Using light and X-ray scattering to untangle complex neuronal orientations and validate diffusion MRI

Disentangling human brain connectivity requires an accurate description of nerve fiber trajectories, unveiled via detailed mapping of axonal orientations. However, this is challenging because axons can cross one another on a micrometer scale. Diffusion magnetic resonance imaging (dMRI) can be used to infer axonal connectivity because it is sensitive to axonal alignment, but it has limited spatial resolution and specificity. Scattered light imaging (SLI) and small-angle X-ray scattering (SAXS) reveal axonal orientations with microscopic resolution and high specificity, respectively. Here, we apply both scattering techniques on the same samples and cross-validate them, laying the groundwork for ground-truth axonal orientation imaging and validating dMRI. We evaluate brain regions that include unidirectional and crossing fibers in human and vervet monkey brain sections. SLI and SAXS quantitatively agree regarding in-plane fiber orientations including crossings, while dMRI agrees in the majority of voxels with small discrepancies. We further use SAXS and dMRI to confirm theoretical predictions regarding SLI determination of through-plane fiber orientations. Scattered light and X-ray imaging can provide quantitative micrometer 3D fiber orientations with high resolution and specificity, facilitating detailed investigations of complex fiber architecture in the animal and human brain.


Introduction
Unraveling the complex nerve fiber network in the brain is key to understanding its function and alterations in neurological diseases. The detailed reconstruction of multiple crossing, long-range nerve fiber pathways in densely-packed white matter regions poses a particular challenge. Diffusion magnetic resonance imaging (dMRI) is currently used to derive neuronal orientations in vivo. However, with voxel sizes typically down to a few hundred micrometers in post-mortem human brains (Calabrese et al., 2018;Roebroeck et al., 2018), the resolution is insufficient to resolve individual nerve fibers, and the signal is affected by all brain structures, not only axons. Moreover, the possibly hundreds of fibers within a voxel might have complicated geometries, e.g. crossing or kissing fibers, which poses a particular challenge. Especially notable is that structural connectivity and wiring diagrams of the brain, obtained from dMRI measurements and The scattering of visible light can also be used to reveal crossing nerve fiber orientations ( Figure 1B - Menzel et al., 2020a,b) as it is sensitive to directional arrangements of neuronal axons (~μm diameter). In

Results
Light and X-ray scattering patterns are specific to different fiber configurations To better understand how light and X-ray scattering patterns correspond to each other for different nerve fiber configurations, we analyzed the scattering patterns from SLI and SAXS measurements in a vervet monkey brain section. Figure 2 shows the resulting scattering patterns for four representative points (marked with asterisks in B): (i) unidirectional in-plane fiber bundle in the corpus callosum, (ii) two crossing fiber bundles in the corona radiata, (iii) a sightly through-plane inclined fiber bundle in the fornix, and (iv) a steep out-of-plane fiber bundle in the cingulum. The orientation information is encoded in the variation of the signal intensity as a function of the azimuthal angle φ (going in a circle around the pattern, cf. Figure   2C(i)), plotted as azimuthal profile under each scattering pattern in Figure 2C. Figure 2-figure supplement 1 shows average, maximum, minimum, mean peak prominence and mean peak width of the azimuthal profiles for each pixel measured with SAXS and SLI.
While the SLI scattering patterns show contiguous signal intensity (from center out), the strongest SAXS signal (Bragg peaks) appears along the Debye-Scherrer ring (arrows in Figure 2C), at a specific distance (qvalue) from the center of the pattern that corresponds to the myelin layer periodicity (here 17.5nm)

(Georgiadis et al., 2021).
For in-plane nerve fibers, i.e. nerve fibers that mostly lie within the section plane, the strongest signal in both SLI scatterometry and SAXS is perpendicular to the fiber orientation (red dashed lines in Figure 2B and C(i)), shown in the azimuthal profile as peaks separated by 180°. For the two in-plane crossing fiber bundles in the corona radiata (ii), the peaks in the SLI and SAXS azimuthal profiles similarly indicate the fiber orientations, with each bundle producing two peaks separated by 180° (white/yellow arrows).
For partly out-of-plane fibers, i.e. fibers that have a certain angle with respect to the section plane, such as those in the fornix, the peaks in the SAXS azimuthal profiles are still 180° apart -owing to the Figure 2. Scattering patterns obtained from SLI scatterometry (px = 3μm) and SAXS (px = 100μm) on a 60μm-thick vervet monkey brain section at a coronal plane between amygdala and hippocampus (no. 511

