Numerical Simulation of Shock and Bubble Dynamics in Shockwave Lithotripsy

Theoretical evaluation of the efficacy of stone comminution (and potential for tissue damage) during shockwave lithotripsy requires knowledge of the complex stress fields associated with both the incident focussing shock and the dynamics of cavitation bubbles that it induces. While simple models from geometrical acoustics and subsequent modeling of spherical bubbles in isolation (Gilmore equation) can provide estimates, high‐speed photography in vitro reveals a far more complex flow with bubble number densities that are sufficiently high such that collective effects associated with a cloud of bubbles are important. This talk will describe a modeling effort aimed at estimating stresses from these complex lithotripter generated flow fields. We compute the time‐dependent, compressible, ensemble‐averaged two‐phase flow equations with a finite‐difference scheme. Detailed modeling of the dynamics of bubbles (on the microscale) and high‐order weighted essentially nonoscillatory shock‐capturing schemes are employed. The model is compared to hydrophone and passive cavitation detection measurements, as well as qualitative comparison with high‐speed photography. Finally, we explore collective bubble mechanisms ranging from defocusing and shielding of the stone (for high bubble densities in the focal region) to enhanced stresses due to concerted cloud collapse in a dual‐pulse lithotripsy configuration