Bioelectrical effects of mechanical feedbacks in a strongly coupled cardiac electro-mechanical model

The aim of this work is to investigate by means of numerical simulations the effects of myocardial deformation due to muscle contraction on the bioelectrical activity of the cardiac tissue. The three-dimensional electro-mechanical model considered consists of the following four components: the quasi-static orthotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the orthotropic Bidomain model for the electrical current flow through the tissue; the membrane model of the cardiac myocyte, including stretch-activated currents (ISAC). In order to properly take into account cardiac mechanical feedbacks, the electrical current flow is described in a strongly coupled framework by the Bidomain model on the deformed tissue. We then derive a novel formulation of the Bidomain model in the reference configuration, with complete mechanical feedbacks affecting not only the conductivity tensors but also a convective term depending on the velocity of the deformation. The numerical simulations are based on our finite element parallel solver, which employs both Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton-Krylov-Algebraic Multigrid methods for the solution of nonlinear systems arising from the discretization of the finite elasticity equations. The results have shown that: (i) the ISAC current prolongs action potential duration (APD) of about 10-15 ms; (ii) the inclusion into the model of both ISAC current and the convective term reduces the dispersion of repolarization of about 7% (from 139 to 129 ms) and increases the dispersion of APD about three times (from 13 to 45 ms). These effects indicate that mechanical feedbacks might influence arrhythmogenic mechanisms when combined with pathological substrates.