Ionic parameters identification of an inverse problem of strongly coupled PDE's system in cardiac electrophysiology using Carleman estimates

In this paper, we consider an inverse problem of determining multiple ionic parameters of a 2 x 2 strongly coupled parabolic-elliptic reaction-diffusion system arising in cardiac electrophysiology modeling. We use the bidomain model coupled to an ordinary differential equation (ODE) system and we consider a general formalism of physiologically detailed cellular membrane models to describe the ionic exchanges at the microscopic level. Our main result is the uniqueness and a Lipschitz stability estimate of the ion channels conductance parameters of the model using subboundary observations over an interval of time. The key ingredients are a global Carleman-type estimate with a suitable observations acting on a part of the boundary.