Mathematical Modelling of Unsteady Flows during Ureteroscopy

 

 

Background

Ureteroscopy is quickly becoming the preferred method for the treatment of kidney stones. The procedure involves passing a flexible medical instrument, known as a ureteroscope, through the urinary system to gain access to the kidney (Figure 1). The ureteroscope is hollow along its length, creating a working channel through which irrigation fluid can pass into the body. Once inserted into the patient, working tools are passed down the length of the working channel to access and remove the kidney stones.

Figure 1: Schematic of ureteroscopy.

Ureteroscopy requires constant fluid irrigation to help with distention of kidney cavity, to give a clear field of view for a camera on the tip of the scope. Traditionally, this is done by hanging a bag of saline solution above the level of the scope, creating a pressure gradient to drive the flow. This delivery method is somewhat crude and provides little control, and so recent developments in the field involve using an electronic pump to drive the fluid, giving much control over pressure and flow patterns within the system. The use of these pumps enables the possibility for the flow to be pulsatile or to display other time-dependent behaviors.

The project will use mathematical modelling in combination with experimental approaches to explore the effect of oscillating flows on ureteroscope fluid irrigation. We seek to understand the differences between constant fluid irrigation and the new time dependent flows. We will explore the potential for pulsatile flow to enhance ureteroscopy by establishing a coherent mathematical model of the system.

 

Progress

A mathematical model for oscillatory flow of irrigation fluid throughout the ureteroscopy system (tubing, scope, kidney, sheath) has been produced. We have explored the effect of the oscillations and compared to that of steady flow. The results suggest flows with high frequencies display similar behavior to that of steady flow throughout the entire system. We have found that pressure variations are significantly dampened by the time they reach the kidney (Figure 2), suggesting that the impact of oscillatory flow on the kidney may be negligible for some parameter ranges. Further, we have shown that when a working tool is present the dampening of oscillations is greater; this is because the fluid has a much smaller channel to flow through.

Figure 2: Amplitude of pressure in ureteroscope.

 

Previous research has lead us to also explore how the working tool moves around within the working channel of the ureteroscope. We tackle the problem using a reduced two-dimensional model, where we explore the movement of a tilted plate placed within a channel of fluid. When the tilted plate is free to move vertically and pivot about its centre, the surrounding fluid causes it to travel away from the centre of the channel as well as increase its rotation. The result suggests that the natural position of a working tool is unlikely to be central and coaxial within a working channel. We find that as the working tool moves away from the centre it causes less resistance to the flow, however a larger tilt increases resistance to the flow.

 

Future work

The next aim is to determine the behavior of irrigation fluid within the kidney. We will achieve this by establishing a two-dimensional model of unsteady flows within a cavity. Further to this, we aim to include stone transport into the kidney flow model, to study how the stones are disturbed and moved by the irrigation fluid. Understanding more about the flow within the kidney will allow us to optimise ureteroscope design in order to create more efficient and effective treatment of kidney stones.

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