Myelin water imaging depends on white matter fiber orientation in the human brain

Purpose The multi‐exponential T2 decay of the MRI signal from cerebral white matter can be separated into short T2 components related to myelin water and long T2 components related to intracellular and extracellular water. In this study, we investigated to what degree the apparent myelin water fraction (MWF) depends on the angle between white matter fibers and the main magnetic field. Methods Maps of the apparent MWF were acquired using multi‐echo Carr‐Purcell‐Meiboom‐Gill and gradient‐echo spin‐echo sequences. The Carr‐Purcell‐Meiboom‐Gill sequence was acquired with a TR of 1073 ms, 1500 ms, and 2000 ms. The fiber orientation was mapped with DTI. By angle‐wise pooling the voxels across the brain’s white matter, orientation‐dependent apparent MWF curves were generated. Results We found that the apparent MWF varied between 25% and 35% across different fiber orientations. Furthermore, the selection of the TR influences the apparent MWF. Conclusion White matter fiber orientation induces a strong systematic bias on the estimation of the apparent MWF. This finding has implications for future research and the interpretation of MWI results in previously published studies.

resonance T 2 relaxation time of approximately 10 ms at a field strength of 3 T. In contrast, the T 2 relaxation time of the intracellular and extracellular water is in the range of 30 ms to 60 ms, and the CSF has a T 2 relaxation time of more than 1 second. 5,6 The resulting multi-exponential T 2 signal decay of a white matter voxel can be measured using a multi-echo spin-echo scan and be decomposed into its individual components, resulting in a T 2 spectrum. 7 The area of the T 2 spectrum spanning the short T 2 components, referred to as the myelin water peak, divided by the area of the total T 2 spectrum, is defined as the myelin water fraction (MWF). A strong correlation between the MWF and independent measures of myelin has been demonstrated in various postmortem studies. [8][9][10] Over the past two decades, myelin water imaging (MWI) has been applied to mild traumatic brain injury, 11 aging, 12 spinal cord injury, 13 neonates, 14 and multiple sclerosis, [15][16][17][18] among others.
The human brain's white matter is highly anisotropic. This circumstance is widely exploited in DTI, which allows us to map the brain's complex fiber architecture. 19 The orientation of white matter fibers with respect to the main magnetic field B 0 also affects the magnitude and phase of the complex MRI signal and a wide range of quantitative MRI parameters. Strong orientation effects have been reported for R * 2 relaxation, 20-25 gradient-echo phase, 21,24,26 and QSM. 27 A weak orientation effect also exists for T 1 relaxation. [28][29][30][31] Moreover, due to anisotropy of the cerebral vascular architecture, dynamic susceptibility-contrast perfusion measurements conducted with both gradient-echo 32 and spin-echo sequences 33 show an orientation dependent behavior. The orientation dependency of the gradient-echo signal of white matter is extensively studied and is ascribed primarily to the anisotropy of the magnetic susceptibility caused by the myelinated nerve fibers. 24,25,34,35 The observation that the T 2 signal of white matter shows an anisotropic behavior 25,33,36,37 that depends on the fiber orientation, suggests that MWI is potentially affected as well. Therefore, we investigated whether and to what degree the MWF depends on the angle between the white matter fiber tracts and the main magnetic field B 0 . In the present study, we acquired MWI using a gradient and spin-echo (GRASE) sequence, 38 which is used widely in literature, and the Carr-Purcell-Meiboom-Gill (CPMG) sequence, which is the gold standard. The CPMG sequence was further acquired at various TRs. We show that the apparent MWF depends strongly on white matter fiber orientation, independent of MRI sequence.

| METHODS
Eight healthy volunteers (3 female, 5 male) with a mean age of 26 years (age range = 21-33 years) and without any history of neurological disorder participated in this study, which was approved by the University of British Columbia Clinical Research Ethics Board. All volunteers gave written, informed consent. The MRI was performed on a 3T MR system (Ingenia Elition; Philips Medical Systems, Best, the Netherlands) using a 32-channel SENSE head coil.

