Estimation of shear viscoelasticity via time-domain elastic full waveform inversion in ultrasound shear wave elastography

Abstract

The elastography inversion process typically assumes local homogeneity or ignores viscosity, which can lead to inaccuracies. This study presents a methodology for estimating viscous and elastic properties of a heterogenous media based on time-domain elastic full waveform inversion using the limited data available in conventional ultrasound shear wave elastography (SWE). The proposed method is based on the elastodynamic equation and minimizes a squared residual misfit function. To improve the optimization process, a total viscoelastic search space is considered and a quasi-Newton optimization is employed, where gradients are approximated using the adjoint state method. Additionally, Tikhonov regularization is incorporated to handle noisy and sparse displacement data. The proposed method was evaluated across various scenarios simulating real-world experimental conditions, accounting for noise levels and temporal sampling sparsity of displacement field. Using noisy displacement data from a single slice of three-dimensional volume, imitating the ultrasound SWE, resulted in 2.91% error for elasticity estimation and 23.97% error for viscosity estimation across the field of view. This framework enables the estimation of viscous and elastic properties of heterogeneous media and has shown promising results. Additionally, the optimization was improved, and noisy and sparse displacement data were effectively addressed.