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If the ureter becomes blocked, the resultant increased pressure may be relieved by inserting a double-J stent (a polymer tube, usually punctuated with holes). A major clinical problem associated with stent use is reflux (retrograde flow of urine from the bladder to the kidney), which may result in infections, scarring, and even renal failure. We develop a mathematical model, treating the ureter as an elastic tube and the stent as a permeable rigid tube within it. We investigate how the number of holes in the stent wall affects the total amount of reflux that occurs when bladder pressure rises, by considering the limits of a highly-permeable stent, and an impermeable stent. We find that, in the scenarios we consider, the highly-permeable stent gives rise to less total reflux than the impermeable one.

Original publication




Journal article


J Math Biol

Publication Date





56 - 82


Humans, Models, Biological, Stents, Ureter, Urination