Recent investigations of viscoelastic properties of materials have been performed by observing shear wave propagation following localized, impulsive excitations, and Fourier decomposing the shear wave signal to parameterize the frequency-dependent phase velocity using a material model. This paper describes a new method to characterize viscoelastic materials using group shear wave speeds , , and determined from the shear wave displacement, velocity, and acceleration signals, respectively. Materials are modeled using a two-parameter linear attenuation model with phase velocity and dispersion slope at a reference frequency of 200 Hz. Analytically calculated lookup tables are used to determine the two material parameters from pairs of measured group shear wave speeds. Green's function calculations are used to validate the analytic model. Results are reported for measurements in viscoelastic and approximately elastic phantoms and demonstrate good agreement with phase velocities measured using Fourier analysis of the measured shear wave signals. The calculated lookup tables are relatively insensitive to the excitation configuration. While many commercial shear wave elasticity imaging systems report group shear wave speeds as the measures of material stiffness, this paper demonstrates that differences , , and of group speeds are first-order measures of the viscous properties of materials.

Using a 3D rotational shear wave elasticity imaging (SWEI) setup, 3D shear wave data were acquired in the vastus lateralis of a healthy volunteer. The innate tilt between the transducer face and the muscle fibers results in the excitation of multiple shear wave modes, allowing for more complete characterization of muscle as an elastic, incompressible, transversely isotropic (ITI) material. The ability to measure both the shear vertical (SV) and shear horizontal (SH) wave speed allows for measurement of three independent parameters needed for full ITI material characterization: the longitudinal shear modulus µ L , the transverse shear modulus µ T , and the tensile anisotropy χ E . Herein we develop and validate methodology to estimate these parameters and measure them in vivo, with µ L = 5.77 ± 1.00 kPa, µ T = 1.93 ± 0.41 kPa (giving shear anisotropy χµ = 2.11 ± 0.92), and χ E = 4.67 ± 1.40 in a relaxed vastus lateralis muscle. We also demonstrate that 3D SWEI can be used to more accurately characterize muscle mechanical properties as compared to 2D SWEI.

While ultrasound shear wave elastography originally focused on tissue stiffness under the assumption of elasticity, recent work has investigated the higher order, viscoelastic properties of tissue. This paper presents a method to use group shear wave speeds at a series of derivative orders to characterize viscoelastic materials. This method uses a least squares fitting algorithm to match experimental data to calculated group shear wave speed data, using an assumed material model and excitation geometry matched to the experimental imaging configuration. Building on a previous study that used particle displacement, velocity, and acceleration signals, this study extends the analysis to a continuous range of fractional derivative orders between 0 and 2. The method can be applied to any material model. Herein, material characterization was performed for three different two-parameter models and three different three-parameter models. This group speed based method was applied to both shear wave simulations with ultrasonic tracking and experimental acquisitions in viscoelastic phantoms (similar to the Phase II Quantitative Imaging Biomarkers Alliance (QIBA) phantoms). In both cases, the group speed method produced more repeatable characterization overall than fitting the phase velocity results from the peak of the 2D Fourier transform. Results suggest the linear attenuation model is a better fit than the Voigt model for the viscoelastic QIBA phantoms.

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