Multiple relaxation mechanisms for modeling a broad range of power law ultrasound attenuation in heterogeneous biological tissue

Accurate wave attenuation modeling is crucial for quantitative ultrasound, beamforming, waveform inversion, therapeutic planning, and the quantification of acoustic fields in neuromodulation. Despite its importance, the combined challenges of modeling different attenuation power laws and magnitudes in highly heterogeneous tissue have limited simulation fidelity. We present a multiple relaxation-based model that captures a broad spectrum of power-law attenuation behaviors in complex media, including sub-resolution attenuation effects that cumulatively impact wave propagation and backscatter. Our finite difference time domain (FDTD) framework supports both 2-D and 3-D ultrasound simulations. It integrates multiple relaxation mechanisms with an optimization-based fitting process to replicate target attenuation coefficients and power-law exponents. Dispersion is constrained via Kramers–Kronig relations. Our toolchain leverages a scalable, multi-GPU CUDA backend with a Python interface for rapid and flexible computation. Benchmarking in 2-D demonstrates relative attenuation errors below 10% across a wide range of power laws within 1–20 MHz. In 3-D applications, single-angle plane wave imaging of a mouse brain is completed in under t10 min, while five-angle imaging is accomplished in less than 1 h. This high-fidelity, efficient simulation enables models that require accurate attenuation in finely heterogeneous materials.