A diffraction correction for storage and loss moduli imaging using radiation force based elastography

Abstract

Noninvasive evaluation of the rheological behavior of soft tissues may provide an important diagnosis tool. Nowadays, available commercial ultrasound systems only provide shear elasticity estimation by shear wave speed assessment under the hypothesis of a purely elastic model. However, to fully characterize the rheological behavior of tissues, given by its storage (G') and loss (G″) moduli, it is necessary to estimate both: shear wave speed and shear wave attenuation. Most elastography techniques use the acoustic radiation force to generate shear waves. For this type of source the shear waves are not plane and a diffraction correction is needed to properly estimate the shear wave attenuation. The use of a cylindrical wave approximation to evaluate diffraction has been proposed by other authors before. Here the validity of such approximation is numerically and experimentally revisited. Then, it is used to generate images of G' and G″ in heterogeneous viscoelastic mediums. A simulation algorithm based on the anisotropic and viscoelastic Green's function was used to establish the validity of the cylindrical approximation. Moreover, two experiments were carried out: a transient elastography experiment where plane shear waves were generated using a vibrating plate and a SSI experiment that uses the acoustic radiation force to generate shear waves. For both experiments the shear wave propagation was followed with an ultrafast ultrasound scanner. Then, the shear wave velocity and shear wave attenuation were recovered from the phase and amplitude decay versus distance respectively. In the SSI experiment the cylindrical approximation was applied to correct attenuation due to diffraction effects. The numerical and experimental results validate the use of a cylindrical correction to assess shear wave attenuation. Finally, by applying the cylindrical correction G' and G″ images were generated in heterogeneous phantoms and a preliminary in vivo feasibility study was carried out in the human liver.

Characterization of Viscoelastic Materials Using Group Shear Wave Speeds

“…Two procedures are commonly used to estimate the phase velocity and attenuation from the Fourier transform signal trueu∼false(r,ωfalse). First, as described by Chen, et al [4] and Deffieux, et al [13], the phase of the asymptotic Hankel function (9) varies linearly with the coordinate r , so a linear fit of phase vs. position can be used to measure the wavenumber k and phase velocity c ( ω ) = ω / k. Similarly, the attenuation α ( ω ) can be measured using the exponential decay with position in (9) [14, 15], or by using the Hankel function dependence in (8) [9]. A second method to measure the phase velocity and attenuation is by constructing the two-dimensional Fourier transform (2DFT) of the spatial-temporal shear wave signal and to measure the phase velocity and attenuation from the peak location and width of the 2DFT signal at each specific temporal frequency [8, 16, 17].…”

Accounting for the Spatial Observation Window in the 2-D Fourier Transform Analysis of Shear Wave Attenuation

“…2 can also be compared to shear wave spectroscopy measurements of the phase velocity as described by Deffieux, et al(2009) and attenuation from the decay of the shear wave signal as described by Budelli, et al(2017). Using the asymptotic form of the Bessel function in (5) and including a $\sqrt{x}$ weighting factor, the temporal Fourier transform shear wave signal has the form $$\sqrt{x}\stackrel{\sim }{v}false(x,\omega false)~e^{-ikfalse(\omega false)x}{e}^{-\alpha false(\omega false)x}$$…”

“…Measurements of c ( ω ) and/or α ( ω ) in viscoelastic materials have been reported by many authors including Deffieux, et al(2009), Nenadic, et al(2017), Nightingale, et al(2015) and Budelli, et al(2017). In addition, direct measurements of μ ( ω ) have been reported by several authors including Henni, et al(2010) and Manduca, et al(2001).…”

Distributing Synthetic Focusing Over Multiple Push-Detect Events Enhances Shear Wave Elasticity Imaging Performance

“…This situation is further exacerbated in viscoelastic estimators where researchers often attempt to estimate phase speed of individual shear wave spectral components [49]. Since the energy of a frequency component is much lower than that of the broadband signal, large variances are reported in the literature while estimating viscous attenuation (>50 Np/m in [50]). A common technique to tackle this issue is to use a larger shear wave propagation ROI [49], [51].…”