Inverse problem in electrocardography via the factorization method of boundary value problems

Julien Bouyssier (1) , Nejib Zemzemi (2, 1) , Jacques Henry (1)

1 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
2 IHU-LIRYC

We present a new mathematical approach for solving the inverse problem in electrocardiography. This approach is based on the factorization of boundary value problems method. In this paper we derive the mathematical equations and test this method on synthetical data generated on realistic heart and torso geometries using the state-of-the-art bidomain model in the heart coupled to the Laplace equation in the torso. We measure the accuracy of the inverse solution using spatial Relative Error (RE) and Correlation Coefficient (CC).

Mots clés: Inverse problem; Riccati equations; factorization method; boundary value problems; electrocardiagraphic imaging (ECGI)

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Julien Bouyssier, Nejib Zemzemi, Jacques Henry. Inverse problem in electrocardography via the factorization method of boundary value problems. IEEE 12th International Symposium on Biomedical Imaging (ISBI), 2015, Apr 2015, New York, France. ⟨10.1109/ISBI.2015.7163979⟩. ⟨hal-01222401⟩