Introduction

Anomalous diffusion (AD) broadly refers to situations where the mean square displacement is no longer proportional to diffusion time. Depending on the time scale examined, AD may be transient, which has given rise to the concept of transient AD (tAD)^1,2. Techniques based on tAD, named γ-imaging and α-imaging, have recently been applied to excised human tissue¹ and human brain in vivo², showing sensitivity to local susceptibility differences^{1, 2} and structural disorder^{1, 3, 4}. However, a comprehensive biophysical understanding of tAD parameters is still missing. Among other diffusion techniques, q-space-imaging (QSI) allowed assessment of tissue microarchitecture in mouse spinal cord white matter (MSC-wm)^5,6. Here we compare α and γ and diffusion-micro-MRI parameters with morphologic measures resolved by optical microscopy in MSC-wm tracts, to evaluate the biophysical associations of tAD with the tissue morphology.

Methods

The MSC was extracted from a C57/BL6 mouse and fixed following the procedure in Ong et al.⁶. The sample was scanned on a Bruker Avance 400MHz spectrometer (B0=9.4T, max gradient strength=1.2 T/m; rise time=100 µs) along three orthogonal directions, selecting axial slices at the lumbar and thoracic levels. Diffusion weighted images (DWIs) were acquired with Pulsed Gradient Stimulated Echo (PGSTE) sequences (Fig. 1). DWIs were denoised⁷ to minimize noise-bias by means of MRtrix3 software (http://www.mrtrix.org/). FSL 5.0 DTIFIT routine⁸ was used to measure mean diffusivity (MD), fractional anisotropy (FA), axial (Dpar) and radial (Dort) diffusivity. γ-imaging and α-imaging parameters (mean-γ=Mγ, axial-γ=γpar, radial-γ=γort, γ-anisotropy=Aγ, and Mα, αpar, αort and Aα, computed similarly to DTI) were extracted, by fitting echo attenuation $$$S(q,\triangle)$$$, where q is the wave vector, to models $$$S(q)=A\cdot\exp(-D_{gen}q^{\gamma}\triangle)+c$$$, and $$$S(\triangle)=A\cdot\exp(-D_{gen}q^{2}\triangle^{\alpha})+c$$$ (Dgen=generalized diffusion constant; c=offset). QSI parameters were extracted using the low-q-value approximation (d_ics and d_ecs represent mean displacements in the intra- and extra-cellular spaces) and fitting the Fourier Transform of the normalized signal to a Lorentzian curve (L_ics, proportional to its FWHM)⁵. After MRI the MSC was prepared for histology⁹: 1.5 µm-sections cut at the lumbar and thoracic levels were analyzed with a Zeiss Axioskop light microscope. Axon diameter $$$d_{ax}=2\cdot\sqrt{A/\pi}$$$, where A is the area of an equivalent circle⁶, standard deviation of the axons distribution (SD_ax), effective local axonal density (eld)¹⁰ were measured by means of a custom-made MATLAB script (MATLAB R2016a, The MathWorks, Inc., Natick, Massachusetts, United States), performing 2D-object recognition with selection rules in chosen regions of interest (ROI). The relation between diffusion-micro-MRI parameters and morphologic measures was assessed via Pearson’s linear correlation, rejecting the null hypothesis for P<0.05. All the analyses and computations were performed in MATLAB.

Results

SNR of the denoised images tripled compared to the raw data without significant blurring (Fig. 2). The diffusion-micro-MRI techniques provide different contrasts for MSC-wm (Fig. 3). The morphologic characteristics extracted from histology (Fig. 4) agree well with literature (R²=0.92, P<0.005 for d_ax; R²=0.71, P<0.05 for SD_ax; R²=0.73, P<0.05 for eld). The correlations between diffusion-micro-MRI parameters and the morphology are illustrated in Fig. 5: γ-imaging parameters show the strongest associations with d_ax, SD_ax and eld. None of DTI parameters were found to correlate significantly with SD_ax. Among the α-imaging parameters, axial-α considerably decreases with SD_ax, while radial-γ, as well as QSI-parameters, decrease with eld.

Discussion

The increase of Dort, d_ics and L_ics with d_ax corresponds to literature^5,11. γ-imaging parameters increasing with axon diameter could be due to a progressive dispersion of microtubules and neurofilaments inside the axolemma, reducing the spatial variations in magnetic susceptibility encountered by water molecules during their motion. The decrease of axial-α with SD_ax replicates in vitro and in vivo results^3,12, and it could be the effect of a more pronounced structural disorder in the longitudinal direction, due to axonal varicosities¹². In distinction to standard axonal density, effective local axon density (eld) is not based on axon count, rather on axon neighborhood, considering axon-free regions¹⁰. γ- and QSI-imaging parameters depend on eld, a measure sensitive to aging, as shown in animal studies¹⁰. The ability of diffusion-micro-MRI parameters to mirror the morphology of MSC-wm tracts has clinical potential. In fact both physiologic and pathologic wm degradation translates into alterations of wm morphometry and topology^10,13.

Conclusion

Results reported here provide potentially useful information to elucidate the biophysical meaning of tAD parameters. tAD-micro-MRI and QSI outperform DTI as a means to probe MSC-wm morphology, and have the potential to assess wm tissue integrity.

Acknowledgements

AC, GBB and SC thank A. Gabrielli and J.R. Santos for the interesting discussions concerning effective local density.