B₀-orientation dependent magnetic susceptibility-induced white matter contrast in the human brainstem at 11.7T

Abstract

Purpose

To investigate B₀-field-orientation dependent white matter contrast in the human brainstem based on R₂* and frequency difference (Δf) mapping from gradient-echo (GRE) imaging at 11.7T.

Methods

Multi-echo GRE data were acquired from two fixed human brainstem specimens at multiple orientations with respect to the static B₀-field. The B₀-orientation dependent modulation curves of R₂* and Δf measurements between short- and long- echo time regimes were used to reconstruct maps of 3D white matter orientation vectors. The results were compared with maps from diffusion MRI, susceptibility tensor imaging, and histological staining of the same specimens.

Results

R₂* and Δf maps demonstrated distinct and significant contrast modulation between the corticospinal tract (CST) and transverse pontine fibers (TPF) dependent on B₀-orientation. Interleaved fiber orientations of the CST and TPF could be sensitively resolved based on field-orientation-dependent fitting of the R₂* and Δf measurements. The fitted 3D orientation-vector maps and peak-to-peak amplitude of R₂* and Δf modulation exhibited close correspondence to primary eigenvector and anisotropy maps derived from diffusion MRI. Notably, the amplitude of B₀-orientation dependent R₂* modulation was significantly (p<0.005) higher in CST compared to TPF, while fractional anisotropies were comparable.

Conclusion

Findings demonstrate the potential of B₀-orientation dependent susceptibility-induced R₂* and Δf contrasts to probe tract-specific orientation and microstructure in white matter.

Introduction

MR signal measured from gradient-echo (GRE) experiments combines contributions from the intrinsic spin-spin relaxation rate as well as macroscopic and mesoscopic field inhomogeneities associated with tissue-specific variations in magnetic susceptibility. Phase contrast derived from GRE images, particularly at high-field strengths, has been used to investigate the local magnetic microenvironment of gray and white matter tissue in the brain, e.g., variations in iron or myelin content [1-4]. Recent evidence indicates that GRE-based apparent transverse relaxation rate (R₂*) and phase measurements both exhibit dependence on the local orientation of white matter fibers relative to the external B₀-field [5-10]. While the biophysical origins of these effects are not yet completely understood, mechanisms proposed to explain the observed signal properties include anisotropy of magnetic susceptibility [8,11], the generalized Lorentzian approach for microscopic susceptibility inclusions in tissue [12,13], and a theory including both susceptibility anisotropy and structural tissue anisotropy [14].

In white matter, the microstructure of the myelin sheath has been implicated in the frequency shifts and associated phase contrast in GRE-MRI [15,16]. This notion is supported by the apparent loss of gray-white matter contrast observed in phase images of the ex vivo mouse brain after dysmyelination [17]. Sophisticated quantitative susceptibility mapping (QSM) methods have been introduced to calculate 3D maps of isotropic tissue susceptibilities from non-local phase data, which show excellent correlation with local tissue properties e.g., iron concentration, in deep gray matter tissue [18-23]. However, the underlying assumption of isotropic magnetic susceptibility does not necessarily hold true for white matter, which exhibits significant differences in derived QSM contrasts across different head orientations [24]. Fitting the anisotropic susceptibility in white matter with a rank-two symmetric tensor using susceptibility tensor imaging (STI) has also been proposed [25-27]. In addition to the orientation-dependence of white matter susceptibility, the evolution of GRE signal phase in white matter does not necessarily exhibit a linear behavior with echo time [7,28]. This latter effect has been attributed in part to sub-voxel contributions from white matter microstructure, particularly the contribution from water trapped in myelin lipid bilayers to signal phase (frequency) in the short-TE regime [29,30]. Recent reports [28,31] have shown that GRE-based frequency difference mapping, which measures the deviation from phase linearity between short- and long-TE regimes, can be used to extract the effects of local tissue microstructure and underlying white matter orientation on GRE signal evolution in a manner independent of non-local phase effects, which scale linearly with time.

