Setting boundary conditions on the Khokhlov–Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

Pleiades Publishing Ltd - Tập 62 - Trang 151-159 - 2016
P. B. Rosnitskiy1, P. V. Yuldashev1, B. A. Vysokanov2, V. A. Khokhlova1
1Physics Faculty, Moscow State University, Moscow, Russia
2Mechanics–Mathematics Faculty, Moscow State University, Moscow, Russia

Tóm tắt

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.

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Pleiades Publishing Ltd

Tập 62

151-159

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