Nonlinear Acoustics FDTD method including Frequency Power Law Attenuation for Soft Tissue Modeling

TL;DR

This paper introduces a nonlinear acoustic FDTD model incorporating frequency power law attenuation for soft tissue simulation, efficiently fitting experimental data with minimal computational resources.

Contribution

It presents a novel FDTD approach using relaxation processes to model frequency-dependent attenuation without convolution, suitable for soft tissue ultrasound simulations.

Findings

Two relaxation processes suffice for most soft tissues.

The model accurately fits experimental attenuation data.

Reduced computational resources compared to fractional derivative methods.

Abstract

This paper describes a model for nonlinear acoustic wave propagation through absorbing and weakly dispersive media, and its numerical solution by means of finite differences in time domain method (FDTD). The attenuation is based on multiple relaxation processes, and provides frequency dependent absorption and dispersion without using computational expensive convolutional operators. In this way, by using an optimization algorithm the coefficients for the relaxation processes can be obtained in order to fit a frequency power law that agrees the experimentally measured attenuation data for heterogeneous media over the typical frequency range for ultrasound medical applications. Our results show that two relaxation processes are enough to fit attenuation data for most soft tissues in this frequency range including the fundamental and the first ten harmonics. Furthermore, this model can fit experimental attenuation data that do not follow exactly a frequency power law over the frequency range of interest. The main advantage of the proposed method is that only one auxiliary field per relaxation process is needed, which implies less computational resources compared with time-domain fractional derivatives solvers based on convolutional operators.