Time-Domain Simulation of Ultrasound Propagation in a Tissue-Like Medium Based on the Resolution of the Nonlinear Acoustic Constitutive Relations

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 the exact frequency power law attenuation and the 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 finite differences method and to improve stability when shock waves are present. The numerical code is especially suitable to study high intensity and focused axisymmetric acoustic beams in tissue-type medium, as it is based on the full constitutive relations that overcomes the limitations of the parabolic approximations, while some specific effects not considered 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 solutions, to k-space numerical solutions, and lastly experimental data from a focused beam propagating in a frequency power law attenuation media.