Inverse Problem of Electrocardiography: estimating the location of cardiac isquemia in a 3D geometry

C.E. Chavez (1) , Nejib Zemzemi (2, 3) , Yves Coudière (2, 3, 4) , Felipe Alonso-Atienza (1) , Diegó Alvarez (1)

1 UC3M - Universidad Carlos III de Madrid [Madrid]
2 IHU-LIRYC
3 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
4 IMB - Institut de Mathématiques de Bordeaux

The inverse problem in cardiology (IPC) has been formulated in different ways in order to non invasively obtain valuable infor-mations about the heart condition. Most of the formulations solve the IPC under a quasistatic assumption neglecting the dynamic behavior of the electrical wave propagation in the heart. In this work we take into account this dynamic behavior by constraining the cost function with the monodomain model. We use an iterative algorithm combined with a level set formulation allowing us to localize an ischemic region in the heart. The method has been presented by Alvarez et al in [1] and [4], in which the authors developed a method for localize ischemic regions using a simple phenomenological model in a 2D cardiac tissue. In this work, we analyze the performance of this method in different 3D geometries. The inverse procedure exploits the spatiotemporal correlations contained in the observed data, which is formulated as a parametric adjust of a mathematical model that minimizes the misfit between the simulated and the observed data. We start by testing this method on two concentric spheres and then analyze the performance in a 3D real anatomical geometry. Both for analytical and real life geometries, numerical results show that using this algorithm we are capable of identifying the position and, in most of the cases, approximate the size of the ischemic regions.

Mots clés: Inverse Problem; Electrocardiography Imaging

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

C.E. Chavez, Nejib Zemzemi, Yves Coudière, Felipe Alonso-Atienza, Diegó Alvarez. Inverse Problem of Electrocardiography: estimating the location of cardiac isquemia in a 3D geometry. Functional Imaging and modelling of the heart (FIMH2015), Jun 2017, Maastricht, Netherlands. ⟨10.1007/978-3-319-20309-6_45⟩. ⟨hal-01222385⟩