Prediction of HIFU Propagation in a Dispersive Medium via Khokhlov–Zabolotskaya–Kuznetsov Model Combined with a Fractional Order Derivative

Abstract

High intensity focused ultrasound (HIFU) has been proven to be promising in non-invasive therapies, in which precise prediction of the focused ultrasound field is crucial for its accurate and safe application. Although the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation has been widely used in the calculation of the nonlinear acoustic field of HIFU, some deviations still exist when it comes to dispersive medium. This problem also exists as an obstacle to the Westervelt model and the Spherical Beam Equation. Considering that the KZK equation is the most prevalent model in HIFU applications due to its accurate and simple simulation algorithms, there is an urgent need to improve its performance in dispersive medium. In this work, a modified KZK (mKZK) equation derived from a fractional order derivative is proposed to calculate the nonlinear acoustic field in a dispersive medium. By correcting the power index in the attenuation term, this model is capable of providing improved prediction accuracy, especially in the axial position of the focal area. Simulation results using the obtained model were further compared with the experimental results from a gel phantom. Good agreements were found, indicating the applicability of the proposed model. The findings of this work will be helpful in making more accurate treatment plans for HIFU therapies, as well as facilitating the application of ultrasound in acoustic hyperthermia therapy.

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

“…This is in line with the findings of Gasperini et al (2021) and indicates that more research on the complicated behavior of nonlinear pressure waves emitted or scattered from accelerating sources is needed. For instance, the excitation of the broadband spectrum caused by the oscillating wave emitting boundary likely has an effect on the attenuation of the pressure wave, which is frequency dependent (Chen, 2005;Liu et al, 2018;Jiménez et al, 2015). In order to achieve a more accurate representation of nonlinear waves radiated by oscillating bubbles, the inclusion of transsonic and supersonic background flows, induced by the bubble motion, into the existing modeling framework is one of the most pressing problems.…”

“…Generally, the attenuation of sound waves can effectively be described by power laws of the wave frequencies, which essentially reflects the increase of viscous attenuation with increasing curvature of the wave profile. Thus, the higher harmonics of the wave are attenuated more strongly than the lower harmonics (Chen, 2005;Jiménez et al, 2015;Liu et al, 2018). An idealized shock contains an infinite amount of harmonics.…”

Assessment of Enhanced Thermal Effect Due to Gold Nanoparticles during MR-Guided High-Intensity Focused Ultrasound (HIFU) Procedures Using a Mouse-Tumor Model

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Special Issue on Modelling, Simulation and Data Analysis in Acoustical Problems

“…Medical applications are presented in [3][4][5][6]. Hearing issues are studied by Cucis et al, comparing normal-hearing subjects and cochlear implant users, and Ito et al, regarding the effects of surgical instruments in ear surgery.…”