Temporally and spatially segregated discretization for a coupled electromechanical myocardium model

In this paper, we propose a novel temporally and spatially segregated numerical scheme to discretize the coupled electromechanical model of myocardium. We perform several numerical experiments with activation of a myocardial slab with structural inhomogeneity and evaluate the dependence of numerical errors on the size of spatial and temporal discretization steps. In our study, we show that the spatial step for the mechanical equations h m ⩽2.5 mm yields reasonable results with noticeable errors only in the region of myocardial inhomogeneity. We also show that time step τ m ⩽1 ms can be used for temporal discretization of mechanical equations, and the propagation velocity of the activation and contraction fronts differs from the reference one by no more than 1.3%for such time step. Finally, we show that the increase of time discretization steps of the mechanical equations τ m and the monodomain equation τ e leads to phase errors with opposite signs, and we can compensate these errors by tuning the relationship between the time steps.