Our first objective was to identify suitable ROIs in which 3D FODs can be compared to inherently 2D, coronally sectioned histological data. We focused our analysis on two ROIs with little or no through-plane (anterioposteriorly oriented) fiber orientations containing 1) coherently oriented fibers, or 2) more complex crossing fiber architectures where the DT model is known to be insufficient. The ROIs were selected on the basis of color-coded DT maps, 3D reconstructions of the DT and FOD, and visual inspection of myelin stained histological sections (Figs. 1, 2). The first region selected (ROI-1) was a 1×4 voxel grid within an area of the anterior part (genu) of the corpus callosum containing high densities of within-plane, mediolaterally oriented commissural fibers [46]–[48]. These orientations are apparent from red colored voxels in the color-coded DT maps (Figs. 1A,B). Because the DT model has previously been validated in regions with uniform fiber orientations [12]–[15], this region was used primarily as a benchmark to confirm that both the DT and FOD provided accurate assays of myeloarchitecture in this region. The second region selected (ROI-2) was a 3×4 voxel grid within an area of the deep gray and white layers of the superior colliculus containing transversely oriented bundles of intratectal and tectal afferent and efferent projection fibers [49], [50] (Figs. 1C,D; 2D). Here the color-coded DT maps showed planar “disk-like” diffusion profiles indicative of crossing fibers oriented within in the coronal plane (Fig. 1D. blue color). In both ROIs assessment of the (coronal) histological sections confirmed presence of predominantly in-plane oriented myelinated fibers (Fig. 2C,D), suitable for two-dimensional histological analysis of fiber orientations.

Our second objective was to assess the resemblance of DT and FOD measurements with histological visualizations of myeloarchitecture in the selected ROIs. In ROI-1, 3D DT and FOD reconstructions across all six animals showed the expected “cigar-like” profiles with left-right orientation (Fig. 2E). In ROI-2, 3D DT reconstructions in all six animals confirmed the “disk-like” shape of the DT, and 3D FOD reconstructions indicated the expected crossing fiber patterns (Fig. 2E). The orientation of the FOD reconstructions were highly consistent across animals in both ROIs and with the morphology evidenced in the myelin stained sections (Fig. 2C,D). Taken together, these results demonstrate a high qualitative resemblance between 3D FOD measures and histological observations of crossing fibers which is highly consistent across several animals. To provide a more rigorous quantitative histological validation of this relationship, we continued to perform a detailed voxel-wise quantitative comparison between these measures in ROI-1 and -2 in one of the animal specimens (animal 1).

Our third objective was to quantitatively evaluate the correspondence between high b-value QSI-derived FOD measures (QSI-FODs) and myeloarchitecture in both ROI-1 and 2. As a benchmark for the comparisons we also included DT fiber orientation estimates (DT-FOD) in both regions (see also “Computation of DT-FODs” in the “Materials and Methods” section).

To validate the QSI-FODs, we used a voxel-wise stereological sampling approach to manually record several hundred myelin stained fiber orientations from multiple registered myelin stained histological images (Fig. 3A,B). The angular histogram of all fiber samples (or fiber counts in a given angular bin) within each voxel constitutes the empirical histology-derived FOD (HIST-FOD; Fig. 3C) used as the validation standard to compare against the DT- and QSI-FOD estimates. Prior to comparison, all fiber models were min-max normalized to remove the isotropic component and normalize the maximum amplitude of the respective distributions. The isotropic component was removed because in conventional QSI-FOD measures there is no way to separate the isotropic fiber orientation from the isotropic ADC, and thus if not removed, the QSI-FODs would have a (biased) larger isotropic component compared with the HIST-FODs.

We found that in ROI-1, which contained fibers with relatively homogeneous fiber orientations, both the QSI-FOD and DT-FODs correlated well with the HIST-FODs (average Pearson correlation coefficients r = 0.98; SD = 0.02 for QSI-FODs, and 0.99; SD = 0.01 for DT-FODs, n = 4 voxels; Fig. 4E,F). By contrast, in ROI-2, which contained crossing fibers, the DT-FODs correlated poorly with HIST-FODs (average Pearson correlation coefficients r = 0.16; SD = 0.38; n = 12 voxels), while QSI-FODs correlated substantially better (average Pearson correlation coefficients r = 0.86; SD = 0.07; Fig. 4GH). A non-parametric permutation-based 2-sample t-test revealed that the difference in correlation between the DT-FODs and QSI-FODs were not significant in ROI-1 (p≫0.05), but highly significant in ROI-2 (p<0.0001). These results quantitatively confirm that QSI-FODs provide accurate assays of the underlying myeloarchitecture in regions of both uniform and complex crossing fiber orientations.

