The Journal of the Acoustical Society of America · 1989 · 301 citations · 0 references
Natural SciencesMechanical EngineeringPhysicsAcousticsPlasma PhysicsUltrasoundAcoustic Wave PropagationBubble DynamicsCavitationShock Wave LithotripsyShock WavesUltrasound PhysicsAcoustic Bubble DynamicsAcoustic CavitationBubble CollapseCavitation Bubble DynamicsCavitation Collapse ImpulsesCavitation DynamicsShock Wave GenerationShock Wave Modeling
The focus of an extracorporeal shock wave lithotripter generates an intense acoustic wave that can be modeled as the impulse response of a parallel RLC circuit. The shock wave consists of a zero‑rise‑time positive spike followed by a 6‑µs negative pressure component of ±1000/−160 bar, which drives bubble dynamics via the Gilmore–Akulichev formulation with gas diffusion included. A 1000‑bar negative pressure pulse expands a 1–10 µm bubble over 100× its size for 250 µs, reaching ~1400 µm before violent collapse that emits far‑UV or soft X‑ray photons; gas diffusion does not reduce the collapse pressure but lowers temperature, increases the final radius to ~40 µm, and prolongs ringing, with results sensitive to the pressure ratio and negative‑pressure duration.
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 μs followed by a negative pressure component 6 μs 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-μm range to expand to over 100 times its initial size, R0, for 250 μs, with a peak radius of ∼1400 μm, 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 μm 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.