Sound field prediction of ultrasonic lithotripsy in water with spheroidal beam equations

With converged shock wave,extracorporeal shock wave lithotripsy(ESWL)has become a preferable way to crush human calculi because of its advantages of efficiency and non-intrusion.Nonlinear spheroidal beam equations(SBE)are employed to illustrate the acoustic wave propagation for transducers with a wide aperture angle.To predict the acoustic field distribution precisely,boundary conditions are obtained for the SBE model of the monochromatic wave when the source is located on the focus of an ESWL transducer.Numerical results of the monochromatic wave propagation in water are analyzed and the influences of half-angle,fundamental frequency,and initial pressure are investigated.According to our results,with optimization of these factors,the pressure focal gain of ESWL can be enhanced and the effectiveness of treatment can be improved.