Axon fiber orientation as the source of T1 relaxation anisotropy in white matter: A study on corpus callosum in vivo and ex vivo

Recent studies indicate that T1 in white matter (WM) is influenced by fiber orientation in B0. The purpose of the study was to investigate the interrelationships between axon fiber orientation in corpus callosum (CC) and T1 relaxation time in humans in vivo as well as in rat brain ex vivo.


INTRODUCTION
Gray matter (GM) and white matter (WM) show distinct MRI signals both in relaxometric and diffusion-weighted images owing to the inherent cytoarchitectures, biochemical compositions, and differing hemodynamic and metabolic activities. Although GM at subvoxel spatial scale is commonly treated as an isotropic tissue type in MRI terms, ordered axon fiber tracts and associated cellular structures in WM are responsible for an orientation-dependent (anisotropic) MR signal in relation to the static field (B 0 ) direction. To complement robust measures of microstructure from DTI (i.e., fractional anisotropy [FA] and mean diffusivity [MD]), 1 more advanced diffusion MRI (dMRI) methods have opened access to a number of WM microstructural characteristics, such as fiber orientation, 1 axon diameter, 2 axon density, 3,4 intra-axonal volume fraction, 5,6 and G-ratio. 7 Not only dMRI but also relaxometric MRI informs about WM microstructure in addition to the chemical constituents, such as myelin. 8 It has been reported that T 1 relaxation rate constant (R1 = 1/T1) in spinal cord ex vivo is inversely proportional to axon diameter for the diameter range up to 5 μm. 9 In sections of corpus callosum (CC), where the proportions of large (i.e., 3-5 μm in diameter) and giant axons (>5 μm in diameter) are greater than in the genu where small axons (<1 μm in diameter) dominate, 10 long T 1 is in line with the spinal cord data. 11,12 In WM with such large and giant axons, extracellular space is associated with elevated water content, hence prolonged T 1 . 11 On the other hand, the size of axons per se modulates water mobility, creating conditions where diffusion may influence relaxivity through the so-called volume/surface sinks. 13 Furthermore, de Santis et al. reported that crossing fiber configuration influences T 1 relaxation time in WM in a tract-specific manner. 14 Long T 1 in crossing fiber configuration is thought to reflect myelination properties.
A growing body of evidence links angularly dependent T 1 relaxation in WM in vivo to microstructure. 12,[15][16][17] The studies on orientation dependency of T 1 use dMRI microstructural measures, often FA, to select structurally anisotropic tissue where axon orientation is estimated from the principal diffusion direction. 15,17 The produced angular T 1 plots therefore consist of WM tissue present in different tracts. For example, fibers running parallel to B 0 are prominent in cortico-spinal tract, those perpendicular to B 0 in CC, and an intermediate range of orientations are scattered throughout the WM. 12 As mentioned previously, axon diameter, crossing fibers, and myelination influence T 1 independently of fiber orientation; hence, these approaches used to examine T 1 anisotropy may be biased by tissue structural factors.
To investigate orientation dependency of relaxation unambiguously, relaxation times in ex vivo brain preparations have been measured in tissue sections positioned at different orientations relative to B 0 . [18][19][20] The results from these studies have provided solid evidence for an interrelationship between axon fiber orientation and transverse relaxation, guiding physical modeling of both T 2 * and T 2 anisotropy. 18,19,21 In humans, head tilting has been exploited to reorient given WM tracts in vivo to study the effects of axon tract orientation on T 2 * 22 and T 2 relaxations. 23 In practical terms, one can obtain angle changes up to about 20 • in a standard clinical MRI system or with a special RF hardware. 24 The objective of the present study was to investigate T 1 relaxation and fiber orientation both in vivo and ex vivo. First, T 1 and dMRI microstructural measures were measured in the same CC tracts in vivo, exploiting the inherent variation of fiber orientations within this large WM structure; and second, an ex vivo rat CC preparation was scanned at several orientations in B 0 .

Human subjects
The study received ethical approval from the University of Minnesota Institutional Review Board. Six volunteers with no history of neurological conditions (mean age 27 years, 2 females) consented to participate in the study. All volunteers were scanned both at 3 T and 7 T.

