Time-domain nonlinear distortion of pulsed finite-amplitude sound beam: calculation and experiments

This work aims to validate a time domain numerical model for the short pulse finite amplitude sound beam propagation, radiated by a plane piston, in biological tissue. As it has been shown by Tavakkoli and Cathignol [J. Acoust. Soc. Am. 104, 1998], the method of fractional operators is well suited to account for the different effects: diffraction (Ld), absorption (La), and nonlinear distortion (Ln). The normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two dimensional spatial grid, from the surface of the circular transducer to a specified distance. The complete nonlinear evolution equation is simply derived by a superposition of elementary operators corresponding to the "one effect equation". The surface displacement field of the transducer, measured in water with a laser interferometer, is used as source condition in the fractional step algorithm. The absorption law is measured in the 1 MHz to 10 MHz range in a tissue-mimicking liquid (1,3-Butandiol). The calculations of the acoustical pressure in the near and far field zones in time-domain representation are presented together with time and spectral comparisons between theoretical and experimental pressure waveform on axis.