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We propose a straightforward extension of symbolic transfer entropy to enable the investigation of delayed directional relationships between coupled dynamical systems from time series. Analyzing time series from chaotic model systems, we demonstrate the applicability and limitations of our approach. Our findings obtained from applying our method to infer delayed directed interactions in the human epileptic brain underline the importance of our approach for improving the construction of functional network structures from data.

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.

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.