Abstract Epilepsy has been historically seen as a functional brain disorder associated with excessive synchronization of large neuronal populations leading to a hypersynchronous state. Recent evidence showed that epileptiform phenomena, particularly seizures, result from complex interactions between neuronal networks characterized by heterogeneity of neuronal firing and dynamical evolution of synchronization. Desynchronization is often observed preceding seizures or during their early stages; in contrast, high levels of synchronization observed towards the end of seizures may facilitate termination. In this review we discuss cellular and network mechanisms responsible for such complex changes in synchronization. Recent work has identified cell‐type‐specific inhibitory and excitatory interactions, the dichotomy between neuronal firing and the non‐local measurement of local field potentials distant to that firing, and the reflection of the neuronal dark matter problem in non‐firing neurons active in seizures. These recent advances have challenged long‐established views and are leading to a more rigorous and realistic understanding of the pathophysiology of epilepsy.

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.

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.

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.

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 asynchronous 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.