Stability results for the parameter identification inverse problem in cardiac electrophysiology

Jamila Lassoued (1) , Moncef Mahjoub (1) , Nejib Zemzemi (2, 3)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
3 IHU-LIRYC

In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation. We are interested in proving the stability of the identification of the parameter τ in which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both the PDE and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter τ in giving some observations of both state variables at a given time t 0 in the whole domain and the PDE variable in a non empty open subset w 0 of the domain.

Mots clés: Mitchell-Schaeffer model; Monodomain system; stability result; Ionic parameters Submitted to: Inverse Problems; Parameter identification; Carleman inequality

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Jamila Lassoued, Moncef Mahjoub, Nejib Zemzemi. Stability results for the parameter identification inverse problem in cardiac electrophysiology. Inverse Problems, 2016, 32 (11), pp.1-31. ⟨10.1088/0266-5611/32/11/115002⟩. ⟨hal-01399373⟩