of drift and diffusion coefficients of stochastic processes in case of a limited amount of usable data due to e.g. non-stationarity of natural systems we suggest to use kernel-based instead of histogram-based regression. We propose a method for bandwidth selection and compare it to a widely used cross-validation method. Kernel-based regression reveals an enhanced ability to estimate drift and diffusion especially for a small amount of data. This allows one to improve resolvability of changes in complex dynamical systems as evidenced by an exemplary analysis of electroencephalographic data recorded from a human epileptic brain. [Copyright &y& Elsevier]

This overview summarizes findings obtained from analyzing electroencephalographic (EEG) recordings from epilepsy patients with methods from the theory of nonlinear dynamical systems. The last two decades have shown that nonlinear time series analysis techniques allow an improved characterization of epileptic brain states and help to gain deeper insights into the spatial and temporal dynamics of the epileptic process. Nonlinear EEG analyses can help to improve the evaluation of patients prior to neurosurgery, and with an unequivocal identification of precursors of seizures, they can be of great value in the development of seizure warning and prevention techniques. [ABSTRACT FROM AUTHOR]

The framework of the theory of nonlinear dynamics provides powerful concepts and algorithms to study complicated dynamics such as brain electrical activity (electroencephalogram, EEG). Although different influencing factors render the use of nonlinear measures in a strict sense problematic, converging evidence from various investigations now indicates that nonlinear EEG analysis provides a means to reliably characterize different states of physiological and pathophysiological brain function. We here focus on applications of nonlinear EEG analysis in epileptology. Epilepsy affects more than 50 million individuals worldwide – approximately 1% of the world's population. The disease is characterized by a recurrent and sudden malfunction of the brain that is termed seizure. Nonlinear EEG analysis techniques allow to reliably identify the seizure generating structure (epileptic focus) in different areas of the brain even during seizure-free intervals, to disentangle complex spatio-temporal interactions between the epileptic focus and other areas of the brain, and to define a specific state predictive of an impending seizure. Nonlinear EEG analysis provides supplementary information about the epileptogenic process in humans, contributes to an improvement of the presurgical evaluation of epilepsy patients, and offers a basis for the development of new therapy concepts for seizure prevention. [ABSTRACT FROM AUTHOR]

We investigate the applicability of the permutation entropy H and a synchronization index γ that is based on the changing tendency of temporal permutation entropies to analyze noisy time series from nonstationary dynamical systems with poorly understood properties. Using model systems, we first study the interdependencies of parameters involved in the calculation of both measures. Having identified appropriate parameter settings we then analyze long-lasting EEG time series recorded from an epilepsy patient. Our findings indicate that γ could be of interest for studies on the predictability of epileptic seizures. [ABSTRACT FROM AUTHOR]

Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, however, to what extent stochastic qualifiers of brain dynamics are affected by other endogenous and/or exogenous influencing factors. Addressing this issue, we investigate multi-day, multi-channel electroencephalographic recordings from a subject with epilepsy. We apply a recently proposed criterion to differentiate between Langevin-type and jump-diffusion processes and observe the type of process most qualified to describe brain dynamics to change with time. Stochastic qualifiers of brain dynamics are strongly affected by endogenous and exogenous rhythms acting on various time scales—ranging from hours to days. Such influences would need to be taken into account when constructing evolution equations for the epileptic brain or other complex dynamical systems subject to external forcings. [ABSTRACT FROM AUTHOR]

The Open Access license, which previously read. [ABSTRACT FROM AUTHOR]

Inferring strength and direction of interactions from electroencephalographic (EEG) recordings is of crucial importance to improve our understanding of dynamical interdependencies underlying various physiological and pathophysiological conditions in the human epileptic brain. We here use approaches from symbolic analysis to investigate--in a time-resolved manner--weighted and directed, short- to long-ranged interactions between various brain regions constituting the epileptic network. Our observations point to complex spatial-temporal interdependencies underlying the epileptic process and their role in the generation of epileptic seizures, despite the massive reduction of the complex information content of multi-day, multi-channel EEG recordings through symbolization. We discuss limitations and potential future improvements of this approach. [ABSTRACT FROM AUTHOR]

We investigate assortativity of functional brain networks before, during, and after one-hundred epileptic seizures with different anatomical onset locations. We construct binary functional networks from multi-channel electroencephalographic data recorded from 60 epilepsy patients; and from time-resolved estimates of the assortativity coefficient, we conclude that positive degree-degree correlations are inherent to seizure dynamics. While seizures evolve, an increasing assortativity indicates a segregation of the underlying functional network into groups of brain regions that are only sparsely interconnected, if at all. Interestingly, assortativity decreases already prior to seizure end. Together with previous observations of characteristic temporal evolutions of global statistical properties and synchronizability of epileptic brain networks, our findings may help to gain deeper insights into the complicated dynamics underlying generation, propagation, and termination of seizures. [ABSTRACT FROM AUTHOR]

We compare different centrality metrics which aim at an identification of important nodes in complex networks. We investigate weighted functional brain networks derived from multichannel electroencephalograms recorded from 23 healthy subject under resting-state eyes-open or eyes-closed conditions. Although we observe the metrics strength, closeness, and betweenness centrality to be related to each other, they capture different spatial and temporal aspects of important nodes in these networks associated with behavioral changes. Identifying and characterizing of these nodes thus benefits from the application of several centrality metrics. [ABSTRACT FROM AUTHOR]