Mapping magnetization transfer saturation (MTsat) in human brain at 7T: Protocol optimization under specific absorption rate constraints

To optimize a whole‐brain magnetization transfer saturation (MTsat) protocol at 7T, focusing on maximizing obtainable MTsat under the constraints of specific absorption rate (SAR) and transmit field inhomogeneity, while avoiding bias and keeping scan time short.


| INTRODUCTION
Magnetization transfer (MT) is a unique contrast mechanism enabling detection and quantification of otherwise MRinvisible macromolecules. 1,2 MT is highly correlated with myelination 3 and thus used to study white matter (WM) diseases, most notably multiple sclerosis. 4,5 Contrast is induced by applying high-energy, off-resonance radiofrequency (RF) pulses, targeting the broad absorption line of the rotationally restricted protons bound to macromolecules. This magnetic saturation is then transferred to the free water, where it manifests as a tissue-specific decrease in signal amplitude.
At 7T, the application of MT pulses is curtailed by safety limits of the specific absorption rate (SAR) which increases quadratically with field strength. This limits the achievable signal reduction and the range of any derived metrics. In addition, the more pronounced RF inhomogeneities at 7T may impose a spatial bias. Further, because of the increased Larmor frequency at 7T, it must be avoided that chemical exchange saturation transfer (CEST) resonances overlap with the saturation profile of the off-resonance RF pulse. 6 Due to these challenges, MT-mapping is still relatively uncommon in an ultra-high field (≥7T) in vivo setting, although it has been performed using either a twopool model [7][8][9][10] or through measurement of the Z-spectrum and subsequent multiple-pool analysis at 7T 11 and 9.4T. 12 Nevertheless, the signal reduction by MT-weighting benefits from higher field strength due to the longer T 1 . 2,13 Further, the shift of the macromolecular absorption line with regard to the free water resonance will also increase at higher field strengths. 14 This warrants further investigation of the feasibility of in vivo MT at 7T.
From the MT-weighted (MT-w) signal, semi-quantitative metrics can be derived to describe the MT effect. The MT saturation (MT sat ) represents the fraction of free water saturated by a single MT pulse during repetition time (TR) 15 and care must thus be taken to minimize contributions that confound MT when implementing it. MT sat is obtained from an empirical signal equation of an MT-w spoiled gradient echo, which is supplemented by two spoiled gradient-echo acquisitions with T 1 -and proton density (PD)-weighting (forming a dual flip angle [DFA] experiment). Because of this, MT sat is unbiased by T 1 relaxation (for a small flip angle [FA] and TR << T 1 ) unlike the conventional magnetization transfer ratio (MTR) where T 1 relaxation will counteract MT and reduce contrast. Also unlike MTR, the quadratic dependence of MT on the transmit field 16 cancels out in the algebraic derivation of MT sat , thus inherently compensating for FA inhomogeneities to a large extent. MT sat thus provides a time-efficient alternative to fully quantitative techniques but with increased specificity and contrast compared to MTR. MT sat is mostly used in a multi-parameter mapping (MPM) context, 17,18 for which dedicated processing tools have been developed. 19 Thus far, MT sat has mainly been implemented at 3T where it has been used in a variety of clinical studies. These include research on spinal cord injury, 20,21 effects of aging [22][23][24] as well as multiple sclerosis to assess the g-ratio 25,26 and to discriminate between disability levels. 27 In this study, the steps of optimizing MT-weighting in the context of an MPM protocol for whole-brain imaging are described, explicitly addressing the 7T specific issues of increased SAR and compromised transmit field homogeneity. The developed MT-w sequence was added to an established 7T DFA protocol 28 to obtain MT sat . The choices of MT pulse shape, TR, readout FA and offset frequency are discussed based on separate experiments. Correction for residual effects of transmit field inhomogeneities was also addressed, and efforts were made to maintain a clinically feasible scan time (~5 min) with sub-millimeter resolution. Last, the repeatability of the suggested protocol was tested on a single subject.

