Diffusing-wave spectroscopy in an inhomogeneous object: local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume.

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation [g(2)(τ)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth [M(τ)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(τ). The modulation depth M(τ(i)) at any delay time τ(i) can be measured by short-time Fourier transform of g(2)(τ) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(τ) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(ω), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(ω) corresponding to these regions from the measured region specific M(τ(i))vsτ(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of τ, the match was good only in the initial transients in regard to experimental measurements with ultrasound.