Motivated by the diagnostic value of tissue viscosity beyond elasticity, the goal of this work is to develop robust methodologies based on shear wave elastography (SWE) to reconstruct combined elasticity and viscosity maps of soft tissues out of the measurement plane. Building on recent advancements in full-waveform inversion (FWI) in reconstructing elasticity maps beyond the measurement plane, we proposed to reconstruct a complete viscoelasticity map by novel combination of three ideas: (a) multiresolution imaging, where lower frequency content is used to reconstruct low resolution map, which is then utilized as a starting point for higher resolution reconstruction by including higher frequency content; (b) acquiring SWE data on multiple planes from multiple pushes, one at a time, and then simultaneously using all the data to invert for a single viscoelasticity map; (c) sequential reconstruction where combined viscoelasticity reconstruction is followed by fixing the elasticity map (and thus kinematics), and repeating the reconstruction but just for the viscosity map. We examine the proposed methodology using synthetic SWE data to reconstruct the viscoelastic properties of both homogeneous and heterogeneous tumor-like inclusions with shear modulus ranging from 3 to 20 kPa, and viscosity ranging from 1 to 3 Pa.s. Final validation is performed in silico, where the annular inclusion is reconstructed using noisy data with varying signal-to-noise ratios (SNR) of 30, 20 and 10 dB. While elasticity images are reasonably reconstructed even for poor SNR of 10 dB, viscosity imaging seem to require better SNR. This work, analogous to reconstructing 3D images from 2D measurements, offers a feasibility study for achieving 3D viscoelasticity reconstructions using conventional ultrasound scanners, potentially leading to biomarkers with greater specificity compared to currently available 2D elasticity images.
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