| MT sat
A 3D spoiled gradient-echo MT-w sequence can be described by a simple signal equation to the introduction of MT sat, the fractional decrease in longitudinal magnetization of free water, M z , due to a single saturation event within TR. 15 For small FAs 29 and for T 1 >> TR, the imaging steady-state signal from an MT-w spoiled gradient echo, S MT , is approximated: where MT denotes MT sat , is the readout FA in radians, R 1 = 1∕T 1 and S 0 is the signal amplitude under fully relaxed conditions, ie, TR >> T 1 . Using maps of R 1 and S 0 obtained from a DFA experiment, MT is calculated from S MT : The influence of transmit field inhomogeneities are introduced into Equation (2) through the substitution f T nom = , where f T is the transmit field bias and nom is the nominal FA (set in the user interface). Using this substitution in the equations for S 0 and R 1 in a DFA experiment, one obtains S 0 = S 0,app ∕f T and R 1 = R 1,app f 2 T , where S 0,app and R 1,app are the corresponding estimates obtained with nominal FAs. 29 Equation (2) can be re-written in a similar way: The longitudinal magnetization of the macromolecular pool, M z,b , is reduced by the MT pulse, 1 = B 1 of duration t sat . This is described by differential absorption 16 : where g b 2 ΔT 2,b is the super-Lorentzian macromolecular absorption lineshape, Δ is the MT pulse offset frequency and T 2,b is the transverse relaxation time of the macromolecular pool. Direct saturation of M z can also be described by Equation (4), except with a Lorentzian lineshape governed by T 2 . If no other confounding contrast mechanism is present and the decrease of M z,b (t) during t sat can be ignored, the ensuing transfer renders MT to the macromolecular pool size fraction, F b : Hence, MT will depend not only on macromolecular content, but also on lineshape and transmit field inhomogeneities as well as the apparent transfer rate. 15 However, the square of 1 is mirrored by MT = f 2 T MT,app in Equation (3). This means that by using MT,app one gets a reflection of the macromolecular content, which is inherently compensated for transmit field inhomogeneities, motivating the use of nominal FAs for calculation of MT sat : MT sat henceforth refers to the metric calculated using nominal FAs (Equation (6)).

| RF energy and pulse shape
The power integral ∫ t sat 0 2 1 (t) dt is often used as a surrogate parameter in SAR models. As described above, this integral also governs the energy and induced MT (Equation (5)) of the MT pulse through the differential absorption law (Equation (4)). The power integral can be expressed as: where 1,max is the maximum amplitude of the RF pulse and the rightmost normalized integral depends solely on the normalized RF shape ́1 t ′ . By using sat = 1,max t sat ∫ 1 0́1 t � dt � , the power integral is expressed in terms of sat and t sat , which can be controlled experimentally: where the shape factor: carries the influence of the pulse shape. Note that Q = 1 for a rectangular pulse.

| Noise propagation into the MT sat map
The signal in Equation (1) can be expressed in analogy to the Ernst equation by using R 1,MT = R 1 + MT ∕TR. 30 For a fixed TR and MT pulse, noise propagation from S MT into MT,app is minimized for an optimal readout FA 31 : where MT,max yields the highest signal in the MT-w acquisition and can be obtained by a variable FA experiment and a linear fit to the signals. 29 The full derivation is given in Supporting Information, which is available online. As in the DFA experiment, 28 a global optimization of MT,max is not possible.

| Residual effects of transmit field
inhomogeneities From the f 2 T -dependence in Equation (3) and the 2 1 (t) -dependence in Equation (5), it is clear that MT,app should be compensated for FA inhomogeneities. However, the decrease in M z,b under the duration of the MT pulse (t sat ) will render induced saturation and hence MT smaller than what would be expected from differential absorption (Equation (4)). Thus, MT,app will be somewhat overcompensated by the inherent f 2 T -correction, leading to an underestimation when f T > 1 and an overestimation when f T < 1. This f T dependence of MT,app can be described empirically by a linear dependence 32 : where A and B are phenomenological parameters specific to the MT pulse shape and duration. Equation (11) explicitly contains the nominal FA of the MT pulse, hence A and B can be obtained by varying sat,nom and performing a linear regression of MT,app f T ∕ 2 sat,nom versus sat . Given that the final transmit field-corrected estimate is MT,corr = MT,app f T = 1 = A 2 sat,nom 1 − B sat,nom , the correction takes the form: where the product B sat,nom = C forms a pulse-specific parameter, which is used for post hoc transmit field correction of MT sat .

