The heart muscle is capable of growing and remodeling in response to changes in its mechanical and hormonal environment. While this capability is essential to the healthy function of the heart, under extreme conditions it may also lead to heart failure. In this work, we derive a thermodynamically based and microscopically motivated model that highlights the influence of mechanical boundary conditions and hormonal changes on the remodeling process in cardiomyocytes. We begin with a description of the kinematics associated with the remodeling process. Specifically, we derive relations between the macroscopic deformation, the number of sarcomeres, the sarcomere stretch, and the number of myofibrils in the cell. We follow with the derivation of evolution equations that describe the production and the degradation of protein in the cytosol. Next, we postulate a dissipation-based formulation that characterizes the remodeling process. We show that this process stems from a competition between the internal energy, the entropy, the energy supplied to the system by ATP and other sources, and dissipation mechanisms. To illustrate the merit of this framework, we study four initial and boundary conditions: (1) a myocyte undergoing isometric contractions in the presence of either an infinite or a limited supply of proteins and (2) a myocyte that is free to dilate along the radial direction with an infinite and a limited supply of proteins. This work underscores the importance of boundary conditions on the overall remodeling response of cardiomyocytes, suggesting a plausible mechanism that might play a role in distinguishing eccentric vs. concentric hypertrophy.
Keywords: Actin/myosin interaction; Cardiomyocytes; Growth and remodeling; Multi-scale modeling; Protein availability.
© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.