Crystal aggregation and deposition in the catheterised lower urinary tract
by
Sarah Waters
University of Oxford
Coauthors: Leah Band, Linda Cummings, Jonathan Wattis

Urethral catheters often become blocked with crystals of magnesium struvite and calcium

phosphate. The encrustation can block the catheter, which can cause urine retention in the

bladder and reflux of urine 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 fluid flows from the reservoir through the channel and

out of the system. The crystal particles aggregate, which we model using Becker-Doring

coagulation theory, and are advected through the channel, where they continue to aggregate

and can deposit on the channel's walls. Inhibitor particles also enter the reservoir, and can

bind to the crystals, preventing further aggregation and deposition. In the reservoir, we

assume the crystal concentrations are spatially homogeneous, whereas in the channel we

consider concentrations that vary as a result of advection, diffusion and deposition. We

investigate how the aggregation rate and the influx of inhibitor particles affect the amount

of deposition. For all parameter values, we find that crystals deposit along the full length of

the channel, with maximum deposition at the channel's entrance.

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Date received: May 10, 2008