| METHODS
Experiments were performed on an actively shielded 7T MR system (Achieva, Philips Healthcare, Best, NL) with a head coil of 32 receive and 2 transmit channels with fixed phase setting (Nova Medical, Wilmington, MA). Eight healthy adult subjects (six females, 19 to 37 y old) were scanned after giving informed written consent as approved by the regional Ethical Review Board.
To map MT sat , an MT-w sequence was run in conjunction with a DFA experiment, thus forming an MPM protocol. For all three series, a non-selective 3D RF-spoiled multi-echo gradient-echo sequence was used with in-plane phase encoding anterior-posterior. Isotropic voxels of (0.9 mm) 3 were defined within FOV FH,AP,RL = 230 × 230 × 200 mm 3 (with some variation to match head size). Eight equidistant echoes with fat and water in-phase (multiples of TE = 1.97 ms) were acquired, with alternating readout gradient polarity at a bandwidth of 670 Hz/px. To reduce measurement time, an elliptical k-space coverage was combined with SENSE AP,RL = 2 × 2. The readout RF pulses had a 700 μs asymmetric Gaussfiltered sinc shape to reduce sensitivity to B 0 inhomogeneities and incidental MT effects. 28,33 Other parameters unique to the DFA experiment were α 1 /α 2 = 16°/4° and TR = 18.1 ms. 28 After default automatic adjustment based on the DFA sequence with higher FA, the transmit and receive gain calibration was kept constant throughout the experiment.
Dedicated experiments were performed to study the effect of different sequence parameters on MT sat to obtain the maximum range of MT sat at the 100% SAR level while avoiding bias and keeping scan time short.
FA-mapping was performed using Dual Refocused Echo Acquisition Mode (DREAM) 34 and optimized for the prolonged T 1 at 7T through a slice thickness ratio of 2.0 and a shot interval of 12 s. 35 Acquisition of 48 transverse slices with FOV AP,RL = 240 × 240 mm 2 , voxel size 3.75 × 3.75 × 3.50, slice gap 0.25 mm was accomplished at 4796 Hz/ px readout bandwidth. Three separate DREAM acquisitions with preparation FAs α STEAM,nom = 25°, 40°, 60° were combined offline. 36 Offline processing was performed using MATLAB and FSL. 37 Volumes were averaged across TEs to boost SNR 38 and co-registered using FLIRT. 39,40 MT sat was calculated using Equation (6) and transmit field-corrected using Equation (12) with C as determined below (see Results 4.6) over a common brain mask obtained by BET. 41 Whole-brain histograms were used to evaluate the MT sat maps. Histograms facilitate an intuitive assessment of global changes, where the separation of modes reflects contrast and the broadness reflects SNR. The histograms were typically between −0.5 and 2.5 p.u., using a bin size of 0.01 p.u. For more specific analysis of tissue types, automatic segmentation of WM, gray matter (GM), and cerebrospinal fluid (CSF) was favorably performed on the MT sat maps using FAST. 42 Only pixels with a tissue probability of 1 were evaluated to avoid partial volume effects. CSF was analyzed only within the ventricles.

| Shape of MT pulse
The choice of MT pulse was motivated by previous 3T implementations where a Gaussian with t sat = 4 ms and α sat,nom = 220° was used. 43,44 This MT pulse yields a good compromise between frequency response and short t sat . Since a Gaussian was not available on the system, a similar Gaussian-filtered sinc main lobe was used.
The 4 ms sinc main lobe pulse and a consecutive spoiler added 8.4 ms to the TR of the DFA acquisitions. If α sat,nom = 220° were to be used, the TR would be increased by an additional 13 ms due to SAR limitations. To ensure the shortest possible scan time, α sat,nom was reduced to 180° (the maximum value compatible with TR = 26.5 ms), resulting in a scan time of 4:58 min. This decrease in scan duration will come at the expense of induced MT (see Equation (8)).
To illustrate the choice of pulse shape, four MT pulses with different shapes were compared for identical α sat = 180° and energy (ensuring same MT sat , and same SAR). The compared pulse shapes were (a) a five-lobe sinc (Q = 5.26, t sat = 15.8 ms, B 1,rms = 1.70 μT), which is the default MT pulse shape on the system (b) the implemented sinc main lobe (Q = 1.33, t sat = 4.0 ms, B 1,rms = 3.37 µT), (c) a Gaussian with cutoff at 2% of maximum (Q = 1.61, t sat = 4.8 ms, B 1,rms = 3.10 µT), and last, for reference, (d) a rectangular pulse (Q = 1.00, t sat = 3.0 ms, B 1,rms =3.91 µT). The frequency response profiles were simulated by numerically solving the Bloch equations, ignoring relaxation effects, using the RF Pulse Wizard tool as provided with a copy of Ref. 45.
The nominal α E,MT was determined through pixelwise linear fitting of the four FAs in the brain parenchyma (segmented WM+GM). 46 Thereafter, the median was used to calculate the nominal α opt in Equation (10). The behavior of MT sat in WM, GM, and CSF was studied to identify the occurrence of bias.

