Michalakis A. Averkiou
Lawrence A. Crum
Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105
Mark F. Hamilton
Univ. of Texas, Austin, TX 78712-1063
A theoretical model for the acoustic field produced by commercial lithotripters based on the KZK equation is presented. The KZK equation has been used previously to model high-intensity sound beams in thermoviscous fluids. Both electrohydraulic and piezoelectric lithotripters are considered. To model the acoustic field reflected from ellipsoidal reflectors found in electrohydraulic litho-tripters, geometrical acoustics are used to define a directivity function at the mouth of the reflector. An equivalent focused source with a shading function defined by the directivity function is then assumed as the boundary condition for the KZK equation. A code that solves this equation entirely in the time domain is used to obtain results for the acoustic pressure. The numerical results are compared with previous experiments [Coleman et al., Ultrasound Med. Biol. 13(10), 651--657 (1987)] and good agreement is found. Results for propagation in both water and tissue are presented. Positive pressures of 40--100 MPa and negative pressures of 4--10 MPa are predicted in the focal region. A reflector with a pressure release surface is also considered. In this case the field close to the source is an inverted replica of that of the rigid reflector. However, strong distortion due to nonlinearity affects the rest of field. Negative pressures of 20--30 MPa are predicted in the focal region for this type of reflector. [Work supported by NIH.]