A frequency-specific surrogate for efficient fractional attenuation and dispersion modeling in ultrasound

Fractional-derivative wave equation provides a compact and physically consistent description of power-law attenuation and associated causal dispersion in soft biological tissues, but numerical implementation can be computationally expensive in large-scale time-domain simulations due to the presence of nonlocal operators. We propose a frequency-specific surrogate model in which the fractional loss operators are replaced by a frequency-independent damping coefficient and an effective sound speed. Both parameters are obtained from explicit matching conditions that enforce exact agreement with the fractional reference model at a prescribed central angular frequency ωc.One-dimensional numerical experiments confirm that the surrogate is exact at ωc by construction and achieves high accuracy for narrowband excitations centered around the calibration frequency, while discrepancies increase for broadband signals, as expected. Two-dimensional simulations, including both heterogeneous benchmark media and a realistic breast phantom, further demonstrate the applicability of the proposed approach in complex configurations. The resulting formulation is straightforward to implement within standard PSTD, FDTD, or FEM solvers, and provides a computationally efficient alternative for modeling attenuation and dispersion in narrowband ultrasound applications.