Flow dynamics in a stented ureter

Vesicorenal reflux is a major side effect associated with ureteric stent placement. In a stented upper urinary tract when the bladder pressure rises, such as during bladder spasms (due to irritation caused by the stent) or voiding of the bladder, it drives urine reflux up the ureter, which, in turn, may be a contributory factor for infections in the renal pelvis. We develop a mathematical model to examine urine flow in a stented ureter, assuming that it remains axisymmetric and treating the wall as a non-linear elastic 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 volume increases in response to an increased internal pressure. Fluid enters the renal pelvis from the kidney with a prescribed flux. The stent, ureter and renal pelvis are filled with urine, and the bladder pressure is prescribed. We use the model to calculate the total volume of reflux generated during rises in bladder pressure and investigate how it is affected by the stent and ureter properties.