In vivo measurement of axon diameter distribution in the corpus callosum of rat brain

Abstract

Here, we present the first in vivo non-invasive measurement of the axon diameter distribution in the rat corpus callosum. Previously, this measurement was only possible using invasive histological methods. The axon diameter, along with other physical properties, such as the intra-axonal resistance, membrane resistance and capacitance etc. helps determine many important functional properties of nerves, such as their conduction velocity. In this work, we provide a novel magnetic resonance imaging method called AxCaliber, which can resolve the distinct signatures of trapped water molecules diffusing within axons as well as water molecules diffusing freely within the extra-axonal space. Using a series of diffusion weighted magnetic resonance imaging brain scans, we can reliably infer both the distribution of axon diameters and the volume fraction of these axons within each white matter voxel. We were able to verify the known microstructural variation along the corpus callosum of the rat from the anterior (genu) to posterior (splenium) regions. AxCaliber yields a narrow distribution centered approximately 1 microm in the genu and splenium and much broader distributions centered approximately 3 microm in the body of the corpus callosum. The axon diameter distribution found by AxCaliber is generally broader than those usually obtained by histology. One factor contributing to this difference is the significant tissue shrinkage that results from histological preparation. To that end, AxCaliber might provide a better estimate of the in vivo morphology of white matter. Being a magnetic resonance imaging based methodology, AxCaliber has the potential to be used in human scanners for morphological studies of white matter in normal and abnormal development, and white matter related diseases.

Figure 1

MRI and histological analysis of the corpus callosum. A mid-saggital T₂-weighted MRI of the rat brain with an inset containing the corpus callosum. The corpus callosum is sectioned into five segments from which histological specimens were taken. For each segment a representative electron-microscopy image is given along with the corresponding ADD histogram. Note the difference in ADD along different areas of the structure.

Figure 2

AxCaliber analysis of the rat corpus callosum. (A) A mid-saggital T₂-weighted MRI with an inset containing the ROI (B) and (C) FA and mean ADC maps of the same slice in (A) computed from DTI dataset. (D–F) The volume fractions of each of the AxCaliber components: CSF (D), hindered (E) and restricted/axonal (F). (G) Map of the ADC of the hindered component of AxCaliber. (H and I) Maps of the α and β parameters of the γ-distribution representing the computed ADD.

Figure 3

Axon diameter distribution analysis along the corpus callosum. A mid-saggital T₂-weighted MRI with five regions of interest outlined representing the five segments shown in Fig.1. Each region was consisted of 2 × 3 voxels. The computed ADD from AxCaliber for each voxel within each region is depicted at the bottom. Note the homogenous pattern of ADD within each region and the large differences between them. All ADDs are in the same proportion, the x-axis represents the axon diameters (from 0 to 6 μm) and the y-axis represents the probability (from 0 to 0.3).

Figure 4

Cluster analysis of the axon diameter distribution along the corpus callosum. (A) A mid-saggital T₂-weighted MRI with the AxCaliber clusters superimposed, enlarged at (B). (C) The AxCaliber averaged ADDs for the different clusters given in (A) and (B); note that the colours of the graphs match the clusters’ colours.

Figure 5

Cluster analysis of the axon diameter distribution for different rats (A–C). A mid-saggital T₂-weighted MRI with the AxCaliber cluster superimposed for three different rats. Note that the colours of the clusters for the three rats are matched. Also note the high similarity of the cluster pattern among the rats.

Figure 6

Comparison of AxCaliber with DTI. (A) The indexed DTI maps of the ADC, FA and longitudinal (λ₁) and radial diffusivities [(λ₂ + λ₃)/2] of the same rat shown in Figs 1–3. (B) Correlation between each of the DTI indices and AxCaliber's mean axon diameter (averaged from the computed ADD). Note that the correlations are relatively poor. The statistical significance in correlations was P < 0.00001).