Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank–Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley’57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach—both for the model and the numerics—is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank–Starling mechanism.