Characterization of the cortical myeloarchitecture with inhomogeneous magnetization transfer imaging (ihMT)

BACKGROUND
Myelin specific imaging techniques to characterize white matter in demyelinating diseases such as multiple sclerosis (MS) have become an area of increasing focus. Gray matter myelination is an important marker of cortical microstructure, and its impairment is relevant in progressive MS. However, its assessment is challenging due to its thin layers. While myelin water imaging and ultra-short TE imaging have not yet been implemented to assess cortical myeloarchitecture, magnetization transfer (MT) shows promise. A recent development of the MT technique, ihMT, has demonstrated greater myelin sensitivity/specificity. Here we implemented a 3D ihMT acquisition and analysis to characterize cortical gray matter myeloarchitecture.


METHODS
20 young healthy volunteers were imaged with a 3D ihMTRAGE sequence and quantitative metrics of ihMT (ihMTsat), and dual frequency-offset MT (dual MTsat) were calculated. Cortical surface-based analysis of ihMTsat and dual MTsat were performed and compared. We also compared the cortical ihMTsat map to a cortical surface-based map of T1-weighted images (T1w), defined as a proxy of myelin content.


RESULTS
Cortical ihMTsat and dual MTsat maps were in qualitative agreement with previous work and the cortical T1w map, showing higher values in primary cortices and lower values in the insula. IhMTsat and dual MTsat were significantly correlated but with important regional differences. The ratio ihMTsat/dual MTsat highlighted higher ihMTsat values in the primary cortices and sulci.


CONCLUSION
ihMTsat, a quantitative metric of ihMT, can be reliably measured in cortical gray matter and shows unique contrast between cortical regions .


Introduction
Differences in cortical microstructure can be reflective of function, neuroanatomy, and pathology. A century of research has emphasized the density and distribution of myelin as a particularly valuable marker. The Vogt school pioneered the field of myeloarchitectonics and showed histologically that myelin content varies from one cortical region to another. They used these regional differences to parcellate the cortex and build the first myeloarchitectonic maps ( Braitenberg, 1962 ;Nieuwenhuys, 2013 ). The capabilities of noninvasive imaging offer the possibility of in-vivo studies to assess cortical gray matter (GM) myelination for unbiased 3D mapping, characterization of individual variations, and for the study of development, aging, and disease effects.
A variety of Magnetic Resonance Imaging (MRI) modalities have shown sensitivity to cortical myelin. Proposed contrasts have included T 1 -weighted (T 1 w) images ( Rowley et al., 2015 ) or quantitative T 1 ( Du et al., 2014 ;Jang et al., 2020 ), but to the best of our knowledge, whole brain GM myelin imaging with UTE has not been reported.
Magnetization Transfer Imaging (MTI) is an alternative myelin sensitive imaging technique that reflects exchange of magnetization between macromolecules, including myelin, and free water. A cortical surfacebased study using the magnetization transfer ratio (MTR) has shown promise regarding assessment of cortical myelin content ( Mangeat et al., 2015 ), with results qualitatively in agreement with prior work using other myelin-sensitive contrasts. However, all macromolecules other than those found in myelin contribute to MT contrast, and hence its molecular and diagnostic specificities are reduced, as for example in MS ( Moll et al., 2011 ).
Inhomogeneous magnetization transfer (ihMT) , a novel variant of MT, can selectively image tissues with long dipolar relaxation time (T 1D ) components, such as myelin. The ihMT signal is the difference between the MT signal obtained after single off-resonance frequency saturation of the macromolecular pool, and the one obtained after dual symetric off-resonance frequency saturation using the same RF power. The sensitivity of ihMT to local dipolar order and the ordered structure of multiple lipid bilayers underlying myelin ( Manning et al., 2017 ;Swanson et al., 2017 ;Varma et al., 2015 ) explains the selective ihMT signal from WM ( Girard et al., 2015 ) and ihMT as a potential biomarker of myelin in WM. This selectivity was further validated by correlation with histological fluorescence microscopy ( Duhamel et al., 2019 ). A strong correlation between ihMT and myelin water imaging measures has also been reported ( Ercan et al., 2018 ;Geeraert et al., 2018 ). But ihMT has not yet been applied to characterize the cortex and assess its myelin density.
The aim of this work is to assess whether ihMT can be a valuable tool to observe and quantify cortical myelin content. To answer this question, we implemented a 1.6 mm 3D ihMTRAGE sequence, composed of ihMT preparations combined with a rapid gradient echo (RAGE) sequence . We built cortical surface-based maps of ihMTsat, a quantitative metric of ihMT, and compared them to cortical surface-based maps of T 1 w images, previously proposed as a proxy of cortical myelin content. To gain a better understanding of the unique sensitivity of ihMT to cortical myelin, we also compared cortical surfacebased maps of ihMTsat to those created using the metric of a more conventional MT technique based on the dual-offset saturation, dual MTsat. Finally, we took a first look at the depth dependence of ihMTsat and dual MTsat.

