Journal Article

Flow dynamics in a stented ureter

Jennifer H. Siggers, Sarah Waters, Jonathan Wattis and Linda Cummings

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 1, pages 1-24
Published in print March 2009 | ISSN: 1477-8599
Published online November 2008 | e-ISSN: 1477-8602 | DOI:
Flow dynamics in a stented ureter

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  • Applied Mathematics
  • Biomathematics and Statistics


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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

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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