Computational modeling of coupled cardiac electromechanics incorporating cardiac dysfunctions

Computational models have huge potential to improve our understanding of the coupled biological, electrical, and mechanical underpinning mechanisms of cardiac function and diseases. This contribution is concerned with the computational modeling of different cardiac dysfunctions related to the excitation-contraction coupling in the heart. To this end, the coupled problem of cardiac electromechanics is formulated through the conservation of linear momentum equation and the excitation equation formulated in the Eulerian setting and solved monolithically through an entirely finite element-based implicit algorithm. To model the electromechanical coupling, we use the recently proposed, novel generalized Hill model that is based on the multiplicative decomposition of the deformation gradient into the active and passive parts and on the additive split of the free energy function. This framework enables us to combine the advantageous features of the active-stress and the active-strain models suggested in literature. The proposed coupled approach is further supplemented by the Windkesel-based model to account for the pressure evolution within the ventricular chambers during the cardiac cycle. This allows us to generate the pressure-volume curves as a diagnostic tool to detect possible cardiac dysfunctions and to assess the efficiency of the heart function. The proposed model is employed to investigate different pathological cases that include infarction, eccentric hypertrophy, and concentric hypertrophy. The effects of these distinct cardiac dysfunctions on the pressure-volume curves and on the overall excitation-contraction of the heart are computationally examined and compared to the clinical observations reported in literature.