| Offset frequency
With RF pulses and timings established, the offset frequency of the MT pulse needs to be determined. On one hand, a strong increase in saturation and thus in MT sat is expected at smaller offsets due to the super-Lorentzian lineshape of the macromolecules. 47,48 On the other hand, care must be taken to limit direct saturation and CEST. Thus, Δ was varied through 0.75, 1.0, 1.5, and 2.0 kHz on one subject (19y-old female, α sat,nom = 180°, t sat = 4 ms). Settings of Δ < 0.75 kHz were not employed to avoid direct saturation by the sidebands at 0.48 kHz indicated by the simulations (see the Results section 4.1).
The T 2,b has been shown to be quite similar in WM and GM. 48,49 Hence, it was assumed that WM and GM have comparable absorption lineshapes. The MT-related component of MT sat should therefore vary proportionally with Δ. The difference in average MT sat between WM and GM at the largest Δ = 2.0 kHz (where direct saturation and CEST were assumed negligible) was calculated across all axial slices containing brain pixels. Any disproportionate increase of MT sat , ΔMT sat , in GM relative WM at lower Δ was attributed to either direct saturation in tissue or CEST.

| Negative offset frequency
The lineshape of the macromolecules is shifted with respect to the free water resonance by -2.34 ± 0.17 ppm (−697 Hz at 7T) in WM. 14 To examine how much MT sat can be gained by this asymmetry, the MT pulse was applied with either a positive or a negative offset frequency (Δ = ±2.0 kHz) in one subject (19-y-old female, α sat,nom = 180°, t sat = 4 ms). To take B 0 inhomogeneity into account, the free water frequency offset, f 0 , was also measured. A linear function of MT sat as a function of f 0 (in kHz) was fitted in segmented WM in a slice covering an area above the sinuses. Resulting slopes using Δ = ±2.0 kHz were then compared.

| Residual effects of transmit field inhomogeneities
To determine the correction factor C for the chosen MT pulse, the nominal FA of the MT pulse was varied within a range of α sat,nom = 45°-180° (B 1,rms = 0.87-3.37 μT) in four subjects (three female, 23 to 28 y old). This variation of α sat,nom mimics a variation of f T down to 25% as typically observed in the cerebellum at 7T. 36 The variation of α sat,nom was performed as follows: Subject #1: α sat,nom = 60-180° in steps of 30°. Subject #2: α sat,nom = 120°-180° in steps of 20°. Subject #3 α sat,nom = 60°-180° in steps of 20° with extra measurements at 45°, 90°, 135°. Subject #4: α sat,nom = 80-180° in steps of 10° with an extra measurement at 135°. For subjects #1-#3, each series were acquired twice to increase robustness, resulting in 10, 8, 20, and 12 MT sat maps for the respective subjects. All MT sat maps for a subject were based on a single pair of DFA-derived T 1 -and S 0 maps. In Equation (11), δ MT,app was divided by (α sat,nom ) 2 to obtain C in four ROIs by linear fitting. The ROIs were manually defined symmetrically (left-right) in frontal WM (average across all ROIs and subjects was n pixels = 794 ± 220) and in the caudate head (average across all ROIs and subjects was n pixels = 644 ± 286), where the latter represented GM. When performing the fit, each δ MT,app /(α sat,nom ) 2 data point was weighted by the inverse of the ROI standard deviation for the particular α sat,nom used (ie, points acquired with α sat,nom = 45° were weighted less than points acquired with α sat,nom = 180°). This was done to reduce the influence of noise on the fitting as SNR correlates strongly with α sat . Out of these 4 × 4 = 16 estimates of C, averages for GM (8 ROIs) and WM (8 ROIs) were calculated, as well as a total average, C mean , of all ROIs, to be used for post hoc correction across the entire brain.

| Repeatability
After sequence parameters and f T -correction had been established, the MPM protocol was repeated three times on a single subject to measure repeatability. By all combinations of T 1 -w, PD-w, and MT-w images, this resulted in 3 × 3 × 3 = 27 MT sat maps. Maps of the relative deviation from the mean of all 27 maps were calculated as well as the SD.