Here, we investigate B₀-orientation dependent R₂* and signal frequency contrasts in the fixed human brainstem, which has a complex structure with orthogonally-interleaving fiber populations [32]. Quantitative R₂* and frequency difference maps derived from 3D multi-orientation GRE data at 11.7T were used to probe field-orientation-dependent neuroanatomical contrast. Further, we investigated 3D estimation of voxel-wise white matter orientation maps based on the B₀-orientation dependent R₂* and frequency difference modulation curves, and compared the results with maps from diffusion tensor imaging (DTI), STI, and histology to evaluate the structural basis of susceptibility-induced contrasts. Our results reveal distinct tissue contrasts in the brainstem modulated by B₀-orientation, and 3D estimates of white matter orientation maps that exhibit close correspondence to maps from DTI, and demonstrate the potential to probe tract-specific microstructure in white matter.

Methods

Specimen preparation

Axial slabs (∼1.5 cm thick) at the level of the pons were dissected from the left half of two immersion-fixed (10% formalin) adult human brainstems in the teaching collection in the Department of Neurology (obtained from the Maryland State Anatomy Board). Prior to MRI, specimens were transferred to phosphate buffered saline for 24 hrs, and embedded in a thin layer of agarose (4% weight/volume) gel to minimize tissue deformation. For MRI, specimens were placed in 30-mm-diameter tubes and held in place via cotton gauze inserted into the tubes. The tubes were filled with Fomblin® (Solvay Solexis, NJ, USA) to minimize susceptibility distortion near the specimen surface.

MR data acquisition

MR experiments were conducted on an 11.7T vertical-bore NMR spectrometer (Bruker Biospin, MA, USA) with an actively-shielded micro2.5 gradient system (maximum strength=1000 mT/m), using a 30-mm sawtooth RF transceiver coil. Specimens were first positioned with the long-axis of the brainstem aligned parallel to the B₀-field (denoted for reference as the 0° position). This corresponds to the conventional orientation of the brainstem for human subjects scanned in the supine position on horizontal-bore clinical scanners. 3D data were acquired using a multi-echo GRE sequence with flip angle=45°, 8 echoes, TE1/inter-echo interval=2.8/4 ms, TR=100 ms, and receiver bandwidth 100 kHz. Acquisition time was ∼38 min per orientation at an isotropic resolution of 170×170×170 (μm)³. During imaging, specimen temperature was maintained at 36°C via thermostatically-controlled airflow. Following the first scan, specimens were manually rotated about the anterior-posterior (x-) axis of the brainstem, and data acquired at 11 orientations spanning angles between 0° to 90° relative to B₀ (angular variation about medial-lateral (y-) axis < ±6°). 7 additional images were acquired with orientations of the brainstem long-axis approximately uniformly distributed over a hemisphere about the B₀-axis. First and second order shimming was performed after localizer scans at each orientation to minimize field distortions. For reference, co-registered DTI data were acquired at the same resolution with the specimen in the 0° position, using a 3D diffusion-weighted gradient-and-spin-echo (DW-GRASE) sequence [33] with twin-navigator echoes for phase correction (TE/TR=30/700 ms, turbo factor/EPI factor=4/3, diffusion gradient duration/separation=3.6/12 ms, 2 averages). For fitting of diffusion tensors, one minimally diffusion-weighted (b0) image and six diffusion-encoding directions were acquired with b-value=2000 s/mm².

Image reconstruction and processing

Real and imaginary data were reconstructed in IDL6.4 (ITT Visual Information Solutions) to generate magnitude and phase images. Prior to 3D Fourier transformation, k-space data were apodized by a 10% trapezoidal function to reduce noise and zero-filled to twice the matrix size. R₂* maps were computed for each orientation via linear least-squares fitting of the natural logarithm of multi-echo GRE magnitude data versus TE. Phase maps at odd-numbered echoes were unwrapped using a Laplacian-based unwrapping algorithm [24], and spatially filtered using V-SHARP [19,34] with variable spherical deconvolution kernel size (maximum radius=9 voxels, regularization parameter=0.05) to remove low-frequency background fields. The filtered phase data were normalized by 2πTE to yield maps of the frequency shift referenced to the water center frequency. Frequency difference (Δf) maps at each orientation were calculated by taking the difference between the high-pass filtered frequency shift maps from the 1^st and 7^th echoes (TE=2.8 ms and TE=26.8 ms, respectively). The Δf maps encode the TE-dependent evolution of signal frequency (deviation from linearity of signal phase with TE) at each voxel [7]. Diffusion tensors were reconstructed via multivariate linear fitting in IDL [33] and diagonalized to obtain primary diffusion eigenvector, fractional anisotropy (FA), and direction-encoded color (DEC) maps.

