A three-field, bi-domain based approach to the strongly coupled electromechanics of the heart

We propose a novel, unconditionally stable and fully coupled finite element method for the bidomain based approach to cardiac electromechanics. To this end, the transmembrane potential, the extracellular potential, and the displacement field are treated as independent variables such that the already coupled electrophysiology problem in the bidomain setting is further extended to the electromechanical coupling. In this multifield problem, the intrinsic coupling arises from both excitationinduced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The respective bidomain reaction-diffusion and the momentum balance equations are recast into the corresponding weak forms through a conventional isoparametric Galerkin approach. The resultant set of non-linear residual equations is consistently linearized. The monolithic scheme is employed to avoid stability issues that may arise due to the strong coupling between excitation and deformation. The performance of the put forward framework is further assessed through three-dimensional representative electromechanical initial-boundary value problems.