MRI acquisition
The study was approved by our institutional review board and informed consent was obtained from each volunteer before enrollment. Twenty young healthy volunteers (range, 20 -34 years; mean, 27.7 ± 4.7, 12 females) were recruited and scanned on a 3 tesla Discovery MR750 scanner (GE Medical Systems, Milwaukee, WI, USA) with a 32-channel phased-array head coil (Nova Medical, Wilmington MA, USA) for signal reception.
All subjects were scanned with an identical protocol. First, a 3D T 1 -weighted inversion prepared gradient echo sequence (GE BRAVO) was acquired for anatomic localization, cortical segmentation using the following parameters: 166 axial slices; 1 mm isotropic resolution; matrix, 256 × 256; TE, 3.2 s; TR, 8.2 s; TI, 450 ms; flip-angle (FA), 12°. Phased array UnifoRmity Enhancement (PURE) was applied to correct for non-uniform receiver coils profile. This 3D 1mm 3 T 1 w BRAVO corrected for B 1 inhomogeneity with PURE was defined as a proxy of myelin content and refers to 'T 1 w' in the text. A 3D Fast-Spin-Echo with variable flip-angles (CUBE) T 2 -weighted sequence was acquired for robust brain extraction with the following parameters: 196 sagittal slices; resolution, 1mm 3 ; matrix, 256 × 256; TE, 120 ms; TR, 4800 ms. Next, a recently described  3D ihMTRAGE sequence composed of an ihMT preparation (5 ms off-resonance Tukey-shaped pulses (cosine-modulated for dual-frequency irradiation), Δf =± 7 kHz, singlefrequency B 1,peak = 14 T, RF pulses every 100 ms for 1 s) combined with an MPRAGE sequence (radial-fan beam view-ordering; 1.6 mm isotropic resolution, matrix, 160 × 160; 90 readouts per TR ihMTRAGE ; TE, 1.8 ms; TR, 4.6 ms; TR ihMTRAGE , 2 s; FA = 10°). For enhanced SNR considerations, three repetitions of the single positive ( +Δf) and negative (-Δf) frequency-offset images and 6 repetitions of the dual ( ±Δf) frequencyoffset images, all required to compute the ihMT composite image, were acquired. For quantification purpose, two reference images were also acquired at the beginning of the acquisition. The combined MT and reference image acquisition required a total of 20 min. The first reference image was acquired without any off-resonance pulses, and the second one substituted the ihMT preparation with RF spoiled FA = 25°pulses applied on-resonance every 25 ms for 1 s. Finally, a quick low resolution (matrix, 64 × 64; slice thickness, 6.4 mm) B 1 map was acquired with a previously described Bloch-Siegert sequence ( Sacolick et al., 2010 ) in 2 min.

MRI data processing and surface-based analysis
The quantitative analysis procedure involved three steps: preprocessing, derivation of quantitative ihMT and MT metrics, and evaluation of these quantitative metrics across the cortex using cortical surface-based analysis.

