Numerical Study on Excitation–Contraction Waves in 3D Slab-Shaped Myocardium Sample with Heterogeneous Properties

In this study, we have performed 3D numerical simulations of the excitation and contraction of thin slab-like samples of myocardium tissue. The samples included a narrow region of almost non-excitable tissue simulating impaired myocardium. In the numerical experiments, we considered the heterogeneity of myocardium excitation and the ${\mathrm{Ca}}^{2+}$ activation of its contraction, as well as the orientation of the muscle fibers. Those characteristics varied throughout the thin wall of the sample. The simulations were performed in our numerical framework for the problems of cardiac electromechanics developed recently. The framework was previously tested for the benchmark problems in which formulations took into account only myocardium electrophysiology and passive mechanics. The study could be considered as an approbation of the framework performance with the fully coupled mathematical model of myocardium electromechanics. Here we dealt with the problems requiring a multiscale approach, taking into account cell-level electrophysiology, cell-level mechano-chemical processes, macromechanics (strain and stress) of the 3D sample, and interconnections between the levels. It was shown how the tissue heterogeneity and its strain affected the propagation of excitation–contraction waves in the sample, including, in particular, the formation of spiral waves.