Electroencephalograms in Epilepsy: Complexity 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). We concentrate on EEGs that originate from intracranially implanted electrodes (semi-invasive and fully invasive recording techniques), which provides particularly “clean” signals in terms of noise-level and stationarity. 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 the EEGs: it exhibits trongly significant variations that clearly relate to the time relative to a seizure onset. We mainly address ourselves to hidden properties in these signals, e.g., changes that indicate a seizure cannot be detected by a visual inspection. 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. Finally, we discuss our results within the general context of complex dynamical systems.