Preprocessing of MT and B 1 images
The 3D ihMTRAGE images were preprocessed as follows: (1) realignment of each MT-weighted volume to the reference volume without RF saturation, M 0 , using a 6 degree of freedom rigid registration; (2) registration of the reference volume (M 0 ) to the 3D T 1 w volume using rigid registration; (3) application of the saved rigid transformation to the MTweighted volumes. These preprocessing steps were all performed with FSL (FMBRIB, Oxford, UK).
Using MATLAB (R2017a, MathWorks, Natick, MA, USA) and SPM12 (Statistical Parametric Mapping, Welcome Trust Center for Neuroimaging, London, UK), the Bloch-Siegert B 1 maps were first median filtered with a 21 mm kernel, scaled by a factor of 0.95 to adjust for overestimation of B 1 that occurs when a non-spoiled gradient echo acquisition is used ( Corbin et al., 2019 ) and also registered to the 3D T 1 w using the native T 1 w gradient echo images of the B 1 sequence to derive the anatomic registration.
The 3 repetitions of single frequency-offset +Δf and -Δf images and the 6 repetitions of the dual frequency-offset images were averaged before quantification of ihMT and MT.

Quantification approach for ihMT and dual MT
We adapted the MT saturation approach from Helms et al. (2008 ), Helms and Piringer (2005 ) to derive quantitative ihMT and MT (based on the dual frequency-offset saturation) metrics, unbiased from T 1 and B 1 and independent of sequence timing effects. This approach relies on a model which assumes a short pulse and a relatively long TR such that the effect of each pulse can be considered to be a fractional attenuation of the free pool by the factor (1-) ( Eq. (1) ).
Based on this MT saturation approach, the quantification of ihMT and MT proceeded in several steps. The measured B 1 maps and the two reference images were first fit to determine T 1 in each voxel. Then, the B 1 and T 1 maps were used to determine the saturation parameter, , that fit the attenuation of each MT prepared image relative to the unsaturated image. Finally, the values for different experiments were used to calculate the ihMT and MT metrics. For both fits, we constructed a simple forward model for the spoiled gradient echo excitations and the MT preparation RF pulses (or the reference pulses), as a function of T 1 and B 1 and inverted them using a bisection fitting algorithm with guaranteed convergence to determine first T 1 from the reference images, and then for each MT preparation. Finally, the MT metrics dual MTsat and ihMTsat were calculated from the MT as defined in Eq.
(2) . Since the MT and ihMT saturation effects scale approximately respectively polynomially and quadratically with RF amplitude for our parameters , they were scaled to correct for B 1 variations.
A more detailed description of this quantification is given in the Appendix.

Surface-based analysis
Each subject's 3D T 1 w image was processed using FreeSurfer version 6.0 (http:// surfer.nmr.mgh.harvard.edu) in order to reconstruct the white and pial surfaces and parcellate the cortex. The pipeline did not include skull-stripping which was performed with SPM12, to restrict pial surface manual corrections. Briefly, segmentation of GM, WM and cerebrospinal fluid (CSF) was performed on T 2 w images due to its high contrast between the dura mater and GM. The three classes were added to create a skull-stripped T 2 w image, which was used afterwards to mask the 3D T 1 w image, ihMTsat, dual MTsat and the ratio ihMTsat/dual MTsat. The white surface was also manually corrected for all subjects.
Though all images were already spatially registered, an additional registration of each of the ihMTsat, dual MTsat, ihMTsat/dual MTsat ratio, and T 1 w images to the cortical surfaces was performed using boundary-based registration method. Next, image intensities at several cortical depths (from 10% to 90%, every 10%) between white and pial surfaces were measured. In order to correct for receiver gain differences between subjects, we scaled the individual T 1 w maps by the corresponding cortical mean value. Then, projection of the maps to an across subject average surface ( fsaverage ), averaging across subjects and smoothing along the surface with a 5 mm FWHM Gaussian kernel were performed.
We also used the quantitative T 1 map (from the B 1 and the two reference images) to generate a R 1 (1/T 1 ) map. We generated cortical surface-based maps of R 1 applying the identical surface-based analysis pipeline described at the start of this subsection.

