Interactions of calcium dynamics, muscle forces, and tissue properties in a model of uterine fluid flow and embryo transport

Uterine motility is responsible for carrying out important processes throughout all phases of the female reproductive cycle, including sperm transport, menstruation, and embryo implantation. We present a model of intra-uterine fluid flow in a sagittal cross-section of the uterus by inducing peristalsis in a channel. The peristaltic waveform emerges from the coupling of cellular models to elastic walls and viscous fluid. This is an integrative multiscale spatial model that takes as input the fluid viscosity, passive uterine tissue properties, and a prescribed wave of membrane depolarization. Following Bursztyn et al. [1], the voltage pulse drives the calcium dynamics inside each smooth muscle cell along the uterine walls. This, in turn, drives the formation of cross-bridges in the cell which generate the contractile muscle forces. The forces predicted by this new model are coupled to the elastic channel walls and the viscous, incompressible fluid within the channel using an immersed boundary framework [2].;The main contributions of this dissertation are two-fold. First, we present a modified Hai-Murphy model of uterine smooth muscle cell force generation that accounts for the displacement of myosin cross-bridge heads relative to their binding sites. Second, we couple this microscale model of force generation with an organ level model of the uterine channel that captures the elastic properties of the uterine walls and a viscous, incompressible fluid. We then examine how fluid transport is affected by changes on the molecular and cellular scales. In particular, we show how deficiencies in phosphorylation and calcium uptake affect intra-uterine fluid flow.