基于分数导数研究高强度聚焦超声的非线性声场

摘要

在高强度聚焦超声(high intensity focused ultrasound, HIFU)的研究中,生物组织的衰减和色散性质会对声能量的空间分布产生影响。本文提出应用分数导数修正非线性Khokhlov-Zabolotskaya-Kuznetsov (KZK)方程,研究生物组织中非线性HIFU声场。对三种生物仿体的衰减和声速色散的理论实验研究表明分数导数应用的可行性,在此基础上通过数值仿真分析研究了衰减及声速随频率的变化对HIFU焦域分布的影响。研究结果表明,在计算强非线性聚焦超声时,由于高次谐波的强色散作用,引入分数导数来解决生物组织特殊的衰减以及色散问题可进一步提高HIFU治疗的安全性。%The acoustic energy distribution of high intensity focused ultrasound (HIFU) is influenced by the attenuation and the dispersion of the biological tissue. In this paper we modify the KZK equation according to the fractional wave equation, in order to accurately describe the sound field of HIFU. The theoretical and experimental studies of frequency dependences of attenuation and sound speed examine the validity of the fractional wave equation. Furthermore, the numerical simulation of HIFU field is performed using the modified KZK equation. The results demonstrate that the introduction of the fractional derivative equation could solve the problems of the attenuation and sound dispersion, leading to the accuracy improvement of HIFU therapy.