Asynchronous magnetic resonance elastography: Shear wave speed reconstruction using noise correlation of incoherent waves

FIGURE 1. Numerical simulations of wave speed reconstruction using spatial–temporal correlations. A, Diffuse wavefield simulation using k‐wave, 22 an acoustics library programmed in MATLAB, and characteristic decay in space and time of the correlation function for three sample points. The source code and time‐series images are available as Supporting Information. B, The ratio of the decay in space to the decay in time leads to a pixelwise reconstruction of wave speeds. Three reconstructions are shown for different levels of measurement noise in the form of additive white Gaussian noise. Higher noise levels lead to a systematic overestimation of wave speeds

FIGURE 2. Imaging protocol for asynchronous magnetic resonance elastography (aMRE). Flow chart for the aMRE protocol combines information from two scans designed to separately measure the temporal and spatial properties of a diffuse wavefield. Abbreviations: GRE, gradient echo; MEG, motion‐encoding gradients

FIGURE 3. Snapshots for aMRE protocol on an elastography phantom. A, Illustration of the box‐shaped phantom, the imaging plane, the spherical inclusions of varying stiffnesses, and the finger tapping on the top of the box. A T2‐weighted image is also shown that overlaps the known wave speeds in units of m/s. B, C, The first few reconstructed images of the temporally resolved and spatially resolved phase‐contrast scans. All velocity measurements were sensitized along the phase‐encoding direction

FIGURE 4. Shear wave speed reconstruction of elastography phantom. A, The reconstructed wave speeds sampled at τ=53 ms or f=19 Hz with manually drawn regions of interest for the background and each of the four spherical inclusions. The averaged wave speed is overlaid on each region. B, Plotting true wave speeds against measured wave speed using pixels from the regions of interest show a strong correlation and that aMRE can reconstruct wave speeds. The fitted line is a linear regression using the average of each region of interest and its true wave speed

FIGURE 5. Proof of concept in vivo thigh scan using aMRE and finger tapping. A, B, The first few reconstructed images of the temporally resolved and spatially resolved phase‐contrast scans for a healthy volunteer (male, 29 year old). The entire time series is available as Supporting Information. C, Averaging the absolute velocity over the thigh cross‐section shows that, over time, the phase signal from finger tapping is consistently higher than without tapping over time. The dashed horizontal lines further average the signals in time to quantitatively show the difference between tapping and without tapping

FIGURE 6. Wave speed reconstruction of in vivo thigh scans. Three aMRE protocols were implemented on 2 healthy male volunteers. The wave speeds were sampled at τ≈95 ms or f≈11 Hz for the three scans. Snapshots of the first scan on the left are displayed in Figure 5