Section: New Results

Cardiac Electromechanics

In [1] we study a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction-di↵usion system governing the dynamics of ionic quantities, intra and extra-cellular potentials, and the linearized elasticity equations are adopted to describe the motion of an incompressible material. The coupling between muscle contrac- tion, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. In this paper we prove exis- tence of weak solutions to the underlying coupled reaction-di↵usion system and uniqueness of regular solutions. We close with a numerical example illustrating the convergence of the method and some features of the model.