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

摘要

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{sub}D, absorption and dispersion L{sub}(AD), and nonlinear distortion L{sub}(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{sub}A operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The L{sub}(NL) operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The L{sub}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.