Measurement of the frequency dependent phase velocity and attenuation from the Fourier description of shear wave propagation: Addressing geometric spreading arising from spatially asymmetric Gaussian excitations

Observations of shear wave propagation in a viscoelastic (VE) tissue are typically analyzed by assuming the wave is described as a plane wave, or as the asymptotic form of a wave expanding radially from a cylindrically symmetric source. In this study we present an exact expression for the two dimensional Fourier transform (2D-FT) description of shear wave propagation in a VE material following an asymmetric Gaussian excitation. This expression is used to evaluate the bias in 2D-FT measurements obtained using the plane or cylindrical wave assumptions. A wide range of biases are observed depending on specific values of frequency and aspect ratio R of the source asymmetry. These biases can be reduced significantly by weighting the shear wave signal in the spatial domain to correct for the geometric spreading of the shear wavefront using a factor of x^p. The optimal weighting power p is found to be near the theoretical value of 0.5 for the case of a cylindrical source with R = 1, and decreases for asymmetric sources with R > 1.