The influence of spatial resolution on the spectral quality and quantification accuracy of whole‐brain MRSI at 1.5T, 3T, 7T, and 9.4T

Purpose Inhomogeneities in the static magnetic field (B 0) deteriorate MRSI data quality by lowering the spectral resolution and SNR. MRSI with low spatial resolution is also prone to lipid bleeding. These problems are increasingly problematic at ultra‐high fields. An approach to tackling these challenges independent of B 0‐shim hardware is to increase the spatial resolution. Therefore, we investigated the effect of improved spatial resolution on spectral quality and quantification at 4 field strengths. Methods Whole‐brain MRSI data was simulated for 3 spatial resolutions and 4 B 0s based on experimentally acquired MRI data and simulated free induction decay signals of metabolites and lipids. To compare the spectral quality and quantification, we derived SNR normalized to the voxel size (nSNR), linewidth and metabolite concentration ratios, their Cramer‐Rao‐lower‐bounds (CRLBs), and the absolute percentage error (APE) of estimated concentrations compared to the gold standard for the whole‐brain and 8 brain regions. Results At 7T, we found up to a 3.4‐fold improved nSNR (in the frontal lobe) and a 2.8‐fold reduced linewidth (in the temporal lobe) for 1 cm3 versus 0.25 cm3 resolution. This effect was much more pronounced at higher and less homogenous B 0 (1.6‐fold improved nSNR and 1.8‐fold improved linewidth in the parietal lobe at 3T). This had direct implications for quantification: the volume of reliably quantified spectra increased with resolution by 1.2‐fold and 1.5‐fold (when thresholded by CRLBs or APE, respectively). Conclusion MRSI data quality benefits from increased spatial resolution particularly at higher B 0, and leads to more reliable metabolite quantification. In conjunction with the development of better B 0 shimming hardware, this will enable robust whole‐brain MRSI at ultra‐high field.


| INTRODUCTION
MRSI is a non-invasive method to map concentrations of various biochemical compounds in tissue. Since its introduction, MRSI has evolved into a unique tool that can add valuable information about pathology in many brain disorders. [1][2][3][4][5] In some cases MRSI can even unravel biochemical changes, where conventional MRI appears insufficient. 6 The quality of MRSI data depends strongly on the homogeneity of the main magnetic (B 0 ) field, particularly that within each voxel. 7 B 0 inhomogeneity (ΔB 0 ) increases spectral linewidths, decreases SNR, and leads to poor performance of frequency-selective (suppression) pulses. ΔB 0 are more severe at higher B 0 , and therefore diminish the expected improvements in SNR and spectral resolution when moving to a higher B 0 . 8 To address these problems, ΔB 0 are typically mitigated by superposition of additional magnetic B 0 fields in the form of spherical harmonics 9 and more recently by matrix B 0 shims. 10 One approach-independent of B 0 shimming hardware-is to increase the spatial resolution, which reduces intra-voxel ΔB 0 , but the ability to do so is limited by the available SNR per voxel and the maximum acceptable acquisition time. [11][12][13] The associated spectral resolution improvements have been experimentally investigated in previous studies at ≤3T, but the effects are expected to be even more pronounced beyond 3T.
With the recent advent of whole-brain MRSI at 7T and 9.4T, 14,15 and results that highlight the impact of highresolution MRSI in terms of pathological sensitivity 16,17 at 7T as well as below 7T, [18][19][20][21] it is critical to gain a better understanding of these mechanisms at ultra-high B 0 fields to be able to appropriately optimize whole-brain MRSI protocols. This should be done in a manner that is insensitive to unrelated variations between measurements and where a "gold standard" is available for comparison.
In this study, we created whole-brain MRSI simulation models based on MRI data acquired at 1.5T, 3T, 7T, and 9.4T. These simulation models allowed us to investigate not only how the spectral quality of the MRSI data but also the quantification accuracy, change with spatial resolution, and B 0 field.

| THEORY
The decrease of spectral quality in MRS/MRSI because of either increased ΔB 0 or T 2 shortening is indirectly proportional to the T * 2 relaxation constant. The theory underlying this effect is described in the following sections.

