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.

在心肌建模的背景下，肌节中肌球蛋白头的可用性在心脏周期内发生变化，这有助于器官水平的 Frank-Starling 机制。在本文中，我们提出了一种新方法，可以扩展 Huxley 的 57 肌肉收缩模型方程以合并这种变化。这个扩展是以热力学一致的方式构建的，我们还提出了满足离散水平热力学平衡的自适应数值方法。此外，这整个方法——包括模型和数值——是在分层策略中设计的，能够将微观肌节水平方程与宏观组织水平描述相结合。作为一个重要的说明，将我们的模型与先前提出的简化心脏模型相结合，