The fluid mechanics of ureteroscope irrigation

Flexible ureteroscopy is a minimally invasive treatment for kidney stone removal. The ureteroscope has a central lumen (working channel) for auxiliary instruments (working tools). Successful ureteroscopy requires a good intrarenal view, achieved by irrigation, i.e., driving a saline solution through the working channel via an applied pressure drop. Working tools within the working channel reduce the irrigation flow rate, thus posing a clinical challenge.

We derive a mathematical model, based on systematic reductions of the Navier Stokes equations. We represent the channel and tool as coaxial, non-concentric cylinders of uniform cross-sections. The axial and cross-sectional flow equations decouple and the cross-sectional flow is governed by the 2D Stokes equations.

Geometrical changes to the annular fluid domain affect the relationship between axial flow rate and applied pressure. The position of a working tool is predicted by determining its transverse trajectory subject to an initial perpendicular motion. Results identify an optimal geometry to maximise flow rate for a given pressure drop.