Whole‐Brain Water Content Mapping Using Super‐Resolution Reconstruction with MRI Acquisition in 3 Orthogonal Orientations

<jats:sec><jats:title>Purpose</jats:title><jats:p>Brain water content provides rich tissue contrast comparable to that of longitudinal relaxation time T<jats:sub>1</jats:sub>, but mapping is usually performed at modest resolution. In particular, the slice thickness in 2D mapping methods is limited. Here, we combine super‐resolution reconstruction techniques with a fast water content mapping method to acquire high and isotropic resolution (0.75 mm) water content maps at 3 Tesla.</jats:p></jats:sec><jats:sec><jats:title>Methods</jats:title><jats:p>A high‐resolution multi‐echo gradient echo image is super‐resolution–reconstructed from 3 low‐resolution, orthogonal multi‐echo gradient echo image acquisitions, followed by water content mapping. The mapping accuracy and SNR of the proposed method are assessed using numerical simulations, phantom studies, and in vivo data acquired from 6 healthy volunteers at 3 Tesla. A high‐resolution acquisition with an established mapping method is used as a reference.</jats:p></jats:sec><jats:sec><jats:title>Results</jats:title><jats:p>Whole‐brain water content maps with 0.75 mm isotropic resolution are demonstrated. No bias in the water content values was seen following super‐resolution reconstruction. In the in vivo experiments, a lower SD of the mean water content values was observed with the proposed method compared to the reference method.</jats:p></jats:sec><jats:sec><jats:title>Conclusions</jats:title><jats:p>Super‐resolution reconstruction of multi‐echo gradient echo data is demonstrated, enabling whole‐brain water content mapping with high and isotropic resolution. The accuracy of the proposed method is shown using phantoms and 6 healthy volunteers and was found to be unchanged compared to the conventional acquisition. The proposed method could increase the sensitivity of water content mapping sufficiently to enable the detection of very small lesions, such as cortical lesions in multiple sclerosis.</jats:p></jats:sec>

section_content: Water content in the healthy brain is tightly regulated, 1, 2 and disturbances in the normal homeostasis are indicative of either systemic or local pathology. 4] [5] [6] MRI-based methods offer a way to measure water content, [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] thus enabling the detection of changes in tissue integrity noninvasively and quantitatively. 

Oros-Peusquens et al. described a technique for water content mapping where additional corrections for T 1 weighting are no longer necessary, eliminating the need for additional scans. 10 This is achieved with a 2D interleaved multi-slice multi-echo gradient recalled echo (mGRE) acquisition with a long TR, reducing the acquisition time for water content mapping to within a clinically feasible time. The sequence is usually included in the manufacturer's software on clinical scanners, making this a fast and easy-to-access quantitative method for clinical applications. However, the sensitivity of the method for voxels at interfaces between CSF, gray matter (GM), and white matter (WM) suffers due to partial volume effects. In order to reduce this and increase the sensitivity of the technique to small lesions, isotropic, high-resolution water content maps are desirable. High-resolution mapping is also beneficial for clinical applications where a few additional minutes of measurement time might be justified by the increased diagnostic power, for example, in subtle pathologies such as epilepsy or MS. High resolution can in principle be achieved using 3D water content-mapping techniques. 19, 20 However, for the equivalent quantitative power, these techniques suffer from a substantial increase in acquisition time compared to the simple single-scan 2D technique. 

The resolution in the slice select direction is inherently limited in the 2D mGRE acquisitions with normal pulses due to limited gradient power and deterioration of slice profile performance. Furthermore, the shortest achievable TE increases for thinner slices, which is a disadvantage for this quantitative method as it requires extrapolation of the signal to t = 0. Furthermore, contributions of fast-relaxing water pools, such as myelin water, 13, 14 are better characterized by short TEs. Due to the prolongation of the minimum first TE with decreasing slice thickness and the difficulty in selecting very thin slices, many vendor mGRE sequences have a hard limit on the minimum slice thickness achievable. Specifically, for the mGRE sequence on the 3T MR system used here (sequence name: "gre," 3T PRISMA, Siemens, Erlangen, Germany), the minimum slice thickness is 1. 5 mm, thus precluding the acquisition of water content maps with an isotropic resolution of 1 mm or lower with a single mGRE acquisition. 

