Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression

Abstract

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Given the partially successful existing treatments for epileptiform activity suppression, dynamic mathematical models have been proposed with the purpose of better understanding the factors that might trigger an epileptic seizure and how to mitigate it, among which Epileptor stands out, due to its relative simplicity and high prediction ability. Recent studies using such a model have provided evidence that establishing a feedback-based control approach is possible. However, for this strategy to work properly, Epileptor's parameters, which describe the dynamic characteristics of a seizure, must be known beforehand. Therefore, this work proposes a methodology for estimating such parameters based on a successive optimization technique. The results show that it is feasible to approximate their values, and integrating this system identification approach with observers and controllers can be carried out, which might provide an interesting alternative for seizure suppression in practice in the future.

Epileptic seizure suppression: a computational approach for identification and control using real data

“…This makes it possible to recreate the time signature over time accurately from stored signals, as the case of this work. This result is consistent with a previous study that reconstructed the unmeasurable activity of the Epileptor model based on its measurable activity [21]. The main difference is that this time the reference signal is not dynamically simulated through the numerical integrator, but approximated based on observations of stored signals.…”

“…To assess how close the reconstructed controlled signal is to the desired reference the interdependency between observer and controller: as the first one recreates the real signal computationally, a control input is applied to the recreated artificial signal to verify whether its epileptiform activity can be mitigated. This integration approach has been proposed elsewhere, but for the Epileptor model, and consistent results were obtained [21]. It must be emphasized that the present approach is only carried out because there is no access to the true system.…”

“…This issue is addressed in this work by taking advantage of the concept of Fuzzy Takagi-Sugeno Modeling (FTSM), which states that a nonlinear plant can be exactly reconstructed using linear submodels represented by the so-called Linear Matrix Inequalities (LMIs) [43]. In the case of the observers, they are [21, 43]: where and P obs is a positive-definite matrix [47]. If all of these inequalities are solved simultaneously, then there exists M , thus also assuring the existence of L .…”

“…This issue is addressed in this work by taking advantage of the concept of Fuzzy Takagi-Sugeno Modeling (FTSM), which states that a nonlinear plant can be exactly reconstructed using linear submodels represented by the so-called Linear Matrix Inequalities (LMIs) [43]. In the case of the observers, they are [21,43]:…”

“…[20] proposed a Baysean framework to estimate the epileptogenicity, a parameter responsible for the excitability of the model; Ref. [21], in turn, introduced a successive optimization approach to estimate all of its parameters considering uncertainties and noise. A limitation of the latter approach is that it considers only a reference output of the local field potential (LFP), not real signals.…”