Validation of echo planar imaging based diffusion-weighted magnetic resonance imaging on a 0.35 T MR-Linac

Background and Purpose The feasibility of acquiring diffusion-weighted imaging (DWI) images on an MR-Linac for quantitative response assessment during radiotherapy was explored. DWI data obtained with a Spin Echo Echo Planar Imaging sequence adapted for a 0.35 T MR-Linac were examined and compared with DWI data from a conventional 3 T scanner. Materials and Methods Apparent diffusion coefficient (ADC) measurements and a distortion correction technique were investigated using DWI-calibrated phantoms and in the brains of seven volunteers. All DWI utilized two phase-encoding directions for distortion correction and off-resonance field estimation. ADC maps in the brain were analyzed for automatically segmented normal tissues. Results Phantom ADC measurements on the MR-Linac were within a 3 % margin of those recorded by the 3 T scanner. The maximum distortion observed in the phantom was 2.0 mm prior to correction and 1.1 mm post-correction on the MR-Linac, compared to 6.0 mm before correction and 3.6 mm after correction at 3 T. In vivo, the average ADC values for gray and white matter exhibited variations of 14 % and 4 %, respectively, for different selections of b-values on the MR-Linac. Distortions in brain images before correction, estimated through the off-resonance field, reached 2.7 mm on the MR-Linac and 12 mm at 3 T. Conclusion Accurate ADC measurements are achievable on a 0.35 T MR-Linac, both in phantom and in vivo. The selection of b-values significantly influences ADC values in vivo. DWI on the MR-Linac demonstrated lower distortion levels, with a maximum distortion reduced to 1.1 mm after correction.


Supplementary Material A. Brain Image Segmentation and Registration
The brain volume was extracted from the T1-w images using HD-BET [1] with default parameters.The T1-w images were automatically segmented within the brain masks into the three tissue types cerebrospinal fluid (CSF), gray matter (GM) and white matter (WM) using the FAST function [2] of the FSL software library [3].For each tissue type, a partial volume effect (PVE) image was created by FAST, which contains for each voxel the confidence of the classification to the given tissue on a scale from 0 to 1.The T1-w images were linearly registered and resampled to the distortion-corrected DWI coordinates (to the  = 0 / 2 image) using the function FLIRT [4,5].The same transformation was applied to the brain volume and the PVE segmentation images in order to transform them into the DWI coordinates.After the registration, a threshold of 0.8 was applied to the PVE images in order to create binary masks.For the CSF, we restricted the analysis to the homogeneous region of the ventricles by excluding voxels that were not in the brain mask after a 20 mm erosion thereof.The resulting segmentations on the T1-w image and ADC map for one slice of one subject is shown in figure A.5(a).

DWI Postprocessing
The susceptibility distortion in each DWI was corrected using the Topup function [6] from the software library FSL [3].The function uses image data from the two  = 0 / 2 acquisitions with opposite phase encoding directions to estimate an off-resonance field.The off-resonance field is used to apply a susceptibility distortion correction to the pair of images with opposite phase encoding direction at each b value and gradient direction.The resulting images are substantially more spatially accurate, although distortions due to eddy currents induced by the diffusion gradients are not compensated in this manner.The corrected images were used for further analysis.
The apparent diffusion coefficient (ADC) was calculated for the MR-Linac data using a voxelwise mono-exponential least-squares fit over the signal intensities of the different b-images.The relationship is expressed with the formula   =  0 (− ), where   is the signal intensity at the given voxel for a given b value,  0 is the theoretical baseline intensity of that voxel.Both  0 and ADC were used as variables in the fit.The data points were all weighted equally for the fit.Since images with three different diffusion directions were acquired at the MR-Linac, the data of these acquisitions had to be combined in order to calculate a single, isotropic ADC.This was achieved by calculating for each voxel the geometric mean of the signal intensity across the different diffusion gradient directions at each b value before the ADC fit.At the 3 T scanner, we used the trace-weighted images for the higher b-value, which already combines all diffusion directions.In vivo, ADC values above 4500  2 / (about 1.5 times the ADC of free water at 37°) were considered as measurement errors and thus ignored.(For   , this was the case for about 21% of CSF voxels, 1% of GM voxels and less than 0.01% of WM voxels.For  0,800 and  3 , a failure of fit was the case for less than 0.01% of voxels in all tissues) For DWI at low SNR, the non-zero noise floor that exists in the images can lead to biased intensity values, particularly at images with high b values [7].A correction of the intensities for uniform Rician noise was applied prior to the ADC fit at the MR-Linac with the following formula:   = √ 2 − (2/) 2 , where   is the corrected intensity value at a given voxel,  is the acquired intensity value at the voxel and N is the mean intensity in the background of the image [7].Inhomogeneities in the noise distribution introduced by parallel imaging were neglected in this case.We determined a background mask in the images as a large, manually selected cuboid volume, as shown in Figure A.2.
To quantify the distortion of the images, the off-resonance field estimated by Topup was used to calculate the magnitude of distortion along the phase encoding direction at each point in the image using the formula ∆ = (∆/  )  , where x is the spatial distortion in the phase encoding direction, ∆ is the off-resonance frequency,   is the length of a voxel in the phase encoding direction, and   is the receiver bandwidth per pixel in the phase encoding direction.The latter can be calculated for the ssEPI sequences as   = /(  ), where  is the parallel imaging acceleration factor,   is the number of phase encoding steps acquired (not accounting for partial fourier) and  is the echo spacing.For the sequence at the MR-Linac, we had  = 2,   = 100 and  = 0.8 , therefore   = 25 /.For the sequence at the 3 T scanner, we had  = 2,   = 192 and  = 1.04 , therefore   = 10 /.
The ADC values obtained without Topup correction, shown in Figure A.7, showed similar accuracy of the median for the 3 T scanner.For the MR-Linac, the values for vials 1 and 2 were higher or lower without Topup correction, depending on the phase-encoding direction.The standard deviation of ADC values was always higher without Topup correction.        .The median at the 3 T scanner deviates by less than 1% between the approaches, but the standard deviations are slightly larger without Topup.For the MR-Linac, the medians for vials 3 and 4 also differ by less than 1% between the methods, but for vials 1 and 2, the median is about 1.5% lower or higher without Topup, depending on the phase encoding direction.The standard deviations are also slightly larger without Topup.