SAXS and SLI resolve crossing fibers and show high inter-method reproducibility
We then sought to more precisely compare the in-plane nerve fiber orientations derived from the peak positions in the SAXS and SLI azimuthal profiles, examining the same ~1x2cm² region of the vervet brain (Figure 3 and Figure 3-figure supplement 1). Given the ~33x higher resolution of SLI over SAXS in the presented measurements (3μm vs. 100μm pixels), smaller nerve fiber bundles e.g. in the head of the caudate nucleus (yellow arrow) can be traced. Conversely, out-of-plane nerve fibers in the cingulum (cg), are more sensitively depicted by SAXS.
Despite the different resolutions, the in-plane nerve fiber orientations are highly coincident, not only for unidirectional fibers, but also for fiber crossings (colored lines in Figure 3B To quantitatively compare the in-plane fiber orientations, the SAXS images were linearly registered onto the SLI images, and pixels in which both techniques yield one or two fiber orientations were compared to each other: For each image pixel, the fiber orientations were subtracted (SLI -SAXS), taking the minimum of the two possible pairings in regions with crossing fibers (Figure 4). Figure 4C shows the image pixels for which both techniques yield a single fiber orientation (magenta) or two fiber orientations (green). Figure 4A shows very small angular differences that appear to be uniformly distributed, depicted as absolute angular differences in Figure 4B. While in-plane and slightly inclined fibers (corpus callosum and fornix) as well as major parts of crossing fibers in the corona radiata show mostly differences less than 10°, highly inclined fibers in the cingulum and the corona radiata show absolute differences of 20° and more (white arrows).
The distribution of angular differences for white matter with one and two fiber orientations is shown in Figure 4D (histograms in magenta and green, respectively). The two histograms show a distribution around zero degrees (one fiber orientation: mean ~0.017°, median absolute ~4.1°; two fiber orientations: meañ 0.316°, median absolute ~5.6°). While regions with one fiber orientation yield differences between +/-30°m aximum, regions with two fiber orientations show multiple outliers with differences of +/-45° and more.
As 33×33 SLI pixels with different fiber orientations correspond to one SAXS pixel with a single fiber orientation, larger differences between in-plane fiber orientations are expected, especially in regions with highly varying fiber orientations.  To validate the dMRI-derived fiber orientations, we measured two 80μm-thick vibratome sections (one from the anterior side, Figure 5, and one from the posterior side, Figure 5-figure supplement 2) with 3Dscanning SAXS and computed fiber orientation distributions (Georgiadis et al., 2015(Georgiadis et al., , 2020. To enable a quantitative comparison of the 3D fiber orientations obtained from dMRI and 3D-sSAXS, the dMRI sections corresponding to the physical SAXS-scanned sections (cf. Figure 5B, red rectangle) were identified, and linearly registered to the SAXS data sets. The main fiber orientations per pixel for dMRI and 3D-sSAXS We then performed a more detailed analysis including crossing fibers. First, in the challenging region of the corona radiata, where multiple fiber crossings occur, the dMRI orientations seem to be in high agreement with the directly structural X-ray scattering ( Figure 5G and However, there is a striking difference when it comes to resolving secondary orientations. Diffusion MRI seems to also show multiple fiber orientations per voxel, with a secondary fiber population perpendicular to the main one (albeit with much smaller magnitude), in areas where X-ray scattering shows homogeneous fiber orientations, exemplified in the corpus callosum and in the subcortical white matter nearby the cingulate and the callosal sulci (arrows in Figure 5G,F). Referencing these regions in the higher-

Experimental validation of out-of-plane fiber orientations in SLI
While SLI determines the in-plane fiber orientation with high precision, out-of-plane fiber orientation (inclination) is challenging. Theory suggests that the fiber inclination is directly related to the distance between the two peaks in the SLI azimuthal profile (cf. upper Figure 2C). The peak distance should decrease with increasing inclination, as indicated by the dashed curves in Figure 6G, which were computed from simulated SLI azimuthal profiles for fiber bundles with different inclinations (Menzel et al., 2021a, Figure   7d). The combined measurement of SLI and 3D-sSAXS enables testing of this prediction, given the very high agreement of 3D-sSAXS and dMRI in the human brain sample in regions of out-of-plane fibers ( Figure 5C

