Focused Shear Wave Beam Propagation in Tissue-Mimicking Phantoms

Abstract

Objective: Ultrasound transient elastography (TE) technologies for liver stiffness measurement (LSM) utilize vibration of small, flat pistons, which generate shear waves that lack directivity. The most common cause for LSM failure in practice is insufficient shear wave signal at the needed depths. We propose to increase shear wave amplitude by focusing the waves into a directional beam. Here, we demonstrate the generation and propagation of focused shear wave beams (fSWBs) in gelatin.

Methods: Directional fSWBs are generated by vibration at 200-400 Hz of a concave piston embedded near the surface of gelatin phantoms and measured with high-frame-rate ultrasound imaging. Five phantoms with a range of stiffnesses are employed. Shear wave speeds assessed by fSWBs are compared with those by radiation-force-based methods (2D SWE). fSWB amplitudes are compared to predictions using an analytical model.

Results: fSWB-derived shear wave speeds are in good agreement with 2D SWE. The amplitudes of fSWBs are localized to the LSM region and are significantly greater than unfocused shear waves. Overall agreement with theory is observed, with some discrepancies in the theoretical source condition.

Conclusion: Focusing shear waves can increase the signal in the LSM region for TE. Challenges for translation include coupling piston vibration with the patient skin and increased attenuation in vivo compared to the phantoms employed here.

Significance: Fibrosis is the most predictive measure of patient outcome in non-alcoholic fatty liver disease. Increased shear wave amplitude in the LSM region can reduce fibrosis assessment failure rates by TE, thus reducing the need for invasive methods like biopsy.

Fig. 1.

(a) Cross-sectional schematic of the spherically concave piston. (b) Cylindrical coordinate system ($\mathit{r}$, $\mathit{z}$) and displacement polarizations of a focused shear wave generated by the concave piston; antisymmetric shear wave coalescence results in strong longitudinal (z-polarized) motion in the focal region. (c,d) Imaging configurations for measurement of the (c) transverse and (d) longitudinal components of the motion. Images in each configuration are acquired from outside of the acrylic tank, through the tank wall. Green dashed boxes indicate the imaging regions in each configuration.

Fig. 2.

Block diagram of the signal path (US = Ultrasound).

Fig. 3.

Time snapshot of (a) transverse and (b) longitudinal displacement components of the 200 Hz focused shear wavefield. Displacement data in (a) and (b) are plotted in the imaging regions corresponding to Figs. 1(c) and (d), respectively. Imaging regions and piston are presented to scale in (a) and (b).

Fig. 4.

Measured longitudinal displacement field ${\mathit{u}}_{\mathit{z}}$ along the $\mathit{z}$ axis ($\mathit{r}\hspace{0.17em}=\hspace{0.17em}0$) versus time and propagation distance $\mathit{z}$ in Phantom I, including contributions from both compressional and shear waves, for piston excitation at (a) 200 Hz, (b) 300 Hz, and (c) 400 Hz. Computed shear wave speed ${\mathit{c}}_{\mathit{t}}$ is presented for each frequency. Compressional and shear waves are labeled in each panel.

Fig. 5.

Measured longitudinal displacement field ${\mathit{u}}_{\mathit{z}}$ along the $\mathit{z}$ axis ($\mathit{r}\hspace{0.17em}=\hspace{0.17em}0$) versus time and propagation distance $\mathit{z}$ in Phantoms III–V for piston excitation at 200 Hz. Gelatin (gel) concentration and computed shear wave speed ${\mathit{c}}_{\mathit{t}}$ are presented for each.

Fig. 6.

Beam patterns of the longitudinal shear wave for excitation at (a) 200 Hz, (c) 300 Hz, and (e) 400 Hz in Phantom I. The piston schematic is drawn to scale in the left column. Cross-sections of beam patterns for (b) 200 Hz, (d) 300 Hz, and (f) 400 Hz in the plane perpendicular to the $\mathit{z}$ axis at which each field achieves a maximum value at $\mathit{r}\hspace{0.17em}=\hspace{0.17em}0$. Measured beamwidth (BW) for each frequency is given above each panel.

Fig. 7.

Measurements (black) and best-fit simulations (blue) of longitudinal shear wave displacement amplitude $|{\mathit{u}}_{\mathit{z}}|$ along the beam axis ($\mathit{r}\hspace{0.17em}=\hspace{0.17em}0$) versus propagation distance for the wavefields at (a) 200 Hz, (b) 300 Hz, and (c) 400 Hz in Phantom I. Values of the fit parameters $\mathit{a}$, $\mathit{d}$, and $\mathit{\alpha }$ are given for each frequency. Grey portions in (b) and (c) represent signal that does not correspond to the shear wave and was not used in the curve fitting process.

Fig. 8.

Measurements (black) and best-fit simulations (blue) of longitudinal shear wave displacement amplitude $|{\mathit{u}}_{\mathit{z}}|$ along the beam axis ($\mathit{r}\hspace{0.17em}=\hspace{0.17em}0$) versus propagation distance for the wavefields at 200 Hz in Phantoms III–V. Gelatin (Gel) concentrations are given in each panel.

Fig. 9.

Comparisons along the $\mathit{z}$ axis of the shear wave amplitude in focused (Phantom I) and unfocused beams. (a) Comparison with simulated field for a small flat piston (50 Hz, $a\hspace{0.17em}=\hspace{0.17em}\mathbf{6}\hspace{0.17em}\mathrm{mm}$) modeled after the Fibroscan XL. (b) Comparison with measured (Phantom VI) and simulated fields from a large flat piston (200 Hz, $a\hspace{0.17em}=\hspace{0.17em}\mathbf{19}\hspace{0.17em}\mathrm{mm}$) for which the last axial maximum was approximately matched to the focal length of the focused beam.