GRE data at multiple specimen orientations were spatially registered to the 0° data space using 6-parameter rigid-body mapping in the automated image registration tool [35] implemented in DiffeoMap (www.mristudio.org), followed by affine registration to minimize residual misalignment. The intensity-based registration was driven by the 3^rd echo magnitude images for optimal contrast, and resulting transformation matrices were applied to the R₂*, frequency shift, and Δf maps using tri-linear interpolation for resampling. The 3D transformation matrices were used to calculate the rotation angles and Ĥ_0i vectors (i.e., unit vector along the applied main magnetic field in the specimen frame of reference at the i^th orientation).

Data analysis

The R₂* and Δf measurements at the sampled specimen orientations were fit voxel-wise to generalized models [31]:

$${R_2}^{\ast }=A_{R{2}^{\ast }}{g}_1\left({\theta }_i\right)+B_{R{2}^{\ast }}$$ 1

$$\Delta f=A_{\Delta f}{g}_2\left({\theta }_i\right)+B_{\Delta f}$$ 2

where cos θ_i = |V̅• Ĥ_0i|; θ_i denotes the angle between the local fiber orientation vector V̅ = [v₁, v₂, v₃] in 3D space (to be estimated) and Ĥ_0i. g₁(θ) and g₂(θ) in Eqs. [1] and [2] were modeled as a₁ sin²θ + a₂ sin⁴θ and sin²θ, respectively. The g₂(θ) fitting is based on the assumption that resonance frequency shifts induced by the presence of cylindrically-shaped myelinated nerve fibers exhibit sin²θ dependence on B₀-orientation [12,16,30]. The relationship for R₂* dependence on fiber orientation is relatively less straightforward [6,16,31,36], and was modeled by incorporating a linear combination of sin²θ and sin⁴θ terms in Eq. [1] with a₁ sin²θ + a₂ sin⁴θ normalized to lie in the interval [0,1]. The coefficients A and B represent the peak-to-peak amplitudes of orientation-dependent modulations of R₂* and Δf and corresponding θ-independent baseline offsets, respectively [31]. 5- (or 6-) parameter Levenberg-Marquardt nonlinear least-squares optimization was used to fit the models independently using MATLAB (Mathworks Inc.) to derive estimates of coefficients A, B, and respective 3D fiber orientation vectors at each voxel based on R₂* and Δf measurements. Similar to DTI, where color maps are scaled by FA, R₂* and Δf modulation based fiber orientation maps were scaled by their fitted peak-to-peak amplitudes.

Additionally, the frequency shift data were fit to the six-element susceptibility tensor model [11] at each voxel, by computing the least-squares solution to:

$$\frac{{(\Delta B_z)}_i}{{\mu }_0{H}_0}=F{T}^{-1}\left[\frac{1}{3}{\widehat{H}}_{0i}.FT\left\{\overline{\overline{\chi }}\right\}.{\widehat{H}}_{0i}-{\widehat{H}}_{0i}.\overline{k}\frac{\overline{k}.FT\left\{\overline{\overline{\chi }}\right\}.{\widehat{H}}_{0i}}{k^2}\right]$$ 3

n k-space; where (ΔB_z)_i denotes the measured magnetic field shift at orientation i, μ₀ is the vacuum permeability, k̄ the spatial frequency vector, H₀ the magnitude of the applied magnetic field, χ(x0033F) denotes the rank-2 susceptibility tensor. ΔB_Z in Eq. [3] was calculated from GRE phase data measured at TE=26.8 ms for each orientation. The eigenvalues of the susceptibility tensor (χ₁, χ₂, χ₃), magnetic susceptibility anisotropy (MSA) given by χ_ani=χ₁-(χ₂+χ₃)/2 [26,27], and maps of the primary susceptibility eigenvector corresponding to the most paramagnetic eigenvalue were calculated via eigenvalue decomposition of the voxel-wise fitted tensors using MATLAB.

