Two mathematical models explain the variation in cystometrograms of obstructed urinary bladders

Overdistension of the urinary bladder, secondary to outlet obstruction, causes cellular changes in the bladder wall, including hypertrophy of the smooth muscle cells, which increase bladder mass. To investigate the effects of increased mass on the cystometrogram (CMG), we have developed two mathematical models. In the first model, we assume that mass is added such that the largest bladder volume at zero transmural pressure, the zero pressure volume (ZPV), is constant. It predicts increased pressures and decreased compliance in the CMG. In the second model, we assume that both mass and ZPV increase proportionally. It predicts unchanged pressures, increased compliance, and increased capacity in the CMG. These results allow us to divide animal experiments in the literature into two groups. Cystometrograms performed on animals that have had outlet obstruction induced by a cuff method, inducing a small increase in mass, belong to the first group: hypertrophy with no change in ZPV. Cystometrograms performed on animals that have had outlet obstruction induced by a ligature method, inducing a large increase in mass, belong to the second group: hypertrophy with increased ZPV. We conclude that increased ZPV results from a more severe obstruction which is indicated by the increased capacity and compliance.