Regional analyses
Quantitative comparisons were performed using average values within previously defined cortical regions. We projected the Destrieux cortical atlas from FreeSurfer ( Destrieux et al., 2010 ), composed of 148 Regions of Interest (ROIs, 74 per hemisphere), onto the following cortical surface-based maps previously created: ihMTsat, dual MTsat, ihMTsat/dual MTsat ratio, and T 1 w, from which mean values at 50% depth were extracted. To assess the relationships between ihMTsat and T 1 w or dual MTsat across the brain, we regressed their 148 mean values and performed Spearman's rank correlations. Moreover, to assess the level of myelination across regions, we performed paired Student t-tests across subjects comparing the ihMTsat value in each region to the median ihMTsat value across the regions. The statistical analyses were performed using R (version 3.5).
Furthermore, we took a first look at the depth dependence behavior of ihMTsat, dual MTsat and ihMTsat/dual MTsat for 7 ROIs from the Destrieux atlas (primary cortices, posterior cingulate), believed to be heavily myelinated, though the nominal resolution is not high enough for a precise analysis. To do so, we extracted the mean values for each metric at every 10% depth level starting from 10% and ending at 90%. This range was chosen to consider the potential contamination of WM and CSF due to partial volume effects. We averaged the values from the left and right hemispheres assuming that the depth dependence behavior is not hemispheric-dependent.

Data and code availability statement
Anonymized imaging data will be shared upon request from any interested and qualified investigator after completing a Data Sharing Agreement with Beth Israel Deaconess Medical Center.
The quantitative MTsat / ihMTsat code will be shared upon request from any interested and qualified investigator.

Results
All ihMTsat and dual MTsat maps were of good quality and free of obvious visually apparent artifacts ( Fig. 1 ). A good WM/GM contrast for both maps, albeit more pronounced for ihMTsat, was observed. The corticospinal tract, a heavily myelinated white matter tract, is very bright and highly recognizable on the ihMTsat map.

Assessment of cortical myelin density distribution with ihMTsat
Cortical ihMTsat, sampled at mid-distance between white and pial surfaces, was higher in the primary motor cortices (central sulcus ( S_sulcus ), pre-and postcentral gyri ( G_precentral and G_postcentral )), the primary visual areas such as MT (also called V5) ( S_occipital_ant ), V1 and V2 ( S_calcarine, G_cuneus ), and the primary auditory cortex ( G_temp_sup-G_T_transv ). These elevations relative to the median were respectively significant at p < 0.0001 for S_sulcus, G_precentral, S_occipital_ant and G_temp_sup-G_T_transv, p < 0.002 for G_postcentral and p = 0.04 for the left G_cuneus . Conversely, the insula ( G_insular_short ), known to be lightly myelinated ( Glasser and Van Essen, 2011 ), had low ihMTsat, with a significant reduction relative to the median for G_insular_short ( p < 0.0001). The signal intensities are more variable for association areas. ( Fig. 2 -A,  Supplementary Tables 1&2 ).

Relationship between ihMTsat and dual MTsat
Cortical surface-based ihMTsat and dual MTsat maps show a close spatial distribution ( Fig. 2 -A, Fig. 2 -B, Supplementary Table 1 ), which is further supported by the strong spatial correlation between ihMTsat and dual MTsat values measured in the 74 ROIs of the Destrieux cortical atlas ( = 0.86, p < 0.0001 and = 0.85, p < 0.0001, respectively for the left and right hemispheres) ( Fig. 3 -A , Fig. 3 -B ). However, some regional differences exist. For example, ihMTsat values are relatively higher in the primary auditory cortex, primary visual areas such as V1 and in the central sulcus than dual MTsat values. Those regional differences are emphasized by the cortical surface-based map of the ratio ihMTsat/dual MTsat ( Fig. 2 -C, Supplementary Table 1 ). This ratio brings out the unique information carried by ihMT relative to MT and shows interesting features whose boundaries overlap with regional boundaries from the Destrieux atlas. Relative to dual MTsat, ihMTsat generally has higher values in sulci than gyri. Some significant hemispheric differences are visible in both ihMTsat and dual MTsat. Performing paired t -test across subjects adjusted for multiple comparisons across regions, we found significantly higher ihMTsat and MTsat values on the right hemisphere in the anterior cingulate and inferior frontal regions and significantly higher values on the left hemisphere in a few occipital regions ( Supplementary Table 3 ).

