Abstract
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.
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Acknowledgments
We are grateful to the BBSRC and the University of Nottingham for supporting this project financially. S.L.Waters and J.A.D.Wattis are also grateful to the EPSRC for funding in the form of an Advanced Research Fellowship and a Springboard Fellowship respectively. L.J. Cummings gratefully acknowledges the hospitality of City College New York, Department of Chemical Engineering, during a sabbatical year 2007–2008. We would like to thank J.H. Siggers, K. Heaton, D.M. Grant, R. Bayston and M.C. Bishop for helpful discussions.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Band, L.R., Cummings, L.J., Waters, S.L. et al. Modelling crystal aggregation and deposition in the catheterised lower urinary tract. J. Math. Biol. 59, 809–840 (2009). https://doi.org/10.1007/s00285-009-0253-z
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DOI: https://doi.org/10.1007/s00285-009-0253-z
Keywords
- Urethra
- Bladder
- Catheter
- Encrustation
- Blockage
- Aggregation
- Becker–Döring
- Deposition
- Fluid flow
- Mathematical modelling