Analysis of nonlinear dynamics of healthy and epileptic EEG signals using recurrence based complex network approach

Epilepsy is a neurological condition characterized by sudden occurrences of rapid electrical discharges. Different non-linear methods like correlation dimension, Lyapunov exponent, entropy and more recently recurrence quantification analysis (RQA) have been used to characterize the non-linear dynamics behind interictal (between seizures) and ictal (during seizure) activities. While RQA is sensitive to embedding parameters other non-linear methods mentioned above require long and stationary data. In this study we propose recurrence network (RN) based approach to quantify the non-linear dynamics of the underlying attractors in healthy, interictal and ictal electroencephalographic (EEG) data. The dataset used to test the method is obtained from Department of Epileptology, Bonn University, Germany and consists of altogether 500 signals from interictal, ictal and healthy (eyes open and eyes closed) EEG activity. We compute network measures like clustering coefficient C and path length L on RN derived from EEG time series to characterize the underlying attractor. Our results show that interictal signals are characterized by chaotic attractors and their networks display small world property (high C and low L) while ictal signals are characterized by quasiperiodic attractors with high values of C and L. Further, our results show that for healthy EEG signals with eyes closed, the attractors are highly chaotic while for EEG signals with eyes open the attractors are less complex than fully chaotic attractor. RN based approach for the characterization of nonlinear dynamics of epileptic EEG signals is promising and has advantages over other non-linear approaches as it makes no assumptions about data stationarity, length and is not sensitive to embedding parameters.