Imaging crossing fibers 1 in mouse, pig, monkey, and human brain 2 using small-angle X-ray scattering 3

14 Myelinated axons (nerve fibers) efficiently transmit signals throughout the brain via action 15 potentials. Multiple methods that are sensitive to axon orientations, from microscopy to 16 magnetic resonance imaging, aim to reconstruct the brain’s structural connectome. As billions 17 of nerve fibers traverse the brain with various possible geometries at each point, resolving fiber 18 crossings is necessary to generate accurate structural connectivity maps. However, doing so 19 with specificity is a challenging task because signals originating from oriented fibers can be 20 influenced by brain (micro)structures unrelated to myelinated axons. 21 X-ray scattering can specifically probe myelinated axons due to the periodicity of the myelin 22 sheath, which yields distinct peaks in the scattering pattern. Here, we show that small-angle X- 23 ray scattering (SAXS) can be used to detect myelinated, axon-specific fiber crossings. We first 24 demonstrate the capability using strips of human corpus callosum to create artificial double- 25 and triple-crossing fiber geometries, and we then apply the method in mouse, pig, vervet 26 monkey, and human brains. Given its specificity, capability of 3-dimensional sampling and high 27 resolution, SAXS can serve as a ground truth for validating MRI as well as microscopy-based 28 methods.


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Signals in the brain are transmitted within neurons via action potentials. These are typically 45 initiated in the soma of neurons, and travel through neuronal axons (nerve fibers) until they 46 reach the synaptic clefts where biochemical mechanisms further transmit the signals to the 47 next cell. A major evolutionary step in the signal transmission in the brain came with 48 myelination: oligodendrocytes, an abundant type of central nervous system glial cells found in 49 vertebrates, form processes that "wrap around" neuronal axons (Schwann cells do the same in 50 the peripheral nervous system). The resulting layered structure around axons is called myelin 51 (with a layer periodicity of ~15-20nm) and is an essential component of our brain, constituting 52 ~35% of its dry weight [1]. 53 In the beginning of the 21 st century, the "brain connectome" was conceived [2], [3], with 54 the goal of mapping neuronal connections across the animal and human brain. Given that there 55 are >50 billion neurons in a human brain [4], with more than 100,000 km total length of 56 myelinated fibers [5], each of diameter from 0.1 to 100 micrometers [6] (with most axons being 57 around 1μm in diameter), mapping all their connections is an immensely difficult task, for which 58 we currently do not have the imaging tools. However, multiple technologies have been and are 59 being developed to tackle this problem. 60 Neuronal tracers are considered the gold standard for animal neuronal connectivity, as they 61 trace a number of neuronal paths throughout the animal brain [7], [8], with the mouse brain 62 having been studied and mapped extensively [7], [9], [10]. However, the limited ability to study 63 human brains, in addition to the experimental effort for the multiple injections (and animals) 64 and imaging sessions needed to cover a subset of the neurons of a typical animal brain makes 65 this unique method inconvenient for standard assessment of structural connectivity. 66 At the nanometer level, electron microscopy can image at very high resolutions, providing 67 us with exquisite images of human and animal brain at the sub-cellular level, where even single 68 myelin layers can be clearly distinguished [11]. However, electron microscopy typically needs 69 extended sample preparation procedures, which can alter the sample microstructure. Also, 70 even when used in 3D, electron microcopy typically images a small part of the brain at these 71 very high resolutions, usually extending to much less than 1mm 3 . 72 Alternatively, fluorescence microscopy methods can reach sub-micrometer resolutions, and 73 visualize fibers in extended brain regions [12], while tissue clearing can help image large 74 specimens such as whole mouse or rat brains [13]. However, tissue clearing usually involves 75 tissue distortion and is more difficult for larger and non-perfusion-fixed human tissues. 