An Asymptotic Two-Layer Monodomain Model of Cardiac Electrophysiology in the Atria: Derivation and Convergence

We investigate a dimensional reduction problem of a reaction-diffusion system related to cardiac electrophysiology modeling in the atria. The atrial tissues are very thin. The physical problem is then routinely stated on a two-dimensional manifold. However, some electrophysiological heterogeneities are located through the thickness of the tissue. Despite their biomedical significance, the usual dimensional reduction techniques tend to average and erase their influence on the two-dimensional propagation. We introduce a two-dimensional model with two coupled superimposed layers that allows us to take into account three-dimensional phenomena, but retains a reasonable computational cost. We present its mathematical derivation, show its convergence toward the three-dimensional model, and check numerically its convergence speed.