| T 2 and T 2 * relaxation
The key contributor to spectral quality improvements or degradation is T * 2 relaxation. The measured FID signal at location r in the presence of ΔB 0 is described by Equation 1, where the T * 2 relaxation constant represents the total signal loss because of dephasing over time T * 2 correlates inversely with the broadening of spectral resonances, which determines the associated SNR and spectral resolution loss. The T * 2 constant can be separated into 2 main contributions as shown in Equation 2: the apparent T 2,apparent constant and the T 2,macro constant. The T 2,macro constant represents the macroscopic ΔB 0 inside a voxel volume and therefore can be influenced by changing the spatial resolution in MRSI. Equation 1 can be rewritten as Equation 3, where ΔB 0 (r) represents spatially dependent ΔB 0 .
The T 2,apparent constant is described by Equation 4. The intrinsic T 2,intrinsic represents the homonuclear dipole-dipole interaction between protons, the hyperfine contact interaction with the paramagnetic center, and cross-relaxation. The T 2,Diffusion and the T 2,Exchange describe the contribution of dynamic dephasing, where net magnetization is reduced by diffusion and exchange between regions with different magnetic field strengths. 22 Neither can be experimentally altered. The contribution of dipole-dipole interactions associated with the T 2,intrinsic constant is B 0 -independent, but the remaining effects lead to an overall decrease of T 2,apparent with increasing B 0 . 23 (1) M xy (r,t) = M xy (r,0) e −t∕T * 2 . (2) M xy (r,t) = M xy (r,0) e −t∕T 2,apparent ∫ r e −iγΔB 0 (r)t dr.
with the development of better B 0 shimming hardware, this will enable robust wholebrain MRSI at ultra-high field.

K E Y W O R D S
B 0 field dependency, B 0 inhomogeneities, MR spectroscopic imaging, signal-to-noise, spectral resolution, voxel size | 553 MOTYKA eT Al.

| Spectral quality parameters
High-quality spectra are generally characterized by metabolite signals, which are large compared to the noise level and well-separated. These spectral quality features can be quantitatively described by the SNR (i.e., signal amplitude divided by the SD of noise) and the full-with-at-half-maximum (FWHM) of resonance peaks as a measure of linewidth and/or spectral resolution. The quality of the spectra depends strongly on various acquisition parameters. The signal amplitude is theoretically expected to increase linearly with B 0 because of the Zeeman effect. However, to cover all the important metabolite signals, it is necessary to increase the spectra bandwidth (in Hz) linearly with increasing B 0 field. To achieve a linear increase of SNR, with the assumption of a fixed ADC length, the signal FID has to be multiplied by B 0 and the SD of the noise, σ, modified according to Equation 5 The spatial resolution defines the volume of the signal origin. With decreasing volume, the signal amplitude also decreases. For MRSI with spatial (phase) encoding in 3 dimensions, the SNR per volume is described by Equation 6.
The spectral resolution, represented by the FWHM, can be easily converted into the corresponding T * 2 relaxation constant using Equation 7-assuming a Lorentzian spectral peak shape. The ΔB 0 considered in Equation 3 leads to deviations from this Lorentzian shape inside the voxel, which add additional Gaussian contributions that finally result in in vivo resonances being Voigt-shaped. Nevertheless, linewidths can still be well approximated by Equation 7.

| Quality-of-the-fit parameters
To allow (absolute) metabolite concentrations to be quantified, MRS/MRSI spectra are fit by parametric spectral fitting using e.g., LCmodel. 24,25 The quality of fit for an unbiased estimator is commonly represented by Cramer-Rao bounds, which describe the precision of the parameter estimates from the spectra. 26 Cramer-Rao lower bounds (CRLBs) describe the lowest variance of the estimated concentration of the metabolites in a given spectrum. 24 Low CRLBs may not necessarily reflect reliable or accurate results, but they are a reasonable metric for the quality of fit in the absence of a known concentration gold standard.
If the ground truth concentration of metabolites is known, the estimated concentration from the fit can be directly compared. The absolute-percentage-error (APE) can be calculated for whole MRSI data sets by Equation 8, where c met is the vector of concentration values.

