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Title: Mathematical modelling of fluid flows during ureteroscopic kidney stone removal
Author: Williams, Jessica G.
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2019
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A ureteroscope is a hand-held surgical device. The scope consists of a handle and a long, thin shaft which is inserted through the urethra of the anaesthetised patient; visualisation is provided by a microscopic camera embedded in the scope tip. To prevent stone debris and blood from obscuring the image, a weak saline solution continuously flows from a suspended saline bag, through a long, thin cylindrical channel within the ureteroscope shaft -- the working channel -- and flushes out the kidney. The fluid returns through an access sheath, a rigid tube surrounding the scope shaft. This process is termed irrigation. Remote areas of the kidney are accessed by utilising the flexible scope tip and kidney stones are removed via auxiliary working tools which are passed through the working channel. This thesis is concerned with the mathematics and fluid mechanics of ureteroscopy with an aim to improve surgical visualisation and safety through a mechanistic understanding of irrigation flow rate, kidney pressures, and flow patterns within the kidney as functions of relevant clinical parameters. We commence by modelling flow through an isolated scope, incorporating the effects of saline bag height, scope tip deflection, and working tools. We use a hydraulic network approach to equate irrigation inflow through the working channel with a return flow through the access sheath. We validate mathematical predictions with the results of bench-top and ex-vivo experiments. Flow through the working channel containing a working tool, and flow through the access sheath containing the scope shaft, are modelled as flow through coaxial cylinders, where the position of the inner cylinder is unknown. We determine positions for the inner cylinder and elliptical cross-sections for the ureteroscopic instruments to minimise axial flow resistance, thereby maximising irrigation flow rate for fixed saline bag height. To aid ureteroscope design, we also consider the Stokes resistance to movement of the inner cylinder, highlighting the effects of ellipticity and inner cylinder position. We then characterise the influence of inertial pressures losses (minor losses) -- due to connections between tubular components of ureteroscope irrigation systems -- as quadratic corrections to unidirectional, fully-developed theory. We explore the effect of minor losses with numerical simulations and bench-top experiments. Finally, we turn to modelling flow patterns within the kidney through a combination of numerical simulations and particle image velocimetry experiments. Flow symmetry-breaking is observed and quantified both theoretically and experimentally as a function of Reynolds number and domain length. We use the computed flow fields to simulate the flushing of kidney-stone dust through solutions to an advection-diffusion equation describing the dynamics of a passive tracer. The time required to irrigate the kidney depends on the Peclet number, with relevant scaling law determined by the position and size of flow recirculation zones.
Supervisor: Moulton, Derek E. ; Waters, Sarah L. ; Turney, Benjamin W. Sponsor: InFoMM CDT
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available