Editor's evaluation: Using light and X-ray scattering to untangle complex neuronal orientations and validate diffusion MRI

Abstract

Full text Figures and data Side by side Abstract Editor's evaluation Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract 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. Editor's evaluation This paper presents a valuable cross-validation study of mesoscopic measurements of axonal orientations from three different modalities – small-angle X-ray scattering, scattered light imaging, and diffusion MRI – and is of interest to researchers who want to apply these methods to white matter imaging. The authors show convincing similarities and differences in fiber orientations from all three methods over partial ex vivo brain samples, though the validation of diffusion MRI could be strengthened by considering other fiber reconstruction methods, as only a single diffusion method is investigated. https://doi.org/10.7554/eLife.84024.sa0 Decision letter Reviews on Sciety eLife's review process 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 axonal 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., 2019), the resolution is insufficient to resolve individual nerve fibers, and isolating the anisotropic signal coming from myelinated axons alone is challenging. Moreover, up to hundreds of fibers within a voxel might have complicated geometries, e.g., crossing or kissing fibers, which poses a further challenge. Small-angle X-ray scattering (SAXS) provides myelinated nerve fiber orientations by studying the anisotropy of myelin diffraction (Bragg) peaks in X-ray scattering patterns (Figure 1A and C – Georgiadis et al., 2020; Georgiadis et al., 2021). These are generated by the interaction of the incoming X-ray photons with the layered structure of the myelin sheath, which surrounds nerve fibers in the white matter. The method can be tomographic (SAXS tensor tomography – Liebi et al., 2015; Schilling et al., 2019a; Georgiadis et al., 2021), and 3D-scanning SAXS (3D-sSAXS) can provide 3D distributions of axon orientations in tissue sections (Georgiadis et al., 2020). Recent studies further revealed that SAXS can exploit the modulations in the azimuthal position of the myelin-specific Bragg peaks to resolve crossing nerve fiber populations across species with resolutions of tens of micrometers (Georgiadis et al., 2023). Figure 1 Download asset Open asset Comparison of X-ray scattering (top) and light scattering (bottom) for analyzing nerve fiber structures. (A) Principle of X-ray scattering on a nerve fiber bundle, resulting in a ring at a radial position corresponding to myelin’s periodicity, strongest perpendicular to the in-plane fiber orientation. (B) Principle of light scattering on a nerve fiber bundle, which similarly yields scattered photons perpendicular to the in-plane fiber orientation. (C) Schematic drawing of a 3D-scanning small-angle X-ray scattering (3D-sSAXS) measurement of a brain section, in which raster scanning at multiple angles allows reconstructing 3D fiber orientation distributions for each point of illumination. (D) Schematic drawing of a scattered light imaging (SLI) scatterometry measurement of a whole brain section (left) and reconstruction of a scattering pattern for one selected image pixel (right), which can be performed over the entire image simultaneously. The scattering of visible light can also be used to reveal crossing nerve fiber orientations (Figure 1B – Menzel et al., 2020a; Menzel and Pereira, 2020b) as it is sensitive to directional arrangements of myelinated axons (~μm diameter). In scattered light imaging (SLI) (Menzel et al., 2020a; Menzel et al., 2021b; Reuter and Menzel, 2020) the sample (brain section) is illuminated from many different angles and a camera captures an image of the brain section (Figure 1D, left), in which the intensities of each image pixel vary with the angle of illumination. In this way, a scattering pattern is generated for each micron-sized image pixel (Figure 1D, right). SLI has been shown to reliably reconstruct up to three in-plane fiber orientations for each image pixel (with an accuracy of +/−2.4°; Menzel et al., 2021a) and an in-plane resolution at the micrometer scale (Menzel et al., 2021b). Hence, a combined measurement of 3D-sSAXS and SLI, with the high specificity to myelinated fibers of the former and the high-resolution capabilities of the latter, can potentially provide a gold standard for imaging complex nerve fiber orientations in thin brain sections with micrometer resolution. Here, we present 3D-sSAXS and SLI measurements on the same tissue samples (coronal sections