Dynamics of the upper urinary tract: I. Peristaltic flow through a distensible tube of limited length

A theoretical analysis and numerical solutions are presented for viscosity-dominated flow through a uniform, highly distensible tube with a slit-shaped cross section undergoing peristalsis. At flow rates below an intrinsic upper limit to the peristaltic carrying capacity of the tube, provided that there is always at least one peristaltic contraction wave in the tube, two different types of steady peristaltic flow are possible, with well defined boluses separated by regions where the tube is nearly completely occluded (flow with isolated boluses and flow with boluses in contact). Above this limit two other non-steady types of flow are possible, in which the boluses are less well defined and the contraction waves are in general not completely occlusive (flow with leaky boluses and open-tube flow). In flow with isolated boluses, boluses in contact and leaky boluses, the upstream pressure is determined by the mechanical properties (active and passive) of the tube undergoing peristalsis. In open-tube flow it is primarily determined by the resistance of the outlet from the tube.