Andrey Chuhutin^{1}, Brian Hansen^{1}, Agnieszka Wlodarczyk^{2}, Trevor Owens^{2}, Noam Shemesh^{3}, and Sune Nørhøj Jespersen^{1,4}

To study the relationship between microstructure and disability, 18 ex-vivo spinal cords from a mouse model of MS (EAE) were investigated using DKI and a biophysical model of diffusion. Diffusion data were acquired together with T2* images to delineate lesions. Kurtosis tensors and microstructural parameters were used for statistical analysis using a LME model. The results show a strong relation between disability and kurtosis tensor parameters similar to observations in other hypomyelinating MS models and in patients. Conversely, changes in model parameters, such as extra-axonal axial diffusivity, are clearly different from previous studies using other animal models of MS.

18
(MOG)_{p35–55}-treated
mice (experiment
ethically approved) were
monitored daily and EAE-severity was graded on a 6-point scale, prior
to spinal cord extraction.

Imaging of spinal cords (SC, segments
T8-L6) was performed with a 16.4T Bruker Aeon
Ascend scanner using
a diffusion weighted fast spin echo sequence(credit
to Dr.KD Harkins and Prof.MD Does, NIH-EB019980)^{14–16
}ETL=8,TE/ESP=15/4.23ms,TR=2000ms,$$$\delta/\Delta=$$$1.5/10ms
and b=0.2,0.3,0.5,0.6,0.9,1,1.2,1.5,1.8,2.1,2.5ms/µm^{2},
voxel size
0.5x0.035x0.035mm^{3}.

T_{2}^{*}-weighted
images for manual WM,
GM and lesion delineation^{17},
were acquired using
FLASH
pulse sequence
with
TE=5ms.

Images were denoised^{18}
and corrected for
Gibbs ringing^{19}.
In WM, shells up to $$$b_\mathrm{max}=2.5$$$msµm^{-2} and
GM
up to
$$$b_\mathrm{max}=1.2$$$msµm^{-2} were
fit^{20}
with Weighted
Linear Least Squares^{21},
to
yield diffusion
and kurtosis tensors^{8}.
Tensor
parameters were calculated according
to^{8,9},
which
yielded parameters
of Watson Standard Model(WSM), assuming
Watson distribution of neurites^{22,23}.
Only
the ‘plus’ branch^{22,24,25}($$$D_\mathrm{a}>D_{\mathrm{e},\parallel}$$$)
was
considered.

10 WM
parameters (DKI:$$$D_\parallel$$$, FA,$$$K_\parallel$$$,$$$K_\perp$$$, and WSM:$$$D_{\mathrm{e},\perp}$$$,$$$D_{\mathrm{e},\parallel}$$$,$$$D_\mathrm{a}$$$,$$$f$$$,$$$\kappa$$$)
and
2 GM parameters $$$\bar{D}$$$ and $$$\bar{W}=\frac{\mathrm{Tr}\left(\mathbf{W}\right)}{5}$$$
^{9,26,27}
were estimated.

The voxels from all
spinal cords were analyzed with linear mixed effects model^{28,29}(Wilkinson notation^{30}: $$$p_i \sim g\cdot s +l +\left(s\cdot g | a\right)+\left(l|a\right)$$$,
where diffusion
parameters are
$$$p_i$$$, grade $$$g$$$,
segment $$$s$$$,
lesion $$$l$$$,
animal $$$a$$$).
For each of
the ‘fixed’ effects, ANOVA p-values
were calculated post-hoc.

In GM, $$$\bar{W}$$$ depended
significantly on disability grade, in line with human studies^{10,31–33}
and the cuprizone
model^{12}.
Changes in $$$\bar{W}$$$ indicate
GM pathology, that
could be due to
neuronal degeneration and myelin loss.

In NAWM, $$$K_\perp$$$ and $$$D_\perp$$$ were most robust parameters distinguishing between disability
grades, which has been observed in other MS models^{11,13,14}.
An increase in $$$D_\perp$$$ agrees with chronic demyelination studies^{11,13,14}.
Human studies associated it with demyelination^{34}
and axonal loss^{35}.

Among WSM parameters, $$$D_{\mathrm{e},\parallel}$$$ and axonal water fraction($$$f$$$, a biomarker of axonal loss^{36})
affected the EAE-grade most. This is in contrast with hypomyelination
models^{11,12,37},
where effects
on $$$D\mathrm{a}$$$ and
$$$D_{\mathrm{e},\perp}$$$ were
the strongest. Technical differences (i.e. using SC or
particular ‘branch’ of the WSM
model^{22,37,38}) aside,
the prominent
role of $$$D_{\mathrm{e},\parallel}$$$ may result from different mechanisms underlying tissue
degeneration in hypomyelination models compared to EAE. The increase
in extra-axonal diffusivities can be explained by axonal damage,
glial cells structure changes, and myelin loss, that cause lowered
tortuosity in the extra-axonal
space. This
novel observation
indicates $$$D_{\mathrm{e},\parallel}$$$ as
a key parameter that
may prove
important for MS and EAE disability characterization

- Inside WM lesions, no biomarker was found to correlate with disability.
- In NAWM and GM, the relationship between disability and DKI/DTI metrics was similar to other hypomyelinating MS models and ex-vivo MS tissue.
- A combination of strong increase in $$$D_{\mathrm{e},\parallel}$$$ and a
potentially-verifiable change in $$$f$$$ is
clearly distinct in comparison to other MS animal models.