Regions of interest (ROIs) for quantitative analysis were defined using ROIEditor (www.mristudio.org), and were based on co-registered DEC maps reconstructed from DTI to delineate specific fiber tracts. Statistical comparisons of R₂* and Δf measurements were performed based on Wilcoxon rank-sum tests using IDL6.4.

Histological processing

Following MR experiments, specimens were paraffin-embedded and sectioned serially into 10-μm thick sections. Select alternate slides were stained using Luxol fast blue (LFB, for myelin) and Bielchowsky's silver impregnation method (for labeling axons and neurofibrils) as described previously [37]. Histological slides were imaged under a Zeiss AxioObserver.Z1 microscope (Carl Zeiss Microscopy, NY, USA) using a 5× objective.

Results

Fig. 1 shows R₂* and frequency shift maps for two representative orientations of the brainstem axis (0° and 89°). In the pons (DEC map in Fig. 1a), longitudinal fascicles of the corticospinal tract (CST) interweave orthogonally through medio-laterally running transverse pontine fibers (TPF). At the 0° specimen orientation, CST fibers were oriented parallel to B₀ and exhibited significantly (p < 0.001) lower R₂* values compared to pontine fibers perpendicular to B₀. At 89°, this contrast was found to be reversed, with a drastic increase (p < 0.001) in R₂* measurements observed in the CST (ΔR₂* = 23.1 ± 3.2 s^-1) relative to TPF, which in turn showed a corresponding decrease in R₂* (ΔR₂* = -17.3 ± 2.2 s^-1) compared to the 0° position (Fig. 1b). Frequency shift maps at the 0° specimen orientation revealed negative (diamagnetic) frequency shifts for TPF with respect to the CST, with a reversal of the relative polarity observed at 89° (Fig. 1c). This inversion of contrast between the two fiber groups can be distinctly seen in Fig. 1, which shows specific tracts highlighted at each orientation.

Figure 1.

B₀-orientation dependent modulation of R₂* and frequency shift (f) contrasts in the human brainstem. Axial sections at the level of the pons show comparison of fitted R₂* (b) and f maps at TE=16.8 ms (c) for two representative orientations of the brainstem axis (0°, 89°) relative to the external B₀ field. The maps reveal a distinct inversion of R₂* and frequency shift contrasts between the corticospinal tract (CST) and transverse pontine fibers (TPF) at the two orientations, with no apparent change evident in gray matter (GM) areas. The respective fiber orientations of the two white matter groups can be seen in the corresponding direction-encoded colormap derived from DTI on the left (red: anterior-posterior, green: medial-lateral, blue: superior-inferior).

Fig. 2 shows results of frequency difference (Δf) mapping for one representative specimen orientation (long-axis of the brainstem parallel to B₀). The B₀-field is oriented perpendicular to the plane of the sections for the sampling orientation shown. The Δf maps exhibited local contrast specific to white matter regions (Fig. 2d), which showed significant dependence on fiber orientation relative to B₀. Comparison with the LFB-stained histological section (Fig. 2e) reveals relatively large frequency differences specific to myelinated fibers perpendicular to B₀, as evidenced by close correspondence of the resulting Δf contrasts to LFB staining of in-plane myelinated TPF fibers (Fig. 2d-e). Plots of R₂* and Δf measurements in the CST and TPF as a function of angle between the brainstem axis and B₀ are shown in Fig. 3, and demonstrate distinct orientation-dependent modulation of both R₂* and Δf contrasts. The relative contrast between the two fiber groups was found to reach extrema at specimen angles close to 0° or 90° with respect to B₀, with progressive minimization of the contrast observed at angles approaching 45° (Fig. 3a-b). Scatter plots of voxel-wise R₂* and Δf measurements at acquired specimen orientations versus angle made by the corresponding DTI primary eigenvector with B₀ (Fig. 3c-d) illustrate strong dependences of R₂* and Δf on local fiber orientation.

Figure 2.

