Synopsis

In this study, we segmented large axons from high resolution 3D synchrotron images of the monkey splenium. We simulate the intra-axonal MRI diffusion signal of both the segmented geometry and a simplified, corresponding cylindrical geometry, and calculate the corresponding axon diameter indices. The axon diameter index is well estimated in the simplified geometry, but is overestimated in the more complex segmented geometry, potentially due to variations in axon diameter and non-uniform trajectories. Lastly, we present the observation that segmented axons, which all have average diameters >2 µm, seem to experience similar absolute diameter variations.

Introduction

The diameter of a myelinated axon modulates its conduction speed ¹. Diameters and densities of axons in white matter are thus indicators of brain performance, and a better understanding of how these properties compare in healthy/diseased conditions is important. Diffusion magnetic resonance imaging (MRI) provides non-invasive 3D insight into live brain microstructure. By designing biophysical models of the tissue architecture, axon diameter distributions (ADD) and densities can be estimated. These models e.g. ActiveAx ^{2, 3} and AxCaliber ⁴, often represent axons as parallel, straight cylinders with a distribution of diameters. Axon diameters are commonly overestimated by diffusion MRI when compared to histology and electron microscopy (EM) ^{3, 5}, potentially due to both microstructural and mesoscopic effects e.g. diameter variations and non-parallel axons. To improve axon diameter and density estimates with diffusion MRI, knowledge concerning realistic axon morphologies is required. EM has high in-plane resolution, but suffers from long acquisition times, small field of view (FOV) and damage to tissue when slicing samples to obtain 3D volumes. Synchrotron radiation imaging (SRI) offers a non-destructive, high-resolution, large-FOV, 3D alternative.

In this study, we image samples from the corpus callosum of a monkey brain, previously studied with ActiveAx ², with SRI. We segment large axons and observe axon diameter variation along a length of 150 µm. Furthermore, we compute the diffusion weighted (DW) signal arising from 1) the segmented axons and 2) a simplified substrate consisting of parallel cylinders. From these signals, we calculate an axon diameter index, $$$a’$$$.

Methods

Synchrotron Imaging

Splenium samples from a 32-month old female perfusion fixed Vervet monkey brain ² were stained with 0.5% osmium tetroxide (OsO4) to give contrast to the myelin and embedded in EPON. X-ray phase contrast tomography (PCT) was performed on the samples at beamline ID16A of the European Synchrotron Research Facility (ESRF). The PCT produced 75 nm isotropic resolution 3D volumes (2048³ voxels), with a cylindrical FOV of diameter and length 150 µm with an acquisition time of ~4h.

Segmentation

Large axons were roughly segmented in ITK-Snap. The axons were then automatically segmented by feeding their centerlines into a layered surface segmentation method that we have developed at the Technical University of Denmark and which detected axon-myelin boundaries. Manual correction was performed where needed. 54 meshes of axons longer than 110 µm were generated from the segmentations.

Simulations

Two substrates were used for simulations: 1) the 54 segmented axons and 2) 54 parallel cylinders with diameters equal to the average diameters of the corresponding segmented axons. The diffusion-weighted (DW) signals from these were simulated using an in-house Monte Carlo Simulator ⁶. The ex-vivo diffusivity was set to 0.6$$$\cdot$$$10^-9 m²/s and the optimised ActiveAx 3-shell protocol described in ² was employed.

Model Fitting

The simulated signals were fitted to a straight cylinder model with a Grid Search (GS) approach. We used the Camino toolkit ⁷ to generate DW signals from cylinders with diameters between 0.20 µm – 8.00 µm at intervals of 0.05 µm. These bounds were chosen to reflect the expected axon diameter range in the splenium of the monkey corpus callosum. The GS reported the axon diameter index ², $$$a'$$$, which was the diameter of the cylinder whose signal was most similar (minimum mean-squared-error) to that of the simulated DW signal.

Results and Discussion

Figure 1 shows the diameter variations and trajectories of some axons in a sample from the monkey splenium. In Figure 2, we see that axon diameters and trajectories can vary considerably along a single axon, and that the straight cylinder model is not representative of the real axon morphology. Furthermore, we see that the quoted diameter is dependent on the diameter quantification method.

The diameter variation along axons was studied by normalizing all 54 axon diameter distributions and subtracting the respective median diameters. Although the axons had average diameters varying between 2.1 µm to 4.1 µm, Figure 3(a) surprisingly seems to suggest that they all experience similar diameter variations, regardless of diameter.

Figure 3(b) shows the average axon diameter distribution of the segmented axons. The volume-weighted mean axon diameter was 3.0 µm. For the axon segmentation, $$$a’$$$ was estimated to be 3.6 µm. This over-estimation is potentially caused by the diameter variations and non-straight trajectories present in the true, segmented axons. For the less complex simplified cylindrical substrate, $$$a’$$$ was estimated to be 2.9 µm, closely agreeing with the true mean axon diameter.

Conclusion

Synchrotron imaging enables super high resolution 3D reconstruction of axon geometries in a large field of view. The subsequent analysis of the segmentations can be used to increase our understanding of axon morphology and potentially develop improved biophysical models for microstructure imaging with diffusion MRI.

Acknowledgements

References

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