76 Furthermore, the use of structure tensor analysis, typically accompanying these direct 77 microscopy methods for deriving orientation information, is prone to artifacts due to structures 78 other than axons and can be difficult to apply in dense white matter regions where intensity 79 gradients are small. 80 Imaging methods that directly probe axon orientations overcome many of these issues. 3D 81 Polarized Light Imaging (3D-PLI) exploits the birefringence of myelin to derive fiber orientations 82 in tissue sections at micrometer resolution, with the possible field of view extending to the 83 entire human brain [14]. However, it cannot recover crossing fibers within a pixel, though in-84 plane pixels are sometimes small enough to still resolve individual bundles crossing one another 85 over several pixels (Zeineh et al. [15], Fig 4). Furthermore, the determination of the out-of-86 plane angle by 3D-PLI is challenging. Polarization-sensitive optical coherence tomography  OCT) in serial, back-scattered mode also provides high-resolution orientation information based 88 on the birefringence of myelin [16], [17] while facilitating image registration, but the method 89 has otherwise similar limitations to 3D-PLI. Scattered light imaging (SLI) [18] partly overcomes 90 those challenges, being able to resolve fiber crossings with micrometer resolution, while also 91 providing information on out-of-plane fiber angles. However, SLI is a new method that still 92 needs validation, especially regarding the quantification of the out-of-plane fiber angles. 93 Finally, the most commonly used method to provide brain-wide structural connectivity is 94 diffusion magnetic resonance imaging (dMRI) [ repetitive structure such as myelin, they constructively interfere at specific angles, forming 104 Bragg peaks (hereafter referred to as "myelin peaks"). Moreover, this constructive interference 105 happens at the plane formed between the photon beam and the direction of periodicity of the 106 repeated structure. In the case of myelin layers, this plane is perpendicular to the nerve fiber 107 orientation. This allows the use of the location of the peaks on the detector for determining the 108 orientation of the myelinated axons (cf. Fig. 1  The pig brain was extracted from a female 10-week-old micro-Yucatan minipig, following 150 institutional approval. The brain was immersion-fixed in 4% PFA for a month. A coronal slab was 151 cut out of the left hemisphere, and a vibratome (VT1000S, Leica Microsystems, Germany) was 152 used to cut 100-μm sections. The section together with a minute amount of PBS was placed 153 between #1 cover slips, which were then glued around the edges to avoid sample drying. 154 The vervet monkey brain section was obtained as described in Menzel  For scanning, similar to the mouse sections, the human brain section was immersed in PBS and 167 enclosed within two thin Kapton films, surrounded by a metal frame. 168 All animal procedures were in accordance with the National Institutes of Health guidelines 169 for the use and care of laboratory animals and in compliance with the ARRIVE guidelines. 170

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Each section was raster-scanned by the X-ray beam (details in Each scattering pattern was then segregated into 72 azimuthal segments (5 o steps). The signal 181 intensity modulation along the radial direction was obtained for each segment. Photon counts 182 from pixels in 180-degrees opposite segments were averaged due to the center-symmetry of 183 the pattern. This also allows filling in missing information from the regions that correspond to 184 detector electronics (dark bands in scattering patterns, cf. Fig. 1). 185 The myelin-specific signal for each segment was isolated using procedures similar to those 186 described in Georgiadis et al. (2021) [28], i.e. by fitting a polynomial to the radial signal intensity 187 curve, and isolating the 2 nd order myelin peak (within the red ring in Fig. 1), which is the most 188 prominent peak in myelin scattering patterns [28]. This allowed creating azimuthal profiles for 189 each point, plotted in Fig  The determination of fiber orientations using 3D-PLI was done in an unstained section of a 224 different C57BL/6 mouse brain. The mouse brain was immersion-fixed in 4% buffered PFA. After 225 cryoprotection (20% glycerol), the brain was deep frozen at −70°C. The brain was serially 226 sectioned along the coronal plane at 60 µm thickness using a cryotome (Leica Microsystems, 227 Germany). Sections were mounted on a glass slide, embedded in 20% glycerol, cover-slipped 228 and sealed with nail polish. The protocol was approved by the institutional animal welfare 229 committee at the Research Centre Jülich, in accordance with European Union (National 230 Institutes of Health) guidelines for the use and care of laboratory animals. 