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Tissue viscoelasticity is becoming an increasingly useful biomarker beyond elasticity and can theoretically be estimated using shear wave elastography by inverting the propagation and attenuation characteristics of shear waves. Estimating viscosity is often more difficult than elasticity because attenuation, the main effect of viscosity, leads to poor signal-to-noise ratio of the shear wave motion. In the present work, we provide an alternative to existing methods of viscoelasticity estimation, based on peaks in the frequency–wavenumber (f–k) domain, which are considered more robust against noise compared with other features in the f–k domain. Specifically, the method minimizes the difference between simulated and measured versions of two sets of peaks (twin peaks) in the f–k domain, obtained first by traversing through each frequency and then by traversing through each wavenumber. The slopes and deviation of the twin peaks are sensitive to elasticity and viscosity, respectively, leading to the effectiveness of the proposed inversion algorithm for characterizing mechanical properties. This expected effectiveness is confirmed through in silico verification, followed by ex vivo validation and in vivo application, indicating that the proposed approach can be used effectively in accurately estimating viscoelasticity, thus potentially contributing to the development of enhanced biomarkers. 

We utilize Full Waveform Inversion (FWI) framework to convert shear wave elastography (SWE) measurements on multiple planes to a single three-dimensional (3D) image of elasticity using gradient optimization to adjust the elasticity map until the mismatch between simulated and measured particle velocities is minimized. Several ideas are brought together to ensure the robustness and effectiveness of the proposed FWI: correlation-based matching between measurements and simulation, high-fidelity finite element simulation of 3D shear waves in incompressible elastic media, multi-resolution parametrization to help with convergence, multi-frequency continuation for finer resolution imaging, and multi-push illumination. With the help of in silico and phantom validation studies, the algorithm is shown to be effective in providing images outside the measurement plane, including reconstructing full 3D images from 2D.