Probing microstructure with different tomographic methods: Comparing dMRI and X-ray scattering-derived parameters in mouse and human brains
Marios Georgiadis1,2, Dmitry S. Novikov1, Manuel Guizar-Sicairos3, Marianne Liebi3,4, Vivianne Lutz-Bueno3, Benjamin Ades-Aron1, Timothy M. Shepherd1, Aileen Schroeter2, Markus Rudin2, and Els Fieremans1

1NYU Langone Medical Center, New York, NY, United States, 2ETH Zurich, Zurich, Switzerland, 3Paul Scherrer Institute, Villigen, Switzerland, 4Chalmers University of Technology, Gothenburg, Sweden


Despite MRI’s coarse resolution, diffusion MRI (dMRI) enables probing cellular microstructure. Advanced dMRI acquisition and biophysical modeling can provide microstructural metrics related to disease processes, and spherical harmonics (SH)-based orientation distribution function (ODF). Yet, these still need structural validation, and a gold standard for quantifying microstructure, particularly fiber dispersion, is missing. X-ray scattering directly probes tissue microstructure, exploiting the ~17nm myelin repeat distance, and can also represent ODF in a SH basis. Here, we show good correspondence between SH coefficients from dMRI and X-ray scattering on a mouse brain, with analysis on human samples and histological validation to follow.


While resolution in MRI is at the millimeter (humans) or hundreds of micrometers (rodents) range, diffusion MRI (dMRI) provides an excellent tool for investigating microstructure properties, since movement of water molecules at usual echo times happens in the micrometer scale (Fig. 1A). Recent dMRI techniques have enabled extracting brain microstructure metrics related to disease processes (demyelination, axonal loss, beading, oedema and inflammation)1-3, and rotationally invariant parameters4,5 from spherical harmonics (SH)-based orientation distribution functions (ODFs), which can be used as input for fiber tracking. However, all these MRI metrics need structural validation. The recently developed Small-angle X-ray scattering tensor tomography (SAXSTT)6,7 technique (Fig. 1C) exploits myelin sheath periodicity to provide myelin content, fiber directionality and orientation distribution8 based on SH. In this study, we combine these two fundamentally different methods to derive and compare the same microstructural parameter, the SH-based P2 invariant4,5, representative of fiber ODF anisotropy.


The brain of a healthy, 5-month-old C57BL/6 mouse was scanned ex vivo using a receive cryo-coil at the 9.4T Bruker MRI scanner in the Animal Imaging Center of ETH Zurich. Diffusion encoding was applied along 200 diffusion directions (Fig. 1D): 20 for b-value=1μm/ms², 40 for 2μm/ms², 60 for 3μm/ms² and 80 for 4μm/ms², with isotropic voxel size 75μm.

SAXSTT experiments were performed in the cSAXS beamline of Paul Scherrer Institute (PSI), Switzerland, according to Liebi et al.5 (isotropic voxel size: 150μm, beam energy: 16.3KeV, 267 projections, Fig. 1E). The X-ray dose of 105Gy deposited on the brain was below doses used in previous rodent brain experiments8. The myelin-specific signal, corresponding to myelin sheath periodicity (~17.5nm), was identified and isolated9. dMRI and SAXSTT results were registered to a common template, together with a detailed anatomic atlas10,11, for further analyses.

ODF SH coefficients $$$P(n) = \sum P_{lm} Y_{lm}(n)$$$ were derived for both methods. The P2 invariant from dMRI RotInv analysis4 is derived as a Euclidean norm of all 2nd order SHs. In order to directly compare the parameters from the different modalities, SAXSTT-derived S20 was converted to P2 using the inverse Funk-Radon transform (FRT) ( $$$S_{2m} \propto -\frac12 P_{2m}$$$ ), owing to the fact that SAXSTT measures the FRT of the myelinated-fiber ODF, i.e. a “doughnut” rather than a “stick”, (cf. Fig. 1A,C). Both signals have been additionally normalized from 0 to 1.