1. Bakshi, R. et al. MRI in multiple sclerosis: current status and future prospects. Lancet Neurol. 7, 615–625 (2008).

2. Polman, C. H. et al. Diagnostic criteria for multiple sclerosis: 2010 Revisions to the McDonald criteria. Ann. Neurol. 69, 292–302 (2011).

3. Filippi, M. et al. Association between pathological and MRI findings in multiple sclerosis. Lancet Neurol. 11, 349–360 (2012).

4. Inglese, M. & Bester, M. Diffusion imaging in multiple sclerosis: research and clinical implications. NMR Biomed. 23, 865–872 (2010).

5. Miller, D. H., Thompson, A. J. & Filippi, M. Magnetic resonance studies of abnormalities in the normal appearing white matter and grey matter in multiple sclerosis. J. Neurol. 250, 1407–1419 (2003).

6. De Stefano, N. et al. Brain damage as detected by magnetization transfer imaging is less pronounced in benign than in early relapsing multiple sclerosis. Brain 129, 2008–2016 (2006).

7. Kipp, M., Nyamoya, S., Hochstrasser, T. & Amor, S. Multiple sclerosis animal models: a clinical and histopathological perspective. Brain Pathol. 27, 123–137 (2016).

8. Jensen, J. H., Helpern, J. A., Ramani, A., Lu, H. & Kaczynski, K. Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn. Reson. Med. 53, 1432–1440 (2005).

9. Jensen, J. H. & Helpern, J. A. MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed. 23, 698–710 (2010).

10. Bester, M. et al. Non-Gaussian diffusion MRI of gray matter is associated with cognitive impairment in multiple sclerosis. Mult. Scler. J. 21, 935–944 (2015).

11. Falangola, M. F. et al. Histological correlation of diffusional kurtosis and white matter modeling metrics in cuprizone-induced corpus callosum demyelination. NMR Biomed. 27, 948–957 (2014).

12. Guglielmetti, C. et al. Diffusion kurtosis imaging probes cortical alterations and white matter pathology following cuprizone induced demyelination and spontaneous remyelination. NeuroImage 125, 363–377 (2016).

13. Jelescu, I. O. et al. In vivo quantification of demyelination and recovery using compartment-specific diffusion MRI metrics validated by electron microscopy. NeuroImage 132, 104–114 (2016).

14. Kelm, N. D. et al. Evaluation of diffusion kurtosis imaging in ex vivo hypomyelinated mouse brains. NeuroImage 124, Part A, 612–626 (2016).

15. Beaulieu, C. F., Zhou, X., Cofer, G. P. & Johnson, G. A. Diffusion-weighted MR microscopy with fast spin-echo. Magn. Reson. Med. 30, 201–206 (1993).

16. West, K. L. et al. Experimental studies of g-ratio MRI in ex vivo mouse brain. NeuroImage 167, 366–371 (2018).

17. The spinal cord: a Christopher and Dana Reeve Foundation text and atlas. (Academic, 2009).

18. Veraart, J., Fieremans, E. & Novikov, D. S. Diffusion MRI noise mapping using random matrix theory. Magn. Reson. Med. 76, 1582–1593 (2015).

19. Kellner, E., Dhital, B., Kiselev, V. G. & Reisert, M. Gibbs‐ringing artifact removal based on local subvoxel‐shifts. Magn. Reson. Med. 76, 1574–1581 (2015).

20. Chuhutin, A., Hansen, B. & Jespersen, S. N. Precision and accuracy of diffusion kurtosis estimation and the influence of b-value selection. NMR Biomed. 30, e3777 (2017).

21. Veraart, J., Sijbers, J., Sunaert, S., Leemans, A. & Jeurissen, B. Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls. NeuroImage 81, 335–346 (2013).

22. Jespersen, S. N., Olesen, J. L., Hansen, B. & Shemesh, N. Diffusion time dependence of microstructural parameters in fixed spinal cord. NeuroImage (2017). doi:10.1016/j.neuroimage.2017.08.039

23. Novikov, D. S., Veraart, J., Jelescu, I. O. & Fieremans, E. Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI. NeuroImage 174, 518–538 (2018).

24. Novikov, D. S., Fieremans, E., Jespersen, S. N. & Kiselev, V. G. Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. NMR Biomed. 0, e3998 (2018).

25. Hansen, B. & Jespersen, S. N. Recent Developments in Fast Kurtosis Imaging. Front. Phys. 5, (2017). 26. Hansen, B., Lund, T. E., Sangill, R. & Jespersen, S. N. Erratum: Hansen, Lund, Sangill, and Jespersen. Experimentally and Computationally Fast Method for Estimation of a Mean Kurtosis. Magnetic Resonance in Medicine 69:1754-1760 (2013). Magn. Reson. Med. 71, 2250–2250 (2014).