A preliminary evaluation of the depth dependence of ihMTsat and dual MTsat
Though our resolution was insufficient to precisely evaluate the laminar depth dependence of ihMT, a preliminary evaluation showed promising differences between ihMT and MT. The decrease of ihMTsat with depth into the cortex follows a two-slope pattern with a rapid decrease from the white surface to 50% depth followed by a slower decrease from the mid-distance to the pial surface in almost every chosen ROI ( Fig. 4 -A, Supplementary Table 4 ). Conversely, the dual MTsat decrease does not follow a specific pattern ( Fig. 4 -B, Supplementary Table  5 ). Especially dual MTsat values in both precentral and postcentral gyri seem to decrease faster closer to the GM. The ratio ihMTsat/dual MTsat follows a similar, but more prominent, two-slope pattern as ihMTsat ( Fig. 4 -C, Supplementary Table 6 ).

Relationship of ihMT to cortical variation of T 1 -weighted signal
T 1 -weighted signal intensity also varied considerably across cortical regions. Primary cortices (primary motor cortex, primary visual areas, primary auditory cortex) have higher T 1 w intensities than the rest of the brain ( Fig. 5 -B, Supplementary Table 1 ), a feature also visible on ihMTsat map ( Fig. 5 -A, Supplementary Table 1 ). However, T 1 w and ihMTsat differed considerably in spatial distribution in other regions, as supported by the absence of spatial correlations between ihMTsat and T 1 w values measured in the 74 ROIs of the Destrieux cortical atlas ( = 0.05, p = 0.7and = − 0.06, p = 0.6, respectively for the left and right hemispheres) ( Fig. 3 -C , Fig. 3 -D ).
In addition to the T 1 w signal, we also obtained T 1 information from the T 1 maps that were part of our ihMTsat quantification approach. These can also be compared to ihMTsat. As described in the Appendix, these T 1 maps are very sensitive to errors in the measured B 1 . Our B 1 mapping procedure, using an unspoiled Bloch-Siegert method, has been shown to overestimate B 1 , especially in CSF ( Corbin et al., 2019 ), raising questions about the T 1 map reliability. Fortunately, the ihMTsat and MTsat measures are much less vulnerable to this error (see Appendix). For completeness, we have included correlations between R 1 measured from the T 1 maps and our other measures ( Supplementary Fig. 1 ) and the cortical surface-based map of R 1 ( Supplementary Fig. 2 ) in supplementary data.