-E).
We performed a pixel-wise comparison of the out-of-plane fiber orientation angles α from 3D-sSAXS ( Figure 6A,B) and the peak distances Δ from SLI ( Figure 6D,E), both for one vervet brain section (A,D) and one human brain section (B,E). The 3D-arrows in Figure 6A indicate the 3D orientation of the nerve fibers computed by 3D-sSAXS for four selected regions. The images in Figures 6C,F show the corresponding 3D fiber orientations from the dMRI measurement of the human brain sample for reference.
When comparing the inclination angles to the corresponding SLI peak distances in Figure 6D-E (evaluated for regions with a single detected fiber orientation), it becomes apparent that regions with inplane fibers (cc) contain many image pixels with large peak distances (blue: Δ > 170°), whereas regions with out-of-plane fibers (cg) contain many image pixels with notably smaller peak distances (green/yellow: Δ < 140°) -especially in the human cingulum. To quantify this effect, we plotted the SLI peak distances against the corresponding 3D-sSAXS inclinations for all evaluated image pixels (see scatter plots in Figure 6G; data points are shown in similar colors as the corresponding outlines in 6D-E; the insets show the representative SLI azimuthal profiles and corresponding peak distances alongside the dashed-line theoretical prediction).
The scatter plots confirm a decreasing peak distance with increasing fiber inclination for most regions, matching the prediction by simulations. The broadly distributed points from the cingulum might be due to the fact that the peak distance in regions with highly inclined fibers is harder to determine due to less pronounced peaks (cf. Figure 2C(iv)). The data points in the white matter of the human cingulate gyrus (CiG) differ the most from the theoretically predicted curve (brown data points in Figure 6G): While SAXS yields similarly high fiber inclinations as in the cingulum (magenta data points), the SLI peak distances are much larger (mostly between 160-180°). The large number of gray pixels (surrounded by brown outline in Figure   6E) indicates the existence of crossing fibers. The dMRI orientation distribution functions ( Figure 6F) reveal indeed that -in addition to the cingulum bundle with highly inclined fibers (in blue) -the cingulate gyrus is interspersed with a transverse rather in-plane fiber bundle (in red), which explains the large SLI peak distances in some regions of the white matter cingulate gyrus.

Discussion
We performed Scattered Light Imaging (SLI) and small-angle X-ray scattering (SAXS) measurements on the same vervet monkey and human brain sections and compared our human section results to high-resolution ex vivo dMRI measurements of the same sample. This allowed us to cross-validate the techniques across different scales and to identify possible limitations -both on the macroscopic scale (dMRI) and the microscopic scale (SLI): Using the 2D-fiber orientations from SLI as high-resolution reference, we found that SAXS yields reliable nerve fiber crossings, while dMRI tends to overestimate the amount of crossing fibers.
Taking the main out-of-plane fiber orientations from dMRI and SAXS into account, we could show that SLI provides information about 3D-fiber orientations, but is still limited in the quantification of the out-of-plane angles, especially in regions with crossing fibers. Thus, the combination of the unbiased resolving power of SAXS with the high-resolution power of SLI may best provide a reliable reference for neuronal connectivity maps, and a gold standard to which techniques such as dMRI can be compared.

Existing methods to identify fiber orientations and tracts
A large variety of neuroimaging techniques exists to study nerve fiber architectures in the post-mortem brain. Some techniques (just as SLI and 2D-SAXS) analyze thin tissue sections to assess brain tissue structures. Histological staining allows to study nerve fiber organizations with fine structural detail (Amunts show the analysis of one vervet brain section (no. 511, cf. Figure 2B); the images on the right show the analysis for one human brain section (posterior section, cf. blue rectangle in Figure 5B). 3D-sSAXS and dMRI images were registered onto the corresponding SLI images (the fornix in the vervet brain section was additionally shifted between the SLI and  colored asterisks in D and G). The SLI profiles were centered for better comparison; the ticks on the inset x-axis denote azimuth steps of 15°. The dashed curves indicate the predicted SLI peak distance obtained from simulated scattering patterns of fiber bundles with different inclinations (Menzel et al., 2021a, Figure 7d).
To assess microscopic fiber structures in 3D volumes (without sectioning), tissue clearing followed by labeling and fluorescence microscopy imaging is commonly used. In recent years, it has served as validation for dMRI data (Marowski et al., 2018; Stolp et al., 2018; Goubran et al., 2019; Leuze et al., 2021). However, the clearing process causes tissue deformation (Leuze et al., 2017). Moreover, it is only feasible for smaller sample sizes (clearing solution and many antibodies cannot fully penetrate large brain samples), and it fails to disentangle densely packed nerve fibers. Other methods to study nerve fiber structures in 3D and microscopic detail (without clearing) are two-photon fluorescence microscopy (Zong et  All described techniques require subsequent tractography to follow the course of fiber tracts. Tracer studies allow visualization of fiber tracts from their beginning to the end (Lanciego et al., 2000), but can only identify specific fiber pathways per experiment and are limited to animal brains. The only ways to follow fiber bundles in ex vivo human brains are Klinger's dissection (Wysiadecki et al., 2019;Dziedzic et al, 2021), where accuracy is limited to the macroscopic scale, or tracer injection, which is slow and impractical (Hevner & Kinney, 1996; Lim et al., 1997a&b).

