高频聚焦超声声场和温度场的仿真研究*

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题，基于Westervelt方程和Pennes传热方程，使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异，然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下，当换能器输出声功率超过5 W时，声波传播的非线性效应不可忽视(p<0.05)；当声功率从5 W增大到15 W时，非线性模型与线性模型预测的温度偏差从20%增加到34.703%；高频聚焦超声波的非线性行为比低频更加显著，基频能量向高次谐波转移的程度增大，声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%；高频换能器参数的改变对组织中声场和温度场分布的影响较大，换能器焦距从12 mm减小到11.2 mm，焦点处最高温度增加了77%。结果表明，7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。

Simulation study of high frequency focused ultrasound sound field and temperature field

This study aims to explore the sound propagation of 7 MHz high-frequency focused ultrasound commonly used in clinical practice in multi-layer biological tissues and the law of biological heat transfer in ms time. Based on the Westervelt equation and Pennes heat transfer equation, the nonlinear thermal viscous acoustic propagation and heat transfer model of multi-layer tissues irradiated by high-frequency focused ultrasound was established by the finite element method. Firstly, the difference between linear model and nonlinear model are analyzed. Then the influence of the acoustic parameters of the transducer on the sound field and temperature field is explored under the nonlinear model. The simulation results show that the nonlinear effect of acoustic wave propagation can not be ignored when the output sound power of the transducer exceeds 5 W at 7 MHz frequency (p<0.05). When the sound power increases from 5 W to 15 W, the nonlinear and linear models'' temperature deviation increases from 20% to 37.7%. The nonlinear behavior of the high-frequency focused ultrasonic wave is more significant than that of the low frequency, and the degree of fundamental frequency energy transfer to the higher harmonic increases. The ratio of the fourth harmonic to the fundamental wave reaches 7.33% and 12.12% when the sound power is 10 W and 15 W, respectively. The change of the high-frequency transducer''s acoustic parameters significantly impacts the distribution of the sound field and temperature field in the tissue. The focal length of the transducer decreases from 12 mm to 11.2 mm, and the maximum temperature at the focal point increases by 77%. The results show that the influence of the fourth harmonic should be considered in the nonlinear propagation of 7 MHz focused ultrasound. The multi-layer tissue nonlinear simulation model proposed in this paper can provide a theoretical reference for optimizing high-frequency transducer parameters and formulating a safe and effective preoperative treatment plan.