Stability of the Ionic Parameters of a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology

Abstract

This paper presents an inverse problem of identifying two ionic parameters of a nonlocal reaction-diffusion system in cardiac electrophysiology modelling. We used a nonlocal FitzHugh-Nagumo monodomain model which describes the electrical activity in cardiac tissue with the diffusion rate assumed to depend on the total electrical potential in the heart. We established at first, the global Carleman estimate adapted to nonlocal diffusion to obtain our main result which is the uniqueness and the Lipschitz stability estimate for two ionic parameters \((k,\gamma )\).