After performing the necessary post-processing steps to ensure high dMRI data quality12-14, microstructural parametric maps characterizing intra- and extra-axonal diffusivity, kurtosis and fiber ODF rotational invariants were produced according to 15 and 4 (Fig. 2). SAXSTT reconstruction provided myelin content and parametric maps of the brain (Fig. 3).
Whole-brain voxel-to-voxel comparison shows weak correlation between dMRI and SAXSTT P2 (Pearson’s R=0.21) (Fig. 4A). Analysis of multiple white and gray matter ROIs (Fig. 4B,C) shows that P2 values are region-wise correlated (Fig. 4D-F): white matter-dominated areas (eg. corpus callosum, cerebral peduncle, anterior commissure) have significantly higher P2 values in both modalities than gray matter regions such as the thalamus or somatosensory cortex areas. Correlation of ROI average values is very high (R=0.94) (Fig. 4F).


The use of two fundamentally different methods, dMRI and SAXSTT, has been demonstrated for assessing the same microstructural tissue parameter: the SH P2 coefficient, main indicator of fiber anisotropy. Whole-brain voxel-to-voxel comparison results in a weak correlation (Fig. 4A), presumably due to the signal being sensitive to noise coming from registration, partial-volume effects, which both add to the inherent sensitivity of the derived SH coefficients, a result high-order non-linear fitting. Another contributing factor to low correlation is the fact that the two methods derive ODFs measuring fundamentally different tissue properties. However, after the coefficients are rendered directly comparable (via FRT and normalization) (Fig. 4B), ROI analysis shows a remarkably high correlation (R=0.94, Fig. 4F). Cancelling of the previously mentioned “noise” effects by averaging in each ROI contributes to the high correlation. Although this result is very promising, especially if one considers the complete orthogonality of the methods used and of the phenomena exploited, it needs further analysis, using more samples (in number and diversity) and validation by the destructive “ground truth” methods, 2D and 3D histology –both steps are planned (Fig. 5).


This study investigated correlation of structural parameters characterizing the fiber ODF, derived by high-order fitting of signal ODFs retrieved from two fundamentally different methods: dMRI and X-ray scattering. A surprisingly high correlation was found for the SH P2 coefficient, which characterizes local tissue anisotropy. Such investigations aim to enhance the understanding of the structural underpinning of dMRI parameters, and aim to validate ex vivo novel metrics that enhance fiber tracking by directly providing spherical harmonics coefficients, so that these can be eventually used in vivo.


Research was supported by the Early Postdoc.Mobility Fellowship of the Swiss National Science Foundation and the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under award number R01NS088040.


  1. Fieremans, E., et al. Diffusion distinguishes between axonal loss and demyelination in brain white matter. in ISMRM. 2012. Melbourne, Australia: Proceeding of International Society of Margnetic Resonance in Medicine.
  2. Jelescu, I.O., et al., In vivo quantification of demyelination and recovery using compartment-specific diffusion MRI metrics validated by electron microscopy. NeuroImage, 2016.
  3. Budde, M.D. and J.A. Frank, Neurite beading is sufficient to decrease the apparent diffusion coefficient after ischemic stroke. Proc Natl Acad Sci U S A, 2010. 107(32): p. 14472-7.
  4. Novikov, D.S., et al., Mapping orientational and microstructural metrics of neuronal integrity with in vivo diffusion MRI. arXiv preprint, 2016(arXiv:1609.09144).
  5. Reisert, M., et al., Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach. NeuroImage, 2017. 147: p. 964-975.
  6. Liebi, M., et al., Nanostructure surveys of macroscopic specimens by small-angle scattering tensor tomography. Nature, 2015. 527(7578): p. 349-352.
  7. Schaff, F., et al., Six-dimensional real and reciprocal space small-angle X-ray scattering tomography. Nature, 2015. 527(7578): p. 353-356.
  8. Georgiadis, M., et al. MRI vs. X-ray scattering: comparative study of myelin distribution, fiber direction and white matter tracts in mouse brain. in ISMRM 25th Annual Meeting. 2017. Hawaii, 22-27 April 2017.
  9. Jensen, T.H., et al., Brain tumor imaging using small-angle X-ray scattering tomography. Physics in Medicine and Biology, 2011. 56(6): p. 1717-1726.
  10. Jensen, T.H., et al., Molecular X-ray computed tomography of myelin in a rat brain. NeuroImage, 2011. 57(1): p. 124-129.
  11. https://wiki.mouseimaging.ca/display/MICePub/Mouse+Brain+Atlases#MouseBrainAtlases-Dorr-Steadman-Ullmann-Richards-Qiu-Egan(40micron,DSURQE).
  12. Dorr, A.E., et al., High resolution three-dimensional brain atlas using an average magnetic resonance image of 40 adult C57Bl/6J mice. NeuroImage, 2008. 42(1): p. 60-69.
  13. Ades-Aron, B., et al., Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) in ISMRM. 2016: Singapore.
  14. Veraart, J., et al., Denoising of diffusion MRI using random matrix theory. NeuroImage, 2016. 142(Supplement C): p. 394-406.
  15. https://github.com/NYU-DiffusionMRI/Diffusion-Kurtosis-Imaging.
  16. Fieremans, E., J.H. Jensen, and J.A. Helpern, White matter characterization with diffusional kurtosis imaging. NeuroImage, 2011. 58(1): p. 177-188.
  17. http://infinity-imagined.tumblr.com/post/4720654940/a-cross-section-of-a-bundle-of-nerve-fibers.
  18. https://people.csail.mit.edu/sparis/sh/.