In response to this problem, we present a technique to increase the spatial resolution of the water content maps by combining information from multiple low-resolution images commonly termed as a super-resolution reconstruction (SRR). 4] [25] [26] [27] [28] The technique presented in this paper is based on those proposed by Poot et al. 29 The 3 main acquisition schemes for multi-slice SRR are: (1) multiple LR acquisitions with a subpixel shift in the slice-select direction 28 ; (2) multiple LR acquisitions with different slice select directions rotated around the phase-encoding direction, each with a low through-plane resolution 26, 27, 30 ; and (3) 3 orthogonal anisotropic LR acquisitions. 25, 31 In the current work, the 3 orthogonal anisotropic LR acquisition scheme was selected in combination with the conjugate gradient-based SRR technique as it affords efficient sampling of the higher frequencies in all 3 orthogonal directions. As pointed out by Scheffler, 22 due to the Fourier-encoding nature of the MR acquisition and the equivalence of k-spaces acquired with an in-plane subvoxel shift, the improvement in resolution by SRR is limited to the slice selection direction. Hence, this work was aimed at improving the through-plane resolution. 

The impact of the SRR acquisition and reconstruction on accuracy and resolution of the water content values was assessed and quantified with the help of simulations and phantom studies. Based on evaluations from 6 healthy volunteers, simulations, and phantom studies, we show that an isotropic HR mGRE image can be accurately reconstructed from a set of 3 orthogonal LR mGRE acquisitions, allowing water content mapping to be subsequently carried out to produce high-resolution water content maps of isotropic voxel size.
section_name: INTRODUCTION

section_name: THEORY

section_content: The SRR model we propose here is an extension of the SRR model in Ref. 29 for mGRE images and reconstructs an HR mGRE object from multiple LR mGRE acquisitions. 21, 30 Given a set of N LR mGRE magnitude images (LR 1, …., LR N ), it is possible to reconstruct a single HR mGRE magnitude image (HR) as follows. Let S (ns ⋅ M × 1) be the signal intensities of the th LR image (LR ), where ∈ {1, …, N}; ns is the number of voxels at each echo of the LR image; and M is the number of echoes in the mGRE image. Let O(m ⋅ M × 1) be the vector of the HR object that we aim to reconstruct, where m is the number of voxels in the HR image. The acquisition of S can then be modeled as:

where e (ns ⋅ M × 1) represents the noise corresponding to the th LR image and X (ns ⋅ M × m ⋅ M) is the transformation matrix that maps O to the th LR image. In Ref., 29 the transformation matrix X ′ (ns × m) is obtained for the case of a 3D GRE image using a method based on a set of shear transforms. In the current work, the implicitly constructed X ′ was replicated for the case of 4D GRE images to form X. Also note that S was vectorized in such a way that the voxels from the different echoes are concatenated 1 after the other. The acquisition of the vector S(ns ⋅ M ⋅ N × 1), containing all LR image voxels from all the LR images, can be modeled as:

with

. 

. 

The problem of estimating O is then reduced to a minimization problem of finding the optimum O such that the squared difference between the predicted LR images and the actual LR images is minimized. However, because of the large number of unknown voxels to be estimated, and due to the presence of noise, the least-squares problem is ill-conditioned. Hence, a Laplacian regularization was used by adding an additional term in the above least squares problem as follows:

where K is an operator that computes the partial second derivatives of O. This regularized least-squares problem was solved efficiently using the conjugate gradient method. 32 With the exception of the incorporation of the multiple echoes, the remaining theory and approach to the solution, including the choice of regularization and the conjugate gradient solver, are identical to what was described in Ref. 29
section_name: Super-resolution reconstruction for mGRE

section_content: Water content mapping
section_name: 2.2

section_content: Reference method (long-TR method)

