An equivalent source model for simulating high intensity focused ultrasound fields using a nonlinear parabolic equation

Abstract

The nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation is commonly used for simulation of nonlinear focused fields generated by medical ultrasound transducers. Axially symmetric codes can be easily implemented on personal computers with simulation times on the order of tens of minutes even for the most extensive simulations of shock formation conditions. However, model accuracy can be limited for high intensity focused ultrasound sources with large convergence angles. In previous studies, it was shown that nonlinear parabolic modeling can provide good matching with measurements and full diffraction modeling in the focal region for both single element piston sources and multi-element arrays. Boundary conditions for the modeling were adjusted by varying the aperture of an equivalent planar source with a uniform pressure magnitude and a phase distribution for parabolic focusing. With this approach, there were slight discrepancies in the lateral pressure distributions in the focal plane. Here, it is proposed that an additional variation in the position of the equivalent source enables matching both axial and lateral distributions of the real HIFU sources with higher accuracy. Several examples are presented to compare modeling and measurements of the fields generated by laboratory and clinical HIFU transducers. [Work supported by RSF 14-12-00974 and NIH EB007643.]