| Experimental data
All MRSI simulations were based on acquired data (i.e., ΔB 0 maps, anatomic maps, and fat maps), which were used to simulate FID signals of metabolites and lipids. For this purpose, the same 5 healthy volunteers (age = 24-33 y, 4 male, 1 female) were measured on 4 MR scanners of different B 0 (1.5T Magnetom Aera, 3T Magnetom Prisma, 7T Magnetom, and 9.4T Magnetom; all Siemens Healthineers, Erlangen, Germany), with 4 different coils (1.5T, 20-channel receive coil array and 3T, 64-channel receive coil array both with body coils for transmission, both Siemens Healthineers; 7T, a 32-channel receive coil array combined with a volume coil for transmission, Nova Medical, Wilmington, MA; 9.4T, a 31-channel receive coil with a 16-channel parallel transmit coil system). 27 Internal review board approval and written informed consent were obtained from all volunteers.

2.
The same metabolite FID was assigned to every voxel inside the brain mask. 3. The lipid FID was assigned to each voxel in the fat mask, but the amplitude of the lipid FID was scaled based on the respective fat fraction indicated by the fat map. 4. ΔB 0 obtained from respective experimental ΔB 0 maps were applied via Equation 9, where term FID 0 (x,y,z,t) represents the FID signal of the initial MRSI model at a specific position (x,y,z) and term ΔB 0 (x,y,z) represents the B 0 deviation in this voxel. The creation of the simulation phantom is summarized in Figure 1.
For each simulation model and volunteer, MRSI acquisitions with different spatial resolutions were simulated in the k-space-time-domain (kx, ky, kz, t) by cutting the inner part of the k-space to achieve the desired spatial resolutions and adding Gaussian noise. Three different spatial resolutions were simulated, with isotropic voxels of a nominal size: 10 × 10 × 10 mm 3 , 5 × 5 × 5 mm 3 , and 2.5 × 2.5 × 2.5 mm 3 . The SD of the Gaussian noise was SBW-dependent (i.e., scaled based on Equation 5). Finally, the simulated MRSI data were spatially filtered by a Hamming window and fitted using LCModel. 24

| Evaluation
For the data evaluation, ~200 regions of interest (ROIs) were obtained from T 1 -weighted MRI scans using Freesurfer's cortical and white matter parcellation (APARC). 52 The ROIs were merged into 8 large regions: frontal lobe, parietal lobe, occipital lobe, temporal lobe, cerebellum, subcortical white matter (WM), subcortical gray matter (GM), and brain stem and then were also co-registered to 3T image space ( Figure 2).
The quality of spectra was characterized in terms of the FWHM and the SNR normalized to voxel volume. FWHM was calculated via a MATLAB script from the LCModel's fit of NAA, but not directly obtained from the LCmodel output. SNR was computed as the amplitude of the fitted NAA peak divided by the SD of the noise, which was calculated from a metabolite-free region of the spectra between 5 and 6 ppm. SNR values were then normalized to the voxel volume (nSNR) of the highest spatial resolution by factors derived from Equation 6. The nSNR and FWHM maps of the high and the intermediate-resolution were resampled to the low resolution to allow pairwise comparison of the results between different spatial resolutions.
CRLBs and APEs were used as quality parameters for the fit and to evaluate quantification accuracy, which inherently contains the effects of lipid leakage through the PSF. Voxels in which the CRLBs of metabolites were higher than 10% were excluded because of low precision. Because the input concentration values in the simulation model were constant across the whole brain, it was expected that the output values would also be constant. The gold standard for estimation of APEs was the median metabolite concentration across those voxels in which CRLBs were below 10%. APEs of metabolites were calculated for every voxel. CRLBs were used to calculate the confidence interval of concentration values (concentration value ± 2*CRLB). Voxels in which the APEs of metabolites were higher than 2 times the CRLB were excluded (low accuracy). Finally, voxels with sufficient quality were counted and converted to volume. The volume after APE thresholding was compared to the volume after CRLB thresholding for both metabolite values and their ratios.

