New approach for solving electrocardiography imaging inverse problem with missing data on the body surface

Mohammed Addouche (1) , Nadra Bouarroudj (2) , Jacques Henry (3) , Fadhel Jday (4) , Nejib Zemzemi (3)

1 Université Aboubekr Belkaid - University of Belkaïd Abou Bekr [Tlemcen]
2 Département de Mathématiques [Oran]
3 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
4 Umm Al-Qura University

In this work, we provide a new mathematical formulation for the inverse problem in electrocardiography imaging. The novelty of this approach is that we take into account the missing measurements on the body surface. The electrocardiography imaging is formulated as a data completion problem for the Laplace equation. The Neumann boundary condition is given at the whole body surface. The difficulty comes from the fact that the Dirichlet boundary condition is only given on a part of the body surface. In order to construct the electrical potential on the heart surface, we use an optimal control approach where the unknown potential at the external boundary is also part of the control variables. We use the method of factorization of elliptic boundary value problems combined with the finite difference method. We illustrate the theoretical results by some numerical simulations in a cylindrical domain. We numerically study the effect of the size of the missing data zone on the accuracy of the inverse solution.

Mots clés: electrocardiography imaging; inverse problem; missing data; Factorization method; incomplete data; optimal control

Domaines: Modélisation et simulation

Mohammed Addouche, Nadra Bouarroudj, Jacques Henry, Fadhel Jday, Nejib Zemzemi. New approach for solving electrocardiography imaging inverse problem with missing data on the body surface. Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc 10-13 mai 2017, May 2017, Hammamet, Tunisia. ⟨hal-01567821⟩