Electroencephalograms in epilepsy: analysis and seizure prediction within the framework of Lyapunov theory

Abstract Epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system. Therefore, the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms. We extract chaos-indicators such as Lyapunov exponents and Kolmogorov entropies from different types of electroencephalograms (EEGs): this covers mainly intracranial EEGs (semi-invasive and invasive recording techniques), but also scalp-EEGs from the surface of the skin. Among the analytical methods we tested up to now, we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure. We also evaluate the time-evolution of the dissipation in these signals: it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset. This article is mainly devoted to an assessment of these methods with respect to their sensitivity to EEG changes, e.g., prior to a seizure. Further, we investigate interictal EEGs (i.e., far away from a seizure) in order to characterize their more general properties, such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions. Generally we use multichannel reconstruction, but we also present a comparison with the delay-embedding technique.