Viscoelastic properties of the contracting detrusor. I. Theoretical basis

This paper presents the theoretical basis for estimating the detrusor's viscoelastic properties using the small-amplitude oscillatory perturbations technique. Three possible configurations of the simplest second-order lumped-parameter model of the bladder were analyzed to derive equations of the parameters incremental resistance (R) and incremental elastance (K) in terms of the experimentally measurable magnitude and phase of hydrodynamic stiffness. In model I, single viscous, elastic, and inertial elements were assumed to to be connected in series. In model III the elastic and viscous elements were connected in series, but the inertial element was connected in parallel. With the assumption of a spherical geometry of the bladder, equations were also derived to obtain the bladder wall mechanical properties, spring incremental constant (S), and muscle incremental viscosity (b) as functions of bladder volume and the hydrodynamic properties R and K. Integration of the incremental equation describing the viscous component yields an expression that fits well the force-velocity experimental data from bladder strips reported by others. This finding suggests that muscle viscosity measured with the small-amplitude oscillations and analyzed with the proper theoretical model may be related to the force-velocity characteristics of the muscle. The equations delivered here form the basis for analyzing the experimental data described in the companion paper.