On 3D Numerical Inverse Problems for the Bidomain Model in Electrocardiology

Bedr'Eddine Ainseba (1) , Mostafa Mostafa Bendahmane (2, 1) , Alejandro Lopez (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque

In the inverse problem en electrocardiology, the goal is to recover electrophysiological activity in the heart without measuring directly on its surface (without using catheter interventions). Note that today the inverse computation is frequently used by solving the quasi-static model. This model doesnt take into account the heart dynamic in time and may result in considerable errors in the reconstruction of the solution on the heart. In this paper, a 3D numerical inverse problem constrained by the bidomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction-diffusion system modelling the propagation of the intracelullar and extracellular electrical potentials, and ionic currents, are extended to further consider the effect of an external bathing medium. Thus, we demonstrate that the novel concept of applying electrophysiological data might be useful to improve noninvasive reconstruction of electrical heart activity. Finally, we present numerical experiments representing the effect of the heart dynamic on the inverse solutions.

Mots clés: Non-Homogeneous; Homogeneous; Electrocardiology; Numerical simulation; Inverse problem

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physiologie [q-bio.TO]

Bedr'Eddine Ainseba, Mostafa Mostafa Bendahmane, Alejandro Lopez. On 3D Numerical Inverse Problems for the Bidomain Model in Electrocardiology. Computers & Mathematics with Applications, 2015, 69 ( 4), pp.255-274. ⟨hal-01256825⟩