Electromechanics of the heart: a unified approach to the strongly coupled excitation–contraction problem

Abstract

This manuscript is concerned with a novel, unified finite element approach to fully coupled cardiac electromechanics. The intrinsic coupling arises from both the excitation-induced contraction of cardiac cells and the deformation-induced generation of current due to the opening of ion channels. In contrast to the existing numerical approaches suggested in the literature, which devise staggered algorithms through distinct numerical methods for the respective electrical and mechanical problems, we propose a fully implicit, entirely finite element-based modular approach. To this end, the governing differential equations that are coupled through constitutive equations are recast into the corresponding weak forms through the conventional isoparametric Galerkin method. The resultant non-linear weighted residual terms are then consistently linearized. The system of coupled algebraic equations obtained through discretization is solved monolithically. The put-forward modular algorithmic setting leads to an unconditionally stable and geometrically flexible framework that lays a firm foundation for the extension of constitutive equations towards more complex ionic models of cardiac electrophysiology and the strain energy functions of cardiac mechanics. The performance of the proposed approach is demonstrated through three-dimensional illustrative initial boundary-value problems that include a coupled electromechanical analysis of a biventricular generic heart model.