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

¹ Tunis El Manar University, ENIT-LAMSIN, BP 37, Le Belvédère, 1002 Tunis, Tunisia.
² INRIA, Bordeaux Sud-Ouest, 200 Avenue de la vielle Tour, 33405 Talence Cedex, France.
³ IHU LIRYC, Electrophysiology and Heart Modeling Institute, Pessac, France.

^* Corresponding author: nejib.zemzemi@inria.fr

Received: 1 October 2018
Accepted: 2 October 2018

Abstract

In this paper, we consider an inverse problem of determining multiple ionic parameters of a 2 × 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.