| Shape of MT pulse
The FWHMs in the frequency responses ( Figure 1, panel C) were very similar for all of the four MT pulses, yielding Δ 1/2 = 0.28, 0.30, 0.29, 0.27 kHz for the five-lobe sinc, sinc main lobe, Gaussian and rectangular pulse at their respective pulse durations. The sinc main lobe still showed small sidebands (1.6%) at ±0.48 kHz (21.6% for the rectangular pulse) which imposes a lower limit on Δ to avoid direct saturation. The time-inefficient nature of the five-lobe sinc is demonstrated by the square of the B 1 amplitude (Figure 1, panel B) where very little saturation is created by the sidelobes. The increase in t sat by 11.8 ms compared to the sinc main lobe would increase acquisition time by ~45%. If a fixed TR = 26.5 ms and t sat = 4 ms was imposed, the frequency response of the five-lobe sinc was very wide (Δ 1/2 = 1.31 kHz at α sat = 91° and 100% SAR). These features confirmed that the appropriate shape of the MT pulse is a shaped single lobe (here a Gauss-filtered sinc main lobe).

| Readout FA
The MT sat maps obtained with different readout FAs were highly consistent (Figure 2). Like at 3T, 15 a systematic positive shift of MT sat with increasing α nom is observed where MT sat in WM increased by 0.12 p.u. at α nom = 8° compared to at α nom = 2°.
The nominal value of α MT,max in the brain parenchyma, spatially correlated to f T , 28 had a median of 12.4°, which would require α nom ≈ 7° for optimal noise progression. In the CSF, progressive saturation at higher α nom due to long T 1 leads to lower SNR and a consecutive positive shift due to Rician noise distribution.
A nominal readout FA of α nom = 4° was deemed a suitable compromise between yielding good SNR in the brain parenchyma, limiting the observed bias (average MT sat in WM of 1.28 ± 0.15 p.u. vs. 1.38 ± 0.17 p.u. for α nom = 8°), and preserving a distinct CSF mode in the histograms. This value was thus chosen for the final protocol.

| TR
Increasing TR resulted in only a minor increase of MT sat at TR = 40.3, 45.0 ms in WM ( Figure 3). Thus, the shortest possible TR = 26.5 ms allowed by the pulse sequence timing at t sat = 4 ms was chosen for the protocol.

| Offset frequency
As expected, MT sat increased strongly as Δ was decreased ( Figure 4). However, the modes of GM and WM appeared

| Negative offset frequency
At an offset frequency of Δ = -2.0 kHz, a larger MT sat was observed compared to Δ = +2.0 kHz ( Figure 6). Average MT sat increased by 45% in WM (1.14 ± 0.16 vs 1.65 ± 0.20 p.u) and by 35% in GM (0.49 ± 0.17 vs 0.66 ± 0.16 p.u.). This observation is in accordance with the shift of the macromolecular absorption line to lower frequencies.
Residual B 0 inhomogeneities shift f 0 to higher frequencies in most of the brain (82%/71% of WM/GM pixels). In these pixels, a negative Δ will increase the distance to free water (Δf 0 ) and to resonances underlying relayed Nuclear Overhauser Effects (rNOE), and thus reduce contributions from these effects. This is reflected by a negative correlation of MT sat to f 0 (-1.0 p.u. per kHz) for Δ = -2.0 kHz in WM in an axial slice close to the sinuses (Figure 7). For Δ = +2.0 kHz, a positive correlation (+0.6 p.u. per kHz) is observed when the distance to free water and CEST resonances decreases at higher f 0 . To maximize MT sat , the MT pulse was applied at Δ = -2.0 kHz in the finalized protocol.

| Residual effects of transmit field inhomogeneities
The average C across all ROIs was C mean = 0.34 ± 0.11. There was no significant difference (P = .25 for a two-tailed student's t-test) between average C in WM/GM ROIs (0.31 ± 0.09/0.37 ± 0.09). The average coefficient of determination was r 2 = 0.20 ± 0.12 across all fits. Figure 8 shows scatter plots of δ MT,app / (α sat,nom ) 2 versus α sat for an example subject, the fitted line, and corresponding C estimate for each of the 4 ROIs. A figure of all four subjects is provided in Supporting Information Figure S1. The decrease of δ MT,app /(α sat,nom ) 2 as a function of local α sat illustrates the additional f T dependence introduced by reduction of M z,b during the MT pulse. The best fit under the constraint that the combination of slope and intercept results in C = C mean = 0.34 is also shown. This fit is still in agreement with experimental data since an incremental change in slope and intercept of the line can result in rather large changes in C.
MT sat maps, before and after correction, of one subject (28-year-old male) acquired with the finalized protocol (Supporting Information Table S1) are shown in Figure 9. Substructures within the basal ganglia are clearly delineated and cortical boundaries are well defined. Before correction, however, locations of increased MT sat coincide with those of low transmit field amplitude. This bias was alleviated after the correction which also distinctly narrowed the WM mode in the histogram. MT sat appeared to be somewhat blurrier in peripheral cortical areas where f T < ~0. 6. In areas with f T < ~0.3, MT sat was indistinguishable from noise, indicating the limit of the method at 7T.