MRI
A Siemens MAGNETOM Prisma 3T system with a 32-channel head coil and a Siemens MAGNETOM 7T scanner with a Nova Medical single-transmit/32-receivechannel head coil was used. At 3 T, dMRI images were acquired using the Human Connectome Project Lifespan Protocol 25 with the parameters given in Table 1. A B 0 field map was acquired using a spin-echo EPI sequence with TR = 8000 ms, TE = 66 ms, and 2-mm 3 isotropic resolution. A B 1 map was also acquired at resolution of 4 × 4 × 8 mm 3 using the manufacturer's routine. At 7 T, diffusion MRI images were acquired at higher spatial resolution using the Human Connectome Project Young Adult Protocol 26 with the parameters given in Table 1. An MP2RAGE sequence was used to acquire images for T 1 mapping both at 3 T and 7 T with the sequence parameters in Table 1. Anatomical T 1 -weighted MPRAGE images were acquired at isotropic 0.8-mm 3 (3 T) and 1.0-mm 3 (7 T) resolutions for tissue-type segmentations.

Image preprocessing
dMRI scans were corrected for distortions caused by eddy currents, susceptibility-induced off-resonance artifacts, and subject motion using TOPUP and EDDY in FSL. 27,28 A DTI model was subsequently fitted to the corrected data using DTIFIT in FSL, 29 to compute the DTI measures (FA, MD, and V 1 ) using b = 0 s/mm 2 and b = 1500 s/mm 2 images at 3 T and b = 0 and b = 1000 s/mm 2 at 7 T. The option of fitting the tensor with weighted least squares was used in DTIFIT. Fiber-to-field-angle (θ FB ) maps were computed from the principal direction of diffusion using the principal eigenvector V 1 images and direction of B 0 as described elsewhere. 17 The orientations and volume fractions of multiple fiber populations (first fiber = F1 and second fiber = F2) were estimated from 7T dMRI scans using BedpostX in FSL. 30 The neurite dispersion and density imaging pipeline in MATLAB 6 was used to create orientation dispersion index (ODI) and neurite density index (NDI) maps from 7T dMRI. The SNR was computed for diffusion images using the procedure described in Descoteaux et al. 31 as implemented in DIPY. 32 A mask encompassing the midsagittal portion of the entire length of CC in anterior-posterior direction was used to measure SNR in images (Table S1). It is evident from Table S1 that even in the worst case, the SNRs in images at 3 T and 7 T were above the noise floor bias. 33 T 1 and S 0 (a proxy for M 0 obtained from zero TI of the MP2RAGE data fits) maps were computed as previously described. 17

Segmentation of the CC
We segmented CC for the region of interest (ROI) analyses using the JHU ICBM 1-mm atlas. 34 The genu (ROI 1), midbody, and splenium (ROI 5) were segmented first from the atlas, and then the midbody was manually segmented into three subregions, the anterior midbody (ROI 2), the posterior midbody (ROI 3), and the isthmus (ROI 4) 34 ( Figure 1), to match the reported axon diameter distribution as closely as possible. 10,11 The masks of these five subregions of the CC were registered to the native T 1 and FA spaces separately by registering the JHU-ICBM 1-mm FA map to the respective maps, and by applying the corresponding transformations to these CC masks. These ROI masks are referred to as the lateral ROIs, which project laterally up to 19 mm for ROIs 1-4 and up to 26 mm for ROI 5 from the midsagittal line. The linear (FLIRT) and nonlinear (FNIRT) registration algorithms from FSL 35 are used for the registration. We also created a second set of five CC masks by limiting the coverage to only the midsagittal section, by eroding the five masks to 4 mm on both sides of the midsagittal line ( Figure 1). These ROI masks are referred to as the midsagittal ROIs. For analyses of quantitative MRI data in ROIs, the midsagittal ROI masks were subtracted from the lateral ROI masks in image space to generate the so-called large ROI masks to be used parallel to midsagittal ROI masks. Anatomical match of both large and midsagittal masks with the CC in both T 1 and FA maps was visually inspected. If needed, the masks were corrected by 1-3-voxel layers to eliminate overlap with surrounding GM and/or CSF. Volumes of the resulting ROIs are shown in Figure S1. The mean and SD of T 1 and diffusion microstructural measures were extracted from these masks using FSL. 35