Phase processing and generation of frequency difference (Δf) maps. From left to right, axial sections through the brainstem illustrate: a) the raw phase data, b) unwrapped phase after Laplacian unwrapping, c) frequency shift (f) map at TE=26.8 ms after SHARP-filtering, d) corresponding Δf map calculated from the 1^st and 7^th echoes (f_{TE=26.8 ms}- f_{TE=2.8 ms}), e) Luxol fast blue (LFB)-stained section at approximately the same axial level as the MRI slice shown in a-d. The B₀ field is oriented perpendicular to the plane of the sections for the sampling orientation shown. Note the relatively large frequency difference apparent in fibers oriented perpendicular to B₀, as evidenced by comparison with staining of in-plane myelinated transverse pontine fibers (TPF) in the LFB section.

Figure 3.

a-b) R₂* and frequency difference (Δf) measurements in the CST and TPF white matter groups plotted as a function of rotation of the brainstem axis with respect to the static B₀-field. Data points are mean measurements over regions-of-interest in the CST (filled circles) and TPF (hollow circles), plotted for 12 sampling orientations with specimen rotation about the x-axis (angular variation about y-axis ≤ 6°). Error bars represent standard deviations over voxels in each ROI. Representative regions for the two fiber groups are indicated in the axial T₂-weighted section on the left. c-d) Scatter plots of voxel-wise R₂* and Δf measurements from multiple specimen orientations plotted against angle measured between the B₀-axis and the corresponding primary diffusion eigenvector from co-registered DTI data. Data points plotted are measured R₂* and Δf values at single voxels in the CST (blue) and TPF (orange), from 3D GRE data at 12 specimen orientations with respect to the B₀-axis.

Fig. 4 shows representative results of 3D estimation of orientation vector and A_R2* maps from voxel-wise fitting of the multi-orientation R₂* data to Eq. [1], along with corresponding FA and DEC maps from DTI. Fitting of the experimental R₂* measurements to Eq. [1] with sin⁴θ and sum of sin²θ, sin⁴θ terms yielded adjusted R² values that were not significantly different (p>0.05 based on the F-statistic in voxels with FA ≥ 0.6), indicating that incorporating the sin²θ term did not significantly alter the goodness of fit when accounting for the number of fitting parameters (results of fits shown in Sup. Fig. S1). Regions exhibiting a higher degree of orientation-dependent modulation of R₂* appear hyperintense in the A_R2* maps (Fig. 4b). A close correspondence is apparent between contrast in the voxel-wise fitted A_R2* map and the parametric FA map from DTI (Fig. 4a, b). The fitted A_R2* values were strongly correlated with FA values (r=0.65, p<0.001) in voxels with FA>0.2. Notably, the CST exhibited a significantly (p<0.005) higher peak-to-peak amplitude of R₂* modulation with B₀-orientation compared to TPF (A_R2* map in Fig. 4b), which was consistent across both brainstem specimens. The corresponding orientation map estimated from Eq. [1] (Fig. 4b) shows interleaved fiber orientations of CST and TPF that could be sensitively resolved and exhibit close agreement with the DEC map derived from DTI (Fig. 4a-b).

Figure 4.

Estimation of white matter orientation maps based on B₀-orientation-dependent R₂* modulation in the brainstem. a) Representative axial slice showing DEC and FA maps^† reconstructed from DTI, b) Corresponding orientation vector map and peak-to-peak amplitude of R₂* modulation (A_R2* map) from voxel-wise fits of the R₂* data at multiple specimen orientations to Eq. [1]. 3D vector components estimated in Eq. [1] are scaled by the fitted A_R2* parameter at each voxel to generate the orientation map. Red, green, and blue represent orientations along anterior-posterior, medial-lateral, and superior-inferior axes, respectively, in both (a) and (b). ^†Note that the relative smoothness of the DTI maps in (a) is due to the wider point-spread-function of 3D-GRASE acquisition along the phase encoding directions, as discussed in ref. [33].

Results from fitting of frequency difference measurements to Eq. [2] based on sin²θ dependency are shown in Fig. 5, which shows A_Δf and scaled orientation vector maps along with corresponding DTI-derived FA and DEC maps. The fitted orientation map (Fig. 5b) reveals interdigitating orientations of CST and TPF in the pons sensitively delineated based on Δf modulation with B₀-orientation (Fig. 5, white arrows), which are in close agreement with the respective orientations resolved in the DEC map from DTI (Fig. 5a). Pronounced differences are also apparent, particularly in regions surrounding dense blood vessels (Fig. 5, white asterisks). Fitted A_Δf values showed a substantial correlation with FA in the mid-pons (r=-0.41, p<0.001) in voxels with FA>0.2. The correlation between A_Δf values and FA was relatively poor (r=-0.16) in regions surrounding blood vessels, although these regions exhibited moderately high FA values (0.46±0.13).