| Statistics
The FWHM and nSNR values from all volunteers were merged to create a large data set for each combination of B 0 and spatial resolution. For every B 0 , results from different spatial resolutions were compared using the Wilcoxon signed-rank test. All tests were performed on the data from the whole volume and different anatomical sub-regions.
For the comparison of the 3 spatial resolutions, the resulting P-values were corrected using the Bonferroni correction and the level of significance was assumed at P ≤ 0.05.

| RESULTS
The results of the FWHM evaluation are presented in Figure  ppm for low, intermediate, and high resolution, respectively. This effect can also be seen on the FWHM maps in Figure  4, which show that the most pronounced linewidth improvements with increased spatial resolution are achieved in regions of strong ΔB 0 , such as the frontal lobe. At 7T, the hotspot of high FWHM values in the frontal lobe (~0.1 ppm) at intermediate resolution was mitigated by increasing spatial resolution similar to the FWHM values found in other subregions (~0.05 ppm). The situation was similar at 3T; the hotspot at intermediate resolution (up to 0.15 ppm) was reduced, although a residuum of the hotspot was present. The median FWHM in different brain regions (after downsampling to the same spatial resolution) and the contribution to this FWHM that originated from ΔB 0 (in %) are summarized in Table 1.
Median FWHM values decreased with increasing spatial resolution at each B 0 and in most brain regions. Comparing the median values of the FWHM over whole brains, the decrease caused by increasing spatial resolution was the highest at 7T (~2.3-fold reduction from 0.075 ppm for the low resolution to 0.033 ppm for the high resolution; P < 0.001) and was lowest at 1.5T (~1.6-fold reduction from 0.139 ppm for the low resolution to 0.084 ppm for the high resolution; P < 0.001). In a few brain regions, the increase in spatial resolution had no effect on the FWHM. For instance, there were no significant differences at 7T (P = 0.06) and 9.4T (P = 0.92) in the brain stem region between low and intermediate resolution or at 1.5T in the subcortical WM region between intermediate and high resolution (P = 0.997).
The results of the nSNR are presented in Figure 5 in the form of histograms normalized to the covered volume. For higher B 0 , the right tail of the nSNR distributions was shifted toward higher nSNR values. For instance, the third quartiles for the intermediate resolution were 9.26, 14.17, 18.41, and 20.58 for 1.5T, 3T, 7T, and 9.4T, respectively. The nSNR distributions became smaller and broader, meaning that the increase of nSNR was not generalized in the whole volume. This effect was also reflected by an increase of the IQRs The volumes in percentage for which the quality-of-fit parameter criteria (CRLBs <10% and APE <20%) were fulfilled are presented in Table 3 for 2 metabolites and their ratios. The fraction of brain volumes with sufficient quality increased with increasing spatial resolution in both metrics. The increase was larger in the case of APE. For example, for tNAA at 7T, the fractions were 37%, 63%, and 74% for low, intermediate, and high resolution, respectively, whereas for CRLBs, the fractions were 74%, 80%, and 82% for the same resolutions. The fractions thresholded by CRLBs increased with increasing B 0 field for both metabolites and each spatial resolution by 10-15% when increasing the B 0 field from 1.5T to 9.4T. However, the fractions thresholded by APE increased with increasing B 0 field only for intermediate (+6% by increasing B 0 from 1.5T to 7T and 9.4T) and high resolution (+16% by increasing B 0 from 3T to 7T and 9.4T). In case of low resolution, the decrease was up to 10%. In general, the fractions were lower in case of APE for both metabolites. However, by taking the ratio between tNAA and tCr the fractions thresholded by both metrics were similar especially at 7T and 9.4T for high spatial resolution with ~78%. The difference between volumes thresholded by CRLBs and by APEs for tCr and tNAA increased with increasing B 0 and decreased with increasing spatial resolution (Figure 7).

