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 $\omega_c$.One-dimensional numerical experiments confirm that the surrogate is exact at $\omega_c$ 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.