Construction of axisymmetric equivalent sources to facilitate the simulation of nonlinear acoustic fields in therapeutic ultrasound

The development of new clinical applications of therapeutic ultrasound has been accompanied by efforts to standardize simulation methods for predicting nonlinear ultrasound fields. Although software tools for simulating nonlinear ultrasound propagation are increasingly available, computational burdens remain high, especially for fields characterized by strong focusing and significant harmonic content. Because nonlinear effects in such fields accumulate primarily over a short axial distance within the focal lobe, the nonlinear field can be approximated by considering an equivalent source with a similarly shaped focal lobe in the linearly focused beam. If an axisymmetric equivalent source can be identified, even strongly nonlinear fields can be accurately simulated with minimal computational burden using the Khokhlov-Zabolotskaya- Kuznetsov model. This approach has been implemented and validated in water for several real sources using only a simple set of linear field measurements to characterize the focal lobe of each source. To demonstrate the breadth of utility of this approach, holograms of non-axisymmetric fields distorted by phantoms were also used to define equivalent sources and estimate in situ nonlinear fields. Fast holography measurements combined with equivalent-source simulations can efficiently characterize the impact of different phantom geometries on nonlinear fields. [Work supported by NIH R01EB025187 and R01EB007643, and RSF 19-12-00148.]