# Along-axon diameter variation and axonal orientation dispersion revealed with 3D electron microscopy: implications for quantifying brain white matter microstructure with histology and diffusion MRI

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## Abstract

Tissue microstructure modeling of diffusion MRI signal is an active research area striving to bridge the gap between macroscopic MRI resolution and cellular-level tissue architecture. Such modeling in neuronal tissue relies on a number of assumptions about the microstructural features of axonal fiber bundles, such as the axonal shape (e.g., perfect cylinders) and the fiber orientation dispersion. However, these assumptions have not yet been validated by sufficiently high-resolution 3-dimensional histology. Here, we reconstructed sequential scanning electron microscopy images in mouse brain corpus callosum, and introduced a random-walker (RaW)-based algorithm to rapidly segment individual intra-axonal spaces and myelin sheaths of myelinated axons. Confirmed by a segmentation based on human annotations initiated with conventional machine-learning-based carving, our semi-automatic algorithm is reliable and less time-consuming. Based on the segmentation, we calculated MRI-relevant estimates of size-related parameters (inner axonal diameter, its distribution, along-axon variation, and myelin *g*-ratio), and orientation-related parameters (fiber orientation distribution and its rotational invariants; dispersion angle). The reported dispersion angle is consistent with previous 2-dimensional histology studies and diffusion MRI measurements, while the reported diameter exceeds those in other mouse brain studies. Furthermore, we calculated how these quantities would evolve in actual diffusion MRI experiments as a function of diffusion time, thereby providing a coarse-graining window on the microstructure, and showed that the orientation-related metrics have negligible diffusion time-dependence over clinical and pre-clinical diffusion time ranges. However, the MRI-measured inner axonal diameters, dominated by the widest cross sections, effectively decrease with diffusion time by ~ 17% due to the coarse-graining over axonal caliber variations. Furthermore, our 3*d* measurement showed that there is significant variation of the diameter along the axon. Hence, fiber orientation dispersion estimated from MRI should be relatively stable, while the “apparent” inner axonal diameters are sensitive to experimental settings, and cannot be modeled by perfectly cylindrical axons.

## Keywords

3*d*electron microscopy Axonal diameter variation 3

*d*axon segmentation Corpus callosum Fiber orientation distribution Axonal diameter distribution

*g*-Ratio Diffusion coarse-graining Diffusion time-dependence

## Notes

### Acknowledgements

We would like to thank the NYULH DART Microscopy Lab Alice Liang, Kristen Dancel-Manning and Chris Patzold for their expertise in electron microscopy work, Kirk Czymmek and Pal Pedersen from Carl Zeiss for their assistance of 3*d* EM data acquisition, and Marios Georgiadis for the discussion of the myelin structure change caused by tissue preparations. It is also a pleasure to thank Markus Kiderlen from Aarhus University and Valerij Kiselev from University Medical Center Freiburg for a discussion on the relation between 2-dimensional and 3-dimensional axonal dispersions; Markus Kiderlen has also kindly provided the reference on the relation between the Steiner compact and the cosine transform of the FOD discussed in Appendix C. Jelle Veraart is a Postdoctoral Fellow of the Research Foundation - Flanders (FWO; grant number 12S1615N). Research was supported by the National Institute of Neurological Disorders and Stroke of the NIH under award number R21 NS081230 (Fieremans, E., Novikov, D. S., and Kim, S. G.) and R01 NS088040 (Fieremans, E. and Novikov, D. S.), and was performed at the Center of Advanced Imaging Innovation and Research (CAI2R, http://www.cai2r.net), an NIBIB Biomedical Technology Resource Center (NIH P41 EB017183, Fieremans, E., Novikov, D. S., and Kim, S. G.).

### Funding

This study was supported by the National Institute of Neurological Disorders and Stroke of the NIH under award number R21 NS081230 (Fieremans, E., Novikov, D. S., and Kim, S. G.) and R01 NS088040 (Fieremans, E. and Novikov, D. S.), and was performed at the Center of Advanced Imaging Innovation and Research (CAI2R, http://www.cai2r.net), an NIBIB Biomedical Technology Resource Center (NIH P41 EB017183, Fieremans, E., Novikov, D. S., and Kim, S. G.).

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical approval

All procedures performed in studies involving animals were in accordance with the ethical standards of New York University School of Medicine. All mice were treated in strict accordance with guidelines outlined in the National Institutes of Health Guide for the Care and Use of Laboratory Animals, and the experimental procedures were performed in accordance with the Institutional Animal Care and Use Committee at the New York University School of Medicine. This article does not contain any studies with human participants performed by any of the authors.

### Informed consent

Not applicable.

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