Analyzing the normal and epileptic output of a neural mass model based on cyclic-small gain theorem.

This study presents a new application of the Cyclic-Small Gain Theorem (CSGT) to analyze the behavior of a Neural Mass Model (NMM), which is utilized to study brain activity related to epilepsy. The model is reformulated as an interconnected network of dynamic subsystems, which made CSGT applicable to this context. It is shown that whenever the CSGT conditions are satisfied, the model is input-to-state stable, and epilepsy cannot occur. Furthermore, the proposed method guarantees normal activity even with increased amplitude of noise, as long as the stability conditions of CSGT are verified. In this way, system instability can be considered indicative of the occurrence of epilepsy. The behavior of an interconnected network consisting of two epileptic columns and a healthy column is analyzed using the proposed method to study the propagation of epileptic activity between regions. The results show that, when the healthy column satisfies the CSGT conditions, it remains stable and unaffected by its epileptic counterparts. The study emphasizes the importance of the CSGT as a protective measure against epileptic activity and provides insights for designing control interventions using electric brain stimulation.