Theoretical Analysis of Power-Law Stress Relaxation and Calcium-Dependent Passive Mechanics in Cardiac Muscle

This study investigates the passive viscoelastic mechanical properties of cardiac muscle by introducing a theoretical model that explains the power-law kinetics of passive stress decay. The model accounts for two parallel processes contributing to passive mechanics: an elastic component and a viscoelastic component designed to simulate stress/strain-mediated unfolding of serial domains in the titin molecule. Under stress, serial globular domains within the elastic region of the titin molecule reversibly unfold. This unfolding phenomenon contributes to both hysteresis (a lag in stress between loading and unloading) and preconditioning effects in simulated striated muscle mechanics. Moreover, experimental evidence indicates that stress relaxation in cardiac muscle follows a power law, and that the muscle’s nonlinear stress-strain relationship and hysteresis behavior are calcium-dependent. To analyze these mechanical phenomena, we simulate the apparent viscous element as a mesoscopic-scale ensemble of chains, each composed of serial globular domains that unfold in a stress-dependent manner. Although the model was developed to represent the behavior of titin, it equivalently represents any contributing process involving a linked series of domains that undergo stress-mediated unfolding. By providing a unified basis for the observed viscoelastic and preconditioning effects, calcium dependency, and power-law stress relaxation phenomena, this study offers a novel theoretical basis for understanding and simulating the role of titin in striated muscle mechanics.