231 Polarimetric measurements of the section were done using the polarizing microscope LMP-232 1 (Taorad GmbH, Germany). The LMP-1 provides a field of view of 2.7 × 2.7mm 2 and a pixel size 233 of 1.3μm. Whole mouse brain section scans were carried out tile-wise using a movable 234 specimen stage and a rotating polarizing filter. For each tile, a stack of 18 images was acquired 235 at equidistant rotation angles (±10°) within the range of 0° to 170°. The measured intensity 236 profile for an individual pixel across the stack of image tiles describes a sinusoidal curve that 237 depends on the spatial orientation of fibers within this pixel. The physical description of the 238 light intensity profile was derived from the Jones calculus for linear optics and represents the 239 basis for orientation analysis, as detailed in [32]. 240 3 Results with some parts having fibers running almost horizontally (cyan). In one such region, at the 250 middle-left of the overlapping region, the fibers seem to cross at almost 90° ( Fig. 2A/B, point 251 [ii]). In the upper part of the overlap region, fibers from the two strips seems to cross at angles 252 ~50 o to 60 o (cf Fig. 2A  The mouse brain scanning SAXS data analysis using SLIX yielded a detailed fiber orientation 281 map for the 25μm-thin section (Fig. 3A,B,E, the latter shows a zoomed-in view of the region of 282 the box from B), revealing intricate crossings in myelinated brain areas. In the white matter, 283 caudoputamen (CPu) fibers merge with the corpus callosum (cc), while some (white arrows) 284 cross the lateral corpus callosum and the external capsule (ec) en route to the cortex, 285 specifically the supplemental somatosensory area (SSs) (anatomic regions delineated on 3D-PLI 286 in D). These crossings can also be inferred from the fiber tract trajectories seen using 287 micrometer-resolution imaging of a section at a ~300μm anterior plane from a different mouse 288 with 3D-PLI (Fig. 3C,D, taking into account that 3D-PLI has limited sensitivity to crossing fibers 289 within a pixel). They are more clearly visible in the axons seen by the tracer studies depicted in 290 Fig. 3F-H, from the Allen Mouse Brain Connectivity Atlas [7] (https://connectivity.brain-291 map.org/), corresponding to experiments 297945448-SSs and 520728084-SSs, which include 292 injections in the supplemental somatosensory area. These axons can be clearly seen crossing 293 primarily the lateral side of the corpus callosum and the external capsule to reach the 294 caudoputamen. 295 At the same time, crossings at the edge of the cortex, at the molecular layer, are also visible 296 with scanning SAXS, where myelinated fibers running circumferential to the brain surface to 297 connect to radial fibers from the rest of the cortex (yellow arrow in Fig. 3B), with the 298 circumferentially oriented axons also visible in 3D-PLI (yellow arrow in Fig. 3C). 299

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Contrary to the commonly studied lissencephalic rodent brain, the pig brain is 317 gyrencephalic, meaning it has a folded structure containing gyri and sulci. This together with its 318 bigger size results in a greater number of myelinated fibers with higher structural complexity of 319 fiber tracts and multiple tract crossings (Fig. 4). The main regions of crossing fibers are enclosed 320 in dotted boxes in Fig. 4B (labelled (i), (ii), and (iii)), and zoomed-in in Fig. 4C. The regions seem 321 to be rich in 2x-fiber crossings, while some triple crossings can also be observed.   The orientation analysis in the vervet brain section produced detailed maps of single and 340 crossing fiber bundles (Fig. 5). Maps of the brain are seen in Figs 5A superior-inferior direction). 348 The cortex is known to contain myelinated axons, with complex fiber architecture that can 356 include crossings. Along these lines, apart from the crossings in primarily white matter regions 357 shown in Figure 3 and also depicted here in Fig. 6C, multiple crossings were also detected in 358 gray matter regions of the mouse brain. Figure 6D displays part of the mouse cortex, where 359 myelinated fibers radiate from the corpus callosum towards the periphery in all parts of the 360 cortex. In addition, fibers are observed running through the cortex in a direction tangential to 361 the corpus callosum (e.g. Fig. 6D, in mostly left-right direction, dashed colored arrows show the 362 radial axon orientations, depicted by color-encoded lines). 