Discussion
These results highlight both the sensitivity of ihMT, enabling robust imaging at spatial resolution sufficient to resolve the cortex, and its specificity to cortical myeloarchitecture. The ihMT signal is believed to mainly reflect lipid membrane density ( Duhamel et al., 2019 ), which is very high in myelinated tissue. Myelin density is also known to be an important indicator of cortical architecture ( Nieuwenhuys, 2013 ) with higher myelination in primary cortices. Hence, our finding of higher ihMTsat in primary motor, auditory, and visual cortices is consistent with the myeloarchitecture of the cerebral cortex.
Though ihMT shared strong similarities to a more conventional MT measure, as supported by the strong correlations between ihMTsat and dual MTsat across regions, clear regional differences exist and are highlighted by the cortical surface-based map of the ratio ihMTsat/dual MTsat. Both contrasts are sensitive to myelin but since MT is also equally sensitive to other tissue macromolecules, ( Duhamel et al., 2019 ), this ratio likely provides an indication of the fractional myelin content. IhMTsat shows higher relative values compared to dual MTsat in primary cortices (primary motor cortex, primary visual areas and primary auditory cortex). Even outside the primary cortices, the ratio ihMTsat/dual MTsat shows an interesting pattern, which follows the boundaries of the Destrieux atlas (based on separation of gyral and sulcal regions) from FreeSurfer ( Destrieux et al., 2010 ). Higher ihMTsat/dual MTsat is mainly located in sulci. Neuroanatomical studies have generally shown a thicker but less densely myelinated layer of the cortex in    ( Hilgetag and Barbas, 2006 ;Horiuchi -Hirose and Sawada, 2016 ). Spatial differences are also observed in cortical depth dependence, with ihMTsat decreasing more rapidly than dual MTsat with distance from the white matter surface. Further study of the depth dependence at higher spatial resolution is nevertheless needed to better probe the depth dependence of these measures and to clarify this relationship. Though the physical and anatomical basis of gyral-sulcal and depth dependent contrast will require further study, it does highlight the unique information available from ihMT for microstructural analysis and differentiation of cortical regions.
This work adds to a growing literature on MRI characterization of gray matter microstructural heterogeneity. Previous work with T 1 w/T 2 w and T 1 w contrasts ( Glasser and Van Essen, 2011 ;Rowley et al., 2015 ;Sereno et al., 2013 ;Sprooten et al., 2019 ) has emphasized the prominence of primary cortices, and these findings are reproduced with our T 1 w analysis here. Though primary cortices are also prominent in the ihMTsat measure, the intensity of the contrast and the distribution of the signal across the entire cortex is quite different, resulting in a poor correlation across the regions of the Destrieux atlas. This lack of correlation has previously been reported in WM between T 1 w/T 2 w and another myelin-sensitive MRI technique, myelin water imaging ( Arshad et al., 2017 ;Uddin et al., 2018 ). Both teams suggested that compared to myelin water fraction, T 1 w/T 2 w would represent a more general measure of tissue microstructure, such as variation in caliber and packing density of the axons. This difference could also be partly explained by the sensitivity of T 1 w/T 2 w to iron. Indeed, iron and myelin are colocalized in the cortex, especially in primary cortices ( Edwards et al., 2018 ;Fukunaga et al., 2010 ) but this colocalization is imperfect ( Fukunaga et al., 2010 ). Using quantitative magnetic susceptibility (QSM) and conventional MT, Marques et al. created a model to separate signals from myelin and iron and reconstructed a myelin map and an iron map ( Marques et al., 2017 ). The iron map shows higher iron content mostly in primary cortices, similar to a T 1 w/T 2 w map, while the patterns of the myelin map and our ihMTsat map are more similar.
This initial study of cortical ihMT is not without limitations. Importantly, the spatial resolution of 1.6 mm is higher than the average cortical thickness but low enough that partial volume effects may contribute to the analysis. This is especially true in the thinner cortex of the primary visual cortex. However, comparison of the regional distribution of cortical thickness and our MT measures yielded low correlation (R 2 < 0.3) (Supplementary Fig. 3), suggesting this is not a major problem for our mid-thickness analysis. The analysis of cortical thickness dependence of the MT and ihMT measures is almost certainly affected at some level by partial volume effects. Such effects could blur higher resolution structure and also include some signal from nearby white matter, which has previously been shown to vary with cortical region and age ( Salat et al., 2009 ). Still the differences between MT and ihMT depth profiles observed in this preliminary analysis, that should be equally affected by partial volume, suggest unique sensitivity of ihMT to cortical microstructure.
Though a vendor correction for surface coil nonuniformity was applied to our T 1 w image, it was still imperfectly corrected for biases related to transmit field inhomogeneity. Our primary focus was to characterize ihMT and MT distribution and the T 1 w image was acquired primarily for tissue segmentation. Improved methods for bias correction and especially quantification of T 1 are recommended for studies of cortical contrast. However, we included results from our T 1 w images knowing this drawback and the resolution effect (1mm 3 versus 1.6 mm isotropic) because they showed similar contrast to earlier work using T 1 contrast in the cortex and could readily be displayed on the same subject atlas.
Our MTsat measure differs significantly from measures in other MT studies and care should be taken in direct comparison. We used a high frequency offset for the MT saturation, 7 kHz, compared to most MT studies that use 2 kHz or lower. More recently, however, higher offset frequencies have been advocated to remove bound pool T 2 effects in quantitative MT studies ( Yarnykh et al., 2014 ). Additionally, we used brief pulses with longer repetition times to increase the ihMT signal . Indeed, with these high-power pulses, the MTsat is no longer linear in applied power. Finally, we used a quantitative MTsat measure that differs substantially from the more conventional MT ratio. For all these reasons, our findings may differ from those obtained with other methods.
Another challenge is that understanding of and quantification methods for ihMT are rapidly evolving, making comparison across studies difficult. Recent work has emphasized the presence of a distribution of dipolar relaxation times in tissue ( Carvalho et al., 2020 ) which can be differentially emphasized by the sparseness and intensity of the applied power Varma et al., 2018 ) and by the choice of dipolar relaxation time weighting in the dual frequency saturation ( Carvalho et al., 2020 ;Duhamel et al., 2019 ;Prevost et al., 2017 ;Varma et al., 2018 ). While standardization of methods is clearly important, the ability to characterize different tissue components by vary-ing the saturation opens up new possibilities for the study of tissue microstructure.

