Estimating short-run and long-run interaction mechanisms in interictal state.

We address the issue of analyzing electroencephalogram (EEG) from seizure patients in order to test, model and determine the statistical properties that distinguish between EEG states (interictal, pre-ictal, ictal) by introducing a new class of time series analysis methods. In the present study: firstly, we employ statistical methods to determine the non-stationary behavior of focal interictal epileptiform series within very short time intervals; secondly, for such intervals that are deemed non-stationary we suggest the concept of Autoregressive Integrated Moving Average (ARIMA) process modelling, well known in time series analysis. We finally address the queries of causal relationships between epileptic states and between brain areas during epileptiform activity. We estimate the interaction between different EEG series (channels) in short time intervals by performing Granger-causality analysis and also estimate such interaction in long time intervals by employing Cointegration analysis, both analysis methods are well-known in econometrics. Here we find: first, that the causal relationship between neuronal assemblies can be identified according to the duration and the direction of their possible mutual influences; second, that although the estimated bidirectional causality in short time intervals yields that the neuronal ensembles positively affect each other, in long time intervals neither of them is affected (increasing amplitudes) from this relationship. Moreover, Cointegration analysis of the EEG series enables us to identify whether there is a causal link from the interictal state to ictal state.