Quantification of the shielding of kidney stones by bubble clouds during burst wave lithotripsy

Bubble clouds can shield kidney stones from insonification, and limit stone breakage during burst-wave lithotripsy (BWL), a recently proposed technique that uses focused ultrasound pulses with an amplitude of O(1-10) MPa and frequency of O(0.1) MHz. We use numerical simulations to quantify the magnitude of such shielding. In the simulations, we solve for the radial evolution of Lagrangian bubbles coupled to a compressible fluid using volume-averaging techniques. The resulting equations are discretized on an Eulerian grid. In particular, we quantify the reduction in acoustic energy flux incident on a rigid, plane wall that models the stone surface. We consider a burst wave with an amplitude of 6 MPa and a bubble cloud of diameter O(1) mm. The size distribution of nuclei, the number density of bubbles, and the distance of the cloud from the wall are varied, We show that a cloud containing O(10) bubbles with a diameter of O(10) um can reduce the total energy flux by more than 50%, largely independent of distribution of nuclei. Finally, we compare the simulation results with high-speed images and hydrophone measurements of bubble clouds from companion experiments. [Work supported by NIH 2P01-DK043881.]