Conclusion
This work has demonstrated that ihMT, previously emphasized in studies of white matter, can provide unique and potentially important quantification of cortical gray matter. The results can complement the findings of other approaches in studies of normal myeloarchitecture and provide a new quantitative measure for pathology in diseases that affect gray matter, including progressive multiple sclerosis and Alzheimer's disease.

Declaration of Competing Interest
D.C.A. receives research support from GE Healthcare. Additionally, he receives postmarket royalties through his institution from GE Healthcare, Siemens Healthineers, Philips Medical, Hitachi, and Animage LLC for patents related to the PCASL technique.

Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.neuroimage.2020.117442 .

Appendix
MTsat and T 1 were quantified using the following model ( Fig. A1 ). The effect of a RF pulse applied on-resonance at time 0 followed by a wait, T rp , on the equilibrium longitudinal magnetization, is given by: After n pulses, the magnetization is given by In the limit of large n, small flip angle and short T rp , this becomes In the MTsat model, the effect of an off-resonance MT pulse repeated every T rs is modeled as a saturation factor, . Similarly, And for n large, small, and T rs short, These are identical to the equations for an on-resonance pulse with the substitution = 1 − cos = 2 si n 2 ( 2 ) ≈ 2 2 (A6) In the limit of n large, and small, and T rs short compared to T 1 , we can quantify from an MT-weighted image using one reference image with zero flip angle (S 0 ) and one with flip angle (S ).
We see that using the nominal flip angle already corrects for B 1 . This approach removes T 1 and B 1 effects simultaneously and a B 1 map is not needed for quantification of MTsat. If you have a B 1 map, you can calculate the T 1 from the two reference images. But this T 1 measurement will be majorly affected by an imperfect B 1 map.
In the case of a shorter preparation such that steady state is not reached, the qualitative behavior is similar but the solution must be calculated numerically by inverting a physical model for the magnetization as a function of T 1 and or . The calculation was performed by stepping across 4 time periods: the wait before the RF preparation, w p , the preparation time, nT rp , the delay before acquisition, w d , and the acquisition time, mT r . Where is the readout flip angle, T r is the readout repetition time and m is the number of readout pulses per segment. For , replace cos( ) with 1-and T rp with T rs . For reasonable parameters, the ratio of the reference images is a monotonic function of T 1 and the ratio of the MT image to the 0°reference image is a monotonic function of . These can readily be solved at each point of the image by a robust bisection method.
We can simulate the effect of an error in measured B 1 on the measured T 1 and . T 1 is strongly affected but is much more mildly affected by the error.