Figure A. 1 :
Figure A.1: Head & neck coil setup with immobilization device for brain imaging at the MR-Linac.

Figure A. 2 :
Figure A.2: (a) A slice of the  = 0 / 2 acquisition for one volunteer with the prescan normalize filter applied.(b) The same slice without prescan normalize filter.In both cases, the purple region represents the manually selected background region.The images are shown with the same intensity window to highlight differences in the background noise pattern.

Figure A. 3 :
Figure A.3: Temperature correction scheme for ADC values described in the manual of phantom 1.

Figure A. 4 :
Figure A.4: (a) A slice of the ADC map of the ADC phantom acquired with the MR-Linac along with four contoured vials.(b) The same contours shown on the ADC map acquired with the 3 T scanner.(c) Box plots of signal intensity values after noise correction divided by the baseline signal S0 (as obtained from the fit) at the MR-Linac for the vials and b-values.Median ADC value trajectories and trajectory intervals containing 95% of ADC values are shown.

Figure A. 5 :
Figure A.5: (a) T1-w scans, ADC maps and segmentations for both scanners for one subject.(b) Box plots of signal intensity values after noise correction divided by the baseline signal S0 obtained from the fit for one subject at the MR-Linac for the tissues and only the two b-values 0 / 2 and 800 / 2 .Median ADC value trajectories and trajectory intervals containing 95% of ADC values are shown.(c) ADC values for each subject and in each tissue calculated at the MR-Linac using different methods and at the 3 T scanner.Kernel density estimation was created with silverman bandwidth estimation.Median ADC values shown as vertical lines in each

Figure A. 6 :
Figure A.6: (a) Histograms comparing the   values for each volunteer subject and in each tissue calculated at the MR-Linac with and without noise correction.Kernel density estimation was created with silverman bandwidth estimation.The vertical lines represent the median ADC value in each case.Subjects 2 and 6 were not reconstructed without the prescan normalize filter, therefore the background noise is underestimated, leading to a smaller noise correction.(b) The same histograms, but for  0,800 .

Figure A. 7 :
Figure A.7: ADC values determined in phantom vials using distortion corrected image (topup) compared to using only one phase-encoding direction, AP or PA, without distortion correction (no topup).The median at the 3 T scanner deviates by less than 1% between the approaches, but the standard deviations are slightly larger withoutTopup.For the MR-Linac, the medians for vials 3 and 4 also differ by less than 1% between the methods, but for vials 1 and 2, the median is about 1.5% lower or higher without Topup, depending on the phase encoding direction.The standard deviations are also slightly larger without Topup.

Table A .
1: Imaging parameters of the MRI sequences used on both devices.

Table A .
2: The p-values of the two-tailed paired Wilcoxon signed-rank tests between the different ADC measurements to compare the mean and median ADC values within each VOI for all subjects.Repeated pvalues are a result of the same outcome of the test statistic.