Ex vivo rat brain
Animal procedures were approved by the Finnish Animal Experiment Board. An adult male Wistar rat under deep isoflurane anesthesia was transcardially perfused with saline for 2 min (30 mL/min) followed by 4% paraformaldehyde in 0.1-M phosphate buffer, pH of 7.4 (30 mL/min), for 25 min. The brain was removed from the skull, post-fixed in paraformaldehyde solution and 1% glutaraldehyde overnight, and stored at +4 • C. The brain was cut symmetrically around the midline into a 6-mm-wide sagittal slab. The specimen was prepared for MRI from the slab by cutting a section through posterior CC using a 6-mm biopsy punch. Before MRI, the specimen was washed in phosphate buffered saline for at least 12 h at +4 • C. The cylindrical sample was placed in a sample holder, 20 inserted into a 9.4T vertical magnet interfaced to a VnmrJ 3.1 Agilent DirectDrive console (Varian Associates, Palo Alto, CA, USA). A 19-mm quadrature RF volume transceiver (RAPID Biomedical, Rimpar, Germany) was used for signal transmission and reception. In the holder, automatic rotations around the cranio-caudal axis of the rat are accomplished. 20,36 This effectively changed the preferential fiber orientation in CC with respect to B 0 .

MRI
Three-dimensional dMRI images collected from the sample were immersed in perfluoropolyether (Galden HS 240; Solvay Solexis, Italy) using a spin-echo EPI sequence at the initial 0 • orientation (left-right axis of the rat approximately aligned with B 0 ), covering the entire specimen, with slice orientation matching the rat axial plane (Table 2). T 1 relaxation time measurements were conducted at nominal rotations of 0 • , 30 • , T A B L E 2 MRI pulse sequence parameters for ex vivo brain specimen at 9.4 T.
The 7T S 0 . # p < 0.05 relative to ROI 1; *p < 0.01 relative to ROI 1; & p < 0.05 relative to large ROI; + p < 0.01 relative to large ROI; Student's paired t-test. Data are presented as mean ± SD for 6 volunteers. ROIs are numbered in Arabic numerals. 45 • , 60 • , 75 • , 90 • , 105 • and 120 • , and repeated at 0 • at the end of the experiment to estimate temporal stability. The images for T 1 maps were collected using an inversion-recovery fast spin-echo (IR-FSE, adiabatic full-passage hyperbolic-secant pulse) sequence in every other slice of the diffusion scans (to reduce magnetization transfer [MT] contamination and slice cross-talk). The T 1 maps were additionally measured using a Look-Locker gradient-echo sequence (IR-LL, adiabatic full-passage hyperbolic-secant pulse) in a single-slice mode ( Table 2). All MRI scans were performed at 20 • C.
The dMRI images were corrected for image distortions and eddy currents using TOPUP and EDDY in FSL, respectively. T 1 maps for each rotation were calculated using two-parametric fit for IR-FSE and three-parametric fit with LL correction according to Deichmann et al. 37 for the IR-LL and the respective signal equations. All T 1 maps were coregistered to the T 1 scan at nominal 0 • rotation using rigid-body transformation in Elastix. 38 The diffusion-weighted images, also acquired at a 0 • rotation, were coregistered to the same T 1 image using an affine and a symmetric image-normalization registration computed with Advanced Normalization Tools (ANTs version 2.3.5). 39 Diffusion tensor maps were estimated from the diffusion-weighted images using nonlinear least squares. 40 T 1 and dMRI data from ex vivo preparation are shown in Figure 6 and Figure S3 from two coronal slices encompassing midsection and anterior splenium volumes in anterior-posterior direction.

