Modelling the Influence of Ureteroscopes on Urological Flows and Stone Dynamics


A common, minimally invasive procedure for the removal of kidney stones is flexible uretero-renoscopy. This involves inserting a hand-held medical instrument, a flexible ureteroscope, to the location of the stone via the urethra, which provides passage through the bladder to the upper urinary system. 

One of the primary challenges of ureteroscopic procedures is visualisation within the kidney environment as this requires irrigation with a weak saline solution, both to clear the field of view of debris, and to open up the ureter to provide access for the scope. This irrigation is typically achieved by hanging a saline bag above the scope to provide a continuous flow through the ureteroscope and into the kidney, with a return flow through an access sheath. However, the details of the flow, specifically its impact on intrarenal pressure and stone visualisation and movement, are hard to determine.  

This is where mathematical modelling has significant potential value, as a physics based model can provide intuition for fundamental system behaviour. We aim to model the flow of irrigation fluid through the ureteroscope by considering systematic reductions of the Navier-Stokes equations and using a combination of analytical and numerical techniques to rigorously address questions of design and optimality.


We have derived mathematical models to describe the irrigation flow through a ureteroscope in various configurations, motivated by pipe flow theory, and tested the validity of these models with laboratory experiments, demonstrating good agreement. We have shown that bends at the tip of the flexible scope have a minimal effect on flow and that auxiliary working tools provide a large resistance to flow that is highly dependent upon their position within the channel.

Understanding the impact of auxiliary working tools within the ureteroscope channel has led us to explore the effects of domain geometry on flow rate. We have found that elliptical, rather than circular, channel cross-sections provide higher flow rates, and that there is an optimal shape that results in maximal axial flow. This result has led us to address other aspects of fluid mechanics with low Reynolds number flows, including the effects of domain geometry on the movement of working tools within the flow field. 

Future Work

Future work will focus primarily on modelling the behaviour of the irrigation fluid as it exits the ureteroscope and enters the kidney and other parts of the urinary system. It will be of particular interest to study the behaviour of irrigation fluid within an enclosed renal cavity containing kidney stones.