Accounting for the spatial observation window in the two-dimensional Fourier transform analysis of shear wave attenuation

摘要

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the two-dimensional Fourier transform (2DFT) of the shear wave signal and measuring the phase velocity c(ω) and attenuation α(ω) from the peak location and full width at half maximum (FWHM) of the 2DFT signal at discrete frequencies. However, when the shear wave is observed over a finite spatial range, the 2DFT signal is a convolution of the true signal and the observation window, and measurements using the FWHM can give biased results. In this study, we describe a method to account for the size of the spatial observation window using a model of the 2DFT signal and a nonlinear, least squares fitting procedure to determine c(ω) and α(ω). Results from the analysis of finite element simulation data are in agreement with c(ω) and α(ω) calculated from the material parameters used in the simulation. Results obtained in a viscoelastic phantom demonstrate that the measured attenuation is independent of the observation window and are in agreement with measurements of c(ω) and α(ω) obtained using the previously described progressive phase and exponential decay analysis.