| Magnetic resonance imaging acquisition
A 3D T 1 -weighted sequence with TE = 4.9 ms, TR = 9.8 ms, flip angle = 8°, resolution = 0.8 × 0.8 × 0.8 mm 3 , FOV = 256 × 256 × 180 mm, compressed SENSE factor = 3.6, and acquisition time = 5:50 minutes was acquired for anatomical overview. Compressed SENSE is a combination of compressed sensing 39,40 and SENSE. 41 For the calculation of fiber orientation, a DTI sequence with TE = 60 ms, TR = 4111 ms, b-value = 700 s/mm 2 , 60 diffusion directions, resolution = 2.3 × 2.3 × 2.4 mm 3 , FOV = 224 × 168 × 224 mm, multiband factor = 2, 42 SENSE factor = 2.1, and acquisition time = 4:19 minutes was acquired. The MWI was performed using the following sequences: (1) a GRASE sequence with TR = 1073 ms, SENSE = 2.5, three gradient echoes per spin echo, receiver bandwidth = 100 kHz (non-EPI) and 350 kHz (EPI), and acquisition time = 11:29 minutes; (2) a CPMG sequence with TR = 1073 ms and acquisition time of 09:43 minutes; (3) a CPMG sequence with TR = 1500 ms and acquisition time = 13:33 minutes; and (4) a CPMG sequence with TR = 2000 ms and acquisition time = 18:04 minutes. All CPMG sequences were accelerated with a CS factor of 7, 43 and all MWI sequences had 48 echoes with the first echo at TE = 8 ms, ∆TE = 8 ms, spatial resolution = 0.96 × 0.96 × 2.5 mm 3 , and FOV = 230 × 120 × 180 mm. The DTI and MWI sequences were acquired in axial orientation without angulation. Due to the long data-acquisition times, not all sequences were acquired in all volunteers. A summary of all acquired sequences for each volunteer, including their acquisition times, is provided in Supporting Information Table S1. All MRI data are available from the authors upon reasonable request.

| Image analysis
The DTI data were analyzed with the FMRIB Software Library (FSL v5.0.9). [44][45][46] Distortions induced by eddy currents and head motion were corrected by FSL's eddy_ correct. FSL DTIFIT was used to calculate the diffusion tensor model, and therefore the eigenvalues and eigenvectors.
For MWI analysis, the T 2 distributions were computed using a regularized nonnegative least-squares algorithm with stimulated-echo correction and a T 2 range of 8 ms to 2.0 seconds. 6 as a T 2 distribution, in which the myelin water T 2 is defined as the T 2 times of the distribution between 8 ms and 25 ms. The intracellular and extracellular water T 2 is defined as the T 2 times above 25 ms. The cutoff between the two water pools was set to 25 ms, which was based on the measured T 2 distributions. The apparent MWF was calculated as the ratio of the myelin water T 2 to the entire T 2 components.
The T 1 and DTI was linearly registered to the MWI using FLIRT. FSL's vecreg was used to register the first eigenvector to the MWI space. The fiber orientation was calculated from the angle between the first eigenvector and the direction of the main magnetic field B 0 . 21 Brain extraction was performed using FSL's brain extraction tool (bet), and FSL's FAST was used to generate a white matter mask, which was eroded with a 3 × 3 × 3 kernel. The apparent MWF, myelin water T 2 , and intracellular and extracellular water T 2 were computed as a function of local fiber orientation θ. The fiber orientations were divided into 18 intervals of 5° between 0° (parallel to B 0 ) and 90° (perpendicular to B 0 ). To compute apparent MWF (θ), voxels from across the entire white matter were pooled for each angle interval, to reduce the influence of tract-specific differences in apparent MWF.

| Statistical analysis
All parameters were tested for normal distribution using the Shapiro-Wilk test. A t-test was used to determine the significance of differences between GRASE and CPMG. To test whether the fiber angle and TR had a significant effect on apparent MWF and T 2 , an analysis of variance was used. All statistical analyses were performed using R (version 3.5.1; The R Foundation for Statistical Computing).

