This study included 25 healthy control subjects (12 females, age (mean ± standard deviation) of 25.4 ± 2.4 years). They were recruited at the University Medical Centre Hamburg-Eppendorf and screened for neurological or psychiatric illness. The study was in agreement with the Declaration of Helsinki and was approved by the local ethics committee (Ärztekammer Hamburg #PV5141).

Each subject was scanned twice within 1 week in a whole-body 3T Tim TRIO MR scanner (Siemens Healthcare, Erlangen, Germany) using the body RF-coil for transmission and a 32-channel radiofrequency (RF) head coil for signal reception, respectively. The MR acquisition on both scan days included a multi-parameter mapping (MPM) (Weiskopf et al., 2013; Callaghan et al., 2015b) and a diffusion-weighted imaging (DWI) protocol. The MPM protocol consists of three differently weighted 3D-multi-echo spoiled gradient echo sequences (Siemens FLASH). The echo train length and flip angle for the proton density (PD) weighted, T1-weighted, and magnetization transfer (MT) weighted sequences were 8/6, 8/21, and 6/6°, respectively. The MT-weighted sequence had a Gaussian RF pulse (2 kHz off resonance with 4 ms duration and a nominal flip angle of 220°). All other sequence parameters were the same for the three sequences: repetition time (TR) 25 ms, echo spacing, resolution 0.8 mm isotropic; field of view (FoV) 166 × 224 × 256 mm³, readout bandwidth 488 Hz/pixel, partially parallel imaging using the GRAPPA algorithm was employed in each phase-encoded direction (anterior-posterior and right-left) with 40 reference lines and a speed up factor of two, total acquisition time: ∼25 min. The B₁+ field reference map was acquired using the three-dimensional echo-planar imaging (3D EPI) method, including field maps for distortion correction (Lutti et al., 2010).

The DWI sequence was a twice-refocused single-shot spin-echo EPI scheme (Reese et al., 2003), consisting of 12 non-diffusion-weighted images (b₀ images), equidistantly distributed across the diffusion weighted images. The diffusion-weighted images were acquired at two b-values (1000smm2 and 2000smm2), sampled along 60 unique diffusion-gradient directions within each shell. The entire protocol was repeated with identical parameters but with reversed phase encoding direction (anterior-posterior) to correct for susceptibility-related image distortions (blip-up, blip-down correction). In total, 264 images were acquired per subject (120 diffusion-weighted images, 12 b₀ images, each acquired twice). Other acquisition parameters were: 86 slices with no gap, TR = 7.1 s, TE = 122 ms, an isotropic voxel size of (1.6 mm)³, FoV = 224 × 224 × 138 mm³, 7/8 partial Fourier imaging in phase encoding direction, readout bandwidth. To accelerate the data acquisition, GRAPPA (in-plane acceleration with factor two) and simultaneous multi-slice acquisitions (“multiband,” slice acceleration factor two) (Feinberg et al., 2010; Moeller et al., 2010; Xu et al., 2013) were used as described in Setsompop et al. (2012). The image reconstruction algorithm was provided by the University of Minnesota Centre for Magnetic Resonance Research. The total acquisition time was ∼37 min.

MT_sat maps were generated in the SPM-based hMRI toolbox (Tabelow et al., 2019). Note that the hMRI toolbox also generates additional maps of longitudinal (R₁) and effective transverse relaxation rates (R2⋆) and PD. Three MT_sat maps were generated: (i) MTsatNO maps, without B₁+ correction; (ii) MTsatB1 map, using the reference B₁+ field map for correction (Lutti et al., 2010); and (iii) MTsatUN maps, using the data-driven UNICORT approach for B₁+ estimation (Weiskopf et al., 2011; see Supplementary Figure 2). UNICORT is a probabilistic framework for unified-segmentation based correction of R₁ maps for B₁+ inhomogeneities. The framework incorporates a physically informed generative model of smooth B₁+ inhomogeneities and their multiplicative effect on R₁ estimates (Weiskopf et al., 2011). Parameters used in UNICORT such as the smoothness and regularization were optimized for R₁ B₁+ correction in a 3T scanner (i.e., Tim Trio scanner—Weiskopf et al., 2011).