RESULTS
T 1 , θ FB , and normalized S 0 values from the two sets of CC ROIs at 3 T (Figure 2A,C,E) and 7 T ( Figure 2B,D,F) are shown. Typical T 1 histograms from ROIs 1, 3, and 5 are shown at 3 T and 7 T ( Figure S2). The quantitative MRI data from ROI 1, encompassing the genu, was used as a reference for measured MRI parameters to other ROIs, because most axons (>70%) in this section are small (<1 μm) and the axon diameter distribution is narrow. 10 T 1 values in ROIs 2-5 were longer than in ROI 1 both at F I G U R E 3 Difference in MRI measures between large and midsagittal ROIs of corpus callosum from 3 T (A,C,E) and from 7 T (B,D,F). The light blue bars in (A) and (B) show the estimated ΔT1 from global WM T 1 angular plots shown in Figure 4C,D. Data are presented as mean ± SD for 6 volunteers. ROIs are numbered from 1 to 5 in Arabic numerals.
3 T and 7 T (Figure 2A,B). In the midsagittal ROIs 1-5, T 1 s were shorter than those in the respective large ROIs at 3 T and in midsagittal ROIs 3-5 at 7 T (Figure 2A,B). The θ FB values in all midsagittal ROIs were greater than those in the respective large ROIs both at 3 T and 7 T ( Figure 2C,D). S 0 values in both large and midsagittal ROIs 2-5 were greater than those in ROI 1 at 3 T ( Figure 2E,F). At 7 T, S 0 values in large ROIs 2-5 were greater than in large ROI 1; in large ROI 2, S 0 was greater than in the midsagittal ROI ( Figure 2F).
The θ FB data in Figure 2C,D show differences between midsagittal and large ROIs, as in the former axon fibers run almost perpendicular to B 0 (θ FB > 80 • in all midsagittal ROIs). The differing fiber orientations in the same CC sections make it possible to examine quantitative MRI measures within given tracts at inherently varying θ FB without head rotations. The difference in T 1 (Figure 3A,B) and S 0 ( Figure 3E,F) between the large and the midsagittal ROIs are shown. In Figure 3C,D, the differences in θ FB between the midsagittal and the large ROIs are shown to obtain positive values. The θ FB values were greater by about 6 • in the midsagittal than in the large ROI 1, but by about 20 • in the midbody and by about 12 • in splenium ROIs at both fields. The angular dependency of T 1 in global WM as a function of FA is shown in 2D plots at 3 T ( Figure 4A) and 7 T ( Figure 4B). We can estimate ΔT1 for the measured Δθ FB in each ROI pair using the angular one-dimensional plots of T 1 versus θ FB from global WM with comparable FA as measured in CC ( Figure 5A). From the T 1 angular plots ( Figure 4C,D), estimated ΔT1 in ROI 1 were 3.7 ± 0.7 ms and 5.8 ± 0.8 ms at 3 T and 7 T, respectively. The measured and estimated ΔT1 values are in agreement in ROIs 2, 4, and 5 at 3 T ( Figure 3A) and in ROI 2 at 7 T ( Figure 3B). Instead, the measured ΔT1 in ROI 3 at 3 T and in ROIs 3-5 at 7 T were approximately 2-3-fold greater than the estimated ones ( Figure 3A,B).
The ΔS0 values were negative in all ROI sets at 3 T (i.e., greater in large than in midsagittal ROIs, but only in ROI 2 at 7 T) ( Figure 3E,F). The data from these two sets of ROIs of the given CC section indicate that orientation of axon fibers with respect to B 0 and within the same fiber tracts may directly influence T 1 . Specifically, in sections of CC containing chiefly small axons, the measured and estimated ΔT1 agree with each other, but in sections with high number of large and giant axons they do not. These results suggest that large axon diameters and/or other microstructural characteristics may confound the relationship between fiber orientation and T 1 in some sections of CC.
