Bannon, Nicholas A.

Shear wave elastography generates shear waves with an acoustic radiation force to obtain estimates of the shear wave speed. Shear wave elastography often utilizes time-of-flight calculations that apply cross-correlations or time-to-peak methods to obtain estimates of the shear wave speed in the time-domain. However, these time-domain methods fail to consider the effect of dispersion caused by the shear viscosity, which can introduce substantial errors into estimates of the shear wave speed. To solve this problem, a new viscoelastic method for estimating shear wave parameters in the time-domain is introduced. The performance of the new method, which is applied to shear wave particle velocity waveforms, is established by evaluating a simulated three-dimensional viscoelastic Green's function model for shear waves in the time-domain. Results show that the new viscoelastic time-domain method is applicable to locations outside of the push beam region at the focal depth and throughout a two-dimensional plane. The results also indicate that estimates of the shear wave speed are either comparable to or significantly improved relative to values obtained from cross-correlations while simultaneously providing estimates of the shear viscosity in the time-domain.

Shear wave elasticity imaging is a non-invasive imaging modality that characterizes the mechanical properties of soft tissue, such as the shear wave speed or shear modulus. Present time-domain methods for shear wave parameter estimation divide the propagation distance by the propagation time to obtain an estimate of the shear wave speed. However, soft tissues are viscoelastic, and the shear viscosity frequently produces large errors in the estimated shear wave speed. To address this problem, a simplified time-domain model for shear wave parameter estimation in viscoelastic media is applied to simulated three-dimensional (3D) shear waves in a viscoelastic medium, where these 3D simulations require high performance computing to evaluate an approximate time-domain Green’s function solution of Navier’s equation that employs a Kelvin-Voigt rheological model. Parameters for the time-domain model are determined from an optimization procedure, then the shear wave speed is estimated from estimated time delays that account for the shear viscosity. Estimates of the shear wave speed are shown at the focal depth and in a two-dimensional region for various parameter combinations. The simplified time-domain viscoelastic model consistently yields smaller errors for the shear wave speed than cross-correlations while simultaneously providing estimates of the shear viscosity.

Time-domain estimates of the shear wave speed are obtained by performing cross-correlations or by evaluating the time-to-peak for two laterally separated shear wave particle velocity waveforms, where the distance divided by the propagation time yields an approximate value for the shear wave speed. Challenges associated with these time-domain estimation approaches include increasing errors as the shear viscosity increases and the absence of an estimated value for the shear viscosity parameter which is responsible for the rapid attenuation of shear waves in soft tissue. To obtain a time-domain estimate of the shear viscosity that also provides an estimate for the shear wave speed, a nonlinear least squares estimation approach is applied to three-dimensional (3D) shear wave particle velocities computed for a shear elasticity of 1.5 kPa, shear viscosities of 1, 2, 3, and 4 Pa.s, and a realistic simulated 3D acoustic radiation force excitation. The results show cross-correlations tend to over-estimate the value of the shear wave speed, the nonlinear least squares approach tends to under-estimate the value of the shear wave speed, and the nonlinear least square approach produces more accurate estimates as the shear viscosity increases. Two-dimensional maps of each estimated parameter are also shown.

Rapid simulations of three-dimensional (3D) shear wave propagation in viscoelastic media with a Kelvin-Voigt model are enabled by Green’s functions accelerated with graphics processing unit parallelization and high-performance computing resources. Cross-correlation analysis of the wave motion yields an estimate of shear elasticity, where the errors in the estimated values increase with rising shear viscosity. To reduce errors in the shear elasticity estimates, a nonlinear least-squares routine that accounts for the effects of propagation, attenuation, and dispersion is applied to 3D simulated shear wave data in viscoelastic media. The nonlinear least-squares approach also yields an estimate of the shear viscosity when applied to simulated particle velocity waveforms. Post-processing, cross-correlation analysis, and the nonlinear least-squares routine are evaluated on a desktop computer using MATLAB. Estimation of viscoelastic parameters is performed at the focal depth for several combinations of shear elasticity and shear viscosity. The errors in the estimated shear elasticities obtained from the nonlinear least-squares routine and cross-correlation are determined as a function of the input shear elasticity and shear viscosity values. The estimates provided by the nonlinear least-squares routine for shear elasticity and shear viscosity are shown to approach the simulation input values for each combination of viscoelastic parameters.