Abstract.
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.
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References
Carew, E.O., Pedley, T.J.: An active membrane model for peristaltic pumping: Part I – Periodic activation waves in an infinite tube. J. Biomech. Eng. 119, 66–76 (1997)
Culkin, D.J., Zitman, R., Bundrick, W.S., Goel, Y., Price, V.H., Ledbetter, S., Mata, J.A., Venable, D.D.: Anatomical, functional, and pathologic changes from internal ureteral stent placement. Urol. 40 (4), 385–390 (1992)
Dauleh, M.J., Byrne, D.J., Baxby, K.: Non-refluxing minimal irritation ureteric stent. Br. J. Urol. 76, 795–796 (1995)
Elsherif, A.: Fracture of polyurethane double pigtail stents – an in vivo retrospective and prospective fluoroscopic study. Br. J. Urol. 76 (1), 108–114 (1995)
Finney, R.P.: Experience with new double-J ureteral catheter stent. J. Urol. 120, 678–681 (1978)
Gorman, S.P., Tunney, M.M.: Assessment of encrustation behaviour on urinary tract biomaterials. J. Biomat. App. 12, 136–166 (1997)
Gorman, S.P., Jones, D.S., Bonner, M.C., Akay, M., Keane, P.F.: Mechanical performance of polyurethane ureteral stents in vitro and ex vivo. Biomat. 18 (20), 1379–1383 (1997)
Griffiths, D.J.: Dynamics of the upper urinary tract: I. Peristaltic flow through a distensible tube of limited length. Phys. Med. Biol. 32 (7), 813–822 (1987)
Griffiths, D.J., Constantinou, C.E., Mortensen, J., Djurhuus, J.C.: Dynamics of the upper urinary tract: II. The effect of variations of peristaltic frequency and bladder pressure on pyeloureteral pressure/flow relations. Phys. Med. Biol. 32 (7), 823–833 (1987)
Knudsen, L., Gregerson, H., Eika, B., Frøkiær, J.: Elastic wall properties and collagen content in the ureter: An experimental study in pigs. Neurourol. Urodyn. 13, 597–608 (1994)
Mundy, A.R., Stephenson, T.P., Wein, A.J.: (Editors). Urodynamics: principles, practice and application. 2nd ed. Edinburgh: Churchill Livingstone, 1994
Nancollis, G.H.: Crystallisation theory relating to urinary stone formation. World J. Urol. 1, 131–137 (1983)
Patel, U., Kellett, M.J.: Ureteric drainage and peristalsis after stenting studied using colour Doppler ultrasound. Br. J. Urol. 77, 530–535 (1996)
Seymour, H., Patel, U.: Ureteric stenting - Current status. Semin. Intervent. Radiol. 17, 351–366 (2000)
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Revised version: 8 August 2003
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Cummings, L., Waters, S., Wattis, J. et al. The effect of ureteric stents on urine flow: Reflux. J. Math. Biol. 49, 56–82 (2004). https://doi.org/10.1007/s00285-003-0252-4
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DOI: https://doi.org/10.1007/s00285-003-0252-4