Observers for Phenomenological Models of Epileptic Seizures

Progress towards effective treatment of epileptic seizures has seen much improvement in the past decade. In particular, the emergence of phenomenological models of epileptic seizures specifically designed to capture the electrical seizure dynamics in the Epileptor model is inspiring new approaches to predicting and controlling seizures. These new models present in various forms and contain important but unmeasurable variables that control the occurrence of seizures. These models have been used mostly as nodes in large networks to study the complex brain behaviour of seizures. In order to use this model for the purposes of seizure forecasting or to control seizures through deep brain stimulation, the states of the model will need to be estimated. Although devices such as EEG electrodes can be related to some of the states of the model, most remain unmeasured and would require an observer (as defined in control theory) for their estimation. Additionally, we would like to consider the case for large nodes of systems where the number of electrodes is far smaller than the number of nodes being estimated. In this paper, we provide methods towards obtaining the full states of these phenomenological models using nonlinear observers. In particular, we explore the effectiveness of the Extended Kalman Filter for small networks of nodes of a smoothed sixth order Epileptor model. We show that observer design is possible for this family of systems and identify the difficulties in doing so.Clinical relevance-The methods presented here can be applied with an individual epileptic patient's EEG to reveal previously hidden biomarkers of epilepsy for seizure forecasting.