The elastic behavior of the urinary bladder for large deformations

The purpose of this paper is to investigate the theoretical basis for the pressure-distension behavior of the urinary bladder. A finite strain theory is developed for hollow spherical structures and it is shown that the Treloar model is a good prototype only for rubber balloons. The pressure-extension ratio relationship is inverted to lead a general form of strain energy function, and fitted by an empirical relation involving one exponential. The following form of strain energy function is derived: W(lambda, lambda, lambda -2) = C1 (P(1), a) + P(1)C2 (a, lambda)ea(lambda -1). Where C1(P(1), a) is a constant (N m-2), P(1) is the initial pressure, a is the rate of pressure increase and C2 (a, lambda) a third degree polynomial relation. P(1) and a are experimentally determined through volumetric pressure-distension data. It is verified that this type of energy function is also valid for uniaxial loading experiments by testing strips coming from the same bladder for which P(1) and a were computed. There is a good agreement between the experimental points and the theoretical stress-strain relation. Finally, the strain energy function is plotted as a function of the first strain invariant and appears to be of an exponential nature.