Modelling spherical and axisymmetric vapour bubbles arising in the treatment of kidney stones #

Sophie Abrahams, Bing Yang, Jessica Williams, Ben Turney, Robin Cleveland, Sarah Waters, Derek Moulton

11:50 Tuesday in 3Q68.

Part of the Mathematical medicine session.

Abstract #

Laser lithotripsy, a common treatment for kidney stones, involves passing a flexible scope containing an optical fibre into the kidney where laser pulses are fired to fragment the stone into pieces small enough to flush out. Laser energy is also transferred to the surrounding liquid, resulting in the production of vapour bubbles. Although bubbles can in some cases have negative effects, they can be utilised to make stone fragmentation more efficient.

This multi-physics system involves bubble nucleation, phase-change, energy transfer and fluid-structure interaction; we simplify this by considering the expansion and collapse of a single bubble, exploiting the natural symmetry for further reductions. For a spherical bubble, the liquid and vapour are treated as distinct regions, employing the Rayleigh-Plesset equation coupled to energy conservation with novel modelling of the laser as a spatio-temporal source of heat energy. In contrast, the axisymmetric case is considered as a two-phase flow, utilising the finite volume and volume of fluid methods.

Through numerical and analytical methods alongside experimental work, we determine the effect of laser power and pulse pattern on the size, shape and duration of bubble produced, providing a framework to guide the development and usage of lasers clinically.