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

2.1 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 FAs²⁹ and for T₁ >> TR, the imaging steady-state signal from an MT-w spoiled gradient echo, , is approximated:

(1)

where denotes MT_sat, is the readout FA in radians, and is the signal amplitude under fully relaxed conditions, ie, TR >> T₁. Using maps of and obtained from a DFA experiment, is calculated from :

(2)

The influence of transmit field inhomogeneities are introduced into Equation (2) through the substitution , where is the transmit field bias and is the nominal FA (set in the user interface). Using this substitution in the equations for and in a DFA experiment, one obtains and , where and are the corresponding estimates obtained with nominal FAs.²⁹ Equation (2) can be re-written in a similar way:

(3)

The longitudinal magnetization of the macromolecular pool, , is reduced by the MT pulse, of duration . This is described by differential absorption¹⁶:

(4)

where is the super-Lorentzian macromolecular absorption lineshape, is the MT pulse offset frequency and is the transverse relaxation time of the macromolecular pool. Direct saturation of can also be described by Equation (4), except with a Lorentzian lineshape governed by . If no other confounding contrast mechanism is present and the decrease of during can be ignored, the ensuing transfer renders to the macromolecular pool size fraction, :

(5)

Hence, 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 is mirrored by in Equation (3). This means that by using 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:

(6)

MT_sat henceforth refers to the metric calculated using nominal FAs (Equation (6)).

2.2 RF energy and pulse shape

The power integral is often used as a surrogate parameter in SAR models. As described above, this integral also governs the energy and induced (Equation (5)) of the MT pulse through the differential absorption law (Equation (4)). The power integral can be expressed as:

(7)

where is the maximum amplitude of the RF pulse and the rightmost normalized integral depends solely on the normalized RF shape . By using , the power integral is expressed in terms of and , which can be controlled experimentally:

(8)

where the shape factor:

(9)

carries the influence of the pulse shape. Note that for a rectangular pulse.

2.3 Noise propagation into the MT_sat map

The signal in Equation (1) can be expressed in analogy to the Ernst equation by using .³⁰ For a fixed TR and MT pulse, noise propagation from into is minimized for an optimal readout FA³¹:

(10)

where 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 is not possible.

2.4 Residual effects of transmit field inhomogeneities

From the -dependence in Equation (3) and the -dependence in Equation (5), it is clear that should be compensated for FA inhomogeneities. However, the decrease in under the duration of the MT pulse () will render induced saturation and hence MT smaller than what would be expected from differential absorption (Equation (4)). Thus, will be somewhat overcompensated by the inherent -correction, leading to an underestimation when and an overestimation when . This dependence of can be described empirically by a linear dependence³²:

(11)

where and are phenomenological parameters specific to the MT pulse shape and duration. Equation (11) explicitly contains the nominal FA of the MT pulse, hence and can be obtained by varying and performing a linear regression of versus . Given that the final transmit field-corrected estimate is , the correction takes the form:

(12)

where the product forms a pulse-specific parameter, which is used for post hoc transmit field correction of MT_sat.

3.1 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.

3.2 Readout FA

To empirically adjust the readout FA, α_nom was varied through 2°, 4°, 6°, 8° in one volunteer (34-year-old female, α_sat,nom = 180°, t_sat = 4 ms, Δ = +2.0 kHz). TR was slightly increased to 27 ms for all series to accommodate the slight increase in SAR for α_nom = 8°.

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.

3.3 TR

To corroborate the choice of the shortest possible TR = 26.5 ms at t_sat = 4 ms, TR was varied through 26.5, 31.1, 35.6, 40.3 and 45.0 ms on one volunteer (24-y-old male, α_sat,nom = 180°, t_sat = 4 ms, Δ = −2.0 kHz). It was of interest to assess whether MT_sat increased at higher TR, and if so, how much. Resulting acquisition times were 04:58, 05:49, 06:40, 07:33, and 08:26 min, where 08:26 min was deemed to be the maximum acceptable.

3.4 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 (19-y-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.

3.5 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 B₀ inhomogeneity into account, the free water frequency offset, f₀, was also measured. A linear function of MT_sat as a function of f₀ (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.

3.6 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 T₁- and S₀ 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.

3.7 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 T₁-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.

4.1 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 B₁ 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).

4.2 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 T₁ 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.

4.3 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.

4.4 Offset frequency

As expected, MT_sat increased strongly as Δ was decreased (Figure 4). However, the modes of GM and WM appeared increasingly shifted to higher MT_sat resulting in a proportionally larger increase in GM relative WM. The proportion of MT_sat in GM relative WM was 0.47/0.50/0.57/0.62 at Δ = 2.0/1.5/1.0/0.75 kHz. This indicates some confounding saturation effect added on top of MT. This shift in observed MT_sat, ΔMT_sat, followed the increase in CSF very well (Figure 5), indicating that direct saturation of the free water contributes to the increasing MT_sat in tissue. The absolute value of Δ was thus set to 2.0 kHz to limit contributions from non-MT sources, predominantly direct saturation, like at 3T.^{43, 44}

4.5 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 B₀ inhomogeneities shift f₀ 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 (Δ–f₀) 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 f₀ (–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 f₀. To maximize MT_sat, the MT pulse was applied at Δ = –2.0 kHz in the finalized protocol.

4.6 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 r² = 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.

4.7 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 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

5.1 Shape of MT pulse

The implemented sinc main lobe is very similar to the default at General Electric MRI systems⁵³ 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 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.

5.2 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

5.3 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}

5.4 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 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 T₂ of the free pool as observed in myelin water and iron-rich structures which decreases at higher field strength. However, the geometric mean T₂s 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.

5.5 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 B₀. 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 B₀ offset (represented by f₀) which mostly shifted Δ– f₀ 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 B₀-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, |f₀| 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

5.6 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°³²). 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.

5.7 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 B₀. 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

5.8 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.