The reverberant shear wave (RSW) technique offers a promising framework for elastography. In this study, to characterize fibrotic fatty livers at different fibrotic stages, we employed an autocorrelation (AC) estimator within the RSW framework to evaluate shear wave speed (SWS) of viscoelastic media. To this end, we utilized both simulation and experimental approaches and excited the RSW field in a medium within each approach at the frequency of 150 Hz: (i) the finite element (FE) simulation of a RSW field in a 3D model of a whole organ fatty liver and (ii) the RSW experiments on two castoroil- in-gelatin phantoms fabricated in the lab. In the FE simulations, to represent a more realistic liver model, a thin adipose fat layer and a muscle layer were added as viscoelastic power-law materials on top of the liver model. The SWS estimation from the RSW simulation was compared with predictions from the theory of composite media for verification. For the RSW experiments on phantoms, the SWS estimations were compared with the SWS results obtained from performing the stress relaxation test as an independent modality. The simulation results showed that the RSW-based AC estimator provides good estimates of SWS, within >90% accuracy compared with theory. Also, the RSW estimator results from the phantom experiments at different background stiffness levels provided some experimental support for the utility of the RSW estimator. These results demonstrated that the AC estimator is sensitive to the changes in viscoelastic properties of viscoelastic media.
Purpose: The study of speckle from imaging systems has a rich history, and recently it was proposed that a fractal or power law distribution of scatterers in vascularized tissue will lead to a form of the Burr probability distribution functions for speckle amplitudes. This hypothesis is generalized and tested in theory, simulations, and experiments.
Approach: We argue that two broadly applicable conjectures are sufficient to justify the applicability of the Burr distribution for speckle from a number of acoustical, optical, and other pulse-echo systems. The first requirement is a multiscale power law distribution of weak scatterers, and the second is a linear approximation for the increase in echo intensity with size over some range of applicability.
Results: The Burr distribution for speckle emerges under a wide variety of conditions and system parameters, and from this one can estimate the governing power law parameter, commonly in the range of 2 to 6. However, system effects including the imaging point spread function and the degree of focusing will influence the Burr parameters.
Conclusions: A generalized pair of conditions is sufficient for producing Burr distributions across a number of imaging systems. Simulations and some theoretical considerations indicate that the estimated Burr power law parameter will increase with increasing density of scatters. For studies of speckle from living tissue or multiscale natural structures, the Burr distribution should be considered as a long tail alternative to classical distributions.
Purpose: Recent theories examine the role of the fractal branching vasculature as a primary site of Born scattering from soft normal tissues. These derivations postulate that the first-order statistics of speckle from soft tissue, such as the liver, thyroid, and prostate, will follow a Burr distribution with a power law parameter that can be related back to the underlying power law, which governs the branching network. However, the issue of scatterer spacing, or the number of cylindrical vessels per sample volume of the interrogating pulse, has not been directly addressed.
Approach: Speckle statistics are examined with a 3D simulation that varies the number density and the governing power law parameter of an ensemble of different sized cylinders. Several in vivo liver scans are also analyzed for confirmation across different conditions.
Results: The Burr distribution is found to be an appropriate model for the histogram of amplitudes from speckle regions, where the parameters track the underlying power law and scatterer density conditions. These results are also tested in a more general model of rat liver scans in normal versus abnormal conditions, and the resulting Burr parameters are also found to be appropriate and sensitive to underlying scatterer distributions.
Conclusions: These preliminary results suggest that the classical Burr distribution may be useful in the quantification of scattering of ultrasound from soft vascularized tissues and as a tool in tissue characterization.
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