15 Christopher developed a nonlinear propagation model to account for wave diffraction, absorption, dispersion, and nonlinearity, though a limit on peak negative pressure needs to be set in the model calculation. 14 Coleman and colleagues used the Burger's equation, which is a one-dimensional version of the Khokhlov–Zabolotskaya–Kuznestsov (KZK) equation to model the focused LSW and diffractive effects were considered by assuming the sound field as a Gaussian beam. Hamilton developed a linear model to simulate the pressure wave form along the lithotripter axis, which provides useful insight on the evolution of different LSW components during wave converging toward the lithotripter focus. Attempts of modeling the acoustic field of an electrohydraulic shock wave lithotripter have been carried out by several groups. Theoretical modeling of the propagation and focusing of lithotripter shock wave (LSW), and bubble dynamics in a lithotripter field is important for understanding the working mechanisms of SWL and for design optimization of the lithotripters. 6 Efforts have been under way to improve the design of lithotripter shock wave sources to improve stone comminution while reducing concomitantly the collateral renal injury. 5 – 9 Following SWL, although most young adult patients recover well, a subgroup of patients, such as pediatric and elderly patients, and patients with pre-existing renal function impairment, are much more susceptible to SWL-induced chronic injury. 3īoth clinical and basic studies have shown that SWL can produce acute renal injury, such as hematuria, kidney enlargement, renal and perirenal hemorrhage and hematomas, especially with the much higher pressure output of the third-generation lithotripters.
2 – 4 The first-generation Dornier HM-3 lithotripter is still regarded by most urologists in the US as the gold standard of SWL. 2 In spite of this great success and the fact that several new generations of lithotripters have been introduced for clinical use, no fundamental improvements in SWL technology that can lead to better treatment efficiency with reduced tissue injury have been accomplished in the past two decades. 1 Currently, approximately 75% of stone patients are treated by SWL alone and another 20% by SWL in conjunction with endoscopic procedures. Since its invention in the early 1980s, shock wave lithotripsy (SWL) has revolutionized the treatment for renal and upper urinary stones. This model may be used to guide the design optimization of reflector geometries for improving the performance and safety of clinical lithotripters. Altogether, the equivalent reflector model was found to provide a useful tool for the prediction of pressure wave form generated in a lithotripter field. Coupling the simulated pressure wave form with the Gilmore model was carried out to evaluate the effect of reflector geometry on resultant bubble dynamics in a lithotripter field. It is interesting to note that when the interpulse delay time calculated by linear geometric model is less than about 1.5 μs, two pulses from the reflector insert and the uncovered bottom of the original HM-3 reflector will merge together. Furthermore, the primary characteristics in the pressure wave forms produced by different reflector geometries, such as that produced by a reflector insert, can also be predicted by this model. The simulated pressure wave forms, accounting for the effects of diffraction, nonlinearity, and thermoviscous absorption in wave propagation and focusing, were compared with the measured results and a reasonably good agreement was found.
The pressure wave form generated by the spark discharge of the HM-3 electrode was measured by a fiber optic probe hydrophone and used as source conditions in the numerical calculation. The ellipsoidal reflector of an HM-3 lithotripter is modeled equivalently as a self-focusing spherically distributed pressure source. A theoretical model for the propagation of shock wave from an axisymmetric reflector was developed by modifying the initial conditions for the conventional solution of a nonlinear parabolic wave equation (i.e., the Khokhlov–Zabolotskaya–Kuznestsov equation).