27. Hansen, B., Lund, T. E., Sangill, R. & Jespersen, S. N. Experimentally and computationally fast method for estimation of a mean kurtosis. Magn. Reson. Med. 69, 1754–1760 (2013).

28. Gelman, A. & Hill, J. Data analysis using regression and multilevel/hierarchical models. (Cambridge University Press, 2007).

29. Goldstein, H. Multilevel statistical models. (Wiley, 2011).

30. Wilkinson, G. N. & Rogers, C. E. Symbolic Description of Factorial Models for Analysis of Variance. J. R. Stat. Soc. Ser. C Appl. Stat. 22, 392–399 (1973).

31. Zackowski, K. M. et al. Sensorimotor dysfunction in multiple sclerosis and column-specific magnetization transfer-imaging abnormalities in the spinal cord. Brain 132, 1200–1209 (2009).

32. Agosta, F. et al. In vivo assessment of cervical cord damage in MS patients: a longitudinal diffusion tensor MRI study. Brain 130, 2211–2219 (2007).

33. Raz, E. et al. A Better Characterization of Spinal Cord Damage in Multiple Sclerosis: A Diffusional Kurtosis Imaging Study. Am. J. Neuroradiol. 34, 1846–1852 (2013).

34. Klawiter, E. C. et al. Radial diffusivity predicts demyelination in ex vivo multiple sclerosis spinal cords. NeuroImage 55, 1454–1460 (2011).

35. Naismith, R. T. et al. Increased diffusivity in acute multiple sclerosis lesions predicts risk of black hole. Neurology 74, 1694 (2010).

36. Fieremans, E., Jensen, J. H. & Helpern, J. A. White matter characterization with diffusional kurtosis imaging. NeuroImage 58, 177–188 (2011).

37. Jelescu, I. O., Veraart, J., Fieremans, E. & Novikov, D. S. Degeneracy in model parameter estimation for multi‐compartmental diffusion in neuronal tissue. NMR Biomed. 29, 33–47 (2015).

38. Hansen, B. et al. White matter biomarkers from fast protocols using axially symmetric diffusion kurtosis imaging. NMR Biomed. 30, e3741 (2017).

39. Chuhutin, A. et al.
Diffusion Kurtosis Imaging maps
neural damage in
the EAE model
of multiple sclerosis. ArXiv2460999 Q-bio. (2018).

Figure 1. Animal
disability grade against lesion load relative volume (number of
voxels in lesions per voxels number in the corresponding segment WM)
averaged per sample in SC WM. Bar plots correspond to different
segments of spinal cord. One barplot represents average over all the
segments. Voxel size is $$$6.1\cdot10^-4\mathrm{mm}^3$$$,
an average segment volume is ~3000 voxels for mid thoracic, ~5000 for
lower thoracic and ~8000 for lumbar segments. Data consists of 5
samples (low grade), 3 (intermediate grade), 5 (high grade), 5
(control). Error bars depict standard error
within
samples. There was no significant differences between the
EAE-disability groups.

Figure 2. Examples
of parameter maps for the diffusion and kurtosis tensors parameters
in mid-thoracic segments of spinal cord. Each of the columns (from
left to right) corresponds to different grades of EAE disability:
control animal, low grade, intermediate grade and high grade of EAE.
Rows correspond to different measured parameters (from top to
bottom): mean diffusivity, mean kurtosis, FA, axial diffusivity,
radial diffusivity, radial kurtosis, parallel kurtosis, the upper row
depicts the delineation of spinal cord on the background of FA map.

Figure 3. Examples
of parameter maps for the modeling parameters in mid-thoracic
segments of spinal cord. Each of the columns (from left to right)
corresponds to different grades of EAE disability: control animal,
low grade, intermediate grade and high grade of EAE. Rows correspond
to different measured parameters (from top to bottom): axonal water
fraction, axonal diffusivity, axial extra-axonal diffusivity, radial
extra-axonal diffusivity and concentration parameter of Watson
distribution, the upper row depicts the delineation of spinal cord on
the background of FA map.

Figure 4. The
results of the fit of the linear mixed effects model. For each of the
studied parameters (in rows), the following are presented in columns:
p-values for coefficients of grade, lesion, segment and
segment*lesion, grade fixed effect estimates and the results of the
FDR multiple comparison test. Since lesions were registered only in
WM, the coefficients of lesion are absent in GM (NaN). The details of the analysis see in ^{39}.

Figure 5. Post-hoc
analysis of parameters in GM and NAWM. For each of the FDR
significant parameters in the rows a post-hoc analysis (2 sample
t-test, corrected for multiple comparison) was carried out to
identify significantly different groups. The results are encoded in
the table with the notation: 1 control-low, 2 control-intermediate, 3
control-high, 4 low-intermediate, 5 low-high, 6 intermediate-high. Only parameters that feature significant results in both linear mixed model and post-hoc analysis are presented.
The details of the analysis see in ^{39}.