Figure 1.
Relationship between stiffness and signal-to-noise ratio (SNR).
a. In the noise-free case, measured stiffness will slightly overestimate the true stiffness due to discretization errors. The calculated stiffness then drops as noise increases. The SNR correction algorithm iteratively searches for the true stiffness that fits the measured stiffness and measured SNR. b. Example histogram of SNR within the brain. The distribution of SNR within the brain has a long right tail. Three summary measures of SNR were evaluated for the SNR correction algorithm: the mode (left-most arrow), the median of the most likely SNRs (middle arrow), and the median (right-most arrow).
Figure 2.
a. A curl wave image calculated with traditional postprocessing methods is shown in the top-left panel, while one calculated with adaptive methods is shown in the top-right. Note the edge discontinuities in the image on the left compared with that on the right. The elastogram calculated with traditional postprocessing in the bottom-left panel shows a larger edge-related bias (3 voxels wide) as compared to the elastogram calculated with adaptive processing in the bottom-right (1 voxel wide). b. Using traditional postprocessing methods, 3 erosions are required to completely remove edge-related bias. c. Using adaptive methods, no edge-related bias is apparent.
Figure 3.
Finite element model (FEM) simulations.
a. The true stiffness maps given to the FEM are shown on the left with increasing atrophy from top to bottom. The corresponding elastograms are shown on the right after downsampling the wave images to 3 mm resolution, calculating the curl, smoothing and calculating stiffness with a direct inversion algorithm. Voxels near the edge of the brain provide underestimates of the true stiffness. Increasing atrophy causes a systematic bias toward underestimated stiffness. b. Using traditional postprocessing methods, this bias can only be completely removed by eroding the ROI by 3 voxels from every edge. c. Using adaptive postprocessing methods, the edge-related bias is removed after only 1 erosion of the ROI.
Figure 4.
Effects of the SNR correction algorithm on noise-related bias.
a. Errors for the test-retest data are shown in the top panel. The markers represent the average inversion error over all exams before (red) and after (blue) SNR correction, and the bars represent the range from percentile 2.5 through 97.5 for each region (F=frontal lobes, O=occipital lobes, P=parietal lobes, T=temporal lobes, D=deep GM/WM, C=cerebellum). Two ROIs had a significant difference between μ0 and μn, as well as a significant relationship between inversion error and SNR (global and frontal). The parietal lobe ROI had only a significant relationship between inversion error and SNR. The absolute value of the errors was decreased by the algorithm in every ROI and the average error was never larger than 0.29%. b. For cross-validation, errors in the elderly cohort are shown in the bottom panel. The parietal lobe ROI had a significant relationship between inversion error and SNR, but no ROI had significant differences between μ0 and μn in this sample.
Figure 5.
Summary of the regional MRE pipeline.
a. The steps for regional stiffness measurement are summarized in the left panel. b. Example images are shown in right panel. At the top is the magnitude image from the MRE data with the frontal lobe ROI outlined in green. Below that image is the ROI-specific wave image, followed by the ROI-specific elastogram.
Figure 6.
Example images of the global ROI.
A T1 weighted image is shown in the top-left, and the corresponding T2 weighted magnitude image from the MRE data is shown in the bottom-left. In the top-center panel is the full brain mask in red, the brain mask after 1 erosion in green and the brain mask after 3 erosions in blue. The difference between the green and blue masks indicates the number of voxels saved by using adaptive methods while incurring no edge-related bias. In the bottom-center panel is the warped atlas in MRE space (red=frontal lobes, green=occipital lobes, blue=parietal lobes, yellow=temporal lobes, cyan=deep GM/WM, the global ROI is the union of all ROIs except for the cerebellum). The wave image is shown in the top-right panel, and the resulting elastogram after 1 erosion is in the bottom-right panel.
Figure 7.
Summary plot of the repeatability of regional brain stiffness measurements.
Each region contains 10 columns (corresponding to the 10 volunteers sorted by average global stiffness) and each column contains 3 markers (corresponding to the 3 MRE exams). The results indicate high test-retest repeatability (summarized in Table 2).
Figure 8.
Median stiffness as a function of SNR and ROI size.
As the ROI size increases, the median stiffness remains constant but the precision of the stiffness measurement improves.