Figure 5.

Estimation of fiber orientation maps of the brainstem based on frequency difference (Δf) mapping at multiple specimen orientations with respect to B₀. DEC and FA maps from DTI are shown in a coronal view through the pons in the left panel (a-a′). Corresponding fitted orientation vector and Δf amplitude parameter (A_Δf) maps from fitting of the 3D-GRE phase data at sampled orientations to Eq. [2] are shown in the right panel (b-b′). White arrows indicate interdigitating fiber orientations of the CST and TPF resolved in the fitted Δf orientation and DEC maps. Asterisks indicate regions containing dense blood vessels, where apparent differences are discernible between the DTI and fitted Δf maps. Red, blue, and green represent anterior-posterior, superior-inferior, and medial-lateral orientations, respectively, in (a) and (b).

Quantitative A_R2* and A_Δf values for the two specimens are summarized in Table 1, along with FA and MSA values for comparison. ROIs for quantitative measurements in the CST and TPF in Table 1 were confined to voxels with angles of 0°±4° and 90°±4° between the B₀-axis and primary eigenvector from co-registered DTI data in the 0° space, respectively, to ensure maximal angular sampling from 0° to 90° for fibers in each ROI at the acquired specimen orientations. This was done to reduce possible bias introduced by sampling orientations in the comparison of A_R2* and A_Δf measurements. The CST exhibited a significantly (p<0.005) higher peak-to-peak amplitude of R₂* modulation with B₀-orientation (A_R2*) compared to TPF for both specimens. In comparison, no significant differences were observed in FA and MSA values between the two white matter groups (Table 1). Fitted A_Δf values were also slightly higher for CST compared to TPF (Table 1), but this difference was not statistically significant (at the p<0.01 level).

Table 1. FA, fitted A_R2^*, A_Δf, and MSA values for the two brainstem specimens.

ROI	FA	AR2* (s-1)	AΔf (Hz)	MSA (ppm)	FA	AR2* (s-1)	AΔf (Hz)	MSA (ppm)
	Specimen A				Specimen B
CST	0.69 ± 0.05	23.3 ± 2.1*	-4.42 ± 0.81	0.019 ± 0.007	0.71 ± 0.06	24.2 ± 1.5*	-5.16 ± 0.83	0.027 ± 0.008
TPF	0.67 ± 0.04	17.5 ± 1.8*	-3.67 ± 0.52	0.017 ± 0.006	0.72 ± 0.04	16.6 ± 1.1*	-4.48 ± 0.63	0.025 ± 0.006
GM	0.06 ± 0.01	3.3 ± 0.8	-0.43 ± 0.18	0.003 ± 0.001	0.11 ± 0.02	2.5 ± 0.2	-0.98 ± 0.62	0.006 ± 0.001

Values shown are mean ± standard deviation of measurements over ROIs in the CST, TPF, and gray matter nuclei (GM). ROIs in the CST (and TPF) were defined based on co-registered DEC maps, and confined to voxels with primary eigenvector orientations parallel (and perpendicular) to the B₀-axis at the 0° specimen position, to ascertain maximal angular sampling of fiber orientations relative to B₀ for each white matter group (angular variation within each ROI ≤ ±4°). GM ROIs were defined in pontine nuclei delineated in DTI trace maps. MSA values listed are from STI fitting of the phase data at TE=26.8 ms.

^*denotes statistically (p<0.005) significant differences in the fitted A_R2* values from Eq. [1] observed between the CST and TPF white matter groups.

