The effect of urinary bladder shape on its mechanics during filling

Despite the normal variation in the shape of the urinary bladder, it has always been modeled as a sphere. We have investigated whether its steady-state pressure-volume relation would be significantly different if it were a spheroid. From pressure-volume curves of anesthetized dogs, we deduced stress-strain constitutive relationships for the bladder wall material. We then solved the equilibrium equations for prolate and oblate spheroids with these constitutive relationships and predicted stress, strain, and volume at 120 different transmural pressures and eight different eccentricities of both types of spheroids. The pressure-volume relation of the prolate spheroid never differed very much from that of a sphere. However, an oblate spheroid made of urinary bladder material is significantly more compliant than either a prolate spheroid or a sphere made of the same material. Applications include identification of the position of highest stress in the bladder wall, estimation of material properties of urinary bladders, and determination of the physiological signal indicating bladder fullness.