| RESULTS
The T 2 distributions plotted for different fiber angles of a representative subject are shown for CPMG in Figure 1A and for GRASE in Figure 1C. The distributions exhibit the F I G U R E 1 T 2 distribution of a representative subject at different fiber angle intervals for Carr-Purcell-Meiboom-Gill (CPMG) (A) and gradient and spin echo (GRASE) (C). Please note that the distribution is dominated by the intracellular and extracellular water peak. The myelin water peak and the cerebrospinal fluid peak are represented by increased signal intensity at the left and right border of the plot, respectively. In the lower row, the cumulative signal intensity is plotted as function of T 2 times for CPMG (B) and GRASE (D). The zoomed inserts in (B) and (D) show how the integral is maximal for low angles and reaches a minimum for angles approximately 50° to 60°. The vertical dashed line indicates the cutoff of 25 ms used in the present study. The typically used cutoff of 40 ms results in a larger orientation dependency in apparent myelin water fraction (MWF) typical large peak from intracellular and extracellular water, the small myelin water peak at short T 2 relaxation times, and a small peak from CSF at very long T 2 relaxation times. The plotted T 2 distribution highlights the intracellular and extracellular water peak, whereas the myelin water peak and CSF peak are represented by increased signal intensity at the left and right border of the plot, respectively. The zoomed inserts display the systematic angle dependency of the distribution. Figure 1B,D shows the cumulative intensity of the distribution ranging from T 2,min = 8 ms to T 2 = T 2,max , computed as the integral of the area under the T 2 distribution from T 2,min to the respective T 2 time normalized by the total area of the T 2 distribution. The zoomed insert shows how the integral differs between fiber angles and between the CPMG and GRASE sequence.
Representative maps of the angle between white matter fibers and B 0 and the corresponding apparent MWF maps are shown in Figure 2 for a single subject. Overall, the GRASE and CPMG sequences provide comparable results, although using a CPMG sequence resulted in higher apparent MWF.
The relationship among the apparent MWF, myelin water T 2 , intracellular and extracellular water T 2 , and the white matter fiber orientation is shown in Figure 3. In general, the apparent MWF decreased with increasing fiber angles and reached a minimum between 50° and 60°, followed by an increase toward angles of 90° ( Figure 3A). The apparent MWF varied by approximately 35% for the GRASE sequence, and by approximately 22% for the CPMG sequence. Using a GRASE sequence resulted in a stronger orientation dependency of the apparent MWF. Myelin water T 2 ( Figure 3B) and intracellular and extracellular water T 2 ( Figure 3C) increased with increasing fiber angle up to a maximum between 15° and 25° followed by a decrease. Between GRASE and CPMG, there was a significant difference in the orientation dependency of the apparent MWF (P = .002) and the myelin water T 2 (P < .001). The orientation dependency of F I G U R E 2 Representative fiber angle and apparent MWF maps, acquired using a CPMG and GRASE sequence, of a single subject | 2225 BIRKL et aL.
the intracellular and extracellular water T 2 (P = .79) showed no significant difference between the two scan types.

| Effect of TR
By increasing TR from 1073 ms to 1500 ms and 2000 ms, the orientation-dependent apparent MWF decreased across all regions, as shown in Figure 4. In general, TR had a significant influence on the orientation-dependent apparent MWF (P < .001), myelin water T 2 (P < .001), and intracellular and extracellular water T 2 (P < .001), as shown in Figure 5. The shape of the orientation-dependent apparent MWF, myelin water T 2 , and intracellular and extracellular water T 2 was similar but shifted with increasing TR. The effect of TR is further evident by plotting the global white matter mean of the apparent MWF ( Figure 6A), myelin water T 2 ( Figure 6B), and intracellular and extracellular water T 2 ( Figure 6C). For example, the apparent MWF decreased by 21.5% from 0.079 at TR = 1073 ms to 0.062 at TR = 2000 ms (P = .006), as shown in Figure 6A.

