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

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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.