Fig. 6 compares representative maps of FA, A_R2*, A_Δf, and MSA for the same axial slice, and corresponding estimates of 3D vector maps scaled by the respective scalar indices. The STI data shown are from tensor fitting of GRE phase data at TE=26.8 ms. To measure quantitative differences in estimated vector orientations across the maps, the angles made by the respective voxel-wise fitted 3D vectors with the corresponding DTI primary eigenvector were calculated. Mean angular differences were found to be 8.7°±4.8° for R₂*, 14.2°±8.1° for Δf, and 18.7°±11.5° for STI fitting with respect to the DTI primary eigenvector (for white matter voxels with FA≥0.6). Comparison of zoomed-in sections through the mid-pons in an area relatively free of dense blood vessels in Fig. 6i-k demonstrates very fine crossing myelinated fibers resolved in the fitted R₂* and Δf based maps, which exhibit close agreement with DTI data (Fig. 6i) and underlying fiber orientations seen with silver-impregnation at the same axial level (Fig. 6l).

Figure 6.

Comparison of white matter orientation maps estimated from DTI, B₀-orientation dependent modulations of R₂* and Δf, and fits using the susceptibility tensor model (STI). Color-coded orientation maps (a-d) and corresponding FA, A_R2*, A_Δf, and MSA parametric maps (e-h) are shown in the same axial slice through the brainstem. Red, blue, and green represent vector orientations as indicated by the color index. White asterisks (in c, d) denote tissue regions containing dense blood vessels. i-k) Zoomed-in views of the region indicated by the white box in panel (a) demonstrate very fine crossing fiber structures in the mid-pons resolved in the DTI data (i) and in corresponding results from voxel-wise fits of the experimental R₂* and Δf data to Eqs. [1] and [2], respectively (j, k). l) Corresponding silver-stained section at the same axial level as the panels in (i-k) is shown for comparison. Scale bar = 1.5 mm.

Discussion

The effect of white matter microstructure on GRE signal phase and magnitude evolution has been investigated recently [16,31,38]. Here, we found distinct contrast between CST and TPF fibers based on R₂* modulation with B₀ orientation - with significantly higher A_R2* evident in the CST versus TPF, while no significant difference in FA was observed between these (Fig. 4, Table 1). Interestingly, the fitted θ-independent offset (B_R2*) maps (Sup. Fig. S1) showed negligible contrast between the CST and TPF, although they exhibited clear contrast between gray and white matter regions. Theoretically, the B_R2* maps can be interpreted to represent the rate of signal decay when all fibers are aligned parallel to B₀ (although not anatomically feasible). This finding suggests that the observed contrast between the CST and TPF is entirely encoded in their respective dependencies on B₀-orientation - which has important implications for probing fiber-specific white matter microstructure, as discussed below.

In our study, the dependence of R₂* on B₀ orientation could be approximated closely by a sin⁴θ modulation. This suggests that for the TE range (0-30.8 ms) used here, signal dephasing in the extra-axonal compartment is in the quadratic regime described in refs. [31,36,39]. Based on simulations, Wharton and Bowtell [31] showed that a pure sin⁴θ fit yields a good approximation for R₂* dependence on B₀, when contributions to signal decay from the myelin compartment can be ignored. Based on our observations (Fig. 3) and published estimates of short-T₂ of myelin water component (∼6 ms at 7T) for in vivo human brain [40], this is a reasonable assumption for fixed tissue at 11.7T, where T₂* is even shorter. However, a precise form of relationship underlying R₂* dependence on B₀ orientation is likely to depend significantly on sequence parameters, particularly on TE. For instance, a recent theoretical study suggested that signal contributions specific to the myelin sheath are expected to exhibit oscillatory and decaying components [16]. In addition, the transition time from quadratic to linear dephasing regimes for cylindrically-shaped perturbers in white matter is itself dependent on orientation (θ) [36].

As seen from Δf maps (Fig. 2), the temporal phase evolution in brainstem white matter was not linear, particularly for fibers at larger angles to the B₀-field. This observation is consistent with previous findings reported in freshly excised [31] and in vivo [28] brain tissues. The specificity of relatively strong frequency differences to white matter fibers aligned perpendicular to B₀ is clearly demonstrated in our data by comparison with histological staining (Fig. 2). Moreover, as shown in Figs. 3 and 5, Δf contrast between CST and TPF fibers was found to modulate significantly with B₀ orientation, which could be used to sensitively reconstruct their interdigitating orientations that showed close agreement with primary eigenvector maps from DTI. A significant θ-dependency was not observed in tissue regions surrounding blood vessels in Δf maps as compared to R₂* data (Fig. 6). This effect could possibly stem from time-dependent dephasing associated with magnetic fields induced by the dense network of microscopic blood vessels traversing this region [41].

