Flow dynamics in a stented ureter

Sarah Waters Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, 24–29 St Giles’, Oxford OX1 3LB, UK Jonathan Wattis and Linda Cummings Department of Mathematical Science, New Jersey Institute of Technology, Newark, NJ 07102, USA Email: j.siggers{at}imperial.ac.uk Received on July 19, 2007. Revised on August 23, 2008. Accepted on August 28, 2008. Vesicorenal reflux is a major side effect associated with uretericstent placement. In a stented upper urinary tract when the bladderpressure rises, such as during bladder spasms (due to irritationcaused by the stent) or voiding of the bladder, it drives urinereflux up the ureter, which, in turn, may be a contributoryfactor for infections in the renal pelvis. We develop a mathematicalmodel to examine urine flow in a stented ureter, assuming thatit remains axisymmetric and treating the wall as a non-linearelastic membrane. The stent is modelled as a rigid, permeable,hollow, circular cylinder lying coaxially inside the ureter.The renal pelvis is treated as an elastic bag, whose volumeincreases in response to an increased internal pressure. Fluidenters the renal pelvis from the kidney with a prescribed flux.The stent, ureter and renal pelvis are filled with urine, andthe bladder pressure is prescribed. We use the model to calculatethe total volume of reflux generated during rises in bladderpressure and investigate how it is affected by the stent andureter properties.