The goal of elastography is to map the mechanical properties of soft tissues associated with health and disease. The mechanical property of interest in this work is the complex shear modulus, composed of a real part, the storage modulus, which is a measure of elasticity, and an imaginary part, the loss modulus, which is a measure of viscosity. Together, they determine the speed and attenuation of shear waves in the medium. Elastography techniques based on either ultrasound imaging or MRI can image shear wave propagation and thus are capable of measuring shear wave speed and attenuation.
Dispersion, or the frequency-dependence of material parameters, is a primary confounding factor when comparing measurements between different shear wave elastography implementations. Prior attempts at quantifying this frequency-dependence suffered from inaccurate modeling assumptions and low signal-to-noise ratios (SNR). To overcome these limitations, a high-fidelity forward model of shear wave propagation in homogeneous media was developed. The model is an exact semi-analytical solution of Navier's equation and is well-suited for acoustic radiation force impulse shear wave elastography (ARFI-SWE) because it does not require precise knowledge of the strength of the source, nor its spatial or temporal distribution. Unlike models used in ARFI-SWE heretofore, it accounts for the vector polarization of shear waves and exactly represents geometric spreading of the shear wavefield, whether spherical, cylindrical, or neither. Furthermore, it is material-model independent, i.e. it makes no assumption about the frequency-dependence of material parameters. It overcomes the problem of low SNR through spatial averaging and enables estimation of the frequency-dependent complex shear modulus over a wider frequency range than has hitherto been possible. This improved ARFI-SWE was named Shear Wave Rheometry (SWR). By combining SWR with a novel torsional vibration rheometry, dispersion in tissue-mimicking gels was quantified from 1--1800 Hz. The measurements show sizable frequency-dependent variation in the shear modulus of gelatin, a material often assumed to be non-dispersive based on narrow-band measurements. SWR measurements in ex vivo bovine liver tissue yielded complex shear modulus estimates from 25--250 Hz and showed that liver tissue exhibits significant dispersion in this frequency range: a factor of 4 increase in the storage modulus and a factor of 10 increase in the loss modulus. Quality metrics showed that liver tissue can be reasonably approximated as homogeneous and isotropic for ARFI-SWE measurements in this frequency range.
Results demonstrate that accounting for dispersion is essential for meaningful comparisons of measurements between systems. Moreover, improved tissue characterization enabled by SWR may have clinical relevance, for example, in the diagnosis and monitoring of chronic liver disease
