Numerical modeling of axially symmetric focused fields generated by ultrasound surgery transducers using a wide-angle parabolic approximation

A numerical algorithm for calculating ultrasound fields radiated from axially symmetric focused sources was developed on the basis of a wide-angle parabolic approximation of the Helmholtz equation. A numerical solution for the field of an axially symmetric spherical radiator with an aperture of a = 5cm, focal length F = 9cm, and the frequency f = 1MHz was obtained. The solution was compared to those obtained using the full diffraction formulation and with conventional parabolic equation. The results showed that the relative error in pressure amplitude at the focus was 1–2% for a wide-angle parabolic approximation and 10–12% for the conventional parabolic approximation comparing to the exact Rayleigh integral solution. Calculation time for a wide-angle model was comparable to conventional parabolic model, and was an order of magnitude less than calculating the exact solution using the Rayleigh integral.