The Mathematical Institute, University of Oxford, Eprints Archive

Modelling crystal aggregation and deposition
in the catheterised lower urinary tract

Band, L. R. and Cummings, L. J. and Waters, S. L. and Wattis, J A D (2009) Modelling crystal aggregation and deposition
in the catheterised lower urinary tract.
Mathematical Biology .



Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker–Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel’s walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel’s entrance.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:908
Deposited By: Ruth Preston
Deposited On:25 Mar 2010 14:53
Last Modified:29 May 2015 18:35

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