363  The human hippocampus is a gray matter structure with numerous interwoven white 374 matter pathways of immense complexity and importance to memory formation, which are 375 altered in neurodegeneration and diseases such as Alzheimer's disease and epilepsy. Analysis of 376 the human hippocampus section provided detailed maps of myelinated axon orientations 377 across hippocampal subfields and the various hippocampal fiber tracts, as demonstrated in 378 Figure 7. 379 Figure 7A shows the color-encoded main fiber orientation for each pixel (achieved by 380

by orientation-encoded colored bars for each 2x2 pixel set. C-D) Zoomed-in images of the left and right corona radiata from
adjusting SLIX parameters to only detect the main peak in the line profiles, cf. Methods), 381 revealing part of the complex anatomy of the hippocampus and the geometry of its fiber 382 bundles. Primary fiber orientations are also depicted visually in Figure 7B, in both white and 383 gray matter areas. The main white matter tracts can be seen there, including the 384 alvear/forniceal (alv), perforant (p), stratum radiatum lacunosum and moleculare (srlm), 385 endfolial (ef) and superficial entorhinal (se) pathways. Subicular fibers heading to/from the 386 alveus ( Fig. 7C) are also seen crossing the gray matter. In Figure 7D, the cyan box in (B) is shown 387 in higher resolution, demonstrating secondary and tertiary orientations of myelinated axons 388 within white matter pixels. Multiple fiber orientations can be seen in most white matter pixels, 389 meaning that in the complex hippocampal anatomy and connectivity, each pixel rarely contains 390 fibers from a single bundle. For instance, the perforant pathway (p) is seen crossing the angular 391 bundle within the parahippocampal gyrus (phg) just below the subiculum (sub), and reaching 392 the superficial entorhinal (se) pathway within the stratum radiatum lacunosum and moleculare 393 (srlm) and crossing the subicular forniceal bundle (alv) from 7C. 394  comparison to MRI, and quantification of myelin levels, orientation, and integrity in volumetric 409 specimens [28]. 410

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Given the experimental conditions and analysis tools presented in this study, the current 412 limit of detection seems to be approximately 25°-30°. This resolving power depends on a few 413 factors: first, the signal-to-noise ratio; if less photons impinge the sample, it is possible that 414 noise in the azimuthal profiles could hamper peak detection. However, the current experiments 415 with typical experimental conditions in scanning SAXS seem to yield signals with a high signal-416 to-noise ratio, which are expected to be robust to such effects. Secondly, there is an inherent 417 resolving limit to the method, which depends on the "fiber response function", i.e., the angular 418 distribution of the signal coming from a single coherent, unidirectional fiber bundle. In theory, 419 the SAXS signal from a single straight fiber would be exactly at 90 degrees to the fiber 420 orientation and have an azimuthal profile with two peaks of minimal width. However, in 421 practice myelinated axons have some curvature and undulations, and each pixel probed by the 422 beam contains multiple fibers with a certain orientation distribution. Under these 423 circumstances, the effective fiber response function has an azimuthal profile with a distribution 424 similar to the peaks in Figures 1 or 2. Taking these considerations as well as data from the 425 current experiment into account, we speculate that the crossing angle detection could be lower 426 at approximately 20 o ; possible improvements to the 25 o -30 o presented here could come from 427 higher signal-to-noise ratio experiments (i.e. using higher flux) or even more sensitive peak 428 detection algorithms, as discussed below. Finally, another case where crossing fibers can 429 remain undetected is a scenario where the secondary fiber population contains considerably 430 less myelinated axons (lower number of axons, or axons with a lower degree of myelination). In 431 that case, its scattering peak might not be able to be detected, unless the signal-to-noise ratio is 432 very high or a micrometer-resolution scan can visually resolve the myelinated axons contained 433 in different tracts. Such resolution can be attained by decreasing beam diameter and motor 434 step size, or by use of other orientation-sensitive microscopy methods, such as scattered light 435 imaging

