Fig 1.
(A) Original 3D FatNav volume acquired at 4 mm isotropic resolution. (B) A low-resolution 3D FatNav volume was obtained from the ACS lines obtained from the original data via the iFFT. (C) To calculate the B1 maps, the low-resolution 3D FatNav volume was divided by the root-sum-of-squares of all channels’ coil volumes. (C) The B1 field maps of one channel calculated for one dataset. Maps were calculated for each channel of all the five datasets using the correspondent ACS lines acquired prior to the scan. Notice how the field is smooth close to the fat layer, but the SNR degrades rapidly towards the centre of the brain.
Fig 2.
Schematic representation of the process performed to calculate the 3D FatNavs tracking accuracy for 225 different combinations of motion parameters (ranged between 0–40 mm translations and 0–20° rotations).
One set of 6 motion parameters were applied to the high-resolution 3D FatNav volumes (obtained via GRAPPA reconstruction) using SPM. The transformed 3D FatNav volumes were multiplied by the B1 maps to find the transformed volume for each coil. Each volume was then undersampled using an acceleration factor of R = 16 (4x4) and re-reconstructed using GRAPPA to simulate the final corrupted 3D FatNav volumes if head motion occurred during the scan. By co-registering the initial high-resolution volume and the corrupted volume it was possible to find the estimated motion parameters if 3D FatNavs were used. These motion parameters were compared to the real motion parameters applied to find the residual motion (or estimation error). The same steps were repeated for all motion traces for each dataset. The residual motion was averaged across the three datasets to find the 3D FatNavs tracking accuracy, from which it was possible to estimate the residual motion from any new motion trace via linear interpolation.
Fig 3.
Smooth and rough motion parameters.
Example of smooth (A) and rough (B) motion parameters randomly generated with RMS = 2.25 mm and RMS = 5.53° and RMS = 2.01 mm and RMS = 1.88° for translations and rotations.
Fig 4.
Summary of the process used to test the 3D FatNavs tracking accuracy on MPRAGE images, together with an example for a set of smooth motion parameters.
A total of 192 motion traces were generated, 96 for smooth motion and 96 for rough motion, within a range of 0–40 mm translations and 0–20° rotations. For each motion trace, the residual motion was found via linear interpolation of the 3D FatNavs motion accuracy previously found (Fig 2). The residual motion was then applied to the motion-free MPRAGE volume. The image quality assessment was performed using the GE metric and evaluation from an observer using a scale between 1 to 4, with 4 denoting no visible motion artifacts.
Table 1.
Summary of the statistical analysis.
Fig 5.
Comparison between 3D FatNavs volume before and after GRAPPA "re-reconstruction".
The figure shows the effect of mismatched ACS data to the 3D FatNavs volumes for four different levels of motion (tables on the left): parallel imaging artifacts are shown to increase with the amount of motion. The “Transformed 3D FatNav volumes” are obtained after applying the motion parameters using SPM. The volumes are then multiplied by the B1 maps and undersampled using an acceleration factor R = 16. The “Corrupted 3D FatNav volumes” are obtained by reconstructing the undersampled volume.
Fig 6.
Multinomial logistic regression between image evaluations and the GE in case of smooth and rough motion for dataset (A) 1, (B) 2 and (C) 3. All evaluations, from 1 to 4, are plotted as blue vertical lines, while each colored Gaussian waveform represents the probability of falling in one of the four evaluation’s categories: category 4 (no visible artifacts) in purple, category 3 (some motion artifacts) in yellow, category 2 (strong motion artifacts) in orange and category 1 (severe motion artifacts) in black. Lower entropy values corresponded to higher category rating and, therefore, to a better image quality.
Table 2.
One-way ANOVA test.
Fig 7.
Estimated motion level at each category boundary.
The motion levels were estimated as the average across the three datasets for smooth and rough motion in the cases of 3D FatNav-based correction or without motion correction. 3D FatNav-based correction shows a high tolerance to motion, whereas the image quality decreases faster for MPRAGE images without motion correction. Category definition: 4 = no visible motion artifacts, 3 = some motion artifacts, 2 = strong motion artifacts and 1 = severe motion artifacts.
Table 3.
Statistical parameters of the linear regression model.
Table 4.
RMS values at image quality category boundaries.
Fig 8.
Comparison of the linear and non-linear model fitting of the GE values as a function of the mean FD in case of smooth and rough motion.
The mean FD values were estimated from the residual motion resulting after 3D FatNav-based motion correction for dataset (A) 1, (B) 2 and (C) 3. The mean FD values estimated from the rough motion case are much larger (up to 12 mm for Dataset 3) compared to the FD range displayed for smooth motion. Nevertheless, the non-linear model is shown to fit the data more accurately than the linear model both for smooth and rough motion. This is corroborated by the estimated R-squared values for the three datasets: the estimated values for smooth and rough motion were 0.91/0.88/0.87 and 0.87/0.78/0.75 using the linear regression model, and 0.95/0.97/0.97 and 0.98/0.98/0.98 when using non-linear regression model, showing a clear improvement in the fitting when the latter is adopted.
Fig 9.
Comparison between mean FD values for smooth and rough motion parameters.
The mean FD values were estimated using the residual motion (remaining motion after 3D FatNavs motion correction) in presence of smooth (blue dots) and rough (orange dots) motion for datasets (A) 1, (B) 2 and (C) 3. A logarithmic regression model (described in Fig 8) was fitted to the data and is plotted as a continuous red line. The mean FD is shown to differentiate between smooth and rough motion, except for mean FD values up to ~1.2 mm which are shown to overlay. This suggests that, if appropriately scaled, the FD metric could be adopted to measure the quantity of motion as well as to discern between types of motion which occurred during an MRI acquisition.