| DISCUSSION
In this study, we successfully modeled MRSI data sets of various spatial resolutions and B 0 field strengths using experimentally obtained data from 5 volunteers to investigate the effects of spatial resolution and B 0 strength on data quality. The main advantage of using simulated data over entirely experimental studies was that the relative metabolite concentrations were known for all data sets and could be used as the gold standard in the evaluation process.
The benefit of increasing spatial resolution to prolong B + 1 has previously been reported in other areas of MRI 53 ; for instance, in both GRE T * 2 -weighted MRI 54 and GRE-based echo planar imaging in functional MRI studies at 1.5T and 3T [55][56][57] as well as at 7T. 58 In 3D-MRSI at 4T, Li et al. 13 have previously reported a linear decrease in linewidth with the decreasing lateral length of cubic voxels. For in vivo measurements, decreasing the voxel volume from 3.4 cm 3 to 0.42 cm 3 yielded a linewidth decrease from 19.6 ± 2.7 Hz to 7.7 ± 1.3 Hz for NAA. A similar decrease was reported by Gruber et al. 12 at 3T using 3D-MRSI, where a decrease in voxel volume from 0.75 cm 3 to 0.094 cm 3 resulted in a linewidth reduction from 5.3 Hz to 2.9 Hz for the Cr-CH 3 resonance. The FOV of both of these studies was localized in the subcortical region. In contrast, a single-voxel spectroscopy study at 4T and 7T by Tkac et al. 41 reported that when an optimal B 0 -shim is achieved in the parietal or occipital lobe, linewidth can become independent of voxel volume in the range from 1-8 cm 3 . This may be possible with excellent B 0 shim hardware  within voxels and P-values from a comparison of different spatial resolutions for brain sub-regions as well as whole brain are presented.

| 559
MOTYKA eT Al.  The nSNR results of the high and intermediate resolution of all B 0 fields were downsampled to the low spatial resolution to allow pairwise comparison. Median of nSNR of brain sub-regions as well as whole brain and P-values from a comparison of spatial resolutions are presented.
and/or software in some brain regions, but is not achievable with MRSI.
Our results at 3T are in agreement with the linear decrease of FWHM with voxel volume that was reported for MRSI in subcortical regions, 12,13 and showed a decrease of the linewidth from 11.0 Hz to 6.8 Hz for a voxel volume reduction from 1 cm 3 to 0.125 cm 3 . A further decrease of voxel volume to 0.015 cm 3 improved spectral resolution much less (i.e., 5.5 Hz). This suggests that the ability to decrease linewidth by decreasing voxel volume is limited by the finite variation of B 0 within a voxel. 41 Tkac et al. 41 reported that at 7T, the contribution of microscopic susceptibility variations to the FWHM was 5.8 Hz, which is in agreement with our results at 7T. In the high spatial resolution case at 7T, the contribution of ΔB 0 in the subcortical WM region was 5.5 Hz. Increasing the spatial resolution generally decreased the ΔB 0 -dependent contribution to the linewidth. However, even at the highest spatial resolution, ΔB 0 constituted the dominant contribution to linewidth (~70-80%). A large portion of this can be explained by tissue heterogeneity, including bulk susceptibility differences between GM, WM, cerebrospinal fluid, and small vessels and the susceptibility anisotropy (i.e., directionally dependent or tensor nature) of myelin. 59,60 This contribution cannot be eliminated entirely by B 0 shimming.

