Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

Abstract

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T₂ and T₁ times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T₁-T₂ relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm²) and multiple inversion and echo times. A second reduced diffusion-T₂ dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement.

Keywords: T1 relaxation; T2 relaxation; axon radius; brain; diffusion MRI; histology.

FIGURE 1

Transmission electron micrograph of a myelinated axon (adapted) illustrating the employed relaxation model for the intra-axonal space, composed of two pools (arbitrarily colored in green and red for illustrative purposes) in fast exchange (Zimmerman and Brittin, 1957). This model is equivalent to the Brownstein and Tarr (1977) model in the fast diffusion limit. The structured water (Le Bihan, 2007) adjacent to the inner axon surface (red) has a shorter T₂ than the cytoplasmic water (green). As the cytoplasmic water (i.e., axoplasm) interacts with large proteins, organelles, and cytoskeletal elements (LoPachin et al., 1991; Beaulieu, 2002), its T₂ is shorter than pure water. An equivalent model was assumed for the T₁ relaxation. [This transmission electron micrograph was deposited into the public domain by the Electron Microscopy Facility at Trinity College]. This is a file from the Wikimedia Commons, a collection of freely usable media files, under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation (Source: https://en.wikipedia.org/wiki/File:Myelinated_neuron.jpg). This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license (CC BY-SA 3.0). Any copy and remix of the original file must be distributed under the same or compatible license as the original.

FIGURE 2

Orientation-averaged spherical mean signals for each pair of TE and TI (TE, TI) in ms. These images were used to fit the diffusion-relaxation model in Eq. (5).

FIGURE 3

Anatomical location of the two independent histological samples of the first histological dataset (Histology1 and Histology2) taken from eleven regions of interest (ROIs) in the Corpus Callosum. The number of studied axons per sample and ROI are reported for each case. The second sample (Histology2) consisted of axons not included in the first sample (Histology1).

FIGURE 4

Axial slices of the $T_2^a$, $T_1^a$, and K maps estimated from the in vivo diffusion-T₁-T₂ relaxation MRI data in native space (i.e., before registering the images to the reference T1w image). Note that the intra-axonal relaxation times are only meaningful in the white matter because the assumptions underlying the estimation method are invalid in gray matter or CSF. The values of K (in arbitrary units) are higher in the white matter because this parameter is proportional to the intra-axonal volume. We highlight two regions with different intra-axonal relaxation times: the genu of the Corpus Callosum and the corticospinal tract (CST).

FIGURE 5

Linear fitting of the inverse of the intra-axonal T₂ times (y-axis) estimated from the in vivo diffusion-T₁-T₂ MRI data to the inverse of the inner axon radius (x-axis) measured from the first histological sample (Histology1) of the first histological dataset. The scatter plot depicts the mean values computed for all the voxels inside four corpus callosum (CC) regions of interest, corresponding to ROI2, ROI5, ROI8, and ROI10 in the Histology1 sample. The number of axons sampled for each CC ROI is displayed in the legend. The intercept and slope of the regression line were 0.0079 ms^–1 and 0.00116, respectively. The slope of the regression line was significantly different from zero (p = 0.030).

FIGURE 6

Linear fitting of the effective histological radius estimated from the second histological sample (Histology2) of the first histological dataset to the predicted radius from the intra-axonal T₂ times, calculated from the in vivo diffusion-T₁-T₂ MRI data. The scatter plot depicts the mean values computed for all the voxels inside the eleven corpus callosum (CC) regions, corresponding to ROI0-ROI10. The number of axons sampled for each CC ROI is displayed in the legend. The slope of the regression line was significantly different from zero (p = 0.022).

FIGURE 7

Linear fitting of the inverse of the intra-axonal T₁ times (y-axis) estimated from the in vivo diffusion-T₁-T₂ MRI data to the inverse of the inner axon radius (x-axis), measured from the first histological sample (Histology1) of the first histological dataset. The scatter plot depicts the mean values computed for all the voxels inside four corpus callosum (CC) regions, corresponding to ROI2, ROI5, ROI8, and ROI10. The number of axons sampled for each CC ROI is displayed in the legend. The intercept and slope of the regression line were 0.0011 and 0.000087. The p-value for the slope was not statistically significant (p = 0.23).

FIGURE 8

Linear fitting of the effective histological radius determined in the second histological sample (Histology2) of the first histological dataset to the predicted radius from the intra-axonal T₁ times estimated from the in vivo diffusion-T₁-T₂ MRI data. The scatter plot depicts the mean values computed for all the voxels inside the eleven corpus callosum (CC) regions, corresponding to ROI0-ROI10 in the Histology2 sample. The number of axons sampled for each CC ROI is displayed in the legend. The slope of the regression line was significantly different from zero (p = 0.039).

FIGURE 9

Predicted axon radius from intra-axonal T₂ times estimated from the in vivo diffusion-T₂ MRI data for the eleven ROIs (ROI0-ROI10) of the Histology2 sample. Additionally, as a reference, the mean effective histological radius calculated from the three histological samples (Histology1, Histology2, and Histology3) is also reported. Although the number and location of the ROIs used in the Histology3 sample differ from those employed in the Histology1-Histology2 samples, they can be regrouped to cover similar anatomical areas (see subsection “Histological samples” for more details). The histological and T₂-based radii follow the expected “low-high-low” trend in axon radii. The axon radii from the Histology1-Histology2 samples are consistently higher (about 25%) than those in the Histology3 sample.

FIGURE 10

Axial and sagittal slices of the T₂-based inner axon radius for the three scanned subjects. Subject3 underwent two scans, with scan2 (46 slices) and scan1 (10 slices) representing the in vivo diffusion-T2 and diffusion-T1-T2 MRI data, respectively. All maps were normalized to the reference T1w image, where the histological CC ROIs were defined, and the predicted radii were plotted over the reference image. A white matter mask was used to suppress voxels in gray matter or cerebrospinal fluid.