For B₁+ correction, we used the following heuristic correction factor as detailed in Helms (2015), and Helms et al. (2021):

where C has been calibrated to be 0.4 for the MT pulse used in this paper. B₁+ can be either measured (MTsatCorr=MTsatB1) or estimated with the UNICORT approach (MTsatCorr=MTsatUN).

The DWI data were processed based on the pipeline described in Ellerbrock and Mohammadi (2018) using the SPM-based ACID toolbox². It included several artifact corrections such as Rician signal bias correction (i.e., denoising) (André et al., 2014), correction for eddy current and motion artifacts (Mohammadi et al., 2010, 2014), and correction for image distortions due to susceptibility artifact using reversed phase encoding (Ruthotto et al., 2012, 2013; Macdonald and Ruthotto, 2018). The corrected images were fitted with the NODDI signal model (Zhang et al., 2012) to estimate the intra-cellular volume fraction (ν_icvf), the isotropic volume fraction (ν_iso), and the orientation dispersion index (ODI) in each voxel.

In this section, our approach to estimating MVF and AVF from the measured MR parameters is introduced. The MR-based MVF (MVF_MR) was assumed to be proportional to MT_sat without intercept, following (Mohammadi and Callaghan, 2020):

The proportionality constant α was estimated from Equation (2) in a region where the histological MVF (MVF_hist) was known. Due to the lack of own histological data, we used published histological data which contain the frequency distribution of inner-axon radius (r) and myelin sheath thickness (m) of 2,400 myelinated fibers in the medullary pyramids of a 71 years old human (see Table 1 in Graf von Keyserlingk and Schramm, 1984). The total volume (TV) of the sample is the sum of the total volume of myelinated axons (TAV_m), unmyelinated axons (TAV_u), myelin volume (TMV), and extra-cellular volume (TEV). TAV_m was calculated as ∑i=1Nmπri2 with i indexing the N_m myelinated axons only, and TMV was computed as ∑i=1Nmπ(ri+mi)2-TAVm. TAV_u, while not reported in Graf von Keyserlingk and Schramm (1984), was found to be approximately 43% of TAV_m for multiple mammals (Swadlow et al., 1980; LaMantia and Rakic, 1990; Olivares et al., 2001; Wang et al., 2008; Liewald et al., 2014). Note that the aforementioned papers typically reported the unmyelinated axons as 30% of the total volume of axons, which corresponds to 43% (= 0.31-0.3⋅100) of TAV_m. EVF was estimated to be 25%, according to Lehmenkühler et al. (1993), Nicholson and Hrabìtová (2017), Tønnesen et al. (2018). Finally, MVF was calculated as

with j indexing all N fibers, yielding MVF_hist ≈ 0.3623. Plugging this value into Equation (2) (assuming that MVF_MR ≈ MVF_hist) along with the group-average MT_sat within the medullary pyramids (see Figure 2 for ROI definition) yielded an α of 0.2496 for MTsatB1, 0.2414 for MTsatUN, and 0.2884 for MTsatNO.

The MR-based AVF (AVF_MR = (1−MVF_MR)AWF_MR) was calculated as

where AWF = (1−ν_iso)ν_icvf is the axonal water fraction estimated from the NODDI parameters (Stikov et al., 2015) and MVF_MR = αMT_sat. The MR g-ratio was then computed according to Stikov et al. (2011, 2015)

Note that three versions of MT_sat, AVF_MR, and g_MR were generated according to notation in section “Data Processing”: (i) MVFMRNO, AVFMRNO, gMRNO for no correction, (ii) MVFMRB1, AVFMRB1, and gMRB1 for B₁+ reference measurement, and (iii) MVFMRUN, AVFMRUN, and gMRUN for UNICORT B₁+ correction.

As g_MR and its constituents (MVF_MR, AVF_MR) are defined only in the WM, we restricted the analysis to the WM by creating binary WM masks (Mohammadi and Callaghan, 2020). WM tissue probability maps (WM-TPM) were created for each subject by segmenting AWF and MTsatB1 using the hMRI toolbox, and taking their intersection according to Mohammadi and Callaghan (2020). In two subjects, the MTsatB1 segmentation was of insufficient quality for segmentation and was replaced by the R1B1 map. A group-specific binary WM mask (WM_group) was generated by averaging all individual WM-TPMs in the MNI space and thresholding it at 0.95.

