Implementing Myocardial Force–Velocity Relation onto a 3D Constitutive Left-Ventricular Model and Solving the Associated Non-convergence Problem

The classical Hill’s model, normally composed of three elements (i.e. two nonlinear springs arranged in series and parallel, with a contractile element) can accurately simulate muscle force generation at various excitation conditions in cellular and tissue levels, including during myocardial contraction. This study develops a method to integrate myocardial force–velocity relationship onto a previously developed 3D left-ventricular finite element model framework, which already incorporates Frank–Starling effect. A damping or delay equation is proposed in this paper, aiming to overcome the non-convergence issue which arises from the direct implementation of instantaneous sarcomere shortening velocity to represent the Hill’s model characteristic. Our simulation result, with the implementation of published force–velocity data, showcased substantial decrease in overall force generated by the myocardium when accompanied by a range of shortening velocities. This computational model serves as a significant improvement in personalized cardiac modelling and has the potential to help us understand multi-scale coupling to simulate the active contraction and relaxation of the heart, with tight interaction between force–velocity and length-dependence relationship of the myocardium.