We also quantitatively evaluated the orientation error of the QSI-FOD peaks in ROI-2 (Fig 5). We found that the peak orientations of the QSI-FODs closely matched the peaks of the HIST-FODs, with an average angular error (across all 12 voxels) of 5.7°; SD 3.8° (Fig 5). The average (acute) intersection angle of the HIST-FOD peaks was θ = 73°; SD = 8° (Fig 5). It should be noted that these results were obtained using a radial-basis function parameterization of the QSI-FODs with a width of σ = 10 (see “Materials and Methods”), which maximized the correlation with the HIST-FODs in ROI-2. However, further testing revealed that the angular error and correlation were relatively robust to variations in σ. When testing a range of σ between 1 and 20, the average angular error and correlation coefficient only varied between 5.4°–6.2° and 0.83 and 0.86, respectively (data not shown).

Animal procedures were approved by the institutional animal welfare committee at the Massachusetts General Hospital, and were in compliance with National Institutes of Health guidelines for the use and care of laboratory animals.

Adult male Sprague-Dawley rats were anesthetized (ketamine hydrochloride 50 mg/kg, and sodium pentobarbital 12 mg/kg, i.p.) and euthanized by transcardial perfusion with 4% paraformaldehyde. The isolated brains were immersed for 4 weeks at 4°C in a solution of 1mM Gd-DTPA (Magnevist®, Bayer HealthCare Pharmaceuticals, Wayne, NJ, USA) in phosphate buffered saline, and positioned in a sealed plastic tube filled with Fomblin® LC8 liquid (Solvay Solexis, Thorofare, NJ, USA) [45]. High b-value QSI data were acquired using a 2D spin echo planar imaging (EPI) sequence on a 4.7T Bruker scanner equipped with a 3 cm solenoid receiver coil. QSI data were collected using a conventional DSI (Cartesian) acquisition scheme. Pulse-sequence parameters for the QSI acquisition were: TR/TE = 650/49 msec, Δ/δ = 23/12 msec, 515 q-space directions, |G|_max = 380 mTm⁻¹, b-max = 30452sec/mm², matrix = 64×64×128, voxel size = 265 µm isotropic. Following MR imaging, the brain was coronally sectioned at 50 µm on a freezing microtome, at an angle closely matching the tomographic images. The right side of the brain was marked with a shallow razor-blade cut in the tissue to ensure correct orientation of the sections. One in four sections was stained for myelin using a standard procedure modified from Woelcke [52], yielding an effective through-plane spacing of 200 µm. High-resolution mosaic images were obtained through UPlanApo 20/0.70 and 40/0.85 dry objectives using a motorized Olympus BX52 microscope running the Neurolucida 7.0 software (Virtual Slice module, MBF Bioscience, Inc, Williston, VT, USA).

As any voxel-wise quantitative comparison requires accurate spatial registration of image data, several measures were taken to minimize the potential error of misalignment. First, care was taken during histological processing to ensure that the coronal sectioning angle matched the tomographic slice orientation. Trigonometric measurements of multiple corresponding anatomical landmarks confirmed that the angle of the histological section plane and tomographical slice orientation only differed by about 2 degrees (rotation around the mediolateral axis), thus allowing direct registration without resampling of the QSI slice orientation. Second, the selected ROIs (procedure described below) were confirmed to have 1) minimal nonlinear distortion in both the histological data (due to histological processing) and QSI data, and 2) consistent myeloarchitecture across multiple coronal (through-plane) sections. Third, a careful and detailed manual registration protocol was performed for both ROIs. Corresponding anatomical landmarks (brain surface, genu and splenium of the corpus callosum, anterior commissure, the ventricular system, the oculomotor nerve, and several mesencephalic and brain stem nuclei) were identified on basis of general gray and white contrast and used to assign relative anterioposterior position coordinates across the whole brain for both image modalities. Then, for each ROI (one in the forebrain at the level of the genu of the corpus callosum, and the other in the brain stem at level of the superior colliculus, see Fig. 1), histological images were manually registered to corresponding QSI images. Groups of corresponding tomographical and histological images from a volume approximating a ∼1 mm thick coronal brain section (corresponding to 4 QSI and 20 histological slices) through both ROIs were assembled as separate layers using the program Adobe Illustrator CS3 (Adobe Systems Inc. San Jose, CA, USA). Each layer was scaled appropriately depending upon the native voxel size. Finally, using the QSI images as a reference, the histological images were individually adjusted using affine transformations to match multiple local gray and white matter landmarks. This final alignment procedure was iterated until optimal spatial matching was achieved.

