Three-dimensional mechano-electrochemical model for smooth muscle contraction of the urinary bladder.

The urinary bladder is a central organ of vertebrates and imposes, based on its extreme deformation (volume changes up to several 100%), special requirements on the overall bladder tissue. However, studies focusing on three-dimensional modelling of bladder deformation and bladder function during micturition are rare. Based on three fields, namely, the membrane potential, calcium concentration, and placement, a mechano-electrochemical-coupled, three-dimensional model describing the contractile behaviour of urinary bladder smooth muscle is presented using a strain energy function. The strain energy functions for the different layers of the bladder wall are additively decomposed into a passive part comprising elastin, the extracellular matrix (ECM), and collagen and an active electrochemical-driven part comprising the contraction of smooth muscle cells (SMC). While the two-variable FitzHugh-Nagumo-type membrane model (FitzHugh, 1961; Nagumo et al., 1962) has been used to describe the membrane potential characteristics, the four-state, cross-bridge model of Hai and Murphy (1988) is implemented into the finite element method for the quantification of the calcium phase. Appropriate model parameters were determined experimentally using 40 tissue strips isolated from porcine bladders. Characteristic orientation-dependent passive and active stress-stretch relationships were identified for muscle strips, including the entire bladder wall structure and those featuring the isolated muscle layer only. Active experiments on the smooth muscle layers revealed higher stresses in the longitudinal (28.9kPa) direction than in the transversal (22.7kPa) one. Additionally, three-dimensional deformation characteristics were recorded from single muscle strips to qualitatively confirm the strip simulations. Three-dimensional simulations at the tissue strip level and the organ level were performed to analyse the interaction among the electrical action potential, calcium distribution, chemical degree of activation, and equivalent von Mises stress.