Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling

Abir Amri (1) , Mourad Bellassoued (1) , Moncef Mahjoub (1) , Nejib Zemzemi (2)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque

In this paper, we prove a stability estimate of the conductivity parameters identification problem in cardiac electrophysiology. The propagation of the electrical wave in the heart is described by the monodomain model coupled to an elliptic equation describing the diffusion of the electrical wave in the whole body. Our result concerns both heart and torso conductivity parameters. The main difficulty that we solve in this paper is related to the transmission conditions between the heart and the torso. We first, establish Carleman estimates for the coupled heart-torso system. Then, using these estimates and the Bukhgeim and Klibanov approach, we prove a Lipschitz stability estimate of cardiac and torso conductivity parameters.

Mots clés: Inverse problem; Stability estimate; Carleman estimate; Cardiac electrophysiology; Conductivity parameters

Domaines: Modélisation et simulation

Abir Amri, Mourad Bellassoued, Moncef Mahjoub, Nejib Zemzemi. Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling. Applicable Analysis, 2021, pp.1-30. ⟨10.1080/00036811.2021.1955861⟩. ⟨hal-03301127⟩