ABSTRACT
Synchronization plays an important role in brain function and dysfunction (Schnitzler and Gross 2005; Uhlhaas and Singer 2006; Buzsáki 2006). A prominent example for pathophysiologic neuronal synchronization is epilepsy together with its main symptom-the epileptic seizure, which re§ects the clinical signs of an excessive and hypersynchronous activity of extended neuron networks in cortex. Gaining deeper insights into the complex spatial-temporal dynamics of seizure generation, spread, and termination calls for analysis techniques that allow one to characterize both strength and direction of interactions between brain regions involved in the epileptic process. Bivariate time series analysis techniques that were developed over the past years (Pikovsky et al. 2001; Boccaletti et al. 2002; Pereda et al. 2005; Stam 2005; Hlaváčková-Schindler et al. 2007; Lehnertz et al. 2009) can be classi–ed into two different groups by which dynamical aspect-strength or direction of interaction-they try to characterize. The investigation of interaction strength, whose application dominated in former seizure prediction studies (Mormann et al. 2007; Osterhage et al. 2008), is mainly concerned with the question of whether there is an interaction between brain regions and how strong it is. Interestingly, these studies indicate seizure precursors in more remote and, in some cases, even contralateral brain areas, thus underlining the importance of brain regions outside the epileptic focus but within an epileptic network that might be responsible for ictogenesis (Lehnertz et al. 2007). More recent developments allow one to characterize the direction of interactions in order to infer possible causal relationships (in a driver-responder sense) between brain regions. We present here two approaches from the latter class of bivariate time series analysis techniques. The –rst approach makes use of our measures for nonlinear interdependence (Arnhold et al. 1999; Quian Quiroga et al. 2002; Chicharro and Andrzejak 2009). Since a characterization of directed interactions in multichannel EEG time series requires computational resources that grow quadratically with the number of recording sites, we approximate nonlinear interdependence with so-called cellular neural networks (CNN) (Krug et al. 2007; Chernihovskyi et al. 2008). The second approach combines the information-theoretic concept of transfer entropy (Schreiber 2000) with concepts from
17.1 Introduction ..........................................................................................................................265 17.2 Measuring Directed Interactions in the Epileptic Brain ......................................................266
