Jelle Veraart^{1,2,3}, Daniel Nunes^{1}, Els Fieremans^{3}, Dmitry S. Novikov^{3}, and Noam Shemesh^{1}

Axon diameter mapping using diffusion MRI in the rat corpus callosum was validated using confocal microscopy with a staining for neurofilaments. When confounding factors such as extra-axonal water and dispersion are addressed, the effective MR axon radii are in good quantitative agreement with histology. However, using MRI, we are limited to the estimation of a single metric representing the entire distribution, which has shown to be dominantly sensitive to the largest axons in the voxel volume of interest.

Axon diameter mapping using diffusion MRI (dMRI) has been a highly
debated topic of research^{1,2}. Discrepancies between histology and dMRI-derived
axon diameters uncovered various confounding factors, e.g. dispersion^{3},
time-dependent extra-axonal diffusion^{4-7}, reduced signal attenuation due to long
diffusion gradient durations^{8,9}, and/or tissue shrinkage^{2}.
Hardware developments and following insights in biophysical modeling promote
the revival of MR axon diameter mapping. In particular, dMRI can become (a) specific to intra-axonal
signal in a high $$$b$$$ regime because the extra-axonal signal decays exponentially
fast^{10}; and (b) predominantly sensitive to the largest
axons^{4} of the underlying distribution because of a volume correction^{4,11}
and the $$$r^4$$$-scaling of the radial signal attenuation of restricted
diffusion inside a cylinder of radius^{5} $$$r$$$ when approaching the
Neuman’s limit^{9}.
A
previous study^{12 }measured human axon radii by evaluating the signal
scaling in an axon-specific $$$b$$$-regime.
The* in vivo *MR results were in good agreement with histological values
reported in literature^{13,14} after accounting for the tail-weighting.
Here, we validate the technique by comparing the MR-derived axon diameters directly
to confocal microscopy.

In the absence of any extra-axonal signal, the powder-averaged diffusion-weighted signal decays as $$\bar{S}(b)\,=\,e^{-bD_a^\perp}\frac{\sqrt{\pi}}{2}\frac{f}{\sqrt{D_a^\parallel}}\,b^{-1/2}\,+\gamma,$$

with
$$$\gamma$$$ a still water signal fraction^{15}, $$$f$$$ the
intra-axonal signal fraction, and $$$D_a^\perp$$$ and $$$D_a^\parallel$$$ the
intra-axonal radial and axial diffusivities, respectively. In each voxel, $$$D_a^\perp$$$
projects the axon radius distribution $$$P(r)$$$ onto a scalar “effective”
radius^{4,12} through the volume correction^{11} and a model of
restricted diffusion inside a cylinder^{5}:
$$r_\textrm{eff}\equiv\sqrt[4]{\langle\,r^6\,\rangle\,/\,\langle\,r^2\,\rangle}.$$

The intra-axonal parallel diffusivity^{16} serves here as a proxy for
the intrinsic diffusivity $$$D_0$$$.

** Samples: **Animal
experiments, preapproved by the institutional and national authorities, were
carried out according to European Directive 2010/63. Three Long Evans rats (Female,
12-weeks-old) were transcardially perfused using 4% paraformaldehyde. The
extracted brains were kept 24$$$h$$$ in 4% paraformaldehyde and washed out
using PBS during two days (changed daily).

** MRI:**
The
samples were scanned on an 16.4T MR scanner (Bruker BioSpin) with
$$$\Delta/\delta\,=\,20/7.1\,\mathrm{ms}$$$ interfaced with an AVANCE
IIIHD console and a micro2.5 imaging probe with maximal gradient amplitude $$$G\,=\,1500\,\mathrm{mT/m}$$$.
Diffusion-weighting was applied using a RARE sequence in the midsagittal plane along
60 gradient directions for a densely sampled spectrum of $$$b$$$-values up to
$$$100\,\mathrm{ms/\mu\,m^2}$$$. Furthermore, $$$\mathrm{TR/TE}\,=2400/30.4\,\mathrm{ms}$$$
and the spatial resolution was $$$100\,\times\,100\times\,850\,\mathrm{\mu\,m}^3$$$.
The
spherically-averaged signals were estimated per $$$b$$$-value using a Rician maximum
likelihood estimator of the spherical harmonic coefficients. We subtracted the
independently estimated (cf. Ref. 17) $$$\gamma$$$ to isolate the
intra-axonal signal.

** Microscopy:** A Zeiss LSM 710 laser scanning confocal
microscope was used for immunohistochemistry image acquisition. A tile scan
using a 10 objective (EC Plan Neofluar, numerical aperture$$$\,=\,0.3,$$$
Zeiss, Germany) was used to cover the Corpus Callosum (CC) (Fig. 1(b)).
Afterwards, 4 ROIs were imaged using a 63 immersion objective (Plan Apochromat,
numerical aperture$$$\,=\,1.4$$$, Zeiss, Germany) in confocal mode, with spatial
resolution of $$$65\times\,65\times\,150\mathrm{nm^3}$$$ and field-of-view of
$$$135\times\,135\mu\,m^2$$$ (Fig. 1(c)). Axons were identified using a neurofilament
staining. The long axes of fitted ellipsoids served as proxies for the
respective axon diameters.

** Accuracy assessment:** The accuracy
of the axon diameter mapping is computed as a function of $$$r$$$ and for the
axon radius distributions extracted from histology (Fig.$$$\,5$$$) using a
simulation framework using the matrix formalism for diffusion signal
attenuation within fully restricted cylinders with our sequence timings18
(Fig.$$$\,2$$$). Errors $$$<25\%$$$ for large $$$r$$$ that are associated to
the missing higher-order terms in Van Gelderen’s model set an upper bound on
the achievable accuracy.

** Experimental validation
of axon diameter mapping: **A visual assessment of the CC-averaged signal
decays in all three samples highlight the apparent deviations from the power law scaling, thereby demonstrating
sensitivity of dMRI signals to the radial intra-axonal signal in this experimental
regime (Fig.$$$\,3$$$). The CC-averaged effective MR radii are highly
consistent across all samples ($$$\hat{r}_\textrm{eff}$$$
in Fig.$$$\,4$$$), with the maps being in good agreement with previously
reported trends of larger axons in the body of the CC in comparison to the genu
and splenium (Fig.$$$\,4$$$). Mesoscopic fluctuations dominate the inter-subject variability.
The quantitative
comparison of the MR- and microscopy-derived effective radii in four locations
of the CC shows differences up to $$$20\%$$$, in agreement with the accuracy
assessment of the simulations (Fig.$$$\,5$$$).

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