A so-called high-SNR WM_group was also defined by taking the intersection of the WM_group and a binary signal-to-noise ratio (SNR) map. Hereby, the latter was used to reduce the number of voxels with unrealistically high values of ν_icvf (ν_icvf≥0.999). In 6 of 25 subjects, an SNR map was created by dividing the mean b₀ image by a single noise estimate in the native space and multiplied by the square root of the number of b₀ images per DWI dataset (n = 12). The noise was estimated within a noise ROI outside the brain in 72 images (6 subjects, both timepoints and 6 b0 images each) using the ACID toolbox, with the values averaged to obtain a single noise estimate. The threshold for SNR maps to create binary SNR map was chosen such that it minimizes the ratio between the number of artifactual voxels where ν_icvf≥0.999 and the total number of voxels in the SNR mask (Figure 3B), yielding a value of 39. This was motivated by the observation that unrealistically high ν_icvf values typically occur in low-SNR areas (Figures 3Aii,iii). This threshold selection represents a trade-off between removing unrealistic voxels while retaining as many voxels as possible.

For the region of interest (ROI) analysis, the JHU-ICBM-DTI-81 WM atlas (Hua et al., 2008) was transformed into the native space using the inverse of the combined deformation field. Two sets of ROIs were defined: (i) whole-WM ROIs and (ii) high-SNR ROIs, used for the main analysis. The whole-WM ROIs included those of the JHU-ICBM-DTI-81 WM atlas that were completely in WM_group defined in 2.6, yielding 43 ROIs (out of 48, leaving out the column and body of the fornix, the left and right cingulum part in the vicinity to the hippocampus, and the left and right uncinate fasciculus). The high-SNR ROIs included only those whole-WM ROIs that overlapped with the high-SNR WM_group to at least 95%, yielding 21 ROIs (Figure 4 and Table 2). For the analyses, group-averaged g_MR, AVF_MR, and MVF_MR were calculated within the WM_group. Note that averaging included both sessions of each subject for all analyses except for the analysis in section “Test-Retest Analysis of the Group-Averaged MR G-ratio, Axon, and Myelin Volume Fraction.”

The group-averaged gMRB1 of the first and second session were compared within the previously mentioned 21 high-SNR ROIs using Bland-Altman plots (Bland and Altman, 1986). In the Bland-Altmann plots, the differences in gMRB1 between the first (gMR1B1) and second (gMR2B1) session (δiretest=(gMR1B1)i-(gMR2B1)i) were plotted against their means (meaniretest=(gMR1B1)i+(gMR2B1)i2), where i is the index of ROI i. Bias captures the offset (δ¯retest=121∑i=121δiretest), while error (ϵretest=1.96⋅120∑i=121(δiretest-δ¯retest)) captures the variation between the first and second scan within the i^th ROI. The computed δ¯retest and ϵ^retest were normalized by the dynamic range (△_DR) of gMRB1 within the high-SNR ROIs, defined as △DR=maxi∈ROI(meaniretest)-mini∈ROI(meaniretest), yielding the relative error (δDR%retest=ϵretest△DR⋅100) and relative bias (δ¯DR%retest=δ¯retest△DR⋅100). The same procedure was also applied to AVFMRB1 and MVFMRB1.

The distinction between bias and error is important, because while a potential bias can be retrospectively corrected, the error in the MR g-ratio method defines its sensitivity to detect differences between individuals, groups, or time points. To reliably capture these differences, the error must be significantly lower than the expected effect size.

Bland-Altman analysis was used to compare g_MR with and without B₁+ correction. In particular, the difference δiB1 in g_MR between (gMRB1)i, when using the reference method B₁+ correction, and (gMRk)i, when using no (k = NO) or UNICORT (k = UN) B₁+ correction: δiB1=(gMRB1)i-(gMRk)i was plotted against their mean: meaniB1=(gMRB1)i+(gMRk)i2, with i being the index of the 21 high-SNR ROIs. The bias and error associated with the lack of (or UNICORT) B₁+ correction are defined as δ¯B1=121∑i=121δiB1 and ϵB1=1.96⋅120∑i=121(δiB1-δ¯B1), respectively.

The computed ϵ^B1 and δ¯B1were normalized by the dynamic range of gMRB1 within the high-SNR ROIs, yielding the relative error (ϵDR%B1=ϵB1△DR⋅100) and relative bias (δ¯DR%B1=δ¯B1△DR⋅100). The same procedure was also applied to AVF_MR and MVF_MR, comparing them to their respective reference method and dynamic range. For MVF_MR, the Bland-Altman analysis was additionally done using the whole-WM ROIs instead of the high-SNR ROIs (see section “Region of Interest Selection”) to assess the influence of including low-SNR voxels in the analysis.

