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

Abstract

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.

Keywords:

• Conductivity parameters
• cardiac electrophysiology
• Carleman estimate
• inverse problem
• stability estimate

2010 Mathematics Subject Classifications:

• Primary 35Q92
• Secondary: 35R30

Acknowledgement

This work has been supported by EPICARD cooperative research program, funded by INRIA international laboratory LIRIMA. The LAMSIN researcher's work is supported on a regular basis by the Tunisian Ministry of Higher Education, Scientific Research and Technology. This work was also supported by the Agence Nationale de la Recherche [grant number IHU LIRYC ANR-10-IAHU-04].

Disclosure statement

No potential conflict of interest was reported by the authors.