from vervet monkey and human brains) and compare them to dMRI outcomes. To capture multiple possible fiber scenarios, we examine brain regions with both unidirectional and crossing fibers – the corpus callosum and corona radiata, respectively. Evaluation of 3D-sSAXS and SLI in a vervet brain section provides a unique cross-validation, but also a very detailed mapping of the single and crossing fiber orientations. Comparison of the results on the human brain sample enables validation of dMRI-derived orientations. Furthermore, we enhance the interpretation of out-of-plane fibers in SLI, using the 3D-fiber orientations from SAXS and dMRI as references. The presented SAXS and SLI results on the same specimens and their cross-validation provide the groundwork for an eventual combined analysis of the two techniques, exploiting the specificity of the former and the resolution of the latter. This combined information could be used to provide reliable nerve fiber orientations and validate dMRI results, towards more accurate brain connectivity maps of the animal and human brain. Results Light and X-ray scattering patterns reflect various nerve 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) a unidirectional in-plane fiber bundle in the corpus callosum, (ii) two crossing fiber bundles in the corona radiata, (iii) a slightly 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, Figure 2C (i)), plotted as azimuthal profile under each scattering pattern in Figure 2C. Figure 2—figure supplement 1 shows the average, maximum, minimum, mean peak prominence, and mean peak width of the azimuthal profiles for each pixel measured with SAXS and SLI. Figure 2 with 1 supplement see all Download asset Open asset Scattering patterns obtained from scattered light imaging (SLI) scatterometry (px = 3 μm) and small-angle X-ray scattering (SAXS) (px = 100 μm) on a 60 μm-thick vervet monkey brain section at a coronal plane between the amygdala and hippocampus (section no. 511). (A) Transmittance image of the whole brain section. (B) Average scattered light intensity of the investigated region (cc: corpus callosum, cr: corona radiata, cg: cingulum, Cd: caudate nucleus, f: fornix, ic: internal capsule). Yellow asterisks indicate the points corresponding to the scattering patterns in C. (C) Scattering patterns from SLI (top) and SAXS (bottom) with azimuthal profiles plotted beneath each pattern, obtained from the pixels indicated in B. (i) unidirectional in-plane fiber bundle in the corpus callosum, with peaks perpendicular to the fiber orientation (red dotted line), lying 180° apart, (ii) two in-plane crossing fiber bundles in the corona radiata, (iii) slightly inclined fiber bundle in the fornix, with SLI peaks <180° apart, and SAXS peaks 180° apart but with lower Bragg peak intensity, (iv) highly inclined fiber bundle in the cingulum, with no SLI azimuthal peak pair and almost isotropic SAXS myelin ring. 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 (q-value) from the center of the pattern that corresponds to the myelin layer periodicity (here 17.5 nm) (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 and SAXS is perpendicular to the fiber orientation (red dashed lines in Figure 2B and C (i)), shown in the azimuthal profile as peaks lying 180° apart. 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 lying 180° apart (white/yellow arrows). In the following, the term ‘peak’ will be used to refer to peaks in azimuthal profiles, so that a pair of azimuthal ‘peaks’ always corresponds to a single fiber orientation. 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 center-symmetry of the pattern -, but become less pronounced with increasing out-of-plane fiber angle (compare peak height of SAXS, Figure 2C (i) vs. (iii)). In contrast, the between-peak distance in the SLI azimuthal profiles decreases with increasing fiber inclination (SLI, Figure 2C (iii)), as also predicted by simulation studies (Menzel et al., 2020a). For out-of-plane fibers that run almost perpendicular to the section plane (Figure 2 point (iv), cingulum), both the SLI scattering pattern and the SAXS myelin ring become almost radially symmetric without significant peaks in the azimuthal profile. In such cases, the information about the in-plane fiber orientations is limited, whereas the out-of-plane angle can be retrieved with scans at different rotation angles using 3D-sSAXS (Georgiadis et al., 2020), and approximated in SLI (Menzel et al., 2021b). 