Evaluation of the power-law impulse response for liver in the time- and frequency-domains

Abstract

Ultrasound attenuation in biological media often follows a frequency-dependent power-law relationship. Power-law attenuation is accompanied by dispersion in which phase velocity also changes as a function of frequency. The power-law wave equation has exact time- and frequency-domain Green's function solutions that are used in numerical evaluations of the Rayleigh–Sommerfeld diffraction integral. These Green's functions contain stable probability density functions that are evaluated in the time-domain using the STABLE toolbox and in the frequency-domain by evaluating the characteristic function of a stable distribution. The impulse response for a circular piston is evaluated on-axis in the time- and frequency-domain using values for human liver. The results show the accuracy of the time-domain impulse response calculation is dependent upon adequate spatial sampling of the piston face. The frequency-domain impulse response exhibits aliasing caused by wrap around of the heavy tail of the stable distribution. Frequency-domain accuracy is dependent upon the spatial sampling of the piston face and the density of the frequency samples. Numerical evaluations show that the frequency- and time-domain calculations converge to the same result. [This work was supported in part by NIH Grant R01 EB012079.]