Values of microstructural measures of FA, MD, F1, F2, ODI, and NDI from 7T dMRI data as well as their differences between the large and midsagittal ROIs are shown ( Figure 5). FA values greater than 0.7 were measured in all CC ROIs, and no difference in FA between midsagittal and large ROIs was observed. ΔMD indicated a higher MD in large than in midsagittal ROIs 2-5 ( Figure 5D). ΔF1 was negative in ROI 5 ( Figure 5F), indicating that the first fiber volume fraction was higher in the midsagittal than the large ROI, whereas ΔF2 was positive in ROI 5 ( Figure 5H), showing that second fiber volume fraction was higher in the large than in midsagittal ROI. The ΔODI values were negative in ROIs 2-4 ( Figure 5J), and ΔNDI values were negative in ROIs 2-5 ( Figure 5L). All in all, the dMRI microstructural data revealed that MD was lower and NDI higher in midsagittal ROIs than in large ROIs 2-5, indicative of tight axon packing and small extraneurite volumes in the former ROIs. 6,41 Furthermore, in ROI 5, F1 was higher and F2 was lower in midsagittal ROI than in the large ROI, indicating a low degree of crossing fiber configuration in splenium midsagittally.
To study orientation dependency of T 1 in the same CC ROIs at multiple rotations in B 0 , an ex vivo rat brain specimen was scanned at 9.4 T. Coronal T 1 maps acquired with IR-LL through the anterior splenium ( Figure 6A) and with IR-FSE through the midsection of splenium ( Figure 6B) are shown. In rat splenium, small axons with narrow distribution in diameter are found. 42 T 1 values were measured in midsagittal (red ROIs in Figure 6A,B) and more lateral ROIs (green ROIs in Figure 6A,B) of the specimen, to mimic the way MRI data were analyzed in human CC in vivo. IR-LL T 1 in the midsagittal ROIs of the two slices were 854.9 ± 4.3 ms and 965.1 ± 8.8 ms for θ FB of 96.9 ± 2.7 • and 94.7 ± 2.2 • , respectively. In the lateral ROIs ( Figure 6A,B), with θ FB of 73.6 ± 5.6 • and 73.9 ± 6.0 • , IR-LL T 1 s were 940.9 ± 7.0 ms and 967.6 ± 7.8 ms, respectively, The IR-FSE T 1 values were 717.0 ± 5.0 ms and 722.1 ± 6.5 ms in midsagittal ROIs and 726.4 ± 7.4 ms and 773.7 ± 7.8 ms in the lateral ROIs. A tendency to long T 1 s in lateral ROIs relative to those in midsagittal ROIs were in line with the in vivo T1 data, as θ FB values in the former ROIs were smaller than in the latter. FA in the anterior splenium was 0.746 ± 0.028, and 0.610 ± 0.067 in the midsection splenium. In the lateral ROIs, the respective FA values were 0.496 ± 0.059 and 0.775 ± 0.042. MD was 0.238 ± 0.086 μm 2 /ms, and 0.401 ± 0.072 μm 2 /ms in the midsagittal ROIs, and 0.296 ± 0.022 μm 2 /ms and 0.368 ± 0.052 μm 2 /ms in the lateral CC ROIs, respectively. T 1 s as a function of θ FB in the midsagittal CC (Figure 6C,E,G,I) and as a function of the rotation angle in GM ROIs ( Figure 6D,F,H,J) are shown. IR-LL T 1 in the midsagittal CC ROI of the anterior splenium showed longer T 1 when θ FB was close to 0 • than that close to 90 • , F I G U R E 6 T 1 maps and T 1 angular plots from an ex vivo rat brain specimens at 9. followed by a turn to longer values beyond 90 • ( Figure 6C). Similarly, IR-FSE T 1 in the midsagittal ROIs of both anterior and midsection splenium ( Figure 6E,I) showed long T 1 when θ FB was close to 0 • compared with the orientation close to 90 • ; however, in these plots, the longest T 1 was observed around 40 • to 50 • . Similar angular patterns were observed in the lateral ROIs (green ROIs, Figure 6A,B) as in midsagittal ROIs, both in IR-FSE and IR-LL T 1 , except that θ FB in these plots was offset by about 74 • due to orientation of the fibers at nominal 0 • rotation ( Figure S3). In GM ROIs ( Figure 6D,F,H,J), no consistent angular patterns in T 1 as a function of the rotation angle were observed, however. The data from ex vivo preparation unambiguously demonstrate the direct effect of axon fiber orientation in B 0 on T 1 .