F I G U R E 7
Boxplot for the brain volumes with sufficient data quality for all volunteers. The blue color codes volumes thresholded by CRLBs and the green color codes the volumes thresholded by APE. Data from all 4 field strengths and 3 resolutions are presented. In every subplot, the first pair of boxplots is the result for the lowest resolution, the second is the result for the intermediate resolution, and the third is the result for the highest spatial resolution. Medians of boxplots thresholded by the same parameter are connected. The results on the 1.5T for all 3 cases did not fulfill quality criteria than a further increase to high resolution (FWHM decreased, at 7T from 0.04 to 0.02 ppm, at 9.4T from 0.03 to 0.02 ppm).
In contrast, regions with severe ΔB 0 , such as the frontal lobe, showed less improvement from increasing spatial resolution from low to intermediate (FWHM decreased at 7T from 0.12 to 0.09 ppm and at 9.4T from 0.12 to 0.10 ppm) than by increasing resolution further from intermediate to high (FWHM decreased at 7T from 0.09 to 0.06 ppm and at 9.4T from 0.10 to 0.07 ppm). This may indicate that very high spatial resolutions are required to truly mitigate intra-voxel dephasing in the most problematic brain regions. Because narrower resonance lines lead to higher SNR, the voxel size has a direct impact on SNR. Previous studies reported the decrease of SNR to be less than expected for smaller voxel volumes. Gruber et al. 12 reported only a 5-fold SNR decrease for an 8-fold decrease in voxel volume.
Our results suggest that MRSI becomes more SNRefficient per volume with decreasing voxel size-with nSNR being higher in almost all regions for all B 0 fields. However, the increase in nSNR was not homogeneously distributed throughout the brain. The biggest improvements, of more than 100%, were measured in the frontal lobe at 3T, 7T, and 9.4T, with a low-to-intermediate increase of spatial resolution. Further increase from intermediate-to-high resolution brought up to 50% higher nSNR at 7T. In more B 0 -homogeneous regions, such as the parietal lobe, the situation was different. Between low and intermediate resolution, nSNR increased only by 8% (at 1.5T) to 30% (at 9.4T), but a further increase to high resolution yielded up to 75% improvement (at 7T).
These results suggest that the improvement in FWHM and nSNR by increasing spatial resolution is complex and depends not only on the region of the brain and tissue heterogeneity, but also on the initial and final spatial resolution.
We found a consistent drop in FWHM (on the ppm scale) with increasing B 0 field from 1.5T to 9.4T, in agreement with an experimental study by Otazo et al. 61 This result was confirmed by a single-voxel MRS simulation study by Deelchand et al. 8 In our results, a region-wise comparison of the FWHM revealed very similar improvement in brain regions with increasing B 0 . For the intermediate resolution, increasing B 0 from 1.5T to 3T yielded an ~30% improvement for all regions except the cerebellum, where improvement was up to 49%. Increasing B 0 from 3T to 7T yielded a further improvement of ~25% for almost all regions except the frontal lobe and cerebellum, where it was ~17%. Surprisingly, the increase of B 0 from 7T to 9.4T had a relatively modest impact of <10% on the FWHM in the parietal, occipital, and temporal lobes, as well as cerebellum. The subcortical WM region showed the highest improvement of ~27%. The consistency of the improvement between different brain regions likely arises from brain structure similarities, whereas deviations from this trend are caused by different B 0 shimming hardware and/or software on each MR scanner.
The fraction of the linewidth, which can be attributed to ΔB 0 , slightly decreased with increasing B 0 , with the biggest decrease found between 7T to 9.4T, where the fraction decreased by up to 9% for the subcortical WM region; however, the fraction in the frontal lobe remained similar (decreased by 2%). These results indicate that, in regions with strong ΔB 0 , there is still the potential to improve linewidth.
With increasing B 0 , the nSNR also increased. Comparing 1.5T with 3T for intermediate resolution, the nSNR increased by ~34%, which is far below the theoretically possible increase of 100%. Similar results were published in the experimental SVS MRS study by Barker et al., 45 who reported a 28% increased SNR when comparing 1.5T versus 3T. For the intermediate spatial resolution at 3T and above, our nSNR values stabilized at ~12. This result is in agreement with those of Deelchand et al., who reported that the SNR-dependence on B 0 above 4T leveled off. 8 However, this effect is not consistent across all brain regions, e.g., the subcortical WM, as well as the temporal and occipital lobes exhibited a slight increase of the nSNR with increasing B 0 , even up to 9.4T.
The PSF of any imaging technique that requires the Fourier transform is defined as the Fourier transform of its sampling points. 23 Even if the number of the sampling points increases (with the spatial resolution), the effects of PSF remain defined in units of voxels. Therefore, the increase of spatial resolution decreases the area (or volume) affected by the lipid leakage through the PSF, which translates into an increase of volume with sufficient data quality. Lipid leakage through the PSF deteriorates data quality, but it does not directly transfer into increased CRLBs. The fractions of the volume thresholded by CRLBs were 2-fold larger compared to fractions thresholded by APE for low resolution at 7T and 9.4T. These effects can be partially recovered by referring to metabolite ratios.
Summarizing all these effects, MRSI benefits several-fold from higher spatial resolution: in increased spectral resolution, increased SNR per volume, and reduced lipid leakage. This translates into improved quantification accuracy. The increase in precision is in agreement with Deelchand et al., 8 who reported that at higher B 0 improved the number of fitted metabolites and lower metabolite CRLBs can be obtained.

