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Mathematical Medicine and Biology Advance Access originally published online on November 5, 2008
Mathematical Medicine and Biology 2009 26(1):1-24; doi:10.1093/imammb/dqn020
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Flow dynamics in a stented ureter

Jennifer H. Siggers{dagger}

Department of Bioengineering, Imperial College London, London SW7 2AZ, UK

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

{dagger} 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 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.

Keywords: vesicorenal reflux; ureteric stent; urodynamics; mathematical modelling; fluid dynamics


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