A Theoretical Study of Cavitation Generated by an Extracorporeal Shock Wave Lithotripter

The intense acoustic wave generated at the focus of an extracorporeal shock wave lithotripter is modeled as the impulse response of a parallel RLC circuit. The shock wave consists of a zero rise time positive spike that falls to 0 at 1 microsecond followed by a negative pressure component 6 microseconds long with amplitudes scaled to +1000 and -160 bars, P+ and P-, respectively. This pressure wave drives the Gilmore-Akulichev formulation for bubble dynamics; the zero-order effect of gas diffusion on bubble response is included. The negative pressure component of a 1000-bar shock wave will cause a preexisting bubble in the 1- to 10-microns range to expand to over 100 times its initial size, R0, for 250 microseconds, with a peak radius of approximately 1400 microns, then collapse very violently, emitting far UV or soft x-ray photons (black body). Gas diffusion does not appreciably mitigate the amplitude of the pressure wave radiated at the primary collapse, but does significantly reduce the collapse temperature. Diffusion also increases the bubble radius from R0 up to 40 microns and extends the duration of ringing following the primary collapse, assuming that the bubble does not break up or shed microbubbles. Results are sensitive to P+/P- and to the duration of the negative pressure cycle but not to rise time.