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 derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction (L) over cap(D), absorption and dispersion (L) over cap(AD), and nonlinear distortion (L) over cap(NL) effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, 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 plane circular transducer to a specified distance. The (L) over cap(A) operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The (L) over cap(A) operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The (L) over cap(D) operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis. (C) 2000 Elsevier Science B.V. All rights reserved.