Towards an efficient computational strategy for electro-activation in cardiac mechanics

The computational modelling of the heart motion within a cardiac cycle is an extremely challenging problem due to (a) the complex multi-scale interaction that takes place between the electrophysiology and electrochemistry at cellular level and the macro-scale response of the heart muscle, and (b) the large deformations and the strongly anisotropic and quasi-incompressible behaviour of the myocardium. These pose an extreme challenge to the scalability of electro-mechanical solvers due to the size and conditioning of the system of equations required to obtain accurate solutions, both in terms of wall deformation and transmembrane potential propagation. In the search towards an efficient modelling of electro-activation, this paper presents a coupled electromechanical computational framework whereby, first, we explore the use of an efficient stabilised low order tetrahedral Finite Element methodology and compare it against a very accurate super enhanced mixed formulation previously introduced by the authors in Garcia-Blanco et al. (2019) and, second, we exploit the use of tailor-made staggered and staggered linearised solvers in order to assess their feasibility against a fully monolithic approach. Through a comprehensive set of examples, culminating in a realistic ventricular geometry, we aim to put forward some suggestions regarding the level of discretisation and coupling required to ensure sufficiently reliable results yet with an affordable computational time.