Measuring the Directionality of Coupling: Phase versus State Space Dynamics and Application to EEG Time Series

Measuring the directionality of coupling between dynamical systems is one of the challenging problems in nonlinear time series analysis. We investigate the relative merit of two approaches to assess directionality, one based on phase dynamics modeling and one based on state space topography. We analyze unidirectionally coupled model systems to investigate the ability of the two approaches to detect driver-responder relationships and discuss certain problems and pitfalls. In addition we apply both approaches to the intracranial electroencephalogram (EEG) recorded from one epilepsy patient during the seizure-free interval to demonstrate the general suitability of directionality measures to reflect the pathological interaction of the epileptic focus with other brain areas.