Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

Abstract

Mapping tissue microstructure accurately and noninvasively is one of the frontiers of biomedical imaging. Diffusion Magnetic Resonance Imaging (MRI) is at the forefront of such efforts, as it is capable of reporting on microscopic structures orders of magnitude smaller than the voxel size by probing restricted diffusion. Double Diffusion Encoding (DDE) and Double Oscillating Diffusion Encoding (DODE) in particular, are highly promising for their ability to report on microscopic fractional anisotropy (µFA), a measure of the pore anisotropy in its own eigenframe, irrespective of orientation distribution. However, the underlying correlates of µFA have insofar not been studied. Here, we extract µFA from DDE and DODE measurements at ultrahigh magnetic field of 16.4T with the goal of probing fixed rat spinal cord microstructure. We further endeavor to correlate µFA with Myelin Water Fraction (MWF) derived from multiexponential T 2 relaxometry, as well as with literature-based spatially varying axon diameter. In addition, a simple new method is presented for extracting unbiased µFA from three measurements at different b-values. Our findings reveal strong anticorrelations between µFA (derived from DODE) and axon diameter in the distinct spinal cord tracts; a moderate correlation was also observed between µFA derived from DODE and MWF. These findings suggest that axonal membranes strongly modulate µFA, which-owing to its robustness toward orientation dispersion effects-reflects axon diameter much better than its typical FA counterpart. µFA varied when measured via oscillating or blocked gradients, suggesting selective probing of different parallel path lengths and providing insight into how those modulate µFA metrics. Our findings thus shed light into the underlying microstructural correlates of µFA and are promising for future interpretations of this metric in health and disease.

Single‐ and double‐Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

“…Note also that recent studies demonstrated that using oscillating gradients rather than Stejskal&Tanner type pulse gradients increase the sensitivity of DDE MRI towards small axons and consequently also improves the agreement between MRI and histology. [92][93][94][95] It should be noted, however, that to achieve the size resolution obtained in the present paper it is important to use strong gradients and have high SNRs. 54,82,83,95…”

A simple estimate of axon size with diffusion MRI

“…Some recent studies have also characterized the distribution of axon diameter as a single representative value ( Veraart et al, 2020 ), while other recent studies have looked to estimate the distribution of axon diameters ( Anaby et al, 2019 ; Romascano et al, 2020 ). Since intra- and extra-axonal water diffusion is sensitive to different measures of axon diameter (see the Appendix ), and given the near linear dependence of Δ D e⊥ on axon size and the near quadratic dependence of Δ D i⊥ , it may be possible to incorporate multiple oscillating gradient, pulsed gradient and/or double diffusion encoding schemes to estimate parameters like the variance of the axon diameter distribution, extra-axonal volume fraction, and/or g-ratio, ( Ianu et al, 2017 ; Kakkar et al, 2018 ; Shemesh, 2018 ). We note that, in some regions of white matter, the distribution of axon diameter may not be well represented by the log-normal distribution used in this and previous studies, and the single-parameter measure for diameter may break down in tissues with axon diameter distributions that are multimodal.…”

Rapid Microscopic Fractional Anisotropy Imaging via an Optimized Kurtosis Formulation

“…By ignoring the third and higher order cumulant terms in deriving equations (4) and (5), μA can be estimated from a single b-shell, reducing scan time; however, ignoring the higher cumulants comes with the cost of potentially introducing a bias to the measurement (Shemesh, 2018). μFA can then be expressed in terms of μA by substituting equation (8) into equation (7):…”

“…Using equation (1) up to the second cumulant term, the powder-averaged linear and mean isotropic signals can be represented as: If it is assumed that the only sources of kurtosis are dispersion in pore size and orientation, then the diffusion coefficient D will be equal between LTE and STE (Szczepankiewicz et al, 2015). By assuming D is the same between LTE and STE signals acquired at the same b-value, Equations (4) and (5) can be substituted into equation (3) to provide an estimate of the scaled difference in variance that notably does not depend on the non-diffusion weighted signal S 0 : Substituting equation (6) into equation (1) provides an estimate of the μFA (Nery et al, 2019): Microscopic anisotropy is defined here based on the difference in signal between linear and isotropic dMRI acquisitions, similar to the equation used in DDE protocols (Ianuş et al, 2018): By ignoring the third and higher order cumulant terms in deriving equations (4) and (5), μA can be estimated from a single b-shell, reducing scan time; however, ignoring the higher cumulants comes with the cost of potentially introducing a bias to the measurement (Shemesh, 2018). μFA can then be expressed in terms of μA by substituting equation (8) into equation (7): …”