In Ref., 10 the water content maps are derived from a spoiled mGRE. Denoising using a principal component analysis-based technique 33 was carried out on the mGRE image. The steady-state signal equation from a voxel of uniform magnetization, M 0, for perfect transverse spoiling can be modeled as:

where S(TE) is the signal at TE; nom is the nominal flip angle (FA); and B1 + is the normalized correction for deviations in the transmit field. S 0 is the signal intensity at time t = 0, and C rec accounts for the inhomogeneities in the receive field. SF is the T 1 saturation factor, which, for the parameters TR = 10s and nom = 90

• as in Ref., 10 becomes negligible for all tissues except CSF. The value of SF is more than 0. 993 for T 1 < 2 s (the upper limit of T 1 in healthy brain tissue at 3 T 34 ). In Equation 5, the corrections from both the transmit field, sin

, and the receive field, C rec, become multiplicative and are therefore combined in a single factor, C bias. This combined transmit-receive correction was computed using SPM12 based on the unified segmentation theory described in Ref. 35 The saturation factor for CSF was computed using T 1 of 4300 ms 36, 37 and a constant B1+ inhomogeneity value of 0. 8, resulting in a steady-state signal reduction value of 0. 90. The B1+ distribution was measured for 2 volunteers using actual flip angle imaging, 38 with very similar results. The B1+ correction value in the center of the head (CSF voxels) was close to 0. 8, and this is the value used for water content calibration to CSF throughout this study. Equation 5 thus simplifies to:

S 0 and T2 * were extracted by fitting the signal decay in Equation ( 7 ) with a mono-exponential function. S 0 is used to calculate the voxel-wise relative water content by normalizing it to the fitted S 0 in the CSF voxels after correcting for the remnant T 1 saturation effect (S 0csf )

F I G U R E 1 Schematic workflow of the proposed method (SRR-H 2 O ). Abbreviation: SRR, super-resolution reconstruction.
section_name: 2.2.1

section_content: The SRR reconstructed HR mGRE image was obtained as described in section 2. 1 from a set of 3 orthogonal LR mGRE images. This image was then used for water content mapping in a manner shown schematically in Figure 1. The method described above (section 2. 2. 1) was used for water content mapping, with 2 modifications: 1) In the reference method, the phase data were used to map the inhomogeneity of the static field, B 0, and to derive a voxel-specific number of echoes to be used to fit the T 2 * decay. 9, 29 Because the SRR-H 2 O method employed here only reconstructs magnitude images and not the phase images, in this work all 11 echoes were included in the T 2 * fitting. 

2) The experiments reported here used TR = 3300 ms and FA = 15

• for reasons that are discussed in section 2. 2. 3. 

These values ensure a T 1 saturation factor of 0. 993 for T 1 < 2 s (within normal brain tissue limits). For CSF, with the SRR-H 2 O method, the SF calculated using Equation 6 becomes 0. 97 as opposed to 0. 90 for the reference method.
section_name: Proposed method (SRR-H 2 O)

section_content: This section compares the SNR and acquisition time of a direct HR acquisition for water content mapping to the SNR and acquisition time of an SRR reconstructed volume in the same total scan time. The mGRE image for water content mapping can be obtained using 2 approaches: 1) a direct HR mGRE acquisition of an isotropic voxel size; or 2) SRR with the 3-orthogonal scheme, whereby 3 orthogonal, anisotropic LR mGRE acquisitions with 3 times the slice thickness (voxel size = vs ⋅ 3) are used to reconstruct a single isotropic mGRE dataset with a voxel size of vs. The optimal through-plane to in-plane ratio of the LR images (known as the anisotropy factor) is application-specific. 39 For the 3-orthogonal acquisition scheme employed here, we use an optimal anisotropy factor of 3. 31 For considerably shorter TRs, if the number of echoes is kept to the maximum allowed (12 echoes), the number of slices might become a limiting factor, thereby favoring the use of approach 2. In order to compare the direct HR acquisition to the SRR acquisition, we chose a protocol in which the 2 high-resolution mGRE images obtained using the 2 approaches have equal acquisition times by setting the TR of the SRR acquisition to one-third of the TR of direct HR acquisition. The FA, α, for all the acquisitions was chosen such that SF = 0. 993 for a T 1 of 2 s. The SNR of the first echo of an mGRE image then depends on the slice thickness (ST) and α:

ST is 3 times higher in the SRR approach than that of the direct HR approach, but α is higher in the direct HR approach. We compared the SNR gain with varying TRs in both approaches by performing a numerical simulation. This theoretically predicted SNR was further validated with 5 scans of a carrageenan phantom using different TRs for both approaches. The results and implications are described in section 4. 1.
section_name: SRR-H 2 O acquisition settings

section_name: METHODS

section_content: The aims of the numerical simulations were the following:

(1) Evaluate the accuracy of SRR-H 2 O method. 

(2) Study the effect of SNR on the accuracy of SRR-H 2 O method. 

(3) Provide an experimental basis for the selection of the regularization factor,, used for the SRR reconstruction. 

Experiments were conducted on a numerical water content phantom, which was generated as described in the Supporting Information Text S1. To evaluate the effect of SNR and the on the accuracy of SRR-H 2 O method, different combinations of SNR and regularization values were studied. The effects of on the mean absolute error (MAE) and on the smoothing of the water content maps were assessed. MAE was calculated by computing the mean of the absolute difference between the water content values obtained from the SRR reconstruction and the ground truth values for all voxels in the 4 compartments. Further, to quantify the effect of on resolution, an edge selected at the interface between compartments 1 and 4 was analyzed. Edge widths were computed with a method proposed by Greenspan et al. 28 The results for the effect of on the MAE obtained from simulations were validated using a phantom. The details are in Supporting Information Text S4 and Supporting Information Figure S2.
section_name: Numerical simulations

section_content: Phantom experiments To assess the improvement in resolution achieved with SRR-H 2 O method, a carrageenan phantom was prepared as described in Ref. 40 The detailed method of preparation is included in the Supporting Information Text S2. The carrageenan phantom had a water content of approximately 70%, achieved by mixing H 2 O/D 2 O in a ratio of 7:3. A cylinder containing distilled water was included for the calibration of water content values. A structure with sharp edges made of Plexiglass was included in the phantom to aid the quantitative assessment of the effective resolution. The edge between the Plexiglass and the medium was characterized with the method proposed in Ref. 28 All statistical analysis was performed using Python 3. 7 (Scipy and Numpy packages).
section_name: 3.2

section_content: Anisotropic LR mGRE images can be used to obtain 1 HR mGRE image using SRR-H 2 O as described above. However, in principle this could also be achieved by performing a zero-padding interpolation in the frequency domain, co-registering the 3 interpolated images, and averaging them to obtain an HR mGRE image from which to perform water mapping. We denote this method by the interpolation-H 2 O method and compare it to SRR results. Water content mapping of the carrageenan phantom was carried out with 3 methods. First, the long-TR method (TR = 10 000 ms, FA = 90

• ) was used to obtain a water content map of voxel size 1. 5 × 1. 5 × 1. 5 mm 3. Second, water content mapping was performed with the SRR-H 2 O method to obtain a water content map of voxel size 1. 5 × 1. 5 × 1. 5 mm 3 from a set of 3 orthogonal LR mGRE images (TR = 3300 ms, FA = 15

• ) acquired with a voxel size of 1. 5 × 1. 5 × 4. 5 mm 3. Third, using the same set of 3 orthogonal LR mGRE images, an HR water content map was obtained using the interpolation-H 2 O method. This was done by zero-padding the LR mGRE images in Fourier space to obtain 3 interpolated HR mGRE images (voxel size = 1. 5 × 1. 5 × 1. 5 mm 3 ) and then coregistering the sagittal and coronal interpolated HR mGRE images to the interpolated transverse HR mGRE image space. The transverse interpolated HR mGRE image and the sagittal and coronal interpolated and coregistered HR mGRE images were then averaged to obtain the final interpolated HR mGRE image. Water content mapping was then performed on this HR mGRE dataset. Because all 3 water content maps obtained with the 3 approaches described above had the same image space and voxel size, it was possible to perform edge analysis of a selected edge in all water content maps. In this case, 4 edges were selected.
section_name: Comparison of SRR-H 2 O to zero-padding interpolation

section_content: Using SRR-H 2 O, quantitative in vivo water content maps were obtained from 6 healthy volunteers (5 male, 1 female; age range: 26 to 30 years; mean: 27. 8 years; SD: 1. 8 years). 

