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Open AccessArticle

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

1
Key Laboratory of Modern Acoustics (MOE), Department of Physics, Collaborative Innovation Centre of Advanced Microstructure, Nanjing University, Nanjing 210093, China
2
The State Key Laboratory of Acoustics, Chinese Academy of Science, Beijing 10080, China
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2018, 8(4), 609; https://doi.org/10.3390/app8040609
Received: 17 March 2018 / Revised: 6 April 2018 / Accepted: 10 April 2018 / Published: 12 April 2018
(This article belongs to the Special Issue Modelling, Simulation and Data Analysis in Acoustical Problems)
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. View Full-Text
Keywords: KZK equation; fractional order derivative; ultrasound hyperthermia; HIFU; acoustic simulation; Kramers–Kronig relation KZK equation; fractional order derivative; ultrasound hyperthermia; HIFU; acoustic simulation; Kramers–Kronig relation
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Liu, S.; Yang, Y.; Li, C.; Guo, X.; Tu, J.; Zhang, D. Prediction of HIFU Propagation in a Dispersive Medium via Khokhlov–Zabolotskaya–Kuznetsov Model Combined with a Fractional Order Derivative. Appl. Sci. 2018, 8, 609.

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