Analytic Quantification of Shilnikov Chaos in Epileptic EEG Data

Abstract

Dynamical Systems Based Modeling (DSBM) is a method to decompose a multivariate signal leading to both a dimensionality reduction and parameter estimation describing the dynamics of the signal. We present this method and its application to EEG data sets of Petit-Mal epilepsies considering Shilnikov chaos as the underlying dynamic interaction. We demonstrate the power of this method compared to conventional decomposition methods like PCA and ICA. Since the fitting quality showed a strong correlation to the ictal phases of the signal, we performed a cross validation on seizure detection with a resulting specifity of 84% and sensitivity of 75%. By applying DSBM in a moving window setup we investigated the comparability of the obtained dynamic models and tested the hypothesis of Shilnikov chaos in terms of linear stability analysis for each of the investigated windows. Thereby we could corroborate the Shilnikov hypothesis for approx. 50% of the relevant windows.