The effect of ureteric stents on urine flow: Is there a better shape?

A problem presented at the UK MMSG Nottingham 2001.

Presented by:
Mr Stuart Graham (Institute of Urology and Nephrology, University College London)
L Cummings, A Gibson, S Graham, P Howell, P Huggins, D Riley, M Simmonds, SL Waters, JAD Wattis, M Williams

Problem Description

The ureter is a muscular tube, lined with epithelium, which transports urine from the renal pelvis of the kidney to the bladder. The ureteric flow in normal conditions is low, at 0.5ml/min. A ureteric stent is a plastic tube that is placed into the ureter to relieve or prevent obstruction. Whilst the stent may be organ- or life-saving in some cases, it presents both patient and surgeon with a new set of problems. Not only may stents be uncomfortable and cause the desire to pass urine often, but they can crust up (encrustation). This may lead to an open operation to remove the stent, and limits the time that stents can be safely left in patients. Presently, stents must be changed if they are to be left long-term every six months. This leads to more operations and the attendant risks. Encrustation mainly happens where stasis of urine occurs, with special regard to the renal pelvis and bladder. The renal pelvis is where most problems originate, as this is the end of the stent that is most difficult to access and remove. Stent design was a somewhat arbitrary process and manufacturers have quickly settled on a curly design known as a "double J".

The study group is asked to consider the following:

  1. What are the flow dynamics through the renal pelvis and pelvi-ureteric junction (PUJ)?
  2. What is the effect of a straight "infinite" stent placed here?
  3. What is the effect of a "double J" stent placed here?
  4. Is there a better shape that allows better flow though this area and lead to less encrustation on the surface?

Study Group Report

The issue of stent encrustation was only briefly considered. Without detailed analysis it was concluded that the main reason for encrustation occurring is that the end curls of the stent are situated in nearly stagnant urine (in the widest parts of the renal pelvis and bladder). Assuming that a faster shear flow past the stent surface would mean less encrustation over a given time period, we suggested changing the design so that, if possible, the whole of the stent lies in regions of appreciable flow speed. Whether or not our suggestion is clinically practical remains to be seen, however.

Regarding question 2, very basic models (assuming Poiseuille flow) were used to derive estimates of the time taken for urine to reflux back along the entire length of the ureter to the kidney, in situations where the bladder pressure is raised above that in the renal pelvis. This was done for two extreme cases: a stent with no holes, and a stent that is extremely porous (e.g. a very fine wire mesh tube). These simple estimates led us to conclude that while there may be some degree of reflux during a bladder twinge, the short duration of the twinge means that urine is unlikely to reflux all the way back to the bladder. During urination however, which can last much longer (and which involves a larger negative pressure differential), total reflux may well occur.

We then went on to formulate a more complicated mathematical model, which treats the ureter as an elastic walled tube, with a rigid porous tube (the stent) inside it. Cylindrical symmetry was assumed, which will of course not be the case in practice. The small aspect ratio of the system enabled us to use lubrication theory to derive explicit evolution equations for the pressures within the stent and ureter, and for the ureter radius. Since these evolution equations are very complicated, we then set about making various asymptotic simplifications. In particular, we again considered the cases of high- and low-porosity stents, to see if we could draw any conclusions about the effect of the holes on the flow. Regarding the reflux issue, which is the major focus of our study, in the two test solutions to our model that we studied it appeared that the holes reduce reflux. Since the holes may also serve a useful purpose in the neighbourhood of the blockage, it seems they are a good design feature.

During the Study Group several experiments were carried out to determine the porosity of a JJ-stent. The results of these experiments agree with what we expect from the mathematics alone.

Download the full report

Follow-Up Activities

The following publications have been written as a result of this problem:

Ureteric stents: Investigating flow and encrustation
SL Waters, K Heaton, JH Siggers, R Bayston, M Bishop, LJ Cummings, DM Grant, JM Oliver & JAD Wattis (2008)
Journal of Engineering in Medicine 222 (4), 551–561.
The effect of ureteric stents on urine flow: Reflux
LJ Cummings, SL Waters, JAD Wattis & SJ Graham (2004)
Journal of Mathematical Biology 49, 56–82.

The following funding for further work has been obtained to investigate aspects of this problem:

Ureteric Stents: Investigating Flow and Encrustation
SL Waters (PI), DM Grant, LJ Cummings, R Bayston, JAD Wattis & SJ Graham
Biotechnology and Biological Sciences Research Council, £302k, October 2003 to September 2006.