Fast spectral algorithm for modeling focused sound beams in a highly nonlinear regime

Abstract

Numerical modeling of high-intensity focused sound beams is important for medical applications of ultrasound. The KZK equation, which may be modified to include relaxation in the time domain or arbitrary absorption and dispersion in the frequency domain, is widely used to model ultrasound beams in tissue. Numerical solutions are available in either the time or frequency domain, but they become time consuming at high intensities when thin shocks are developed. To speed up calculations, a known high-frequency asymptotic result for shocks can be incorporated in the frequency domain algorithm. In comparison with exclusively numerical schemes, the present approach substantially reduces the number of harmonics and thus the computation time [Yu. A. Pishchal’nikov, O. A. Sapozhnikov, and V. A. Khokhlova, Acoust. Phys. 42, 362–367 (1996)]. Focused cw beams radiated from Gaussian and piston sources are simulated in water and biological tissue. The accuracy of the asymptotic approach is verified via conventional numerical methods of solution. It is shown that the present asymptotic method provides accurate results with a considerable reduction in computation time. In combination with conventional numerical schemes, the developed asymptotic method provides an effective tool for investigating focused sound beams for a wide range of parameters. [Work supported by NIH PO1-DK43881, Fogarty Research Program, and CRDF.]