Dynamical regimes underlying epileptiform events: role of instabilities and bifurcations in brain activity

Epileptic seizures represent a sudden and transient change in the synchronised firing of neuronal brain ensembles. While the transition of the collective neuronal activity towards the ictal event is not well understood, some progress has been made using nonlinear time series analysis methods. We present here an analysis of the dynamical regimes of the epileptic activity in three patients suffering from intractable (drug-resistant) seizures, and compare these with the dynamics in rodent epilepsy models. We used the time interval between spikes found in the electroencephalographic recordings as our variable to construct interpeak interval (IPI) time delay plots to study the neuronal interictal (activity between seizures), preictal, and seizure activity. A one-dimensional mapping function was obtained by approximation of the IPI plots with a polynomial. Two main dynamical regimes are obtained from the analysis of the mapping function, derived from the subharmonic bifurcation present in the map: period doubling and intermittency, both of which are observed in human and rat seizures. Hence, our simple model obtained from experimental data captures essential phenomena for the collective dynamics of brain networks, that are found in recordings from human and animal epilepsies. The description of the neuronal dynamics based on one-dimensional maps, widely used in other systems, may prove useful for the understanding of the collective population dynamics of brain activity.