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. 2021 Feb 26;66(5):10.1088/1361-6560/abd5ce.
doi: 10.1088/1361-6560/abd5ce.

Magnetic resonance shear wave elastography using transient acoustic radiation force excitations and sinusoidal displacement encoding

Affiliations

Magnetic resonance shear wave elastography using transient acoustic radiation force excitations and sinusoidal displacement encoding

Lorne W Hofstetter et al. Phys Med Biol. .

Abstract

A magnetic resonance (MR) shear wave elastography technique that uses transient acoustic radiation force impulses from a focused ultrasound (FUS) transducer and a sinusoidal-shaped MR displacement encoding strategy is presented. Using this encoding strategy, an analytic expression for calculating the shear wave speed in a heterogeneous medium was derived. Green's function-based simulations were used to evaluate the feasibility of calculating shear wave speed maps using the analytic expression. Accuracy of simulation technique was confirmed experimentally in a homogeneous gelatin phantom. The elastography measurement was compared to harmonic MR elastography in a homogeneous phantom experiment and the measured shear wave speed values differed by less than 14%. This new transient elastography approach was able to map the position and shape of inclusions sized from 8.5 to 14 mm in an inclusion phantom experiment. These preliminary results demonstrate the feasibility of using a straightforward analytic expression to generate shear wave speed maps from MR images where sinusoidal-shaped motion encoding gradients are used to encode the displacement-time history of a transiently propagating wave-packet. This new measurement technique may be particularly well suited for performing elastography before, during, and after MR-guided FUS therapies since the same device used for therapy is also used as an excitation source for elastography.

Keywords: MRgFUS; acoustic radiation force; elastography; magnetic resonance elastography; shear wave elastography; transient MRE; viscoelastic simulations.

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Figures

Figure 1.
Figure 1.
Pulse sequence timing diagram where the acquisition of data for sine (ϕsin), cosine (ϕcos), and reference (ϕref) images are interleaved on a repetition time level. The magenta line depicts timing of the FUS-induced impulse. For the sine and cosine encodings, the MR pulse sequence timing diagram is identical. However, the cosine encoding is achieved by shifting the timing of the FUS impulse by a π/2 offset relative to the sinusoid motion encoding gradient. For the reference image, no ARF impulse is applied. The reference image is used to correct for background phase change that is not due to ARF-generated displacements.
Figure 2.
Figure 2.
Intermediate calculation steps for the shear wave speed measurement. The cosine and sine phase images are depicted in (a) and (b). A 2D high-pass filtering step is applied to images (a) and (b) and these filtered images are combined using Equation (14) to generate the synthetic phase image. The argument of this synthetic phase image is depicted in (c). The radial derivative of (c) is computed and shown in (d). The shear wave speed map computed from (d) using Equation (17) is shown in (e). The orange ring of increased shear wave speed in (e) is located at a radial distance where the traveling waveform has not had sufficient time to propagate to by the end of the MEG encoding. Hence, regions outside of this position should be excluded from any analysis via masking. The masked shear wave speed map is overlaid on the magnitude image in (f).
Figure 3.
Figure 3.
(a) Shear wave elastography experimental setup. Orientation of FUS transducer, MR imaging volume, and homogeneous phantom are shown in (b). The six ARF excitation locations used for the measurement are depicted as red crosses in (c).
Figure 4.
Figure 4.
Simulation results for scenarios A-F outlined in Table 1. Column 1 highlights the key simulation parameters used. The displacement field, MR phase images, and shear wave speed measurement are depicted in columns 2, 3, and 4, respectively. The horizontal axis in all plots denotes the radial distance, measured from the origin in the x2 = 0 plane. The column 4 plots compare the actual shear waved speed (blue horizontal line) to the shear wave speed estimate made by applying Equation (17) to the simulated MR phase images.
Figure 5.
Figure 5.
Simulations for case F show the effect of the high-pass filtering step where (a) depicts the MR phase values, (b) the calculated shear wave speed estimates, and (c) the shear wave speed measurement error. For all plots, dotted lines represent phase images or shear wave speed measurements in which the 2D spatial high-pass filtering was applied to the phase images. The horizontal axis denotes the radial distance measured from the origin in the x2 = 0 plane. The gray horizontal line in (a) denotes the zero crossing position and the blue horizontal line in (b) denotes the actual shear wave speed of the medium (i.e., 1.5 m/s).
Figure 6.
Figure 6.
Plot grid showing MR image phase (top row), shear wave speed estimate (middle row), and simulated displacement field at the completion of the cosine encoding (bottom row) for 6ms (first column), 12ms (second column) and 18ms (third column) MEG durations. The MEG waveform period was 6ms for all scenarios. Gray vertical dotted line in all plots depicts the location of the peak displacement at a propagation time corresponding to the end of the cosine encoding. For radial distances beyond this peak displacement location, measurement error is large since the propagating shear wave packet hasn’t traveled beyond this position when the cosine encoding ends. For each encoding scenario, more accurate shear wave speed measurements are found for radial distances less than the measurement horizon as defined by the vertical gray lines.
Figure 7.
Figure 7.
Harmonic magnetic resonance elastography measurements performed at six different excitation frequencies are shown in row (a). The mean shear stiffness values, calculated over the 20×20-pixel ROI as depicted in red in the magnitude image, are plotted in (b), where the star denotes the mean value and the error bar denotes the standard deviation over the ROI. The fit-line and estimated values for shear modulus and shear viscosity are also shown.
Figure 8.
Figure 8.
Sine and cosine MR phase images from simulations (a,d) and experimental results (b,d) in homogeneous phantom. Horizontal line plots through the center of each phase image (a,b) and (d,e) are depicted in (c) and (f) respectively, where dashed and solid lines denote the simulated and experimental data, respectively. The 2D maps and line plots show close agreement between the simulated and experimental data.
Figure 9.
Figure 9.
Shear wave speed maps computed from simulation (a, d) and experiment (b, e) show that the high-pass filtering step improves measurement uniformity in a homogeneous phantom. Horizontal line plot through maps (a,b) and (d,e) are depicted in (c) and (f) respectively, where the black dashed and solid line represent simulated and real data, respectively. The line plot is constructed by plotting the measured shear wave speed values positions on the horizontal line going through the center of each image, which coincides with the ARFI excitation location. Vertical red dotted lines in (c) and (f) denote the position of the simulated wave-packet peak when the cosine encoding ends. For positions beyond this location, the shear wave speed estimate is unreliable since the displacement encoding ends before the wave-packet peak has travel to those positions. Comparison of shear wave speed measurement performed on simulated and experimental data is provided to confirm usefulness of simulation approach to assess transient elastography approaches—measurement errors seen in experiment were closely modeled by measurements performed on simulations.
Figure 10.
Figure 10.
Individual masked shear wave speed measurements for each ARF excitation position are shown in (a-f) with composite shear wave speed map overlaid on magnitude image in (g).
Figure 11.
Figure 11.
MR phase (a, b) and individual shear wave speed maps (c) for each ARF impulse location in the inclusion phantom.
Figure 12.
Figure 12.
Reformatted gradient echo magnitude image showing stiffer inclusions in (a) and composite shear wave speed map shown as a color overlaid on the segmented-EPI magnitude image in (b). The coronal slice positions for (a) and (b) were the same. Adding egg white albumin to inclusions makes them readily visible on T1-weighted magnitude images. The shear wave speed map correctly identifies the shape and position of the three stiffer inclusions.

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