Modeling of nonlinear shock wave propagation and thermal effects in high-intensity focused ultrasound fields.

Abstract

Numerical simulations based on the Khokhlov–Zabolotskaya-type equation are currently used to characterize therapeutic high-intensity focused ultrasound fields in water and to predict bioeffects in tissue. Here results from three different algorithms that differ in calculating the nonlinear term in the equation are presented. Shock capturing schemes of Godunov type, exact implicit solution with further extrapolation of the waveform over a uniform temporal grid, and direct modeling in the frequency domain are tested. In the case of weak nonlinearity, all schemes give essentially the same solution. However, at high peak pressures around 50 MPa and strong shocks developed in the focal region, the predictions of acoustic variables and heat deposition become sensitive to the algorithm employed. The parameters of the schemes, such as number of harmonics or temporal samples and the inclusion of artificial absorption that provides consistent results, are discussed. It is shown that the spectral and Godunov-type approaches require about 6 points and implicit time domain approach needs more than 50 points in the shock to be accurate. In all schemes artificial absorption should be employed to obtain acceptable accuracy with fewer points per cycle. [Work supported by the NIH EB007643, ISTC 3691, RFBR 09-02-01530, and NSF 0835795 grants.]