Numerical Simulation and Experiments of Shock Wave Pulse Propagation in the Human Body

基于时域有限差分（FD-TD）方法，提出了一种非常简单的分析冲击波脉冲在人体内非线性传播的数值方法；该问题与体外冲击波碎石的问题密切相关。该方法的基本方程是由连续方程和欧拉运动方程近似求得的关于声压和粒子速度的两个联立偏微分方程。简单地介绍了体积模量中声速的非线性。将该方法应用于与雷肯伯格（Reichenberger）在水中实验装置相吻合的三维数值模型中，即超声波脉冲由电磁激波发生器发射，经声透镜聚焦后，所计算的声压分布与雷肯伯格（Reichenberger）的实测声压分布吻合较好。结果表明，在体积模量中除声速常数项外，再加入与粒子速度成正比的非线性项，进一步提高了模拟结果与实测结果的一致性。该方法可以应用于各种关于非线性和线性超声波传播的问题；媒体并不局限于水。用该方法还可以分析激波脉冲被某些障碍物散射的问题。

A very simple numerical method based on the FD-TD (Finite-Difference Time-Domain) method was developed for analyzing nonlinear propagation of shock wave pulses in the human body ; the problem is closely related to that of extracorporeal shock wave lithotripsy. The basic equations in this method are two simultaneous partial differential equations with respect to sound pressure and particle velocity, which are approximately obtained from the equation of continuity and Euler's equation of motion. The nonlinearity is introduced simply in the acoustic velocity in the bulk modulus. It was verified that when the present method is applied to the three-dimensional numerical model made coinciding with the Reichenberger's experimental setup in water, in which the ultrasonic pulse is radiated from an electromagnetic shock wave generator and is focussed by an acoustic lens, sound pressure distributions calculated by using the present method agree very well with the Reichenberger's measured ones. It was found that when a term proportional to the particle velocity is included as a nonlinear term in addition to the constant term in the acoustic velocity in the bulk modulus, the agreement is further raised between the results simulated and those measured. The method can be applied to a wide variety of problems with respect to nonlinear as well as linear ultrasonic wave propagation ; the media are not limited to the water. The problem of scattering of shock wave pulses by some obstacles can also be analyzed by this method.