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Scanning SAXS has different advantages and shortcomings compared to the multiple other 438 methods employed towards detecting fiber orientations -and crossing fibers-in the animal and 439 human brain. Since diffusion MRI is the only modality which can be applied both in vivo and ex 440 vivo with minimal sample preparation, other methods aim to overcome its shortcomings. 441 Limitations of diffusion MRI mostly stem from the fact that it uses the directional 442 movement of water molecules as a proxy for fiber orientation. As a result, i) it is difficult to 443 translate findings from ex vivo to in vivo, since water content and motility are altered in fixed 444 samples, ii) movement of water is also restricted or hindered by all structures in the brain [33], 445 including membranes of other cells, organelles, extracellular matrix and vesicles, cell 446 cytoskeleton, vesicle walls, while water can passively or actively move across membranes [34], 447 iii) fiber response function is inherently broader compared to SAXS, because even in the case of 448 perfectly aligned fiber population, all the above factors, as well as the movement of water in 449 random directions (to the extent allowed) within the neuronal somata, axons, and in the 450 extracellular space, contribute to an angular dispersion of the signal. In addition, dMRI 451 resolution is typically restricted to hundreds of micrometers per voxel, potentially 452 corresponding to thousands of fibers, further contributing to the angular dispersion. All these 453 make interpretation of diffusion MRI output very challenging and stress the need for validation 454 methods [21]. 455 As described, the main limitation of dMRI is lack of specificity to myelinated axons. This can 456 be provided by scanning SAXS, confocal/multi-photon microscopy (possibly combined with 457 clearing), and polarization-based methods (3D-PLI/PS-OCT plane compared to in-plane resolution, and structure tensor analysis is challenging in dense 481 white matter regions where intensity gradients are low. 3D-PLI can also provide 3D orientation, 482 but the out-of-plane angle can be ambiguous, while SLI yields information on out-of-plane 483 angles, but quantification has not yet been achieved. 484 Finally, SAXS, in its tensor tomography form [26]- [28], is the only method together with 485 MRI that can be performed on intact specimens, with most other methods being limited to 486 sections. Tissue clearing also enables 3D imaging of specimens, but tissue is usually distorted by 487 the clearing process, and samples larger than few millimeters pose challenges in clearing, 488 antibody penetration and imaging. 489

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Crossings in the brains of various species are shown in this study. The mouse brain scan 491 revealed crossings in both white and gray matter. White matter crossings were seen mostly by 492 cortical fibers and crossing the corpus callosum and external capsule on their way to the 493 caudoputamen. The relative scarcity of white matter crossings is expected given the rodent 494 brain relative simplicity compared to gyrencephalic brains. Nevertheless, X-ray scattering was 495 also able to distinguish crossings of myelinated axons in gray matter regions, including 496 tangential fibers crossing the more abundant radial ones [37], only previously reported using 497 tracer studies [7], special microscopy methods with very high resolution The human hippocampus is critical for new memory formation, and shows degraded 520 function in neurodegenerative diseases such as Alzheimer's disease (AD) [53]. However, its 521 location towards the lower part of the brain, next to the mastoid air cells, its complex anatomy 522 [ The study has a number of limitations. First, the ground truth for fiber orientations is an 543 ongoing challenge. We attempted to overcome this by i) validating against strips of 544 unidirectional fibers artificially superimposed to mimic pixels with crossings, noting that 545 scanning SAXS has been proven to work in brain tissue for primary orientation [22], [28], and ii) 546 comparing to a micrometer-resolution 3D-PLI image of a similar region of a mouse brain. 