Ethical approval was obtained from the local ethics committee. Three orthogonal LR mGRE images were acquired with an in-plane resolution of 0. 75 mm × 0. 75 mm and a slice thickness of 2 mm. HR water content maps with an isotropic resolution of 0. 75 mm were reconstructed using SRR-H 2 O method. The SNR of both the phantoms and the in vivo data was close to 30. Based on the results of numerical simulations with SNR = 30, an optimum λ value of 0. 08 was chosen for SRR reconstruction. For comparison, water content maps were also obtained using the long-TR method with an in-plane resolution of 0. 75 mm × 0. 75 mm and a slice thickness of 1. 5 mm, the thinnest allowed by the scanner software. A subsequent upgrade of the scanner software version allowed for the selection of 1 mm thick slices. To compare the performance of the SRR-H 2 O method with the long-TR-H 2 O method at an isotropic resolution of 1 mm, a similar acquisition to that described above was carried out with 1 mm isotropic resolution for 1 volunteer. The imaging parameters for the 1 mm isotropic acquisitions and the obtained results can be found in the Supporting Information Text S3 and Supporting Information Figure S1, respectively. The histograms and mean WM and GM water content values of the 2 methods were compared. The WM and GM masks were generated with SPM12 using the acquired mGRE image for the long-TR method and the SRR reconstructed mGRE image for the SRR-H 2 O method. In this study, the total brain mask was obtained by combining the WM and GM masks. All measurements were made using a Siemens Prisma 3T MRI scanner equipped with a body coil for transmit and a 64-channel receiver coil. The MR acquisition parameters for all the experiments are detailed in Table 1.
section_name: In vivo experiments

section_name: RESULTS

section_content: Figure 2 shows the theoretically predicted curves for the comparison of the SNR of the 2 approaches, under the constraint that the total acquisition time for the HR image (either directly obtained or after SRR) is the same, and the saturation factor for T 1 = 2s is 0. 993 for all acquisitions. The horizontal axis is the acquisition time relative to the direct HR acquisition with TR = 10s. SNR is influenced by the fact that the slice thickness ST of the LR
section_name: SRR-H 2 O acquisition settings

section_content: Relative SNR versus TA for the 2 approaches: SRR and direct HR. The TR of the SRR approach is a third of that of direct HR acquisition to maintain equal TAs for the 2 approaches. All the SNR and TA values are normalized to the SNR and TA of the mGRE dataset obtained at TR = 10,000 ms with the direct HR approach. The curves are the theoretically predicted values, and the dots are the experimentally measured values on the phantom. HR, high-resolution; mGRE, multi-echo gradient recalled echo; TA, acquisition time. 

acquisitions is 3 times that of the direct HR acquisition. Additionally, Figure 2 shows the experimentally obtained SNR values obtained from the carrageenan phantoms as dots, and these agree well with the theoretical prediction.
section_name: F I G U R E 2

section_content: Figure 3 shows the numerical phantom used for the numerical simulations and the simulation results; its geometry is depicted in Figure 3A. Figure 3B shows the ground truth water content distribution. Figure 3C shows water content maps in 3 orthogonal orientations of the ground truth (top), maps from all 3 LR mGRE datasets simulated for SNR = 30 (rows 2 to 4), and the high-resolution water content map (bottom) obtained using the SRR-H 2 O method with = 0. 08. As can be seen, the LR water content maps have a high in-plane resolution (red frame) but a low through-plane resolution, whereas the water content map obtained using SRR-H 2 O method has a high resolution in all 3 orientations. Supporting Information Figure S3 shows that an increase in leads to a less noisy and more smooth water content map. Figure 4 shows the effect of regularization on the MAE and the edge widths of the water content maps. The MAE first decreases with increasing, reaching a minimum, followed by a rise with increasing. As seen in Figure 4A, regularization appeared particularly useful at lower SNR, whereas at higher SNR levels regularization had a minimal effect on MAE (as also shown in 4c), and even intermediate λ values lead to increasing errors. The edge widths show a more complicated evolution but increase with increasing for values above the optimum.
section_name: Numerical simulations

