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Cavity flow characteristics and applications to kidney stone removal

Published online by Cambridge University Press:  07 September 2020

J. G. Williams Open the ORCID record for J. G. Williams [Opens in a new window] ,
A. A. Castrejón-Pita Open the ORCID record for A. A. Castrejón-Pita [Opens in a new window] ,
B. W. Turney Open the ORCID record for B. W. Turney [Opens in a new window] ,
P. E. Farrell Open the ORCID record for P. E. Farrell [Opens in a new window] ,
S. J. Tavener ,
D. E. Moulton Open the ORCID record for D. E. Moulton [Opens in a new window]  and
S. L. Waters Open the ORCID record for S. L. Waters [Opens in a new window]
J. G. Williams*
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, UK
A. A. Castrejón-Pita
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, OX1 3PJ, UK
B. W. Turney
Affiliation:
Nufffield Department of Surgical Sciences, University of Oxford, OX3 9DU, UK
P. E. Farrell
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, UK
S. J. Tavener
Affiliation:
Department of Mathematics, Colorado State University, Oval Drive, CO80523, USA
D. E. Moulton
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, UK
S. L. Waters
Affiliation:
Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG, UK
*
†Email address for correspondence: williamsj@maths.ox.ac.uk
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Abstract

Ureteroscopy is a minimally invasive surgical procedure for the removal of kidney stones. A ureteroscope, containing a hollow, cylindrical working channel, is inserted into the patient's kidney. The renal space proximal to the scope tip is irrigated, to clear stone particles and debris, with a saline solution that flows in through the working channel. We consider the fluid dynamics of irrigation fluid within the renal pelvis, resulting from the emerging jet through the working channel and return flow through an access sheath. Representing the renal pelvis as a two-dimensional rectangular cavity, we investigate the effects of flow rate and cavity size on flow structure and subsequent clearance time of debris. Fluid flow is modelled with the steady incompressible Navier–Stokes equations, with an imposed Poiseuille profile at the inlet boundary to model the jet of saline, and zero-stress conditions on the outlets. The resulting flow patterns in the cavity contain multiple vortical structures. We demonstrate the existence of multiple solutions dependent on the Reynolds number of the flow and the aspect ratio of the cavity using complementary numerical simulations and particle image velocimetry experiments. The clearance of an initial debris cloud is simulated via solutions to an advection–diffusion equation and we characterise the effects of the initial position of the debris cloud within the vortical flow and the Péclet number on clearance time. With only weak diffusion, debris that initiates within closed streamlines can become trapped. We discuss a flow manipulation strategy to extract debris from vortices and decrease washout time.

JFM classification

Biological Fluid Dynamics: Biomedical flows Nonlinear Dynamical Systems: Bifurcation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A16
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Williams et al. supplementary movie

A movie of the experimental technique to `switch’ the direction of the jet, to complement Figure 3 in our manuscript. The movie is at 100 fps.

Download Williams et al. supplementary movie(Video)
Video 305.9 MB