To assess group variability for each correction method, the coefficient-of-variation (CoV) across subjects and sessions was calculated for MVF_MR, AVF_MR, and g_MR in the MNI space after applying tissue-weighted smoothing (Tabelow et al., 2019), yielding: CoVMRB1, CoVMRUN, and CoVMRNO, where MR ∈ {g_MR,AVF_MR,andMVF_MR}. For tissue-weighted smoothing, a full width at half maximum Gaussian smoothing kernel of 6 mm was used. Bland-Altman analysis (see section “Test-Retest Analysis of the Group-Averaged MR G-ratio, Axon, and Myelin Volume Fraction”) was used to compare CoVMRUN and CoVMRNO against CoVMRB1 based on the reference method, yielding bias (δ¯CoV) and error (ϵ^CoV) values. A higher variability across the brain is expected to increase δ¯CoV whereas a higher local variability is expected to increase ϵ ^CoV.

Voxel-wise maps of group-averaged gMRB1, AVFMRB1, and MVFMRB1 in WM are shown in Figure 5. The group-averaged mean and standard deviation of gMRB1, MVFMRB1, and AVFMRB1 in 21 high-SNR ROIs are reported in Table 1 and Figure 6. The dynamic range (△_DR), minimum and maximum values, and mean and standard deviation of gMRB1, AVFMRB1, and MVFMRB1 across ROIs are listed in Table 2. The largest gMRB1 and AVFMRB1 were found in the right anterior limb of the internal capsule (0.688 and 0.384, respectively), while the largest MVFMRB1 was in the genu of corpus callosum (0.445), where also the lowest gMRB1 (0.642) can be found. The lowest AVFMRB1, and MVFMRB1 were found in the right posterior thalamic radiation (AVFMRB1 = 0.308) and in the left external capsule (MVFMRB1 = 0.408), respectively. The △_DR was the smallest for MVFMRB1 (0.037), followed by gMRB1 (0.046) and AVFMRB1 (0.076).

The relative error (ϵDR%retest) and bias (δ¯DR%retest) values of the test-retest analysis are summarized in Table 3 and shown as Bland-Altmann plots in Figure 7. The test-retest analysis revealed a δ¯DR%retest below an absolute value of 8.4% for each metric (gMRB1, AVFMRB1, and MVFMRB1), where the AVFMRB1 showed the lowest δ¯DR%retest with 0.79% (Figure 7 and Table 3). The ϵDR%retest was below 22.2% for each metric, where the AVFMRB1 showed the lowest ϵDR%retest with 20.5% (Figure 7 and Table 3).

The relative error (ϵDR%B1) and bias (δ¯DR%B1) values of the B₁+ correction analysis are summarized in Table 4 and shown as Bland-Altmann plots in Figures 8, 9. For g_MR, compared to the no-correction case, UNICORT showed both lower ϵDR%B1 (UNICORT vs. no correction: 10.9% vs. 37.0%) and δ¯DR%B1 (30.4% vs. −89.1%). For both AVF_MR and MVF_MR, UNICORT yielded lower ϵDR%B1 (UNICORT vs. no correction; AVF_MR: 5.3% vs. 15.8%; 16.2% vs. 59.5%) and lower δ¯DR%B1 (AVF_MR: 14.5% vs. −40.8%; MVF_MR: 48.6% vs. 143.2%). Altogether, the UNICORT correction reduced the bias and error in the MR g-ratio and its constituents by roughly a factor of three. The lower ϵDR%B1 and δ¯DR%B1 associated with UNICORT was also reflected by the fact that values of gMRUN, AVFMRUN, and MVFMRUN (Figure 8, lower panel) lie closer to the unit slope line than values of gMRNO, AVFMRNO, and MVFMRNO (Figure 8, upper panel). When computing ϵDR%B1 and δ¯DR%B1 of g_MR in the whole-WM ROIs (see Supplementary Figure 1), δ¯DR%B1 was consistently lower for both the no-correction case (whole-WM ROIs vs. high-SNR ROIs: 36.5% vs. 143.2%) and UNICORT (13.1% vs. 48.6%), whereas ϵDR%B1 was similar (no-correction: 52.8% vs. 59.5%; UNICORT: 24.0% vs. 16.2%).