section_content: Figure 5A shows the water content map of the multi-compartment cylindrical phantom obtained with the SRR-H 2 O and long-TR-H 2 O methods. As can be seen in Figure 5B, the fitted water content values are in good agreement with the ground truth values. Figure 5C shows the water content map of the carrageenan phantom obtained with the SRR-H 2 O and long-TR-H 2 O methods. 

The optimum was chosen using the results from the simulations. The broader histogram (Figure 5D ) of water content values from the SRR map reflects the lower SNR of the original acquisitions. Figure 6 shows the comparison of the water content maps obtained with the long-TR method, the SRR-H 2 O method, and the interpolation method. Qualitatively, it can be seen that a sharper water content map is obtained with the SRR-H 2 O method as compared to the interpolation method. This proves the advantage of SRR over interpolation with respect to the true resolution of the water content map. This is also proved objectively as the quantitative analysis of the edge
section_name: Phantom experiments

section_content: (A) Water content maps of an ROI in the phantom obtained with the reference (long-TR-H 2 O), proposed (SRR-H 2 O), and the zero-padded interpolation (interpolation-H 2 O) methods, all obtained with an equal scan time. Blurring can be noticed in the interpolation-H 2 O method, while the SRR-H 2 O maps are comparable in quality to the reference method. (B) Sigmoid fit to an edge selected, which is shown as a red line in (A). The steeper the fitted the better the resolution

width of a selected edge in the phantom water content map reveals that the SRR-H 2 O method has a smaller edge width in comparison to the interpolation method. The edge widths [in voxel units] of the 4 selected edges were: long-TR-H 2 O: {0. 94, 1. 07, 1. 43, 1. 82}, SRR-H 2 O: {0. 97, 1. 62, 1. 69, 2. 15}, and interpolation-H 2 O: {2. 26, 2. 35, 2. 55, 2. 58}.
section_name: F I G U R E 6

section_content: Figure 7A shows the whole-brain, high and isotropic resolution (0. 75 mm) water content maps from a single volunteer (25 yrs, male) obtained using the SRR-H 2 O and long-TR-H 2 O methods. The water content histograms of the SRR-H 2 O method and the long TR reference method, shown in Figure 7B, display the usual bimodal distribution of WM and GM values. As seen in Figure 7C, the water content values of both methods match well. The mean ± SD water content values obtained for this volunteer (in percentage units) for each tissue class were WM:69. 7 ± 3. 4 p. u. and GM: 84. 2 ± 4. 7 p. u. using the SRR-H 2 O method; and WM: 70. 7 ± 3. 1 p. u., GM: 83. 5 ± 4. 5 p. u. using the long-TR method (difference not significant). 

Here, the SD describes the width of the distribution. The group mean ± SD of the mean water content values across all 6 volunteers were 68. 7 ± 0. 8 p. u. for WM and 83. 7 ± 0. 6 p. u. for GM with the SRR-H 2 O method; and 69. 3 ± 1. 2 p. u. for WM and 82. 6 ± 1. 1 p. u. for GM with the long-TR method. Here, the SD characterizes the group variability. Hence, across the volunteers, the variance in WM and GM mean water content values was found to be smaller with the SRR-H 2 O method. and 4. 5 p. u. for the long-TR and SRR-H 2 O methods, respectively. Figure 9 shows a comparison of the water content maps obtained with the SRR-H 2 O method against those obtained with the long-TR method. Note that the acquisition time for both methods is similar. There is a noticeable increase in the resolution in the sagittal and coronal orientations in the SRR-H 2 O map in comparison to the up-sampled long-TR-H 2 O map. The structures in the area near the cerebellum and brain stem in the sagittal and coronal orientations are visualized better in the SRR-H 2 O map. This is partly due to the improved contrast between the CSF and brain tissue in SRR-H 2 O as a result of the higher SF value.
section_name: In vivo

