Estimating the local viscoelastic properties from dispersive shear waves using time-frequency ridge analysis

Modulated low-frequency shear waves can be non-invasively generated locally within a medium, by the oscillatory acoustic radiation force resulting from the interference of two focused quasi-CW ultrasound beams of slightly different frequencies. The propagation of such shear waves within a viscoelastic medium is known to be affected by the dispersive effects of viscosity. Specifically, a low-frequency (LF) spectral component was shown to arise with increased viscosities and higher modulation frequencies and appear as a 'slow' wave at the end of the shear waveform. In this paper, the shear dispersion characteristics are studied based on the Pseudo-Wigner-Ville distribution (PWVD) in the time-frequency domain. The ridges of the PWVD are then extracted and used to calculate the frequency-dependent shear speed, by identifying the LF dispersive component both in time and frequency. Using numerical simulations, it is shown that this way of estimating the shear dispersion is more efficient and robust than the conventional phase-delay Fourier method. Thus, more accurate estimates of the local shear modulus and viscosity of the propagating medium could be achieved. The effects of noise on the proposed method are also discussed.