DISCUSSION AND CONCLUSIONS
MRI data from experiments on WM tracts that were rotated to different orientations relative to B 0 , both ex vivo 19 and in vivo, 24 have unambiguously demonstrated the causal effect of fiber orientation on T 2 */T 2 relaxation, whereas evidence for similar orientational influences on T 1 has been lacking. Recent studies suggesting angularly dependent T 1 in vivo have selected WM tissue using diffusion microstructural measures, such as FA, and estimated θ FB from the principal diffusion direction by DTI. 12,15,17 In such experiments, it is conceivable that either physico-chemical factors or axon diameter and density (or both) compromise angular T 1 plots. Here, the T 1 and dMRI data from human CC, which is one of the largest WM tracts in the brain, indicate that axonal fiber orientation per se influences T 1 . In the anterior midbody of CC in vivo, the orientations of axon fibers change within a short distance by up to about 18 • and are associated with a T 1 prolongation that matches the estimated ΔT1 from global WM T 1 data. However, in midbody and isthmus, where large and giant axons are prevalent and axon density is low, the measured T 1 change far exceeds the estimated one, indicating that other microstructural and/or tissue factors are in play as well. Conclusive evidence for the direct effect of fiber orientation on T 1 is obtained by rotations of the same midsagittal CC ROI ex vivo. T 1 in rat CC ex vivo revealed angular T 1 patterns at 9.4 T that closely resemble those observed in human WM in vivo at 7 T. All in all, the current results both from in vivo and ex vivo show that axon fiber orientation influences T 1 relaxation and thus T 1 anisotropy.
Interpreting angular T 1 data from midbody and isthmus of CC in vivo is complicated by the variation of axon diameter and density. In genu, small axons are dominant (>70% of axons are < 1 μm) with narrow diameter distribution, and axon density is high, whereas in somato-motor section and isthmus, large and giant axons are prevalently associated with low axon density. 10,43 The G-ratios estimated both by histological and MRI methods have been reported to be within tight limits (approximately 0.7) across the CC, however. 7 Similarly, myelin water fraction is measured to vary little in CC. 7 Therefore, excluding the axon fiber orientation, the most significant microstructural factors influencing T 1 in CC are the axon diameter and density. We observe that S 0 is higher in ROIs 2-5 than that in ROI 1, paralleling longer T 1 in these ROIs than in ROI 1. These observations support the possibility that high proton density contributes to long T 1 in sections of CC. 11 However, the relationship between high S 0 and long T 1 is not straightforward across the CC, as in splenium the T 1 tends to be shorter than in the midbody despite high S 0 in both sections. In splenium, low MD, high NDI, and high F1 indicate tight packing of axon fibers, low extracellular volume, and low level of crossing fibers, factors that may explain short T 1 in this section of CC relative to midbody. 44 WM tracts in the midsagittal CC in vivo align close to perpendicular to B 0 in the neutral head position in the magnet bore. Midsagittal axons are tightly packed with lower MD and greater NDI than when the tracts begin to fan out toward the hemispheres. As mentioned previously, the latter two differences may confound interpretation of angularly dependent T 1 within the ROIs. Nevertheless, in ROI 2, the measured and estimated ΔT1 match, indicating that in the anterior body, axon fiber orientation and T 1 are closely linked. Histology of the anterior body shows dominant presence of small axons and low number of giant axons. 10 In ROI 5, encompassing the splenium, ΔT1 values matched at 3 T, but the measured ΔT1 was much higher than that estimated at 7 T. In splenium, giant axons are rare; however, the proportion of large axons is significant, 10 which may influence T 1 in a field-dependent manner. In ROI 3, the measured ΔT1 far exceed the estimated values. In CC ROI 3, large and giant axons are present at high proportions. 10 It would be tempting to speculate that the presence of large and giant axons in these sections would make the orientation dependency of T 1 larger than estimated from global WM relaxation data. It should be noted, however, that the use of angular T 1 plots from global WM as a reference for CC may be biased, because giant axons are present in significant numbers only in some WM tracts, such as cortico-spinal tract, superior longitudinal fasciculus, and CC. 43,45,46 All in all, T 1 data from human CC in vivo provide evidence that a change in fiber orientation in the same tract can explain a change in T 1 . However, potential confounds caused by variation in axon diameter and density in some sections of CC complicate drawing a firm conclusion. Therefore, measuring T 1 exactly in the same CC sections at several orientations in B 0 using an ex vivo specimen was considered informative.