A possible source of contribution to the relatively higher angular differences (with respect to DTI) observed in Δf-fitted maps compared to R₂* data in our study (Fig. 6) can also arise from errors propagated during phase preprocessing, and residual RF transmit phase effects [19] that could not be effectively eliminated owing to substantially non-linear behavior of signal phase and hardware constraints on receiver bandwidth which limited the minimum achievable inter-echo spacing at the acquired resolution. Our results in Fig. 6 also demonstrate marginally higher angular differences observed with STI fitting (18.7° ± 11.5°) as compared to Δf-fitted maps (14.2° ± 8.1°) when using DTI data as the reference. However, note that instead of using Δf maps, STI fits the rank-two susceptibility tensor based on frequency-shift (f) maps, which includes the susceptibility-induced nonlocal frequency shift without consideration of microstructure in its theoretical framework, therefore larger errors in the estimation of fiber orientations are not unexpected [30].

The relatively higher degree of θ-dependent R₂* modulation for CST compared to TPF suggests that the contrast mechanism can exhibit potential sensitivity to specific features of underlying white matter microstructure. Based on the hollow cylinder model in ref. [7], signal contribution to B_R2* maps is dominated by the T₂-relaxation constant of axonal and extra-axonal water. Results in Fig. S1 reveal a near absence of contrast between CST and TPF in the fitted B_R2* maps. In comparison, the CST is more prominently highlighted in fitted A_R2* maps compared to the TPF (Figs. 4, S1), and shows relatively higher amplitude of θ-dependent R₂* modulation (Fig. 3, Table 1). No significant differences in FA between the two fiber-groups are seen (Table 1), suggesting that the orientation-dependent amplitude maps can probe specific aspects of white matter microstructure that are distinct from those probed using both T₂-relaxation and diffusion MRI. Possible features that can influence the observed A_R2* and A_Δf contrasts include fiber volume fraction, myelin g-ratio, and ratio of water to lipid layer thicknesses in the myelin sheath, as suggested by recent studies modeling GRE signal evolution [7,16]. Although details on these geometric parameters for CST and TPF fibers are not available and require more detailed electron microscopy analysis, our data indicate that the A_R2* and A_Δf measures are potentially sensitive to tract-specific differences in underlying white matter microstructure.

In conclusion, our findings show significant modulation of R₂* and Δf contrasts in the human brainstem with B₀-field orientation, and demonstrate 3D estimation of white matter fiber orientations based on the observed dependencies. The relative amplitudes of R₂* and Δf modulation observed in CST and TPF further suggest that the anisotropic evolution of GRE contrasts can be potentially used to probe local tract-specific white matter microstructure in the human brain. The orientation-dependence and phase non-linearity observed in our study can also have useful implications for interpretation of QSM data in the human brain.

Supplementary Material

Supp Fig S1

Sup. Figure S1: Fitting of experimental multi-orientation R₂* data from 3D GRE imaging of the brainstem to Eq. [1] with, (from top-down) sin⁴θ, sum of sin⁴θ and sin²θ, and sin⁴θ terms. Panels from left to right show the fitted orientation vector map (V_R2*), peak-to-peak amplitude of R₂* modulation with B₀-orientation (A_R2*), θ-independent baseline offset for R₂* (B_R2*), and the root-mean-squared error (RMSE) calculated from residuals of 5- (or 6-) parameter Levenburg-Marquardt nonlinear least-squares optimization independently at each voxel. The corresponding direction-encoded colormap from DTI is shown at the top left. CST: corticospinal tract, TPF: transverse pontine fibers, GM: gray matter. Colors in V_R2* maps indicate the estimated x, y, and z vector components at each voxel (red: left-right, blue: top-down, green: orthogonal to the plane of the slice). No significant differences in adjusted R² values (p>0.05, using the F-statistic adjusted for degrees of freedom) were evident for fits with the sin⁴θ and sum of sin⁴θ, sin²θ terms in white matter voxels (FA ≥ 0.6). Marginally higher residual values for pure sin²θ fitting when compared to fitting with the sum of sin⁴θ, sin²θ terms are apparent in several WM voxels (FA ≥ 0.6) in the CST and TPF (last panel).