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

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 assays. We use the bidomain model coupled to an ordinary differential equation 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 (k, gamma) 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.

Automated summary

In this paper, the authors investigate an inverse problem in cardiac electrophysiology modeling, where two space dependent ionic parameters of a reaction-diffusion system are determined using multi-electrode array/human induced pluripotent stem cells-cardiomyocytes assays to simulate drug action. The bidomain model coupled with an ordinary differential equation is used, and the FitzHugh-Nagumo phenomenological model is employed to describe ionic exchanges at the microscopic level. The main result of the paper is the uniqueness and Lipschitz stability estimate for the two ionic parameters, achieved through sub-boundary observations over a time interval. The key components include global Carleman-type estimates and suitable observations on a part of the boundary.