| Repeatability
Maps of the relative deviation from the average MT sat and the resulting SD can be seen in Figure 10. The median SD in WM was 0.18 p.u. The variability is most prominent in the inferior F I G U R E 4 Offset frequency. Top row: MT sat maps (left) acquired with Δ = +0.75, +1.0, +1.5, +2.0 kHz and corresponding histograms (right). Bottom row: Bar graph showing mean/SD in segmented ventricular CSF, GM, and WM. Overall MT sat increases strongly with decreasing Δ but there is also a positive shift of MT sat , indicating confounding saturation effects at lower Δ regions of the cerebellum and temporal lobes. These regions suffer from low transmit field amplitude as well as being more susceptible to physiologic noise caused by breathing. 50

| DISCUSSION
At 7T, limits imposed by SAR and an inhomogeneous transmit field (approximately 0.3 ≤ f T ≤ 1.5, see Figure 9) are exacerbated. Nevertheless, we obtained MT sat maps of a quality comparable to 3T, 15,31,43,44 although limitations were observed in areas of low transmit field amplitude (local α sat < ~100°, f T < ~0.6) where MT sat could be somewhat noisier. At very low transmit field amplitude (local α sat < ~60°, f T < ~0.3), reliable estimates for MT sat could not be obtained. In addition to decreasing SNR due to lower α sat , R 1 and S 0 cannot be reliably determined at very low f T by the underlying DFA experiment when the higher local FA decreases below the Ernst angle. 28 It could therefore be beneficial to use multi-channel transmit RF technology and/ or dielectric pads 51 to improve transmit field homogeneity. The threshold value of α sat (here ~60°) depends on MT pulse shape and duration.
To identify systematic variation, we relied on previous experience at 3T and by empirically studying how MT sat in different tissues changed depending on parameter settings. This was done either through qualitative features such as spatial symmetry or separation of tissue-specific modes in the histograms or quantitatively through the comparison of averages derived from automatic tissue segmentation. A previous report 52 was complemented by aspects of TR, offset frequency sign, transmit field correction and repeatability.

| Shape of MT pulse
The implemented sinc main lobe is very similar to the default at General Electric MRI systems 53 with a bell shape similar to a Gaussian. The sinc main lobe compares favorably to the pure Gaussian due to higher normalized energy (Q = 1.33 versus Q = 1.61), while still providing sufficiently narrow frequency response. The frequency response of either pulse for all subjects, see Supporting Information Figure S1. Average f T and individual C for a specific ROI is denoted. The best fit obtained with the constraint C = C mean = 0.34 is indicated by an orange dashed line was very similar, but the Gaussian will lack the small sidebands of the sinc main lobe. Previous work has shown no difference in MT sat for pulses with identical energy, 15 and a sinc main lobe should thus be expected to behave very similar to a Gaussian. Last, it should be noted that MT sat is defined for an instantaneous saturation event which further motivates the choice of a short, time-efficient (low Q) pulse, facilitating short TR and acquisition time.

| Readout FA
A small positive shift of MT sat with increasing α nom has previously been described at 3T. 15 This effect originates from omitted non-linear terms in the approximate signal equation (Equation (1)), accounted for through a positive bias in MT sat .
Regarding the physical interpretation of MT sat , it should be noted that the readout by α may disturb the MT dynamics during TR. By choosing α nom smaller than the optimal 7° regarding SNR, the bias was limited in areas of high f T without sacrificing too much precision. The reduced bias was traded off against decreased SNR in regions of low f T . When targeting a specific structure, noise progression can be optimized to match the local f T . 31

