Introduction

The structure-function relationship in peripheral nerves has been delineated¹, but proves more challenging for axons of the intact central nervous system. The axon diameter (AD) is one variable that affects the conduction velocity (CV), and is therefore interesting to capture non-invasively with MRI. However, MRI is not sensitive to the smallest diameters^2,3, but limited to representing only the larger ones, and does therefore not show the whole picture.
Here, we aim to investigate the structure-function relationship via AD estimation with diffusion-weighted MRI (dw-MRI) and transmission electron microscopy (TEM) and relating these metrics to latencies from optogenetically evoked local field potentials (LFP) of the transcallosal fibers between the primary motor cortices (M1) in rats.

Methods

Surgery
Young male Sprague-Dawley rats were injected with a viral inoculum (AAV5::CaMKIIa−hChR2(H134R)−EYFP) and implanted with an optic fiber in Layer 2/3 of right M1. A stereotrode was implanted at the same depth of the contralateral M1⁴.

Electrophysiological recordings
Transcallosal conduction time (TCT) was estimated from optogenetically evoked responses in M1 after optogenetic stimulation in the contralateral homotopic area⁴. We used the latency of the first positive peak (P1) from the LFP signal as indicative of TCT (fig.1).

For verification, the stimulated transcallosal projection region was revealed with fluorescence light microscopy of a midsagittal section with histology. The pathway length between the bilateral M1s and through the projection region was measured using tractography (fig.2a). Whole-brain ex vivo diffusion weighted MRI (dw-MRI) data were collected with isotropic voxel size (125 µm; 20 axial slices) using a single shell with b-value of 4000 s/mm² (G = 224 mT/m; ∆ = 23 ms; ∂ = 7.5 ms), 61 isotropically distributed non-collinear directions from the Camino tool box⁵. Scans were acquired with echo time (TE) = 38.6 ms and repetition time (TR) = 3592 ms.

The CV was calculated as CV = TCT/Length, which could be used to infer on the corresponding AD through the following relation⁶: $$$\text{CV} = (5.5/g) \cdot d$$$, with d being the inner AD, and assuming a constant g-ratio (g) of 0.7 for CNS^7,8.

Measuring ADs from TEM
Tissue punctures from a midsagittal area were Epon-embedded⁹ (fig.4a) and then sectioned for TEM. TEM images were obtained at x4200 magnification of the M1 callosal projection region (fig.4b). The inner ADs were automatically segmented using AxonDeepSeg¹⁰ (fig.4c), obtaining an AD distribution (ADD) (fig.4d).

AD estimation with dwMRI
A pulsed gradient spin echo (PGSE) protocol was acquired for AD estimation with parameters: gradient strengths G = [500, 550, 590] mT/m, gradient separation ∆ = 18 ms and gradient duration ∂ = 8 ms. It was applied along 50 isotropically distributed directions and gave three unique b-values, b = [17840, 21558, 24783] s/mm². These b-values are high enough to suppress contributions from the extra-axonal space¹¹, and the SMT-3 model¹² could thus be fitted to the powder averaged signal to obtain AD. The intrinsic ex vivo diffusivity was assumed to be $$$D_0 = 0.6 \cdot 10^{-9} \text{m}^2\text{/s}$$$. Voxel values of mean AD above 0.5 µm (1 value excluded) were extracted from a manually drawn ROI in the projection ROI.

Sensitivity simulation
To assess the lower bound of measurable diameter, the sensitivity profile to AD (fig. 2b) of this dw-MRI acquisition was calculated¹². The signals from cylinders were analytically generated for diameters between 0.2 µm and 15.0 µm. Rician noise with a signal-to-noise ratio (SNR) of 100 was added to the signals and the SMT-3 model was fitted to obtain a diameter estimate.

Results and Discussion

The median TCT was 5.6 ms with 0.3 ms mean standard deviation within animals and 1.49 ms between animals. Such latency corresponds to a predicted axon diameter of 0.25 ± 0.09 µm (fig.3)

The ADD segmented from TEM images is shown in fig. 4d along with the gamma-fitted distribution (a = 5.122, b = 0.105). The ADD has a mode of 0.43 µm (mean = 0.54 µm; var = 0.06; skew = 0.88), with few axons being larger than 1.5 µm.

The ADs predicted from the electrophysiological experiments corresponded to the smaller axons up to the mode of the ADDs from histology. These recordings were thus not sensitive to detect latencies corresponding to the larger axons, which might even be underestimated due to shrinkage induced through tissue processing¹³.

With dw-MRI we also estimated the mean volume-weighted ADs in the projection region revealed by tractography between the bilateral M1s, stimulated with optogenetics (fig.5a).

dw-MRI was mainly sensitive towards the larger axon diameter population, not captured with our electrophysiological recordings and only sparsely with histology. The latter might be limited by the FOV to robustly represent the low density of larger axons. The obtained mean ADs from dw-MRI are however all below the lower-bound of about 3.0 µm (fig.5b), indicating that they are likely underestimated, when taking the simulated sensitivity profile (fig.2b) into account.

Conclusion

All modalities (electrophysiology, TEM and dw-MRI) showed large variability and sensitivity. The mode of the ADD measured from TEM corresponds with the AD predicted from the latency of electrophysiology, but not the larger axon population for which dw-MRI appears sensitive towards. Future studies should choose modalities having sensitivity profiles suitable for observing the functional and structural ranges of interest.

References

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