A Continuum Framework for Modeling the Excitation–Contraction Coupling of Smooth Muscle

Sammanfattning: Excitation-contraction coupling of smooth muscle refers to a chain of coupled physiological processes which convert a stimulus to a mechanical response. These processes can be disassociated into ionic transport during cell membrane excitation, activation of myosin light chains, and muscle contraction caused by actin-myosin interaction (filament sliding). This thesis concerns the development of a framework which allows to model the smooth muscle excitation-contraction coupling constitutively by applying the principle of virtual power and dissipation inequality. In doing so, the transport of ions through membrane channels is characterized by an ionic flux and an ionic supply, both governed by an electrochemical potential energy. By letting the Helmholtz free energy to be dependent on the myosin light chain configurations during contraction, the myosin light chain activation process, i.e., myosin phosphorylation, is included. The activation process links the membrane excitation to the filament sliding. A contractile element is presented to replicate the active deformation caused by the filament sliding within the smooth muscle cell. This deformation is coupled to the overall deformation of the muscle tissue by assuming a distinct principal alignment for the contractile elements.By employing this framework, an electro-chemo-mechanical model is derived by which the mechanical response of smooth muscle to an electrical stimulus is determined. This model is evaluated by comparing the model response to the experimental isometric stress data obtained from rat uterine smooth muscle tissue. By implementing this model in a finite element program, human uterine contractions during labor are simulated. This simulation determines important clinical factors, e.g., intrauterine pressure and provides the opportunity to investigate the effect of physiological and structural parameters on the uterine contractility.Finally, a methodology to accommodate individualized parameters from intrauterine pressure measurements is established. This methodology allows to develop models with potentials of being used clinically to diagnose difficulties during labor and delivery.