The Epileptor Model: A Systematic Mathematical Analysis Linked to the Dynamics of Seizures, Refractory Status Epilepticus, and Depolarization Block.

One characteristic of epilepsy is the variety of mechanisms leading to the epileptic state, which are still largely unknown. Refractory status epilepticus (RSE) and depolarization block (DB) are other pathological brain activities linked to epilepsy, whose patterns are different and whose mechanisms remain poorly understood. In epileptogenic network modeling, the Epileptor is a generic phenomenological model that has been recently developed to describe the dynamics of seizures. Here, we performed a detailed qualitative analysis of the Epileptor model based on dynamical systems theory and bifurcation analysis, and investigate the dynamic evolution of "normal" activity toward seizures and to the pathological RSE and DB states. The mechanisms of the transition between states are called bifurcations. Our detailed analysis demonstrates that the generic model undergoes different bifurcation types at seizure offset, when varying some selected parameters. We show that the pathological and normal activities can coexist within the same model under some conditions, and demonstrate that there are many pathways leading to and away from these activities. We here archive systematically all behaviors and dynamic regimes of the Epileptor model to serve as a resource in the development of patient-specific brain network models, and more generally in epilepsy research.