g_MR showed on average smaller CoV than AVF_MR and MVF_MR (Figure 10). In all maps, the CoV was the highest in the deep brain areas. The relative error (ϵCoVCoVB1⋅100) and bias (δ¯CoVCoVB1⋅100) values of CoV with respect to the B₁+ reference measurement are summarized in Table 5 and the error and bias are also displayed as Bland-Altman density plot in Figure 11. For g_MR, compared to the no correction case, UNICORT showed similar ϵ^CoV (UNICORT vs. no correction: 0.6% vs. 0.6%) but lower δ¯CoV (−0.1% vs. −0.4%). UNICORT yielded higher ϵ^CoV (UNICORT vs. no correction; 1.0% vs. 0.8%) and lower δ¯CoV (−0.2% vs. −0.4%) for AVF_MR, and higher ϵ^CoV (1.2% vs. 0.4%) and higher δ¯CoV(−0.5% vs. −0.1%) for MVF_MR. The lower δ¯CoV of g_MR and AVF_MR associated with UNICORT reveals itself as a slight shift of the points toward the unit slope line in the scatter density plot (Figure 12).

MT_sat have been often used as a proxy for the MVF_MR in g-ratio weighted imaging (Mohammadi et al., 2015; Campbell et al., 2018; Ellerbrock and Mohammadi, 2018; Hori et al., 2018; Kamagata et al., 2019), because they are directly linked to the macromolecular pool with an intrinsic correction for underlying longitudinal relaxation time and B₁+ field inhomogeneities effects (Helms et al., 2008). Despite the latter intrinsic correction for B₁+ field inhomogeneities, we found that the residual B₁+ effects on MT_sat map were still observable. In particular, the bias and error of the MR g-ratio (g_MR) was about −89 and 37% higher, respectively, when omitting the B₁+ correction. We found the same trend for MVF_MR and AVF_MR; while the error and bias were even larger for MVF_MR when B₁+ correction was omitted, it was smaller but still substantial for the AVF_MR. We found that omitting B₁ + leads to a substantially higher (more than 10-fold) bias in the MR g-ratio and its constituents when compared to a test-retest analysis of our data (Figure 7 and Table 3). Also, the error due to omitting the B1+ correction was twice as large as the error observed in the test retest analysis for the MR g-ratio and the MVF, whereas for AVF the errors were similar. We expect that the high error will be of particular relevance for group studies because it can be regarded as an error that evolves when replacing the reference method with the alternative method. For comparison, age-related changes assessed by g-ratio weighted imaging (Cercignani et al., 2017; Berman et al., 2018) have been reported to vary between 30 and 100% (in absolute values: g_MR0.02–0.04 (Figure 5 in Cercignani et al., 2017). Consequently, the reported effect size of age-related changes would have become potentially undetectable if the B₁+ field correction has been omitted in the study of Cercignani et al. (2017). The B₁+ effect is particularly relevant for the MR g-ratio method by Cercignani et al. (2017) that combined quantitative MT (Gloor et al., 2008) with NODDI, because the qMT method does not possess an intrinsic correction for B₁+ field inhomogeneities as opposed to the MT_sat methods used here. Note that we reported, for better intuition, the bias and error relative to the dynamic range of the parameters across the investigated white matter (WM) ROIs (the dynamic range of g_MR is △_DR = 0.046; the absolute bias and error can be found in Table 4).

To reduce this source of bias and error, we propose a data-driven approach to correct for B₁+ field inhomogeneities when no B₁+ field measurement is available. To this end, we used UNICORT to estimate the B₁+ field (Weiskopf et al., 2011). We found that using the UNICORT-estimated B₁+ field to correct residual B₁+ field inhomogeneities in MT_sat reduces at the group level the bias and error in the MR g-ratio and its constituents by roughly a factor of three. However, the UNICORT estimated B₁+ inhomogeneity can be erroneous with the error varying across subjects. To assess this variability, we estimated coefficient-of-variance (CoV) maps of g_MR, AVF_MR, and MVF_MR for all three methods. In general, an increased CoV can be found at tissue boundaries (e.g., cerebral spinal fluid to WM) due to slight misregistration between the maps of axonal and myelin markers and/or imperfect normalization (Figure 10). Additionally, we found a strong increase in the bias and error of the CoV of MVF maps (increase in bias: 11% and in error: 18%) when UNICORT B₁+ correction was used as compared to no correction. The CoV of g_MR and AVF_MR did not show a consistent trend: while the bias decreased, the error increased for both parameters. In other words, the UNICORT B₁+ correction leads to higher accuracy in the g-ratio and its constituents but comes at the cost of a lower precision in MVF.

