Theoretical predictions of the acoustic pressure generated by a shock wave lithotripter

A one-dimensional frequency domain model is used to predict the temporal peak acoustic pressures developed near the beam focus during extracorporeal shock wave lithotripsy (ESWL). The model includes consideration of finite amplitude effects, attenuation, diffraction and dispersion, and results are presented for the case of an electrohydraulic source with the beam geometry of the Dornier HM3 lithotripter. Propagation in castor oil, water and tissue is examined. The model predicts that nonlinear effects enhance the peak positive pressure (p+) at the beam focus in 6 cm of tissue in a Dornier type lithotripter by a factor of about 3 above that which would be expected for linear propagation. The negative peak pressure (p-), conversely, is predicted to be depressed by a factor of about 0.7 below the linear theory prediction. The model also indicates the occurrence of excess absorption due to shock formation. This is shown, for a Dornier HM3 type lithotripter, to cause a reduction in the peak positive pressure gain and a broadening of the focal depth as the output of the source is increased. A threshold aperture pressure is identified for a source with the same beam geometry as the Dornier HM3 below which shock formation does not occur. In this region the pressure gain increases and the focal depth narrows as the source output increases. These effects are characteristic of current commercial piezoelectric and electromagnetic lithotripsy fields.