Numerical Modeling of Ultrasound Propagation in Weakly Heterogeneous Media Using a Mixed-Domain Method

A mixed-domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The present method is based on solving an integral equation derived from a Westervelt-like equation. One-dimensional problems are first studied to verify the MDM and to reveal its limitations. It is shown that this method is accurate for cases with small variation of sound speed. A 2-D case is further studied with focused ultrasound beams to validate the application of the method in the medical field. Results from the MATLAB toolbox k-Wave are used as the benchmark. Normalized root-mean-square (rms) error estimated at the focus of the transducer is 0.0133 when the coarsest mesh (1/3 of the wavelength) is used in the MDM. Fundamental and second-harmonic fields throughout the considered computational domains are compared and good agreement is observed. Overall, this paper demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities.