Time-domain simulation of ultrasound propagation in a tissue-like medium based on the resolution of the nonlinear acoustic constitutive relations

TL;DR

This paper introduces a time-domain simulation method for ultrasound in tissue-like media using nonlinear acoustic relations, incorporating relaxation processes to model realistic attenuation and improve computational stability and accuracy.

Contribution

It presents a novel numerical code that models nonlinear ultrasound propagation with realistic tissue attenuation and correction for numerical dispersion, surpassing previous approximations.

Findings

Accurately models frequency power law attenuation in tissues.

Demonstrates improved stability and efficiency in simulating high-intensity focused beams.

Validates results against analytical, numerical, and experimental data.

Abstract

A time-domain numerical code based on the constitutive relations of nonlinear acoustics for simulating ultrasound propagation is presented. To model frequency power law attenuation, such as observed in biological media, multiple relaxation processes are included and relaxation parameters are fitted to both exact frequency power law attenuation and empirically measured attenuation of a variety of tissues that does not fit an exact power law. A computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the numerical method and to improve stability when shock waves are present. This technique avoids the use of high order finite difference schemes, leading to fast calculations. The numerical code is especially suitable to study high intensity and focused axisymmetric acoustic beams in tissue-like medium, as it is based on the full constitutive relations that overcomes the limitations of the parabolic approximations, while some specific effects not contemplated by the Westervelt equation can be also studied. The accuracy of the method is discussed by comparing the proposed simulation solutions to one-dimensional analytical ones, to $k$-space numerical solutions and also to experimental data from a focused beam propagating in a frequency power law attenuation media.