| TR
MT sat should increase with TR as this allows more time for MT to reestablish the equilibrium disturbed by the MT pulse. 53 A similar small increase of MT sat in the TR range 18 ms ≤ TR ≤ 65 ms has been observed at 3T. 15 In this work, the effect was weaker ( Figure 3) which may be due to MT sat being smaller than at 3T. An increase in TR could thus only facilitate an increase in MT sat via increased energy of the MT pulse, which would be beneficial for low f T areas. Modification of the MT pulse would require repeating the optimization procedure, especially the calibration of the transmit field correction (Methods 3.6). We instead opted for a shorter measurement, with TR = 26.5 ms which is only slightly longer than the TR = 23.7 ms used at 3T. 43,44

| Offset frequency
Since fitted macromolecular absorption lines have been found to be similar in GM and WM, we expected a proportional increase of MT sat with decreasing frequency offset, in the absence of confounding contributions. In previous work at 1.5 T, T 2,b has been estimated to 11.8 ± 1.3 μs and F I G U R E 9 Before and after correcting MT sat for residual effects of transmit field inhomogeneities. MT sat map acquired with the finalized protocol before (A) and after (B) correction of residual transmit field effects (C = 0.34) and the FA map used for correction (C). Corresponding histograms are also included (D). In the right periphery (white arrows), SNR is lower due to lower transmit field amplitude (f T < ~0.6). In the right temporal lobe and cerebellum (blue arrows), transmit field amplitude is even lower (f T < ~0.3) and MT sat becomes indistinguishable from noise. Overall, the transmit field correction works well and the homogeneity in WM is improved, as seen in the maps (red arrows) as well as by manifestation of a narrowing of the WM mode in the histogram (red arrows) 12.3 ± 1.6 μs in WM and 11.1 μs in cortical GM. 48 Another study, also at 1.5 T, reported 10.4 ± 0.5 μs in WM and 9.2 ± 0.4 μs in GM. 49 The gradual shift of MT sat at lower Δ is interpreted as being predominantly due to direct saturation in tissue. This interpretation was supported by linear regression of MT sat onto a reference experiment (Δ = +2.0 kHz), as previously applied to harmonize between scanners. 17 This experiment showed that ΔMT sat correlated strongly with MT sat in CSF ( Figure 5). The higher ΔMT sat at Δ = +1.0 kHz (3.4 ppm) is likely due to overlap with the APT frequency at +3.5 ppm and ensuing CEST. It should also be noted that hydroxyl and amine exchange at +2.5 ppm could influence MT sat at Δ = +0.75 kHz, 54 although no obvious overestimation above the line was observed. As Δ = +2.0 kHz corresponds to 6.7 ppm at 7T, we assumed the virtual absence of exchanging resonances as confirmed in rat cortex. 55 Our interpretation of direct saturation cannot be explained by the simulated profile ( Figure 1C), probably because relaxation effects were ignored. Direct saturation is linked to short T 2 of the free pool as observed in myelin water and iron-rich structures which decreases at higher field strength. However, the geometric mean T 2 s of different structures are proportionally shorter at 7T relative to those observed at 3T. 56 Hence, we do not observe tissue-type specific effects.
Arguably, Δ = 2.0 kHz could still be affected by direct saturation. Since ΔMT sat changes gradually with offset frequency, it is not possible to prove the absence of direct saturation. We did not increase Δ beyond 2.0 kHz to avoid further diminishing the already rather weak MT sat and accepted any minor remaining bias. If a wider absolute MT sat difference between tissue types is desired, this could be achieved by decreasing Δ. This would involve some trade-off against a higher degree of direct saturation and various other effects, which would impair specificity to traditional MT.