There are stark differences in physical conditions, such as lower temperature and mean diffusivity ex vivo than in vivo, and physiological state, such as lack of perfusion ex vivo, which inevitably influence MRI signals. The differing physical conditions make it complicated to quantitatively compare relaxometric in vivo and ex vivo data. However, the nature of interrelationships between MRI signals and microstructure can still be evaluated in ex vivo brain, where WM axonal tracts and other cellular components are structurally intact. We have used IR-based pulse sequences with three different readout schemes to measure T 1 . The MP2RAGE sequence consists of an (adiabatic) inversion pulse followed by two gradient-recalled readout modules, where hard read pulses lead to an inevitable MT contribution to the acquired in vivo brain images. In T 1 maps acquired by IR-LL from ex vivo specimen, MT contribution remains inherently low owing to a single-slice acquisition. Similarly, in the IR-FSE images ex vivo, a wide slice gap is expected to minimize MT. Thus, despite likely differing MT contributions in T 1 maps by MP2RAGE and IR-LL/IR-FSE, we observed closely matching T 1 angular plots from global WM in vivo at 7 T and ex vivo rodent midsagittal CC at 9.4 T. It is noteworthy that ex vivo T 1 angular plots obtained by the two IR-based pulse sequences are qualitatively comparable, even when the T 1 values were longer in the IR-LL than in IR-FSE maps. Thus, relaxation anisotropy is a generic phenomenon in WM due to orientation of axon fibers, involving also T 1 in addition to the established anisotropies of T 2 * 21,47 and T 2 . 48 The closely similar angular T 1 patterns in vivo and ex vivo at 7 T and 9.4 T are reassuring in light of the T 1 plots reported from human WM in vivo at 3 T. T 1 by MP2RAGE at 3 T showed no difference in T 1 between parallel and perpendicular fibers ( Figure 4C), 17 in contrast to T 1 by variable flip angle (VFA), where parallel to the field fibers have longer T 1 than those perpendicular to B 0 . 15 The VFA T 1 also lacks the long T 1 hump centered around 40 • -50 • , 15 which is prominent at 3 T ( Figure 4A). 17 T 1 is longer in parallel than in perpendicular fibers in MP2RAGE T 1 plots at 7 T ( Figure 4D). 12 Hence, the recent 12,15 and current observations indicate that T 1 angular plots depend not only on the tissue's orientation relative to B 0 , but also the pulse sequence that is used to measure T 1 (for further discussion, see Kauppinen et al. 12 ).
Several physical models have been developed to deal with the anisotropic T 1 relaxation. 49,50 Common to the models is that they all focus on the T 1 angular pattern with longer values in parallel rather than in perpendicular to B 0 fibers (or the opposite angular pattern in R1 = 1/T1). Two of the models deal with motionally restricted protons in myelin-associated water and membrane and/or axonal structures, 16,50 and one with magnetic-field variation in the myelin-associated water compartment. 49 It has been concluded that while transverse components of field gradients enhance spin eigenstate transitions in myelin-associated water, and thereby T 1 relaxation, this effect is deemed to be too small to account for the experimental T 1 data. 49 With regard to susceptibility in WM, additional sources of field variation may arise from microvasculature and biological iron, as discussed in Schyboll et al. 15 Blood is effectively removed by transcardial perfusion. A close match of T 1 angular plots in vivo and ex vivo tends to downplay the plausible role of Hb as an effector of orientation-dependent T 1 . The role of iron present in oligodendrocytes clustered around axonal fibers 51 remains to be studied.
