Mariam Andersson^{1,2}, Jonathan Rafael-Patino^{3}, Hans Martin Kjer^{1,2}, Vedrana Andersen Dahl^{1}, Alexandra Pacureanu^{4}, Martin Bech^{5}, Anders Bjorholm Dahl^{1}, Jean-Philippe Thiran^{3,6}, and Tim B. Dyrby^{1,2}

^{1}Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark, ^{2}Danish Research Centre for Magnetic Resonance, Hvidovre, Denmark, ^{3}Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, ^{4}The European Synchrotron, Grenoble, France, ^{5}Department of Medical Radiation Physics, Clinical Science, Lund University, Lund, Sweden, ^{6}Radiology Department, Centre Hospitalier Universitaire Vaudois and University of Lausanne, Lausanne, Switzerland

We extract the orientation dispersion (OD) and 3D axon diameter variations of long axons (>100 *µ*m) from an ultra-high resolution, synchrotron X-ray nano-holotomography (XNH) scan of the monkey splenium. From this, we discover a relationship between mean axon diameter and along-axon diameter variations. Monte Carlo simulations are then performed on the intra-axonal spaces (IAS) of different substrates which inherit their morphological features from the segmented axons. These simulations show that the OD significantly affects the transverse apparent diffusion coefficient (ADC_{⟂}) of the axon substrate at diffusion times up to 50 *m*s, while diameter variations do not.

The equivalent diameters of axons were quantified every 150

Three substrates (S) were generated for simulations (as in Figure 3): S1) 54 parallel cylinders, S2) 54 cylinders with orientation dispersion and S3) 54 tubes with OD and diameter changes. The average axon diameters, OD and diameter changes present in the substrates matched the corresponding measurements in each of the 54 XNH-segmented axons. An in-house Monte Carlo simulator

$$\lambda^2_\bot = 2 \cdot \text{ADC}_{\bot} \cdot D_t$$

where $$$\lambda^2_\bot$$$ is the root-mean-square displacement in the transverse direction and $$$D_t$$$ is the diffusion time. The average ADC

$$\lambda^2_\bot =\frac{1}{2} (\frac{D}{2})^2$$

1. Hursh, J. B. Conduction Velocity And Diameter Of Nerve Fibres. American Journal of Physiology-Legacy Content. 1939; 127:131–139.

2. Alexander, D. C. et al. Orientationally invariant indices of axon diameter and density from diffusion MRI. Neuroimage. 2010; 52:1374–1389.

3. Dyrby, T. B., Søgaard, L. V., Hall, M. G., Ptito, M. & Alexander, D. C. Contrast and stability of the axon diameter index from microstructure imaging with diffusion MRI. Magn. Reson. Med. 2013; 70:711–721.

4. Assaf, Y., Blumenfeld-Katzir, T., Yovel, Y. & Basser, P. J. AxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magn. Reson. Med. 2008; 59:1347–1354.

5. Barazany, D., Basser, P. J. & Assaf, Y. In vivo measurement of axon diameter distribution in the corpus callosum of rat brain. Brain. 2009; 132:1210–1220.

6. Caminiti, R., Ghaziri, H., Galuske, R., Hof, P. R. & Innocenti, G. M. Evolution amplified processing with temporally dispersed slow neuronal connectivity in primates. Proceedings of the National Academy of Sciences. 2009; 106:19551–19556.

7. Aboitiz, F., Scheibel, a. B., Fisher, R. S. & Zaidel, E. Fiber composition of the human corpus callosum. Brain Res. 1992; 598:143–153.

8. Andersson M, Kjer HM, Rafael-Patino J, Andersen Dahl V, Pacureanu A, Thiran JP, Bech M, Bjorholm Dahl A, and Dyrby T. Uncovering 3D Axonal Morphologies with Synchrotron Imaging: Impact on Microstructure Imaging with Diffusion MRI. International Society for Magnetic Resonance in Medicine 27th Annual Meeting. 2019.

9. Abdollahzadeh, A., Belevich, I., Jokitalo, E., Tohka, J. & Sierra, A. Automated 3D Axonal Morphometry of White Matter. Sci Rep. 2019; 9:6084.

10. Lee, H.-H. et al. 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. Brain Struct. Funct. 2019; 224:1469–1488.

11. Lee H-H, Fieremans E, and Novikov D. Exploring the effect of varying axonal shape on the transverse diffusion inside EM-reconstructed axons using 3d Monte Carlo simulations. International Society for Magnetic Resonance in Medicine 27th Annual Meeting. 2019.

12. Rafael-Patino, J. et al. Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the substrate complexity and parameter choice on the reproducibility of results. arXiv [physics.med-ph]. 2019.

13. Vangelderen, P., Despres, D., Vanzijl, P. C. M. & Moonen, C. T. W. Evaluation of Restricted Diffusion in Cylinders. Phosphocreatine in Rabbit Leg Muscle. J. Magn. Reson. B. 1994; 103:255–260.