A Generalized Split-Step Angular Spectrum Method for Efficient Simulation of Wave Propagation in Heterogeneous Media.

Angular spectrum (AS) methods enable efficient calculation of wave propagation from one plane to another inside homogeneous media. For wave propagation in heterogeneous media such as biological tissues, AS methods cannot be applied directly. Split-stepping techniques decompose the heterogeneous domain into homogeneous and perturbation parts, and provide a solution for forward wave propagation by propagating the incident wave in both frequency-space and frequency-wavenumber domains. Recently, a split-step hybrid angular spectrum (HAS) method was proposed for plane wave propagation of focused ultrasound beams. In this study, we extend these methods to enable simulation of acoustic pressure field for an arbitrary source distribution, by decomposing the source and reflection spectra into orthogonal propagation direction components, propagating each component separately, and summing all components to get the total field. We show that our method can efficiently simulate the pressure field of arbitrary sources in heterogeneous media. The accuracy of the method was analyzed comparing the resultant pressure field with pseudospectral time domain (PSTD) solution for breast tomography and hemispherical transcranial-focused ultrasound simulation models. Eighty times acceleration was achieved for a 3-D breast simulation model compared to PSTD solution with 0.005 normalized root mean-squared difference (NRMSD) between two solutions. For the hemispherical phased array, aberrations due to skull were accurately calculated in a single simulation run as evidenced by the resultant-focused ultrasound beam simulations, which had 0.001 NRMSD with 40 times acceleration factor compared to the PSTD method.