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 ~1 × 2 cm² region of the vervet brain (Figure 3 and Figure 3—figure supplement 1). Given the ~33 x higher resolution of SLI versus SAXS in the presented measurements (3 μm vs. 100 μm pixels), smaller nerve fiber bundles e.g., in the head of the caudate nucleus (yellow arrow) can be traced in detail by SLI. Conversely, out-of-plane nerve fibers in the cingulum (cg), are more sensitively depicted by SAXS. Figure 3 with 1 supplement see all Download asset Open asset In-plane nerve fiber orientations from small-angle X-ray scattering (SAXS) and scattered light imaging (SLI) measurements of vervet monkey brain section no. 511. (A) Fiber orientation maps showing the predominant fiber orientation for each image pixel in different colors (see the color wheel in the upper right corner): px = 100 μm (SAXS), px = 3 μm (SLI). (cc: corpus callosum, cr: corona radiata, cg: cingulum, Cd: caudate nucleus, f: fornix, ic: internal capsule). (B) Fiber orientations are displayed as colored lines for 5 × 5 px (SAXS) and 165 × 165 px (SLI) superimposed. The length of the lines is weighted by the averaged scattered light intensity in SAXS and SLI, respectively. (C) Enlarged region of the corona radiata, showing fiber orientations as colored lines for 1 × 1 px (SAXS) and 33 × 33 px (SLI) superimposed. The white arrows indicate the main stream of the computed fiber orientations. The in-plane nerve fiber orientations are highly coincident, not only for unidirectional fibers, but also for fiber crossings, depicted as colored lines in Figure 3B, Figure 3—figure supplement 1D, where each vector glyph covers orientations from a grid of 165 × 165 measured pixels that are visually overlaid in SLI, vs. a 5 × 5 pixel grid in SAXS. Further zooming in shows a concordant fiber course in the highly complex corona radiata architecture (Figure 3C, Figure 3—figure supplement 1E): the fibers of the corpus callosum fan out (blue/magenta) while crossing the ascending internal/external capsule (green). To quantitatively compare the in-plane fiber orientations, SAXS images were linearly registered onto SLI images (scaled, rotated, and translated), and pixels in which both techniques yield the same number of fiber orientations (one or two) were compared to each other: For each image pixel, the corresponding 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). The quality of registration is shown in Figure 4—figure supplement 1A: The boundaries of white and gray matter are overall well aligned, only the fornix is slightly shifted (see arrows) and was, therefore, evaluated separately. Figure 4 with 1 supplement see all Download asset Open asset Angular difference between scattered light imaging (SLI) and small-angle X-ray scattering (SAXS) nerve fiber orientations (SLI – SAXS) for vervet monkey brain section no. 511. For evaluation, the SAXS image was registered onto the SLI image (with 3 µm pixel size) and only regions where both techniques yield the same number of fiber orientations were considered. (A) Angular difference displayed for one of the maximum two predominating fiber orientations in each pixel. (B) Absolute angular difference displayed for each image pixel. (C) Regions with one or two fiber orientations for both methods (magenta = 1, green = 2 orientations). (D) Histograms showing the angular difference for pixels with one and two fiber orientations, evaluated in white matter regions excluding the fornix (see regions delineated by white lines in A-C). Figure 4A shows that the small positive and negative angular differences (displayed in shades of red and blue, respectively) appear to be randomly distributed across the tissue. The absolute angular differences are displayed 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 in white matter pixels 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: mean ~0.316°, median absolute ~5.6°). While regions with one fiber orientation yield differences between +/−30° maximum, 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. Comparison to diffusion MRI shows high agreement and small discrepancies Next, we aimed to extend our findings to the human brain and compare our results to diffusion MRI (dMRI) fiber orientations. To enable the analysis of regions with both unidirectional and crossing fibers, we selected a ca. 1 cm thick human brain sample that contains parts of the corpus callosum (cc), the cingulum (cg), the internal capsule (ic), and the corona radiata (cr) (Figure 5A). After high-resolution multi-shell dMRI scanning, we computed traditional diffusion tensors to yield the main fiber orientations (Figure 5C, left), and used multi-shell multi-tissue constrained spherical deconvolution (Jeurissen et al., 2014) to map fiber orientation distribution (Figure 5D, Figure 5—figure