The dipolar model dealing with interactions between protons of myelin-associated water and solid myelin shows that T 1 relaxation of both these types of protons are orientation-dependent. 16 The computations of these interactions in a realistic WM environment prevailing in vivo suggest that the dipolar coupling of protons in myelin-associated water and solid myelin is a viable mechanism to account for the in vivo T 1 angular pattern obtained by VFA MRI at 3 T. 16 The most recent model proposes lateral diffusion of bound protons in cellular and myelin membranes, hence the name lateral diffusion model (LDM), as a potential mechanism of T 1 anisotropy. 50 Interestingly, LDM predicts distinct angular T 1 dependencies of protons residing in cellular membranes to those in axons. The predictions by LDM agree with in vivo observations of axon fiber T 1 angular plots obtained by VFA at 3T (i.e., longer T 1 in fibers with θ FB of 0 • than in those at 90 • ) seen in MP2RAGE at 7T ( Figure 4D). 50 The LDM also provides explanation for B 0 dependency of relaxation anisotropy of bound protons. However, LDM does not predict the presence of long T 1 hump around 40 • -50 • in MP2RAGE data. While our primary aim was to examine the interrelationship between axon fiber orientation and T 1 in WM tracts, and by doing so, to better understand the role of axon fiber orientation in T 1 anisotropy, the angular patterns we recently reported 12 and recorded here are richer in features than predicted by any of the published physical models for T 1 anisotropy. The difference in T 1 between axon tracts at 0 • and 90 • with magnetic field is present in data obtained using IR-based MRI sequences both in WM in vivo and ex vivo, in line with predictions by the dipolar models. 16,50 All in all, our data indicate that multiple mechanisms are in operation behind T 1 anisotropy in WM; thus, further experimental data are required to guide refining physical models for this underexplored MRI contrast.
We recognize some limitations in our MRI approaches to both in vivo and ex vivo settings. First, histological and MRI approaches on axon diameter and density as well as G-ratio have focused on the midsagittal CC. 2,7,10,43 Instead, histological data in lateral CC are not well known. A recent electron micrograph study indicated that axon diameter varies little, and G-ratio remains unchanged within a short distance (in millimeter range) from midsagittal splenium toward lateral tissue. 52 We think that it is fair to assume that both axon diameter and G-ratio in the immediate lateral sections of CC analyzed here were similar to those midsagittally. Second, the IR-based MRI pulse sequences used in in vivo and ex vivo scans differ with respect to signal readout schemes. MP2RAGE and LL sequences share the feature that multiple TIs are acquired after the inversion pulse, and comparison of T 1 data obtained by these two methods is therefore more straightforward than between MP2RAGE and IR-FSE. Nevertheless, all the IR-based pulse sequences provided closely matching angular T 1 plots from WM in vivo and ex vivo. Third, a 9.4T scanner was used for ex vivo scans, a field that is higher than those used in vivo. It is well documented that T 1 in the brain is B 0 -dependent. 53,54 In light of the recent analysis on B 0 dependency of T 1 in brain, a shift from 7 T to 9.4 T will only affect short T 1 component as a linear function of B 0 , but not the long T 1 component. 54 The pulsing conditions used both in vivo and ex vivo were such that the data are strongly weighted for the "bulk water" with long T 1 .
To conclude, we have provided evidence from human CC that a change in inherent orientation within the same axon tracts in B 0 results in estimated change in T 1 in sections where dominant axon diameter is small and axon density high. In sections of CC, where large and giant axons are prominently present, the measured T 1 change is much greater than the estimated one. The data from ex vivo CC demonstrate that rotation of the same WM tissue in B 0 results in T 1 variation as function of θ FB matches those observed in WM in vivo. Thus, the axon fiber orientation in WM should be included as a factor modulating T 1 in standard quantitative MRI.

SUPPORTING INFORMATION
Additional supporting information may be found in the online version of the article at the publisher's website. Table S1. SNRs for diffusion MRI at 3 T and 7 T. Figure S1. Volumes of midsagittal and large regions of interest (ROIs) of human corpus callosum at 3 T and 7 T. Figure S2. T 1 histograms from large ROI 1 (A,G), ROI 3 (C,I), and ROI 5 (F,L) and midsagittal ROI 1 (B,H), ROI 3 (D,J), and ROI 5 (F,L) at 3 T and 7 T. Figure S3. T 1 (in ms) as function of the fiber-to-field angle (θ FB in degrees) in the green ROIs of ex vivo rat corpus callosum shown in Figure 6A,B.
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