547 However, even in the artificial crossings using corpus callosum strips, fibers are not fully aligned 548 within each strip, so ground-truth crossing angles cannot be exactly determined. On the other 549 hand, SAXS yields directional information from myelinated axons directly and with specificity, 550 so the fiber orientations are relatively easily and directly interpreted compared to structural 551 imaging or diffusion MRI, where myelinated-axon-specific orientation analyses include more 552 complex algorithms and more assumptions. 553 SAXS scans can achieve a moderately high resolution while discerning crossing fibers; the 554 highest resolution demonstrated here was in the first mouse brain section, reaching 25 555 micrometers, while resolution was up to 125 micrometers for the vervet brain, much lower 556 than the resolution typically reached in 3D-PLI or SLI. Although SAXS scanning can be performed 557 at very high resolutions, down to nanometer levels [36], practical considerations (beamline 558 capabilities regarding beamsize, and time needed for raster-scanning an extended field of view 559 at such resolutions) limit the resolution to typically tens of micrometers. This is below or at the 560 same order as that of diffusion MRI, with the advantage of specificity to the myelinated fibers, 561 making it thus a very good validation tool for similarly-sized samples. 562 Sensitivity to peak detection in the azimuthal profiles presents a challenge for future 563 improvements. In this study, the SLIX software [30] used the SAXS azimuthal profile data as 564 input, since in SLI photons also scatter anisotropically off material depending on structure 565 orientation, and in both methods the position of the peaks in azimuthal profiles reveals the in-566 plane orientation of the fibers. However, by looking at the azimuthal profiles of pixels 3, 6, and 567 7 in Fig. 2, one can suggest that there are two peaks that are at an angle of ~20 o apart. This 568 could indicate that a more sensitive peak-fitting algorithm, the subject of our future work, could 569 possibly be able to tell these peaks apart, and thus resolve even lower angle crossings. 570 When it comes to tissue preparation for imaging, the presented scanning SAXS experiments 571 were performed on thin sections. Although this is a very common approach used in histology or 572 methods such as 3D-PLI or SLI, in many cases it is not desired, or not feasible. However, with 573 the advent of SAXS tensor tomography [26], [28], such experiments can also be performed 574 tomographically on whole specimens without sectioning. The challenge of computing both the 575 tensor-tomographic reconstruction and depicting multiple fiber orientations per voxel will also 576 be the subject of future investigations. This would provide a tomographic gold-standard in the 577 axonal orientation field and enable a head-to-head validation of diffusion MRI orientation 578 information on the same specimens. 579 Access to scanning SAXS is also a limitation because the required photon flux of micro-580 focused beam is currently only obtainable from synchrotrons. However, several sites worldwide 581 provide appropriate beamlines for collaborative use. Continued improvement of 582 instrumentation and analysis will enable higher sample throughput as well as scanning SAXS 583 experiments on lab SAXS setups. 584

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Accurate and specific imaging of crossing nerve fibers is an important challenge in 586 neuroscience. In the experiments presented here, we use scanning small-angle X-ray scattering 587 (SAXS) to show that detecting crossing fibers is feasible for at least three crossing fiber bundles 588 and crossing angles down to approximately 25°, and applied the method across species, in 589 mouse, pig, vervet monkey, and human brain, in gray and white matter. Overall, as scanning 590 SAXS can provide specificity to myelinated axonal orientations, which are responsible for long-591 distance signal transmission in the brain, it has the potential to become a reference method for 592 accurate fiber orientation mapping. Combination of scanning SAXS with micrometer-resolution 593 imaging approaches, such as 3D-PLI or SLI, taking advantage of SAXS's specificity and 3D-PLI/SLI 594 resolution, could provide ground truth information on fiber orientations, yield accurate 595 structural connectivity maps and be the basis for validation of diffusion MRI signals. 596