Global Lipschitz stability of multiple space dependent ionic parameters for the MEA/hiPSC-CM assays

Abstract

In this paper, we consider an inverse problem of determining two space dependent ionic parameters of a strongly coupled parabolic-elliptic reaction-diffusion system arising in cardiac electrophysiology modeling when simulating drugs action with multi-electrode array/human induced pluripotent stem cells-cardiomyocytes (MEA/hiPSC-CM) assays. We use the bidomain model coupled to an ordinary differential equation (ODE) and we consider the classical phenomenological model in cardiac electrophysiology of FitzHugh-Nagumo to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate for two ionic parameters pk, γq of the model using sub-boundary observations over an interval of time. The key ingredients are a global Carleman-type estimates with a suitable observations acting on a part of the boundary.