An asymptotic two-layer monodomain model of cardiac electrophysiology in the atria: derivation and convergence.

Yves Coudière (1) , Jacques Henry (2) , Simon Labarthe (1)

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

Numerical simulations of the cardiac electrophysiology in the atria are often based on the standard bidomain or monodomain equations stated on a two-dimensional manifold. These simulations take advantage of the thinness of the atrial tissue, and their computational costs is reduce, as compared to three-dimensional simulations. However, these models do not take into account the heterogeneities located in the thickness of the tissue, like discontinuities of the fiber direction, although they can be a substrate for atrial arrhythmia [Hocini et al., 2002, Ho et al., 2002, Nattel, 2002]. We investigate a two-dimensional model with two coupled, superimposed layers that allows to introduce three-dimensional heterogeneities, but retains a reasonable computational cost. We introduce the mathematical derivation of this model, show its convergence toward the three-dimensional model and give some numerical illustration of its interest. Our model would be an efficient tool to test the influence of three-dimensional fiber direction heterogeneities in reentries or atrial arrhythmia without using three-dimensional models.

Mots clés: Cardiac modeling; Atrial model; Surface model; Asymptotic analysis

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Cardiologie et système cardiovasculaire

Yves Coudière, Jacques Henry, Simon Labarthe. An asymptotic two-layer monodomain model of cardiac electrophysiology in the atria: derivation and convergence.. 2016. ⟨hal-00922717v3⟩