A modified Hai-Murphy model of uterine smooth muscle contraction

We extend and analyze the Wang and Politi modified Hai-Murphy model of smooth muscle cell contractions to capture uterine muscle cell response to variations in intracellular calcium concentrations. This model is used to estimate values of unknown parameters in uterine smooth muscle cell cross-bridging. Uterine motility is responsible for carrying out important processes throughout all phases of the nonpregnant female reproductive cycle, including sperm transport, menstruation, and embryo implantation. The modified Hai-Murphy partial differential equation model accounts for the displacement of myosin cross-bridge heads relative to their binding sites. This model was originally developed for the study of airway contractions; we now extended it for use in modeling nonisometric uterine contractions. Our extended model incorporates cross-bridge position and contractile velocity into the original model, resulting in more accurate modeling of the initial stages of contraction and modeling nonisometric contractions. Numerical simulations show that the contraction rate in our extended model is faster than the original Hai-Murphy model. These simulations provide quantitative estimates for the increased level of responsiveness of our extended model to intracellular calcium concentrations. The extended model and new parameter estimates for the cross-bridging can be coupled with uterine flow models to advance our understanding of embryonic motility and intrauterine flow.