Our gMRB1 and AVFMRB1 across the white matter were within the range of the reported values of previous studies (g_MR: 0.64–0.76; AVF_MR: 0.26–0.43 in (Cercignani et al., 2017; Berman et al., 2018). The range of MVFMRB1 was in the upper half of previously reported values (0.17–0.42 in Cercignani et al., 2017). Our slightly higher MVF_MR values might be due to differences in the calibration approach: while we calculated the reference MVF_REF from previously published ex-vivo histology data (Graf von Keyserlingk and Schramm, 1984), Cercignani et al. (2017), used a reference from previously published ex-vivo histology g-ratio data in the corpus callosum and Berman et al. (2018), did not perform any calibration assuming that macromolecular tissue volume and MVF_MR are equal. An error in the calibration constant can lead to a bias in the MVF estimates which in turn leads to an error and bias in the MR g-ratio (Campbell et al., 2018).

As this study calculates the in-vivo MR g-ratio, there is no histological data available from the participants of this study, which could be used for calibration or as a gold standard reference. For calibration of MT_sat to MVF_MR, we estimated the histological MVF (MVF_hist) from published ex-vivo data within the human medulla oblongata (Graf von Keyserlingk and Schramm, 1984). Since the reference MVF_hist and the calibrated MT_sat map were taken from different subjects, this might introduce a systematic bias in the MR g-ratio. However, since we found a relatively good agreement between our g_MR, AVF_MR, and MVF_MR values with previously reported values obtained by a different calibration approach (Cercignani et al., 2017; Berman et al., 2018), we expect that it had a small effect on the results. Moreover, we focused on the effect of omitting B₁+ correction, which will lead to additional inaccuracies in g-ratio weighted imaging, independent of the quality of the calibration.

Although, not reported in previous NODDI-based g-ratio mapping studies (Stikov et al., 2015; Cercignani et al., 2017; Jung et al., 2017; Mancini et al., 2017; Ellerbrock and Mohammadi, 2018; Hori et al., 2018), we found that the intra-cellular volume fraction (ν_icvf) determined with NODDI tends to be biased at small signal-to-noise ratios (SNR < 39), resulting in a ceiling effect, i.e., ν_icvf ≈ 1. To avoid a corresponding bias in g_MR (and AVF_MR), we restricted the analysis to regions with sufficiently high SNR (Figure 3). To investigate whether our findings generalize to low-SNR regions as well, we performed an additional Bland-Altman analysis of MVF_MR in whole-WM ROIs. To this end, a larger set of ROIs was used covering the entire white matter. Although the bias was smaller for the whole-WM as compared to the high-SNR ROI analysis, we found the same trend: the error and bias were reduced when using UNICORT B₁+ correction relative to no correction. Note that the smaller bias for the whole-WM analysis is most probably an artifact of the calibration procedure. Since the ROI used for calibration was not part of the high-SNR ROIs but was part of the whole-WM ROIs, we think it could have reduced the bias in the whole-WM ROI analysis as compared to the high-SNR analysis.

We note that the presented results were based on a customized B₁+ mapping method (Lutti et al., 2010). Using vendor specific protocols for B₁+ and MT_sat mapping may influence the results (Leutritz et al., 2020). Moreover, the calibration factor in Equation (1) may have to be recalibrated for different MT-pulses.

Future studies should investigate the effect of B₁+ correction on MR g-ratio mapping when using alternative biomarkers to estimate AVF_MR and MVF_MR (e.g., Ellerbrock and Mohammadi, 2018). Moreover, there are alternative B₁+ mapping approaches available which might vary in precision (Lutti et al., 2010) and therefore can affect the MR g-ratio values. However, the differences in the precision of these methods are in the order of few percentage and thus much smaller than the effect of omitting the B₁+ field or using the data-driven UNICORT B₁+ estimate (Weiskopf et al., 2011).