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Validating axonal directionality with 3D X-ray scattering
Marios Georgiadis1,2, Dmitry S. Novikov1, Zirui Gao2,3, Manuel Guizar-Sicairos3, Lin Yang4, Shirish Chodankar4, Jelle Veraart1, Ben Ades-Aron1, Choong Heon Lee1, Sunglyoung Kim1, Piotr Walczak5, Jiangyang Zhang1, Aileen Schroeter2, Markus Rudin2, and Els Fieremans1

1NYU School of Medicine, New York, NY, United States, 2ETH Zurich, Zurich, Switzerland, 3Paul Scherrer Institute, Villigen PSI, Switzerland, 4Brookhaven National Laboratory, Upton, NY, United States, 5Johns Hopkins Medicine, Baltimore, MD, United States

Synopsis

Diffusion MRI (dMRI) is sensitive to neuronal alignment, yet its directional signal does not depend only on the fiber orientation distribution function (fODF). Current validation methods for measuring and modeling the ODF have major limitations. Small-angle X-ray scattering (SAXS) produces directly structural signal, specific to myelin’s repetitive structural arrangement. We apply 3D scanning SAXS on mouse brain sections, retrieve fODFs and compare against dMRI-derived axonal directionality. We also apply SAXS-tensor tomography to mouse spinal cord, produce tractography maps and correlate dMRI- and SAXS-TT-derived fODF parameters. These demonstrate SAXS’s potential for providing novel microstructural insights and structurally validating dMRI-derived fODFs.

Introduction

In brain diffusion MRI (dMRI), the anisotropic signal is typically attributed to neuronal directionality, but is also affected by other factors1 such as myelin density, intra- and extra-axonal heterogeneities, cross-membrane water exchange etc. Hence, structural validation is essential for dMRI. Previous validation studies were based on either electron microscopy2,3, which only probes minuscule (sub-mm3) volumes, light microscopy4-6, which provides intensity information not easily translatable to 3D fODF, or brain clearing techniques7-9 whose limitations include heterogeneous tissue deformation or restricted/heterogeneous antibody penetration. Small-angle X-ray scattering (SAXS) produces directly structural signal, specific to myelin’s repetitive structure10. The 3D scanning SAXS (3DsSAXS) and SAXS tensor tomography (SAXS-TT) methods can provide 3D fiber orientation in bone11-14 and mouse brain tissue15-17. Here, we apply 3DsSAXS and SAXS-TT to mouse brain and spinal cord respectively, retrieve the fODFs, generate neural tracts, and compare to the dMRI-derived ODFs.

Methods

A 5-month-old C57BL/6 mouse brain was dMRI-scanned ex vivo (9.4T Bruker animal MRI scanner) with voxel size=75μm, 200 q-space points, b-value=1-4 ms/μm2. Two sections, 25 and 50μm thick, were cut using a vibratome and scanned using 3DsSAXS11 (cSAXS beamline, Paul Scherrer Institute, Switzerland) at 6 rotation angles, with voxel size=25 and 50μm, Ephoton=12.4KeV. The cervical spinal cord from a 50-day-old Rag2-/- mouse was dMRI-scanned (7T Bruker animal MRI scanner), with voxel size=100μm, 160 q-space points, b-value=2-20 ms/μm2. The sample was SAXS-TT-scanned (LiX beamline, Brookhaven National Laboratory) with voxel size=100μm, Ephoton=15.7KeV, 100 projections.

Whole-brain and spinal cord dMRI data were processed using DESIGNER18-20, resulting in diffusion and kurtosis tensors and corresponding parametric maps, Fig. 1. For the 3DsSAXS brain sections, the rank-2 scattering tensor17 was used to derive the scattering ODF, which was converted to the fODF using the FRT, Fig. 2. Similarly, for the spinal cord SAXS-TT data, IRTT17 was used to derive the scattering ODF rank-2 tensors, which were FRT-transformed to fODFs. For probabilistic tractography21,22, a synthetic dMRI dataset was generated from SAXS-TT data based on each voxel’s fODF.

The dMRI- and SAXS-derived rank-2 tensors were used to determine the main fiber direction. P2 invariants were calculated as Euclidean norms of the tensors’ 2nd order spherical harmonics representation23. dMRI data were affine-registered24,25 to SAXS brain sections and spinal cord, with fractional anisotropy (FA) of dMRI and SAXS tensors as contrast.

Results

For the 25μm brain section, the 2D (in-plane) fiber directionality from SAXS and dMRI are compared, Fig. 3, showing good agreement. Small differences, e.g. anatomical discrepancies, can be attributed to sectioning artifacts or imperfect registration, and others, e.g. the low X-ray scattering signal in the myelin-poor cortex, to the different signal-producing mechanisms. For the 50um-thick section, the retrieved 3D orientation from both methods was compared, Fig. 4. Again, directional correspondence is very good, with differences attributed to the aforementioned factors. SAXS-TT-derived spinal cord neural tracts, Fig. 5 top right, agree with known anatomy tracts. The correlation coefficient between FA from both methods is 0.68, whereas the correlation coefficient for P2 is 0.74, Fig. 5 bottom.