supplement 1), including regions with highly aligned fibers as well as distinct fiber crossings. Figure 5 with 5 supplements see all Download asset Open asset Diffusion magnetic resonance imaging (dMRI) measurement of a 3.5 × 3.5 × 1 cm³ human brain specimen (200 μm voxel size) in comparison to measurements with 3D-scanning SAXS (3D-sSAXS) (150 μm pixel size) and scattered light imaging (SLI) (3 μm pixel size) of a 80 μm-thick brain section. (A) Human brain specimen; the bottom image shows the sample measured with dMRI (cc: corpus callosum, cg: cingulum, cr: corona radiata, ic: internal capsule). (B) Posterior brain section with regions measured by 3D-sSAXS (red rectangle) and SLI (blue rectangle). (C) Main 3D fiber orientations from dMRI (left) and 3D-sSAXS (right) for the brain section; dMRI was registered onto 3D-sSAXS (with 150 μm pixel size), see Figure 4—figure supplement 1B. (D) Orientation distribution functions from dMRI, with zoomed-in regions surrounded by rectangles shown in subfigure F. (E) Vector dot product of the dMRI and 3D-sSAXS main fiber orientations, as histogram and map of the studied area. (F) The enlarged regions from subfigure D show the fiber orientation distributions in the corona radiata (rectangle i, orange), a subcortical fiber bundle (rectangle ii, red), and the corpus callosum (rectangle iii, cyan). The fiber orientation distributions are almost identical to the ones shown here also when only high b-values are taken into account, Figure 5—figure supplement 4. (G) In-plane fiber orientation vectors for dMRI (left) and SAXS (right) superimposed on mean SAXS intensity. Vectors of 5 × 5 pixels are overlaid to enhance visibility. Zoomed-in images of the corona radiata region from both methods are shown in Figure 5—figure supplement 3C. (H) In-plane fiber orientations from SLI (multiple fiber orientations are displayed as multi-colored pixels), with zoomed-in areas in boxes (1) and (2). For better readability, fiber orientations in the gray matter are not shown in subfigures C-G. To compare dMRI- with SAXS-derived fiber orientations, we measured two 80 μm-thick vibratome sections (one from the posterior side, Figure 5, and one from the anterior side, Figure 5—figure supplement 2) with 3D-scanning 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 (Figure 5B, red rectangle) were identified, and linearly registered to the SAXS data sets. Figure 4—figure supplement 1B shows the quality of registration: The main features, including the tissue and white/gray-matter boundaries, appear to be overall well aligned. The main fiber orientations per pixel for dMRI and 3D-sSAXS (Figure 5C) show a high correlation, similar to what has been shown in Georgiadis et al., 2020, with a dot product approximating unity (Figure 5E), and a median angular difference of 14.4o over all voxels (9.1o over voxels with fractional anisotropy (FA) >0.2, computed from the eigenvalues of the rank-2 tensor for both methods). 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 fiber orientations seem to be in high agreement with the direct structural X-ray scattering (Figure 5G and Figure 5—figure supplement 3B left): the two methods have a median angular difference of 5.6o in the first orientation, and 6.0o in the second orientation (overall median angular difference 5.8o). This shows that diffusion MRI has the sensitivity to accurately resolve multiple fiber orientations per voxel in the white matter, see also Figure 5D and F (rectangle i, orange in the corona radiata). Next, we turned our focus to areas that appear to have relatively homogeneous fiber populations in SAXS, such as the corpus callosum. The main fiber orientations in these regions were again in high agreement between the two methods, with a median angular difference of 5.7o (Figure 5—figure supplement 3B, right). There was an observed difference in detecting secondary orientations in areas such as the corpus callosum. Unlike X-ray scattering, which shows homogeneous fiber orientations, dMRI seems to show multiple fiber orientations per voxel, with a secondary fiber population perpendicular to the main one (albeit with a much smaller magnitude). This is exemplified in the corpus callosum and in the subcortical white matter nearby the cingulate and the callosal sulci (white arrows in Figure 5G and F). The effect is also visible when calculating fiber orientations using the high b-values only (see Figure 5—figure supplement 4). Referencing these regions in the micrometer-resolution SLI (px = 3 μm, Figure 5H), we confirm the X-ray scattering results and do not observe a second fiber population perpendicular to the main one. We then proceeded to quantify this effect over the entire white matter of the posterior brain section. Comparing the SAXS and dMRI secondary orientations, we observed a 104% (more than double) increase in the voxels with multiple orientations in dMRI. More specifically, secondary fiber orientations within a single voxel were detected in 31% of the total number of voxels by SAXS vs. 64% of the total number of voxels by dMRI (also see Figure 5—figure supplement 5 for a map of the number of orientations per voxel). The anterior brain section similarly showed a 40% increase, while primary orientations were in high agreement as well (Figure 5—figure supplement 2). 