Validation studies of dMRI fiber orientations
To obtain reliable connectivity maps from dMRI, a correct interpretation of the measured diffusion parameters is needed. In recent years, multiple efforts have been undertaken to enhance the interpretation of in vivo dMRI data by using post-mortem techniques as validation that provide connectional anatomy maps (Yendiki et  SAXS and SLI have both shown the potential to determine secondary (crossing) fiber orientations with a higher precision and smaller crossing angles. As they provide directly structural information across extended fields of view on the same tissue sample, they can serve as a standard validation tool for dMRIderived fiber orientations, enabling comparisons in different anatomical regions.
While SAXS uses X-rays with ~0.1nm wavelength interacting with the layered structure of the nervesurrounding myelin sheath, SLI uses visible light with ~0.5µm wavelength interacting with the directional arrangement of nerve fibers. SLI requires several fibers on top of each other to achieve sufficient signal, whereas SAXS works already on individual (myelinated) fibers (Inouye et al, 2014). Also, X-ray scattering always occurs perpendicular to the nerve fibers and the pattern is center-symmetric (cf. Figure 2), while SLI azimuthal profiles with an odd number of peaks cannot be interpreted without taking information from neighboring pixels into account. SAXS allows measurements of samples irrespective of sample thickness, can yield accurate fiber orientations in 3D, and can also be applied tomographically in bulk samples (Georgiadis et al., 2021). SLI on the other hand yields much higher in-plane resolutions (here: 33x) without the time-consuming raster-scanning and can be performed with relatively inexpensive equipment in a standard laboratory.
Despite these differences, SAXS and SLI also have much in common. They are both orientation-specific methods: they directly probe the fiber orientation, without an intermediate step of imaging the tissue structures as in optical or electron microscopy, or using a proxy such as anisotropic water diffusivity in dMRI. This enables to reliably determine the nerve fiber orientations also in regions with densely packed, multi-directional fibers. They also result in similar azimuthal profiles for in-plane fibers, and, as here, the same software can be used to determine peak positions for both techniques. At the same time, both techniques can image similarly-prepared tissue sections, without any staining or labeling, and they are nondestructive, enabling sample reuse.

Identification of false-positive fiber tracts in dMRI
The 2D fiber orientations from the highly-specific SAXS measurement corresponded very well to those from the high-resolution SLI measurement (Figure 3-4), demonstrating the ability of both techniques to serve as ground truth for in-plane fiber orientations in complex brain tissue structures. Registering dMRI, 3D-sSAXS, and SLI data sets of a human brain sample enabled comparisons of fiber orientations from all three methods (Figure 5 and Figure 5-figure supplements 1-3). When comparing the 3D-sSAXS fiber orientations of two brain sections with the corresponding dMRI fiber orientation distributions of the entire tissue sample, we observed a very high correspondence between the primary fiber orientations for each voxel: the dot product is highly skewed towards one, denoting almost perfect co-alignment (Figure 5D,E and Figure 5figure supplement 2), similar to what had been shown previously in mouse brain (Georgiadis et al., 2020). Figure 5E and Figure 5-figure supplement 2) are regions with two strong crossing fiber populations (cf. Figure 5G) corona radiata, the fiber orientations from dMRI and SAXS also seemed to be in high agreement ( Figure 5figure supplement 3B).