| DISCUSSION
We demonstrated that the T 2 relaxation times of both myelin water and intracellular and extracellular water, and therefore the measurement of the apparent MWF, are considerably influenced by the angle between the white matter fiber tracts and the main magnetic field. Furthermore, the TR of the sequence also has an impact on estimating the apparent MWF. Orientation effects of the transverse relaxation signal have been ascribed primarily to dipole-dipole interaction and to magnetic susceptibility effects. In the following, we first discuss both mechanisms qualitatively in the context of previous F I G U R E 5 Apparent MWF (A), myelin water T 2 (B), and intracellular and extracellular water T 2 (C) as function of fiber orientation acquired using a CPMG sequence with a TR of 1073 ms (blue, 8 subjects), 1500 ms (green, 6 subjects), and 2000 ms (orange, 4 subjects). The minimum of the orientation-dependent apparent MWF was between 50° and 60° for all TRs. The shaded areas indicate the 95% confidence interval F I G U R E 6 Global white matter apparent MWF (A), myelin water T 2 (B), and intracellular and extracellular water T 2 (C). The TR has a significant impact on the apparent MWF (P < .001), myelin water T 2 (P < .001), and intracellular and extracellular water T 2 (P < .001). The GRASE sequence was acquired on 7 subjects; CPMG with TR of 1073 ms was acquired on all 8 subjects, with TR of 1500 ms on 6 subjects and TR of 2000 ms on 4 subjects | 2227 BIRKL et aL.
literature. Then, we apply previously presented models to our experimental data to investigate the possible origins of the orientation dependency.
The observed orientation dependency of the apparent MWF is based on the fact that the underlying T 2 distribution depends on the fiber angle. As the estimation of the apparent MWF relies on the separation of the myelin water pool from the intracellular and extracellular water pool in the T 2 spectrum, an alteration of the T 2 spectrum will affect the estimation of the apparent MWF. This is further evident as the myelin water pool and the intracellular and extracellular water pool show a different sensitivity to changes in fiber orientation. Furthermore, as the T 2 spectrum is based on the T 2 relaxation properties per se, the orientation-dependent behavior of the apparent MWF can be related through the orientation dependency of the T 2 spectrum to T 2 anisotropy effects in general.
Orientation dependency of T 2 has been observed in highly ordered tissues, such as cartilage and tendons. [48][49][50][51] Such structures give high T 2 signal when they are oriented near the magic angles, where the term 3 cos 2 θ − 1 describing the z-component of the dipole field approaches zero. When water is bound to highly ordered tissue, the dipolar interactions depend on the orientation of the tissue with respect to the main magnetic field. These dipolar interactions result in a rapid signal dephasing, unless the tissue is oriented at or near the magic angle. In experimental work on tendons, 50,52 where signal increases by several 100% are observed at the magic angle, the orientation-dependent relaxation effects could be modeled according to k·(3 cos 2 θ − 1) 2 . 48,51 Another cause of orientation effects is the magnetic susceptibility of tissue, which has a strong influence on phase and magnitude of the gradient-echo signal. Although the orientation dependency of white matter R * 2 has been studied extensively, [20][21][22]24,25,53 the effect of tissue orientation on R 2 in the brain has been considered weak for a long time. 37,49 One notable exception is diffusion in the vicinity of the anisotropic white matter vasculature, which gives rise to considerable orientation dependency in the measurements of cerebral blood flow and volume using spin-echo dynamic susceptibility contrast. 33 Oh et al reported a weak orientation dependency of R 2 in ex vivo formalin-fixed white matter that is best described by dipole-dipole interaction according to k·(3 cos 2 θ − 1) 2 . 25 Based on their observation, the authors suggested that the apparent MWF should also weakly depend on fiber orientation. However, the angle effects in their R 2 data were small, which could be a consequence of fixation-induced crosslinking, which reduces tissue anisotropy at length scales that are relevant to T 2 relaxation. Furthermore, with the decreased T 2 relaxation times due to tissue fixation 54 and due to the high field strength of 7 T, the shortest TE of 9 ms of their study may be too long to capture orientation effects under these conditions. Formalin fixation also reduces the diffusion coefficient, and therefore the effects of magnetic susceptibility on the spin-echo signal. The orientation dependency of the field inhomogeneities, on the contrary, is not changed by tissue fixation, as demonstrated by various studies on R * 2 in fixed tissue. 25 Knight et al presented a model for the orientation dependency of the spin-echo signal based on the loss of spin coherence due to diffusion through field inhomogeneities. 36,37 This loss of coherence adds to the intrinsic R 2 and results in an additional reduction of the spin-echo signal. For anisotropic perturbers, such as cylindrical structures, the spin-echo signal becomes orientation-dependent. The theory predicts two possible sources of T 2 anisotropy, which are referred to as (1) a sin 4 (θ)-related orientation dependency caused by diffusion-mediated loss of coherence due to susceptibility differences and (2) a sin 2 (θ) orientation dependency related to interactions between susceptibility differences and applied field gradients. 37 Experimentally, Knight et al report the longest T 2 times for white matter fibers parallel to the B 0 , and the shortest T 2 times for white matter fibers perpendicular to B 0 , which is in good agreement with their theoretical framework. These results are also in agreement with our present study, in which we observed the longest T 2 times of both myelin water T 2 and intracellular extracellular water T 2 at low angles, and the shortest T 2 times in tissue perpendicular to the main magnetic field. Note, however, that in our data both the myelin water T 2 and the intracellular and extracellular water T 2 exhibit a small increase between 0° and about 20°, which is not explained by the model by Knight et al. To shed more light on the underpinnings of the orientation dependency of the spin-echo signal, we fitted previously presented models to our measured myelin water R 2 and intracellular and extracellular water R 2 data (Figure 7 and Supporting Information Tables S2 and S3).