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 (upper Figure 2C). The peak distance should decrease with increasing inclination, as indicated by the black 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). Measurements of SLI and 3D-sSAXS on the same tissue sample enable 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). Figure 6 Download asset Open asset Pixel-wise comparison of 3D-scanning SAXS (3D-sSAXS)/diffusion magnetic resonance imaging (dMRI) fiber inclinations and scattered light imaging (SLI) peak distances. The images on the left show the analysis of one vervet brain section (no. 511, 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 with 3 µm resolution (Figure 4—figure supplement 1); the fornix in the vervet brain section was additionally shifted between the SLI and 3D-sSAXS images to account for the slight misalignment between the registered images in this region; only regions with unidirectional fibers were evaluated. (A,B) 3D-sSAXS fiber inclination angles of the vervet and human brain section are shown in different colors for the white matter (blue: in-plane, yellow: out-of-plane, dark gray: gray matter). The 3D-arrows indicate in four selected regions of the vervet brain section the orientation in which the fibers of these regions point out of the section plane. (C) Corresponding dMRI fiber inclination angles of the human brain sample. (D,E) Distance between two peaks in the corresponding SLI azimuthal profiles (cf. inset in G). Only profiles with one or two azimuthal peaks were evaluated (other pixels are shown in light gray). Regions used for the pixel-wise comparison with 3D-sSAXS are surrounded by colored outlines; asterisks mark three representative pixels. (F) dMRI orientation distribution functions of the region marked in C. The dashed lines indicate separation into the three regions in E (cg – cingulum, CiG – cingulate gyrus, cc - callosum). (G) SLI peak distance plotted against the 3D-sSAXS inclination for the corresponding regions marked in D and E for vervet and human brain samples, respectively (data points are displayed in similar colors as the corresponding outlines in D and E). The inset in the left panel shows the SLI azimuthal profiles for the three representative pixels in the vervet brain section (marked by similarly 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). We performed a pixel-wise comparison of the out-of-plane fiber orientation angles α from 3D-sSAXS (Figure 6A and B) and the peak distances Δ from SLI (Figure 6D and E), for one vervet brain section (A, D) and one human brain section (B, E). The quality of co-registration is shown in Figure 4—figure supplement 1. The 3D-arrows in Figure 6A indicate the orientation in which the nerve fibers point out of the section plane, computed by 3D-sSAXS for four selected regions. The images in Figure 6C and F show the corresponding 3D fiber orientations from the dMRI measurement of the human brain sample for reference. The out-of-plane inclination angles from dMRI (Figure 6C) highly agree with those obtained from 3D-sSAXS (Figure 6B). In both coronal brain sections (vervet and human), the fibers in the corpus callosum (cc) are mostly oriented in-plane (dark blue: α<20°), while fibers in the cingulum (cg) are mostly oriented out-of-plane (light green/yellow: α>40°). Fibers in the vervet fornix (Figure 6A) show mostly intermediate inclination angles (light blue: 20°<α<40°). 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 in-plane 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 Figure 6D-E; the insets show the representative SLI azimuthal profiles and corresponding peak distances alongside the black 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 (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) implying a stronger heterogeneity of the fiber architecture: 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 a brown outline in Figure 6E) indicates the existence of crossing fibers. The dMRI orienta