Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams

This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derive d by a superposition of elementary operators corresponding to the 'one effe ct equation'. Diffraction (L) over cap(D), absorption and dispersion (L) ov er cap(AD), and nonlinear distortion (L) over cap(NL) effects are treated i ndependently using a first order operator-splitting algorithm. Using the me thod of fractional steps, the normal particle velocity and the acoustical p ressure are calculated plane by plane, at each point of a two-dimensional s patial grid, from the surface of the plane circular transducer to a specifi ed distance. The (L) over cap(A) operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramer s-Kroning relations. The (L) over cap(A) operator is a time-based transform ation obtained by following an implicit Poisson analytic solution. The (L) over cap(D) operator is the usual Rayleigh integral. We present a compariso n between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmo nics, obtained after spectral analysis. (C) 2000 Elsevier Science B.V. All rights reserved.