Modelling Creep (Relaxation) of the Urinary Bladder

Abstract

Abstract We first present the results of an experiment in which the passive properties of the urinary bladder were investigated using strips of rabbit bladder. Under the assumption that the urinary bladder had orthopaedic characteristics, the strips were taken in the longitudinal and in the circumferential directions. The material was subjected to uniaxial tension, and stress-stretch curves were generated for various rates of deformation. We found that the rates did not have a significantly effect on the passive response of the material. Additionally, the stress-stretch dependence during relaxation of the material when exposed to isometric conditions was determined experimentally. Next, we measured nonlinear stress-stretch dependence to determine the coefficients for this dependence in analytical form using a standard fitting procedure. The same approach was used to obtain the coefficients for the relaxation curves from the experimental data. Two constitutive laws, the nonlinear model for passive response and the creep model, were introduced within the shell finite element for geometrically and materially nonlinear analysis. We provide descriptions of the numerical procedures that were performed by considering the urinary bladder as a thin-walled shell structure subjected to pressure loading. The developed numerical algorithm for the incremental-iterative solution was implemented into the finite element program, PAK. The response of the urinary bladder was calculated for continuous filling, and the numerical and experimental results were compared through cystometrograms (pressure-volume relationships). We also present comparisons of the shapes and volumes of the urinary bladder obtained numerically and experimentally. Finally, the numerical results of the creep response, when placed under constant internal pressure, are provided for various stages of deformation.