Investigation of network brain dynamics from EEG measurements in patients with epilepsy using graph-theoretic approaches

`Small-world' neuronal networks are characterized by strong clustering in combination with short path length, and assist the progress of synchronization and conceivably seizure procreation. In this article we aim to investigate if the brain networks display `small-world' features during seizures, by using graph-theoretic measures as well as scalp EEG recordings from patients with focal and generalized epilepsy. Specifically, we used linear cross-correlation to characterize patterns between nodes in scalp EEG recordings of 5 patients for 3 periods of interest: before, during and after seizure onset. For each period we reconstruct graphs from the linear cross-correlation calculations and use different network measures to characterize the graphs such as clustering coefficient, characteristic path length, betweenness centrality and network small-world-ness. In three (out of five) patients, our results suggest that shortly after seizure onset and in the early postictal period the brain network changes towards a more small-world structure, in agreement with earlier graph-theoretic based results related to epilepsy. However, for one patient the opposite was observed: small-worldness decreased after seizure onset. Finally, for one patient we could observe no differences in the network properties before and after the onset. These preliminary results suggest the potential use of graph-theoretic measures to quantify brain dynamics before and during seizures after further refinements.