Modeling of an electrohydraulic lithotripter with the KZK equation

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Abstract
The acoustic pressure field of an electrohydraulic extracorporeal shock wave lithotripter is modeled with a nonlinear parabolic wave equation (the KZK equation). The model accounts for diffraction, nonlinearity, and thermoviscous absorption. A numerical algorithm for solving the KZK equation in the time domain is used to model sound propagation from the mouth of the ellipsoidal reflector of the lithotripter. Propagation within the reflector is modeled with geometrical acoustics. It is shown that nonlinear distortion within the ellipsoidal reflector can play an important role for certain parameters. Calculated waveforms are compared with waveforms measured in a clinical lithotripter and good agreement is found. It is shown that the spatial location of the maximum negative pressure occurs pre-focally which suggests that the strongest cavitation activity will also be in front of the focus. Propagation of shock waves from a lithotripter with a pressure release reflector is considered and because of nonlinear propagation the focal waveform is not the inverse of the rigid reflector. Results from propagation through tissue are presented; waveforms are similar to those predicted in water except that the higher absorption in the tissue decreases the peak amplitude and lengthens the rise time of the shock.