| Limitations
In agreement with a recent single-voxel simulation study by Deelchand et al., 8 T 1 relaxation changes with increasing B 0 were considered negligible. Not all T 2 values of metabolites were found in the literature. Therefore, metabolites with similar T 2 were grouped together and missing values were extrapolated. In practice, these assumptions should not significantly alter our results since additional line-broadening because of B 0 -and metabolite-dependent T 2 contribute only | 563 MOTYKA eT Al. by 0.9 Hz to 3.2 Hz (based on the B 0 for NAA), whereas the effect of ΔB 0 on line-broadening is in the range of 8-25 Hz. For extracranial lipids, the T 2 values of breast adipose tissue were used, which were available for all field strengths. [47][48][49][50][51] In any case, our simulations were performed for an FID-MRSI sequence, which does not have an echo time. Hence, there is no T 2 -related signal decay.
For simplicity, our simulation model assumed spatial phase encoding in all 3 directions. In fact, several much more time-efficient MRSI encoding strategies exist. [62][63][64] Our MRSI data were simulated without including B 1 inhomogeneities, which potentially could have a significant effect on the SNR at higher B 0 . We decided to do this because different coil geometries, the number of receive channels, and substantially different transmit coils (i.e., body coils, local transmit coils, or parallel transmit coils) make a fair comparison impossible. In practice, experimental studies will be strongly affected by the choice of coils, as observed previously, 61 but results reflect an undesirable mix of B 0and coil-efficiency dependence. Our MRSI data were simulated assuming excellent water suppression. In practice, insufficient water suppression could impair accurate spectral fitting, but simulating this in a more realistic manner requires many assumptions about parameters including water T 1 , B 1 + inhomogeneities, and choice of water suppression technique, which would only distract from the investigation of the B 0 and spatial resolution dependence. This simplification is consistent with a recent single-voxel simulation study by Deelchand et al. 8 The SNR was assumed to increase linearly with B 0 , which was also measured experimentally by Otazo et al. for birdcage coils, but not multi-channel coils, where they observed less than linear increase. 61 In contrast to this, Pohmann et al. 65 reported SNR to scale supralinearly with B 0 (~B 0 1.65 ) for multi-channel coils, which would yield even higher improvement. In our study, we did not report the absolute SNR values, mainly because we were predominantly interested in the effect of the increasing resolution at different B 0 fields and in that case, the normalization to voxel volume is required. Additionally, the amount of signal compared to noise is inherently covered by CLRBs and APE. The quantification precision associated with the fitting process was assessed by CRLBs. This is common in the field of MRS/MRSI, although it is not a good measure of the quantification quality. Fortunately, our simulation model also allowed us to estimate quantification accuracy by comparing the confidence interval of estimated metabolite concentrations against the APE. The absolute values of metabolite concentrations (in mmol) were not used as the gold standard. Instead, in our simulation model-in which a constant concentration across the whole volume was introduced at the beginning-the same constant concentration was assumed as a gold standard to quantify the APE.

| CONCLUSIONS
Our study suggests that moving to high spatial resolution, whole-brain MRSI will improve spectral quality and associated quantification accuracy, which will enable the study of neurochemical changes in the diseased and healthy brain in more detail. Because improvements in data quality were more pronounced at higher B 0 and in more inhomogeneous regions, high resolution and further improved B 0 shimming hardware can be expected to jointly overcome the challenges associated with ultra-high field and thereby enable clinically robust whole-brain MRSI at 7T and higher.

ACKNOWLEDGMENTS
This study was supported by the Austrian Science Fund (FWF): P 30701 and KLI 718.