Simulation of the effects of cavitation and anatomy in the shock path of model lithotripters

We report on recent efforts to develop predictive models for the pressure and other flow variables in the focal region of shock wave lithotripters. Baseline simulations of three representative lithotripters (electrohydraulic, electromagnetic, and piezoelectric) compare favorably with in vitro experiments (in a water bath). We proceed to model and investigate how shock focusing is altered by the presence of material interfaces associated with different types of tissue encountered along the shock path, and by the presence of cavitation bubbles that are excited by tensile pressures associated with the focused shock wave. We use human anatomical data, but simplify the description by assuming that the tissue behaves as a fluid, and by assuming cylindrical symmetry along the shock path. Scattering by material interfaces is significant, and regions of high pressure amplitudes (both compressive and tensile) are generated almost 4 cm postfocus. Bubble dynamics generate secondary shocks whose strength depends on the density of bubbles and the pulse repetition frequency (PRF). At sufficiently large densities, the bubbles also attenuate the shock. Together with experimental evidence, the simulations suggest that high PRF may be counterproductive for stone comminution. Finally, we discuss how the lithotripter simulations can be used as input to more detailed physical models that attempt to characterize the mechanisms by which collapsing cavitation models erode stones, and by which shock waves and bubbles may damage tissue.