Numerical Characterization of Shear Elasticity Values Estimated with the Time-of-Flight Approach

In clinical ultrasound applications, there is a need for accurate estimates of the shear elasticity, which is directly relevant to the characterization of liver fibrosis, cancer, and other pathologies. The time-of-flight (TOF) approach, which is widely used for estimating the shear elasticity, is effective in purely elastic media, but the TOF approach tends to overestimate the shear elasticity in viscoelastic shear wave phantoms and in soft tissues. To determine the range of shear viscosity values over which the TOF approach yields accurate estimates for the shear elasticity, multiple three-dimensional (3D) simulations of the acoustic radiation force and resulting shear wave particle displacement are assessed. The TOF method is evaluated for values of shear elasticity and shear viscosity within the range of values encountered in healthy liver tissue. A realistic 3D model of the acoustic radiation force is calculated using the fast nearfield method and the angular spectrum approach in FOCUS (https://www.egr.msu.edu/~fultras-web), and then the shear waves are simulated in 3D with Green's functions in viscoelastic media on a graphics processing unit (GPU). The TOF method is evaluated within a two-dimensional (2D) cross-section and is based on the Kelvin-Voigt model for a viscoelastic material. The results demonstrate that the accuracy of the TOF method is dependent on the shear elasticity and the shear viscosity, where the accuracy of the TOF method worsens as the shear viscosity increases within the ranges encountered in liver and also worsens as the elasticity increases for a fixed value of shear viscosity.