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    Area of Science:

    • Acoustics
    • Computational physics
    • Biomedical engineering

    Background:

    • Angular spectrum (AS) methods are efficient for wave propagation in homogeneous media but not directly applicable to heterogeneous media like biological tissues.
    • Split-stepping techniques offer solutions for heterogeneous media by decomposing domains and propagating waves in multiple domains.
    • Previous split-step hybrid angular spectrum (HAS) methods were limited to plane wave propagation of focused ultrasound beams.

    Purpose of the Study:

    • To extend split-step hybrid angular spectrum (HAS) methods for simulating acoustic pressure fields from arbitrary source distributions in heterogeneous media.
    • To enable efficient and accurate wave propagation simulations for complex scenarios in biomedical acoustics.
    • To validate the proposed method against established techniques like the pseudospectral time domain (PSTD) method.

    Main Methods:

    • Decomposition of source and reflection spectra into orthogonal propagation direction components.
    • Separate propagation of each spectral component.
    • Summation of all propagated components to reconstruct the total acoustic pressure field.
    • Comparison with pseudospectral time domain (PSTD) solutions for validation.

    Main Results:

    • The extended HAS method efficiently simulates acoustic pressure fields for arbitrary sources in heterogeneous media.
    • Achieved 80x acceleration for a 3-D breast simulation model compared to PSTD, with a 0.005 normalized root mean-squared difference (NRMSD).
    • Accurately calculated skull-induced aberrations for hemispherical phased arrays, achieving 40x acceleration with 0.001 NRMSD compared to PSTD.

    Conclusions:

    • The developed method provides a significant acceleration for simulating acoustic fields in heterogeneous media.
    • The approach is accurate and efficient for applications like breast tomography and transcranial focused ultrasound.
    • This advancement facilitates more complex and faster simulations in biomedical acoustics and wave propagation research.