The regions with low dot product (colored in blue in
However, we observed a discrepancy in regions with more homogeneously distributed fibers, such as in the corpus callosum (arrows in Figure 5G): Diffusion MRI seemed to consistently yield a secondary fiber population perpendicular to the main one, albeit with much smaller magnitude (Figure 5F (ii) and (iii)). Xray scattering did not show such a crossing (Figure 5G right), which was also missing in the micronresolution scattered light imaging (Figure 5H) Such phenomena stress the need for approaches that use micro-structural models to decouple the contributions from intra-and extra-cellular water (Jelescu and Budde, 2017). Using such models could help to separate the hindered diffusion close to these vessel walls and the restricted diffusion within the axons, making the dMRI-derived fiber orientations insensitive to such signals and thus more axon-specific.
Selection of the optimum model that best eliminates these contributions is not within the scope of the current manuscript, but our results show that research in this direction should be pursued in the future, using the directly structural, fiber-specific and/or micrometer-resolution methods presented here as ground-truth data to refine the models.

Experimental validation of out-of-plane fibers in SLI
With the combined measurement of SLI and 3D-sSAXS (and dMRI for the human sample), we were able to provide experimental validation of the predicted decrease in SLI peak distance with increasing fiber inclination. However, it also became apparent that the quantification of fiber inclination based on SLI peak distance alone is challenging: while regions with steep fibers (inclinations > 70°) can be clearly identified by 398 a high degree of scattering and small peak distances (< 90°), the moderate decrease in peak distance for fibers with up to 60° inclination together with the large distribution of measured values (cf. Figure 6G) makes a clear assignment between peak distance and inclination practically impossible. Our study suggests that SLI also has limitations when it comes to regions with inclined crossing fibers (cf. Figure 6E-F, and G on the right). To improve the interpretation, more advanced algorithms are needed. Machine learning models, trained on simulated data sets, could help to improve the interpretation of measured scattering patterns from SLI and yield more reliable estimates (suggested by Vaca et al., 2022).

Conclusion
Disentangling the highly complex nerve fiber architecture of the brain requires a combination of dedicated, multi-scale imaging techniques. We here provide a framework that enables combined measurements of scattered light and X-ray scattering (SLI and SAXS) on the same brain tissue sample, with high agreement between the two methods. The high-resolution properties of the former combined with the high-specificity of the latter enables the detailed reconstruction of multiple nerve fiber orientations for each image pixel, which can provide providing unprecedented insights into brain circuitry. The unique cross-validation of SLI, SAXS, and diffusion MRI on the same tissue sample revealed high agreement between the methods, but also false-positive crossings in MRI. Furthermore, it allowed the experimental validation of out-of-plane fiber orientations in SLI, paving the way for a more detailed reconstruction of 3D nerve fiber pathways in the brain. Due to the simple setup of SLI, any SAXS measurement of a tissue section can easily be combined with a corresponding SLI measurement, significantly enhancing the reconstruction of nerve fiber pathways in the brain, especially in regions with complex fiber crossings.

Materials and methods
Vervet brain sample preparation selected for further evaluation (see Figure 2A and Figure 2-supplement figure 1A). A region from the right hemisphere (16.4×10.9mm²) -containing part of the corona radiata, corpus callosum, cingulum and fornixwas measured with SLI several months afterwards (cf. Figure 2B and Figure 2-supplement figure 1B). For 3D-sSAXS, the brain sections were removed from the glass slides, re-immersed in phosphate-buffered solution (PBS) for two weeks, placed in-between two 170μm-thick (#1.5) cover slips, sealed, and measured in a comparable region (19.0×10.9mm², cf. Figure 2C and Figure 2-supplement figure 1C).

Human brain sample preparation
The human brain (66 year-old female with no known neurological disorders) was obtained from the Stanford ADRC Biobank, which follows procedures of the Stanford Medicine IRB-approved protocol #33727, including a written informed brain donation consent of the subject or their next of kin or legal representative. The brain was removed from the skull within 24 hours, fixed for 19 days in 4% formaledhyde (10% neutral buffered formalin), coronally cut into 1 cm-thick slabs, and stored in PBS for five years. From the left hemisphere, a 3.5×3.5×1cm 3 specimen -containing part of the corona radiata, corpus callosum, and cingulum -was excised (cf. Figure 5A). For dMRI, the specimen was degassed and scanned in fomblin. Five weeks later, the anterior and posterior part of the tissue was cut with a vibratome (VT1000S, Leica Microsystems, Germany) into 80μm-thick sections. Two sections (no. 18 from the posterior side and no. 20 from the anterior side) were selected for further evaluation. For 3D-sSAXS, the brain sections were placed in-between two 150μm-thick (#1) cover slips and measured in a center region of 28.0×18.9mm² for no. 18 (red rectangle in Figure 5B) and 28.0×20.1mm² for no. 20. For SLI, the brain sections were removed from inbetween the cover slips, mounted on glass slides with 20% glycerin, cover-slipped, and measured ten weeks afterwards in a region of 16.4×10.9 mm² containing corpus callosum and cingulum (cf. blue rectangle in Figure 5B).

