Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Abstract

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.

Influence of microphone characteristics on demodulated sound measurement in near field of parametric loudspeaker

“…We used theoretical values as a reference for evaluating measurements because many theoretical analyses have given results that are in reasonable agreement with measurements of nonlinear sound propagation and formed fields. 15,[39][40][41] This may not always be valid. In addition, there is a possibility that the variability of several decibels between the used microphones affected the results.…”

Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles

“…The Westervelt equation [54] for full-wave propagation and the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation [55] , [56] for quasi-planar propagation have both been used as continuum models for the nonlinear propagation of focused ultrasound. The KZK equation corresponds to the limiting form of the Westervelt equation and has been widely used [57] , [58] , [59] , [60] , [61] , [62] , [63] , [64] , [65] , [66] , [67] , [68] , [69] , [70] , [71] , [72] , [73] , [74] , [75] , [77] , [78] , [76] , [79] , [80] , [81] , [82] , [83] , [84] , [85] , [86] , [87] as a computational model for medical applications, owing to its accuracy and usability in numerical calculations. However, the original KZK equation [55] , [56] was derived for propagation in single phase liquids without bubbles.…”

Explicit Predictor-Corrector Method for Nonlinear Acoustic Waves Excited by a Moving Wave Emitting Boundary

“…In addition, the wave frequency is subject to a modulation beyond the linear Doppler shift when the source accelerates relative to the medium, which also causes a certain amplitude modulation (Christov and Christov, 2017;Gasperini et al, 2021). A detailed understanding of the mechanisms leading to the modulation of pressure waves is of particular importance for biomedical applications, where the generation of higher harmonics is associated with a higher attenuation of acoustic energy, which can alter the deposition of heat in biological tissue (Muir and Carstensen, 1980;Bailey et al, 2003;Qiao et al, 2016). In order to investigate the modulation of pressure waves in a nonlinear medium in the presence of an accelerating source causing a nonlinear Doppler modulation, we present a numerical solution method for Eq.…”