Advanced nonlinear approach to quantify directed interactions within EEG activity of children with temporal lobe epilepsy in their time course

Background. The quantification of directed interactions within the brain and in particular their time courses are of highest interest for the investigation of epilepsy. The underlying coordinated neuronal mass activities span functionally diverse and structurally widely distributed cortical and subcortical brain regions, i.e. dynamic, distributed epileptic network can be assumed possibly not fitting in the concept of linearity. Consequently, nonlinear, time-variant, and directed connectivity and synchronization analysis could be helpful to understand processes contributing to the seizure onset and propagation. Methods. The nonlinear convergent cross mapping (CCM) quantifies directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to the EEG of 18 children with temporal lobe epilepsy (TLE), i.e. directed interactions within EEG activity and within specific components of EEG activity (δ-activity and α-activity) are investigated. Linear time-variant multivariate AR modeling was performed for these data to test for subsequent applications of linear AR-based connectivity measures. Results. Linear MVAR models proved to be inappropriate for our data. Time-varying application of CCM revealed that statistically significant nonlinear interactions within the EEG activity and within specific components of the EEG exist in the preictal, ictal, and postictal periods. Distinct time courses of such interactions and differences in the time pattern of interactions occurring in the different components of EEG activity that we investigated discovered the high complexity of the underlying processes. No distinct results could be found concerning the presumed directionalities of interactions. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach. Conclusion. Advanced nonlinear CCM approach was able to uncover time pattern of nonlinear interactions thereby possibly contributing to the further understanding of complex behavior of the brain during TLE. Our investigation may provide deeper insight into physiological state of complex networks, e.g. during the development of an epileptic seizure or the recovery in the postictal state.