ROIs were selected on the basis of 1) color-coded DT maps, 2) 3D DT and FOD reconstructions, and 3) visual inspection of myeloarchitecture. The first ROI (ROI-1) was selected to contain relatively uniform white matter fiber orientations (Figs. 1A,B; 2A). To help find this location, a red-green-blue (RGB) map was created using the primary eigenvector of the DT (“preferred” direction), where each vector element defined the red, green, and blue components of each voxel, respectively. The brightness of this preferred RGB map was determined using a measure of the degree of linear anisotropy, defined as C_l = (λ₁−λ₂)/λ₁ [53], where , , and are the first, second, and third eigenvalues of DT, respectively. Thus, a bright red color in the preferred RGB map indicates a high degree of linear anisotropy with left-right orientation (Fig. 1A,A′). The second ROI (ROI-2) was selected to contain complex crossing fiber orientations (Figs. 1C,D; 2B). To help find this location an RGB map of the third eigenvector (“non-preferred” direction) was created and the brightness of this non-preferred RGB map was defined using a measure of the degree of planar anisotropy, defined as C_p = (λ₂−λ₃)/λ₁ [53]. Voxels with a bright blue color would thus indicate a “disk-like” DT (indicative of crossing fibers) within the image plane ( points through-plane, Fig. 1D,D′). 3D DT and FOD reconstructions provided additional confirmation of apparent crossing fiber architectures that were highly consistent across animals. Finally, the myeloarchitecture in ROI-1 and ROI-2 were microscopically inspected in the original histological sections to confirm the neuroarchitectural patterns suggested by the tomographic data.

The HIST-FODs in ROI-1 and 2 were derived using a systematic random stereological approach adapted from [12]. High-resolution histological images from two consecutive myelin stained sections (spaced at 200 µm) were assembled in separate layers in the Adobe Illustrator file used for image registration (see registration section above). A grid derived from the voxel matrix of the spatially corresponding QSI slice was superimposed onto the histological images. Each voxel domain was further subdivided using a 5×5 rectangular sampling grid. In four systematically positioned sample grids (Fig. 2A,B), individual myelin fiber trajectories were traced as vector lines using Adobe Illustrator. The vector coordinates were exported to Matlab (The Mathworks, Inc. Natick, MA) and HIST-FODs were computed for each QSI voxel by calculating the angular histogram of the line plots (fiber vectors) with a bin size of 1° (360 points) from the four sub regions. To further increase the robustness of the HIST-FODs, corresponding angular histograms from two neighboring myelin sections spaced 200 µm apart were averaged together and the averaged histogram was smoothed with a Gaussian kernel with a FWHM of 8°. In this way, our histological sampling included a through-plane distance approximately corresponding to the depth of a single 265 µm QSI voxel. To quantify the intrinsic degree of fiber spreading within ROI-1 of the corpus callosum, Gaussian distributions were fit to the final angular histograms of each voxel, yielding an average FWHM of approximately 34°.

Since the diffusion tensor (DT) is a model for the apparent diffusion coefficient (ADC), a direct comparison with the HIST-FODs would be misleading. Under the DT model, the fiber orientation is given by a single delta function pointed in the direction of the primary eigenvector. To generate DT equivalent FODs (DT-FODs), the resultant delta functions were convolved with a Gaussian smoothing kernel with a FWHM of 34°. This level of smoothing was chosen to match the intrinsic angular dispersion of fibers within the ROI-1 of the corpus callosum.

To estimate the QSI-FODs, we extend the traditional spherical deconvolution method in Reference [29] to arbitrary (multi-b-value) q-space acquisitions. An axially symmetric tensor model [54] was chosen for the single fiber response function with perpendicular (λ_⊥ = λ₂ = λ₃ = 4.0×10⁻⁵ mm²s⁻¹) and parallel diffusivities (λ_∥ = λ₁ = 3.5×10⁻⁴ mm²s⁻¹) estimated directly from the QSI data in ROI-1, similar to the approach used in [29]. Tikhonov regularization was used to improve the conditioning of the inversion. The FOD solution was parameterized using radial-basis functions, as in Ref [26]. The radial-basis functions themselves are parameterized by the desired FOD reconstruction points and the radial-basis function width parameter σ. For the 3D QSI-FOD reconstructions in Figure 2, a 3^rd order icosahedral tessellation of the sphere was chosen for the FOD reconstruction points (642 vertices) and σ was set to 20. For the 2D QSI-FOD reconstructions in Figures 4 and 5, 360 equally spaced points on the unit circle was chosen for the FOD reconstruction points, and σ was set to 10. This value of σ was chosen because it optimized the correlations with the HIST-FODs in ROI-2. However, we tested a range of different values for σ (from 1 to 20) and found that the average correlations and angular error for the FOD peaks were largely robust to variations in this parameter.

Data plotting and correlation analyses were performed using the standard Matlab statistical toolkit. Correlations were given as Pearson correlation coefficients and where appropriate standard deviations are provided.

Graphical charts were generated using Matlab. Figures were assembled using Adobe Photoshop (CS3) and Adobe Illustrator (CS3).