Figure 1. Measuring SH-based ODFs using dMRI and SAXSTT. A. dMRI derives diffusivities D based on intra- and extra-cellular movement of water molecules. B. Electron microscope image of white-matter axons17, which would produce the dMRI signal in A and the scattering signal in C. C. X-ray probes myelinated axons and produces anisotropic signal corresponding to myelin periodicity. D. Distribution of 220 directions in dMRI scan. E. Distribution of 267 directions in SAXSTT scan, limited by practical inability of sample tilt>50o. F. Representation18 of even SH up to 6th order used to model dMRI and SAXSTT ODFs (SAXSTT uses m=0 SH).

Figure 2. dMRI data analysis. A) Proton density signal, for anatomical reference. Artifact at bottom left, caused by moving bubble, affects all derived parameters. B) Mean kurtosis (MK) is higher in myelin-rich regions, such as the corpus callosum, where diffusion is highly non-linear. Axial kurtosis (AK) values have minor differences in the brain, in contrast to radial kurtosis (RK), which gets amplified in areas with densely-packed, highly aligned myelinated fibers. C) Rotiationally invariant P2, calculated according to4. RotInv P2 is based on higher order fitting of the non-linear signal, and is thus sensitive to noise or artifacts (eg. bottom-left area).

Figure 3. SAXSTT-derived SH coefficients. A) S0 map in a coronal slice. S0 represents the isotropic signal component, and is correlated to myelin content, which is directly measurable via SAXSTT8. B) S20 coronal slice map. S20 is the most important coefficient for representing anisotropy in each voxel. It is mostly negative due to the fact that SAXSTT measures signal ODF, instead of fiber ODF (the two are related by Funk-Radon transform -FRT). C-F. SH coefficient distribution in different brain ROIs, with S0 (blue) more positive in highly myelinated areas and S20 (green) more negative in areas exhibiting stronger anisotropy.

Figure 4. Correlation between SAXSTT- and dMRI-derived P2. A) SAXSTT signal S20 and dMRI fiber RotInv P2 correlation for whole brain. B) Normalized fiber P2 whole-brain histograms, where SAXSTT P2 was derived by subjecting S20 to FRT. C-D) Top and bottom view of brain and analyzed ROIs, colored according to boxes in F. E) Histograms of P2 in two representative brain regions, exhibiting low (primary somatosensory cortex-PSC) or high (CC) anisotropy. F). Correlation between normalized SAXSTT- and dMRI-derived P2. Each box is centered at the mean ROI values, and its edge length is 2 standard deviations along the corresponding direction.

Figure 5. Application on human samples and validation. A-F) First experiments on human white matter sample: dMRI analysis was performed (B,F) providing microstructural parameters including intra- and extra-axonal diffusivities, and RotInv P2. Additionally, the possibility to perform SAXSTT experiments on human tissue (C-D) and extract fiber directionality information (E) was demonstrated. Validation of SH coefficients using 2D (G) and 3D (H) histology is also planned, by extracting the fiber ODF using structure tensor analysis (preliminary analysis of 3D histology, performed using CLARITY, neurofilament staining and confocal microscopy, provided fiber directions in every voxel of the brain used in the study).

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)