section_content: We present a novel method employing SRR to perform isotropic high-resolution water content mapping. We demonstrate water content maps with a nominal isotropic resolution of 0. 75 mm acquired at 3T. An isotropic voxel size of 0. 75 mm was chosen to push the limits of resolution achievable and to demonstrate water content maps at a resolution that has not been previously reported at 3T. The work also demonstrates the use of SRR in multiple-echo mGRE data, an aspect of quantitative imaging that has not been previously investigated. In addition to increasing the resolution, SRR allows a reduction in the first TE of the mGRE acquisition. Consequently, applications where imaging at short TE is required would benefit from SRR. 

For this proof-of-principle demonstration, the parameters of the proposed method were chosen such that the measurement time was very similar to that of an established long-TR (reference) method. 10 In principle, 3D water content mapping techniques could be used as a reference. However, this would not be a fair comparison as the 3D technique would require a substantially longer acquisition time and may introduce additional discrepancies in terms of SNR and B 0 field inhomogeneities on the signal decay. Assuming imaging with very thin slices is feasible, and TR and FA are fixed, acquiring N averages increases the SNR by a factor of √ N. However, acquiring N low-resolution LR images with N times thicker slices and recombining them by SRR increases the SNR by a factor of N (the SNR of low-resolution images). Hence, the proposed method offers a better tradeoff between TA and SNR than averaging. 

Our aim was, however, to demonstrate high-resolution water content mapping acquired without a substantial increase in measurement time. As seen in the simulations and phantom results of Figure 2, for a constant T 1 saturation factor, SNR decreases with decreasing TR because the FA must be reduced accordingly. In the range of TRs from 5 s to 10 s, it is more advantageous to use a direct HR acquisition (when possible) with respect to SNR efficiency. When it is not possible to acquire a direct HR mGRE image, the SRR method can be used; however, this can lead to a substantial loss in SNR. For a TR of 10s for the direct HR acquisition, the corresponding TR for SRR acquisition is 3333 ms. This results in the SNR of the SRR acquisition being 76% of that of direct HR acquisition. 

When applied in vivo, the proposed method gives a narrower range of mean water content values in the WM and GM when compared to the long TR method across the volunteers. For the purpose of using water content mapping as a biomarker for pathological changes, this low SD across volunteers is advantageous. The reason for the roughly twofold reduction in the SD of mean water content per tissue class (Figure 8C ) with the SRR-H 2 O method might be due to a minimization of the impact of physiological noise, such as respiration and blood pulsation, in a short TR acquisition compared to 1 that is 3 times as long. The reduction of the SD also in the LR H 2 O maps (TRA-H 2 O, COR-H 2 O, and SAG-H 2 O), as seen in Figure 8C, further suggests that the decrease in SD is due to a shorter TR and not due to the SRR. This is a very intriguing aspect and deserves further study. The correspondence between a slight broadening of the water content distribution with the proposed method, as seen in the histograms shown in Figure 7B, and the increased separation between WM and GM, along with the decrease of the number of voxels showing partial volume effects (between the WM and GM "peaks"), can be well explained by the increased resolution achieved using the proposed method. We draw attention in particular to the exquisite contrast visible in the brain stem seen in Figure 9, where small WM and GM structures are intermixed. The overall increase in contrast in the maps is mainly due to higher contrast between tissue and CSF, resulting from the lower T 1 saturation factor of CSF voxels obtained with the proposed method. While we have adopted a very simple LR acquisition scheme with 3 orthogonal orientations, there are more possibilities. The optimal acquisition scheme for SRR is an active area of research, and further effort will be made to optimize the acquisition scheme for mapping purposes. The proposed reconstruction method would work with any acquisition scheme. We recommend that the SNR of the original LR images be > 20. As shown, the optimum regularization value of depends on the SNR. For an SNR of 30, we recommend a of 0. 08. A potential extension of the method could be to reconstruct complex mGRE images with SRR to lower the noise floor and allow the use of the reconstructed phase image for correction for B 0 inhomogeneities. To avoid the introduction of any