The classical dipole interaction model 51,55 with an orientation-independent contribution a 1 is which allows us to fit the measured myelin water R 2 and the intracellular and extracellular water R 2 (Figure 7). In the next step, we use the extended dipole-dipole interaction model according to previous studies, 25,48,52 in which the model was used to fit orientation-dependent R 2 according to Fitting model R 2,2 (θ) resulted in a poor fit of the R 2 signal (Figure 7).
The third model S 3 (θ) was based on the theory that Knight et al 37 developed for describing the influence of magnetic susceptibility on the orientation-dependent R 2 signal according to Orientation effects due to interactions between susceptibility differences and applied field gradients contribute to b 3 ·sin 2 (θ), and orientation effects due to diffusion-mediated loss of coherence contribute to c 3 ·sin 4 (θ). This model allowed us to properly fit the myelin water R 2 and intracellular and extracellular water R 2 (Figure 7).
In addition, if we independently investigate the orientation effects relating to sin 4 (θ) and contributions related to sin 2 (θ), we see that this allows us to fit the myelin water R 2 and intracellular and extracellular water R 2 (Figure 7). It should be noted that dipole-dipole interactions expressed by R 2,1 (θ) = a 1 + b 1 (3 cos 2 (θ) − 1) can be rewritten as R 2,1 (θ) = a 1 + 2b 1 − 3b 1 sin 2 (θ), which is also evident as the curves of both model fits superimpose, as shown in Figure 7. Furthermore, model R 2,2 (θ) (Equation 2) can be rewritten as R 2,2 (θ) = a 2 + 4b 2 − 12b 2 sin 2 θ + 9b 2 sin 4 θ, which is in line with model R 2,3 (θ), where a 3 = a 2 + 4b 2 , b 3 = −12b 2 and c 3 = 9b 2 . This supposes that model R 2,3 (θ) also incorporates orientation effects due to dipole-dipole interaction, along with orientation effects due to magnetic susceptibility effects. The fitting parameters of all different models are summarized in Supporting Information Table S2 for myelin water R 2 , and in Supporting Information Table S3 for intracellular and extracellular water R 2 .