Discussion

X-ray scattering and diffusion MRI are two fundamentally different methods, based on the phenomena of photon scattering and water diffusion respectively. However, their signal is based on events taking place at the nano-/micro-structural level, orders of magnitude below their nominal resolution, making both sensitive to the axonal fiber directionality. Here, we extract the fODF from the scattering ODF using a rank-2 tensor17, Fig. 2, and compare its main direction and ODF parameters to the corresponding dMRI outputs. Comparison of axonal directionality in 2 mouse brain sections to the corresponding orientation from the MRI-derived diffusion tensor shows excellent agreement both in 2D (Fig. 3) and in 3D (Fig. 4). We also apply SAXS-TT in a spinal cord sample, and generate anatomy-realistic tractograms from SAXS-TT data, Fig. 5 top right. Finally, we compare ODF parameters from both methods: whereas both FA and P2 show high correlations, correlation coefficient of P2 is higher than that of FA, Fig. 5 bottom. Since the anisotropic signal is generated through very different physical phenomena, the respective method-related isotropic component is incorporated in the calculation of fractional anisotropy but not in P2.

Conclusions

We have derived fODFs using X-ray scattering methods on mouse brain and spinal cord tissue, and compared axonal orientations and ODF parameters with dMRI. Given SAXS’s ability to produce myelin-related signal, 3D fODFs, conduct tomographic investigations, and also on human brain tissue16, 3DsSAXS and SAXS-TT may be broadly applicable not only for validating dMRI orientation or microstructural models and corresponding parameters, but also for providing novel microstructural insights as orthogonal, directly structural methods.

Acknowledgements

Research was partially supported by Swiss National Science Foundation (SNSF) grant numbers P2EZP3_168920, 200021_178788, and by the National Institutes of Health (NIH) award number R01 NS088040. The Animal Imaging Center of ETH Zurich and the Preclinical Imaging Core of NYU of Medicine are acknowledged for enabling the MRI studies.

References

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Figures

Figure 1. dMRI parametric maps generated by performing artifact removal and diffusion and kurtosis tensor fitting using the DESIGNER pipeline18-20. The same slice as in Fig. 3 is shown. (A) Mean diffusivity and (B) mean kurtosis maps delineate the main brain anatomical features, with MK highlighting the restricted diffusion brain compartments. (C) The FA as calculated from the diffusion tensor, implicitly incorporates the tensor’s isotropic component. (D) The P2 anisotropy parameter is calculated as the Euclidean norm of all l=2 components of the spherical harmonics representation of the diffusion tensor23, thus disregarding the isotropic component influenced by the diffusion physics.

Figure 2. Deriving the fiber ODF from X-ray scattering. A pencil beam probes each point on the sample, for different rotation angles θ (top left). The resulting scattering pattern includes a characteristic “myelin ring” at a specific q-range (related to real-space dimensions through q=2π/d), with intensity distribution indicative of myelin content and fiber orientation (top right). Sample rotation θ enables analysis of the scattering signal along different directions (bottom right). Fitting the scattering intensity with a rank-2 tensor17, results in a scattering ODF (bottom center). By applying the Funk-Radon transform (FRT) to it, we can derive the fODF (bottom left).

Figure 3. 2D (in-plane) orientation comparison between SAXS (left) and dMRI (right). Orientation interpreted using the colorwheel. In SAXS, scanning each point at rotation angle θ=0ο produced a scattering pattern, which indicated the 2D fiber orientation. Patterns i and iii are from white-matter areas (dorsal fornix and corpus callosum respectively) and have characteristic anisotropic myelin rings, perpendicular to the in-plane fiber direction. Pattern ii is from the poorly myelinated cortex, and has no visible myelin ring. The dMRI tensors from the same brain virtual section (right) were interrogated along the coronal plane in order to retrieve the in-plane directions.

Figure 4. 3D orientation comparison between 3DsSAXS and dMRI, based on the main orientation of the rank-2 tensors. The part of the section scanned with SAXS was identified in the dMRI dataset, and mirrored, for side-to-side dataset comparison. Overall, there is excellent agreement of the two methods. Differences in the outputs can be seen in terms of anatomy, mainly attributed to sectioning artifacts in 3DsSAXS, and in terms of signal in the cortex, which is not captured by the myelin-dominated SAXS signal. Small circle in lower left part of left image indicates the point analyzed in Fig. 2, bottom row.

Figure 5. SAXS-scanning of the mouse spinal cord at different rotation angles permits 2D orientation analysis of each projection (top left). In-plane fiber orientations of the two projections can be interpreted using the colorwheel. IRTT17 reconstruction provides the rank-2 scattering tensor for each voxel, and its FRT provides the fODF. Generating a synthetic dMRI dataset from the tensor data enables SAXS-TT based tractography21,22 (top right). Bottom: FA and P2 parameters can be derived from the SAXS-TT and dMRI rank-2 tensors. P2 correlation over all sample voxels is higher than that of FA, presumably because FA incorporates a method-related isotropic component.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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