Qualitative comparison of the water content maps obtained with the SRR-H 2 O method and the long-TR method obtained with equal TAs. The long-TR-H 2 O has been zero-padding-interpolated to 0. 75 mm isotropic resolution for a fair comparison. For better visualization, given that the eye is sensitive to contrast-to-noise ratio, both maps were smoothed using a Gaussian blur operator (sigma = 0. 5). Despite the up-sampling of the long-TR-H 2 O map, the better resolution of SRR-H 2 O remains visible, especially in the brainstem (blue arrows) and cerebellum (green arrows). Better contrast is noticeable between the CSF and brain tissue with the SRR-H 2 O owing to the improved SF confounding factors in this proof-of-principle study, no additional acceleration techniques were used in either the long TR or the SRR method. However, in order to improve the SNR of the SRR-H 2 O method to a level which could, for example, enable the detection of small cortical lesions in multiple sclerosis, multiple signal averages in each orientation should be considered. Furthermore, the inclusion of standard acceleration methods in the protocol, such as parallel imaging or partial Fourier acquisition, would help to reduce the total measurement time per SRR-scan to under 10 min. Future work should focus on evaluating the overall effect of signal averaging and acceleration methods on the final SNR and optimizing such acquisitions. Despite the advantages of the proposed method, our study has some limitations: First, due to scanner limitations, the slice thickness of the reference acquisition was a factor 2 larger than the reconstructed slice thickness using the proposed approach. Hence, the water content maps from the 2 methods have similar in-plane resolution but different slice thickness. The slice profile used in this work was a default "smoothed box" function as in Ref. 29 However, in the future, the inclusion of the vendor-specific slice profile would be advantageous. Second, in both types of acquisitions we have avoided using slice gaps, as implemented in the established long-TR method, 10 because of their effect on SRR. This is expected to introduce slice cross-talk effects in the acquisition and impact the quantification. The main effect is expected to be cross talk in the CSF, increasing the saturation of CSF beyond that expected from the TR/FA combination. Third, the effect of head motion between acquisitions has not been corrected for. This could be included in a future step by either co-registering the original LR images (e. g., at an intermediate isotropic resolution, obtained by interpolation) or by including the motion directly in the model and estimating it as part of the reconstruction. The LR images acquired in this study have a relatively thin slice thickness of 2 mm. However, with increasing slice thickness and with higher field strengths, the B 0 inhomogeneities become more pronounced, and failing to correct their effect on the signal decay leads to erroneous water content values. 7 At ultrahigh field strengths, a correction for through-slice B 0 gradients such as the sinc correction approach, using a first-order approximation of through-slice B 0 inhomogeneities, 41 should be incorporated in the SRR reconstruction. A strength of the current study is that the regularization strength has been chosen based on simulation experiments rather than being based on an empirical choice. Nevertheless, a theoretical method to select the regularization value, for example, using the L-curve, 42 could be more robust to differences in hardware and sequence parameters.
section_name: DISCUSSION

section_content: We have presented a method for high-resolution water content mapping employing super-resolution reconstruction. We have assessed the accuracy of this method by comparing it to an established water content mapping method. In addition to practically unchanged tissue-class mean values, the proposed method showed greater consistency between volunteers, with a 40% reduction in SD across volunteers compared to the standard protocol. Thus, our method provides a technique for high-precision and high-resolution water content mapping. It is anticipated that the impact of the method will be accentuated at higher field strengths, where gains in both imaging time and SNR can be expected.
section_name: CONCLUSION

section_name: ACKNOWLEDGMENT

section_content: This work was supported by the European Union 's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 764513. The authors would like to thank Fabian Küppers and Michael Schöneck for help with phantom preparation and Claire Rick for help with English proofreading. Open Access funding enabled and organized by Projekt DEAL.
section_name: ACKNOWLEDGMENT

section_name: SUPPORTING INFORMATION

section_content: Additional supporting information may be found in the online version of the article at the publisher's website.
section_name: SUPPORTING INFORMATION

section_name: Text S1