Scattered Light Imaging
The SLI measurements (cf. Figure 1D) were performed using an LED display (Absen Polaris 3.9pro The SLI scatterometry measurement (used to generate the scattering patterns in upper Figure 2C) was performed as described in Menzel et al. (2021b): A square of 2×2 illuminated RGB-LEDs (white light) was moved over the LED display in 1-LED steps for a square grid of 80×80 different positions, and an image was taken for every position of the square with an exposure time of 1sec. For each position of an illuminating square of LEDs, four shots were recorded and averaged to reduce noise. In the end, for each point of the sample a scattering pattern with 80×80 pixels was assembled (cf. Figure 1D  The angular SLI measurements (used to generate the SLI parameter maps in Figures 3-6, Figure 2 3D-scanning small-angle X-ray scattering 3D-sSAXS (Georgiadis et al., 2015;Georgiadis et al., 2020) was performed at beamline 4-2 of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, with a beam of photon energy E photon =15keV. The vervet brain sections were measured (cf. Figure 1C)  To compute the in-plane fiber orientations (shown in Figures 3-5, Figure 3-figure supplement 1 and   Figure5-figure supplement 3), azimuthal profiles were generated for each scattering pattern of the θ=0°measurement (cf. lower Figure 2C) and analyzed by the same SLIX software, as described below. To generate the azimuthal profiles, the scattering patterns were divided into Δφ=5°-segments, the intensity values were summed for each segment, and the resulting values were plotted against the corresponding 20 of 35 average φ-value. The known center-symmetry of the SAXS scattering patterns was exploited to account for missing parts due to detector electronics.
The out-of-plane fiber inclination angles (Figures 5C and 6A-B) were computed by analyzing the scattering patterns obtained from 3D-sSAXS measurements at different sample rotation angles, as described in Georgiadis et al. (2020).

Diffusion magnetic resonance imaging
The dMRI measurement was performed on a Bruker 11.7 T scanner, using a 12-segment spin-echo echo planar imaging (SE-EPI) sequence at 200μm isotropic voxels, repetition time TR=400ms, echo time TE=40ms, diffusion separation time δ=7ms, diffusion time Δ=40ms, field of view FOV=40×36×21 mm 3 , at 200 diffusionweighted q-space points (20@b=1ms/μm 2 , 40@b=2ms/μm 2 , 60@b=5ms/μm 2 , 80@b=10ms/μm 2 ) and The peak width (Figure 2-figure supplement 1, last row) was computed as the full width of the peak at a height corresponding to the peak height minus half of the peak prominence. The in-plane fiber orientation φ (Figures 3-5, Figure 3-figure supplement 1 and Figure5-figure supplement 3) was computed as the midposition between peaks that lie 180° +/-35° apart. To better analyze multiple crossing fiber orientations, the in-plane fiber orientations were visualized as colored lines and displayed on top of each other (cf. Figure 3 and Figure 3-figure supplement 1). The peak distance (Figure 6D-E) was computed as the distance between two peaks, for profiles with no more than two peaks (profiles with one peak yield zero peak distance).

Image registration
To register 3D-sSAXS onto SLI (Figures 4,6), the 3D-sSAXS parameter maps were upscaled to the SLI pixel size. Linear registration of 3D-sSAXS to SLI sections was performed using FSL FLIRT (https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FLIRT), while angular information and 3D vectors were rotated accordingly. For registering dMRI onto SAXS (Figure 5 and Figure 5-figure supplement 2-3), first the matching plane for each human brain section was identified manually in the scanned MRI volume (different plane for each human brain section), and FSL FLIRT linear registration with 12 degrees of freedom was used for precise alignment of the 2D images. Then, the entire dMRI data set was transformed using the identified rotation and translation parameters (twice, once for each section), and the b-vectors were rotated correspondingly. The MRI sections corresponding to the vibratome section plane were isolated and further analyzed as explained in the 'Diffusion magnetic resonance imaging' Methods section.  Figure 2C: Out-of-plane nerve fibers in the cingulum yield high average scattered light intensities with small signal amplitude (max-min), small peak prominence, and large peak width. In-plane nerve fibers in the corpus callosum yield a large signal amplitude, high peak prominence, and small peak width. In-plane crossing nerve fibers in the corona radiata yield a smaller signal amplitude and less prominent peaks.