| Negative offset frequency
It is customary to apply the MT pulse at a positive Δ. 2,15,48,57 However, it has been shown that the super-Lorentzian absorption line of the macromolecules is shifted toward lower frequencies relative free water resonance. 14 The shift in Hz between peak macromolecular response and free water resonance scales with B 0 . We exploited this asymmetry to considerably increase MT sat (Figure 6), without creating more direct saturation or increasing SAR. The rNOE exchange is present on the negative side of the water resonance and it is possible that some contaminating saturation occurred because of this, even at the rather large offset of Δ = -2.0 kHz (-6.7 ppm). 6 However, based on previously published experimental results from rat cortex in vivo, these effects are expected to be small compared to our MT sat values. 55 In this study, eight consecutive 180° saturation pulses, comparable to our MT pulse (B 1,rms = 2 μT, t sat = 13.8 ms) were applied and the observed saturation due to rNOE amounted to <0.5% at −6.7 ppm. Furthermore, the overall increase in MT sat at Δ = -2.0 kHz cannot be explained by B 0 offset (represented by f 0 ) which mostly shifted Δf 0 toward lower values (ie, Δ = -2.0 kHz away from water). The majority of the observed increase in MT sat is thus interpreted to be caused by a shifted absorption lineshape. The observed B 0 -dependence (Figure 7) could be a combined effect of changing the saturation of macromolecules, CEST as well as direct saturation of free water. The specific influence of rNOE could possibly explain the somewhat stronger correlation for Δ = -2.0 kHz compared to Δ = +2.0 kHz. This difference is in the same order of magnitude as the additional saturation from rNOE exchange based on the experimental results on the rat cortex. 55 Large shifts occur mainly above the nasal sinuses and even in these pixels, strong deviations in MT sat were not observed. In 94% of pixels, |f 0 | was below 100 Hz (0.34 ppm). We thus conclude that an MT pulse with FWHM = 300 Hz (1 ppm) applied at −2.0 kHz (−6.7 ppm) yield a satisfactory safety margin of 2.45 ppm to the closest expected rNOE resonance at −3.75 ppm. 6

| Residual effects of transmit field inhomogeneities
The inherent correction of MT sat was insufficient at 7T due to the strong transmit field inhomogeneities. The post hoc correction clearly improved the homogeneity of MT sat , especially in WM ( Figure 9). In view of the relatively large variation in C observed across the 16 ROIs, we ignored underlying differences in B between GM and WM to perform a global post hoc correction.
This post hoc correction is implemented in the hMRI toolbox, 19 albeit with a different weighting factor (C = 0.40 as derived at 3T for a Gaussian MT pulse of α sat,nom = 220°3 2 ). This control variable should be changed based on MT pulse when using the toolbox. For α sat,nom = 180°, this correction factor would be scaled to C = 180°/220°•0.40 = 0.33 (ignoring small differences in pulse shape and negative frequency offset) which is close to C = 0.34 ± 0.11 determined experimentally in this study. This correction implicitly assumes the absence of confounding contributions to MT sat .

| Repeatability
The high SD in the cerebellum and temporal lobes illustrates the limitation of the method imposed by low transmit field amplitude as well as physiological noise affecting B 0 . The latter, caused by chest movement due to breathing, could potentially be remedied using data-driven post-correction methods of the raw k-space data. 50

| Limitations
Due to the recursive nature of the optimization procedure, parameter settings in some experiments did not reflect the final protocol (Supporting Information Table S1). For instance, the positive frequency offset in experiment 3.4 (Figure 4) demonstrates APT resonance but does not access the upfield rNOE exchange. However, the purpose of this experiment was to minimize direct saturation as a confounding mechanism of saturation. This was then followed by an upfield-downfield comparison. Minor confounding effects are likely to remain, making the semi-quantitative MT sat metric proportional to, albeit not identical to, the bound pool size ratio, F b , modeled by fully quantitative approaches. In the MPM approach, this is traded in against speed and high resolution. In areas of very low transmit field (f T < ~0.3), however, MT sat could not be determined using this fast protocol.

| CONCLUSIONS
This study resulted in the following recommendations for setting up an MT sat protocol at 7T: (a) Short MT pulse with a compact shape and sufficiently narrow frequency response. (b) Small readout FA without punishing SNR too much. (c) Minimum TR (as decided by pulse sequence timing) to maintain short scan time. (d) Absolute offset frequency of 2.0 kHz to reduce confounding direct saturation, CEST, and rNOE exchange. (e) Negative sign of the offset frequency to induce more MT. This is a consequence of the shifted lineshape and benefits from higher B 0 . (f) Separate FA-mapping for post hoc correction.

SUPPORTING INFORMATION
Additional Supporting Information may be found online in the Supporting Information section.

FIGURE S1
Residual effects of transmit field inhomogeneities of all subjects. Correction factor, C, derived through linear fitting (blue solid line) in ROIs placed in the caudate head (columns A, B) and frontal WM (columns C, D), representing GM and WM, respectively. Different rows show separate subjects. Headings denotes average f T and individual C for that ROI. The best fit obtained with the constraint C = C mean = 0.34 is denoted by an orange dashed line TABLE S1 Sequence parameters and transmit fieldcorrection factor, C, for the finalized protocol