Simulation of the second harmonic ultrasound field in heterogeneous soft tissue using a mixed domain method

A mixed-domain method dubbed frequency-specific mixed domain method is introduced for the simulation of the second harmonic ultrasound field in weakly heterogeneous media. The governing equation for the second harmonics is derived based on the quasilinear theory. The speed of sound, nonlinear coefficient, and attenuation coefficient are all spatially varying functions in the equation. The fundamental frequency pressure field is first solved by the frequency-specific mixed domain method, and it is subsequently used as the source term for the second harmonics equation. This equation can be again solved by the frequency-specific mixed domain method to rapidly obtain the second harmonic pressure field. Five two-dimensional cases, including one with a realistic human tissue map, are studied to systematically verify the proposed method. Results from the previously developed transient mixed domain method are used as the benchmark solutions. Comparisons show that the two methods give similar results for all cases. More importantly, the frequency-specific mixed domain method has a crucial advantage over the transient mixed domain method in that it can be two orders of magnitude faster.