Other contributions, such as T 1 relaxation and magnetization transfer, will affect the different T 2 components, and therefore the estimation of the apparent MWF. The dependency of apparent MWF and T 2 on TR could be additionally affected by the different T 1 relaxation times of myelin water and the intracellular and extracellular water. The overall T 1 of white matter at 3 T is about 1100 ms, 56,57 whereas T 1 of myelin water is about 200 ms. [58][59][60] Therefore, myelin water is almost fully relaxed even at the shortest TR used in the present study, whereas the intracellular and extracellular water signal is attenuated and increases with increasing TR. As a result, the apparent MWF decreases with increasing TR. Schyboll et al showed a small orientation dependency in both T 1 and water content measurements, of 2.5% and 0.8%, respectively. 28,31 Interestingly, the shape of the water content curve mirrors the apparent MWF curve in our study. In a very recent paper, the same authors showed that the susceptibility effects of the myelin sheath only cause a very weak orientation dependency in T 1 of about 0.4 · 10 −4 Hz between parallel fibers and fibers at the magic angle. 29 Furthermore, Knight et al also reported that the T 1 of white matter weakly depends on the fiber angle with the highest T 1 near the magic angle of 54.7°. 30 Finally, magnetization-transfer effects may influence the estimation of the apparent MWF. Pampel et al showed that magnetization-transfer experiments in white matter are sensitive to fiber-orientation effects, and therefore affect the estimation of short T 2 components through the fiber orientation dependency of the RF absorption lineshape. In their experiments, they observed a fiber orientation-dependent T 2 of the bound water pool (T 2,b ), with a similar orientation dependency compared to our observed myelin water T 2 . The F I G U R E 7 Different models proposed in literature describing orientation-dependent effects were fitted to the measured myelin water R 2 and intracellular and extracellular water R 2 , acquired using a CPMG sequence with TR = 1073 ms (black curve). The shaded area represents the 95% confidence interval. All fit parameters are summarized in Supporting Information Tables S2 and S3 orientation dependency in T 2,b was attributed to chemical exchange and cross-relaxation effects. 61 One limitation of the study is that we only investigated TR up to 2000 ms, which is approximately two times the T 1 of the long T 1 component. The shortest TR of 1073 ms, on the contrary, was defined by the specific absorption rate of the scan. With the required anatomical T 1 and DTI scans and the comparison with the GRASE approach at 1073 ms, the total scan protocol took approximately 75 minutes. Therefore, the present study is not able answer the question of how apparent MWF behaves in the absence of T 1 weighting. A comprehensive study that explores the effects of TR would require several long scans with TRs of up to 5000 ms, in which T 1 weighting of the intracellular and extracellular water is reduced to less than 2%. Such study may be feasible by not scanning every TR in every participant and with reduced brain coverage and lower spatial resolution, which both make image registration more challenging.
Furthermore, the orientation dependency of GRASE and CPMG were different, particularly at larger angles. The increase in apparent MWF at angles above 54.7° was stronger for CPMG compared with GRASE, which may be due to some R * 2 weighting of the GRASE sequence, leading to a reduction of the signal due to field inhomogeneities created by the myelinated axons at larger angles. Future MWI studies will increasingly use the CPMG sequence with compressed sensing, as it allows for shorter echo spacing and for shorter scan times compared with the GRASE-based approach. 43 The approach of using DTI to determine the fiber orientation and pooling voxels according to their local fiber orientation was previously applied in several studies. 20,21,24,32,62 Because for each angle interval voxels are pooled from across the entire brain, potential confounding effects of tract specific differences in apparent MWF are reduced. Moreover, apparent MWF (θ) of all subjects followed a similar pattern, independently of individual differences in head orientation or white matter anatomy. According to Knight et al, crossing fibers led to a decrease in T 2 compared with voxels containing only a single fiber orientation, which will affect the observed orientation-dependent T 2 , and therefore the estimated apparent MWF. 63 By using high-resolution DTI acquisitions with high b-values and multiple directions, the influence of crossing fibers can be minimized. 19 Our findings have consequences for the interpretation of past results and for future research. The orientation dependency of the apparent MWF might mask longitudinal changes in MWF or changes between cohorts, if whole white matter averages are investigated. A corresponding effect was observed in white matter R * 2 , where only an orientationdependent analysis was able to reveal group differences. 53,62 Kor et al modeled the R * 2 relaxation as a function of white matter orientation, myelin, and iron content, and were able to compute whole white matter myelin and iron content. 53 This approach assumed that the effects of iron are orientation-independent, and that only the myelin sheath gives rise to an orientation-dependent R * 2 . Because variations in iron concentration explain approximately 25% of the measured variance in the apparent MWF, 64 an orientation-dependent analysis accompanied by a model that includes the effects of both myelin and iron may shed further light on the orientation dependency of the apparent MWF.
Our findings suggest that comparison of apparent MWF of individual subjects may exhibit paradoxical results if their head orientation differs. A difference in angle by 10°, for example, would result in a relative difference in apparent MWF by 5% to 7%, which is similar to the reduction in apparent MWF in the normal-appearing white matter in multiple sclerosis over 5 years. 17 In conclusion, our study shows that the T 2 distribution, myelin water T 2 , and the intracellular and extracellular water T 2 , as well as the apparent MWF, depend on white matter fiber orientation. Furthermore, with increasing TR, the overall apparent MWF decreases, while the orientation dependency persists.

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