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Large-scale analysis of brain cell morphometry informs microstructure modelling of gray matter
Marco Palombo1, Daniel C. Alexander1, and Hui Zhang1
1Centre for Medical Image Computing, University College London, London, United Kingdom

Synopsis

Diffusion-weighted MRI (dMRI) is a formidable technique for non-invasively characterizing brain microstructure. Biophysical modelling is often necessary to gain specificity to cellular structure. However, designing sensible biophysical models and appropriate dMRI acquisitions is challenging, especially for gray matter (GM), as little is known about typical values of relevant features of brain-cell morphology contributing to dMRI signal. This study addressed this unmet need: we analysed ~3,500 cells from mouse, rat, monkey and human brains to determine statistical distributions of 13 morphological features relevant to GM microstructure modelling. Illustrative examples demonstrate how this study can inform biophysical modelling.

Introduction

This work provides quantitative information on brain-cell structure essential to design sensible biophysical models of the diffusion-weighted MRI (dMRI) signal in gray matter (GM).

Given its sensitivity to the micrometer length scale, dMRI is a promising in-vivo technique for characterizing the brain microstructure. However, this sensitivity is indirect and biophysical modeling of the dMRI signal in the brain tissue is essential to quantify features of the cellular structure and gain specificity to their changes1-3. Therefore, to design sensible biophysical models and appropriate dMRI acquisitions, it is critical to identify which relevant microstructural features can be measured and what are their typical values.

While substantial effort has been made to answer these questions for white matter by finely characterizing the morphology of axons4-7, there is a lack of in-depth morphological analysis of brain-cell structures of relevance for GM.

Here we address this unmet need by estimating a comprehensive set of morphological features useful to GM microstructure modelling from reconstructions of microscopy data of ~3,500 cells from three species and demonstrate the relevance to biophysical modelling.

Methods

Dataset. We obtained three-dimensional reconstructions (SWC files) of 3,448 brain cells from http://neuromorpho.org, representative of eight cell types: microglia, astrocytes, pyramidal, granule, purkinje, glutamatergic, gabaergic and basket, from mouse/rat, monkey and human (all healthy controls).

Morphometric analysis. We measured 13 morphological features of interest for brain microstructure modelling, according to previous works8-18:

general features
  • BO: the degree of branching of cellular projections,
  • Nproj: the number of primary projections radiating from the soma,
  • Rdomain: the extent of the cellular domain;

soma features
  • Rsoma : the effective radius of soma,
  • ηsoma: the amount of soma surface covered by projection interfaces;

neurite features
  • <Rbranch>s: mean branch effective radius,
  • CVbranch: a measure of branch beading,
  • Lbranch: branch length,
  • S/Vbranch: branch surface-to-volume ratio,
  • <μODbranch>s: a measure of mean branch undulation,
  • <Rc>s: a measure of mean branch curvedness,
  • τbranch: a measure of branch tortuosity.

The reconstructions were analysed using custom scripts in matlab (Mathworks) exploiting functions from well validated suites (TREES19; Blender20; ToolboxGraph21), similarly to22.

Specifically, from the information in the SWC file, we separated the nodes/edges defining the neurites from those belonging to the soma (Fig.1). From the latter, we constructed the three-dimensional surface mesh of the soma to estimate the soma volume which is expressed in terms of the morphological feature Rsoma, as described in Tab.1 and Fig.2.

From the nodes/edges defining the neurites, we identified individual branches as parts of the cellular projections delimited by either branching or termination nodes (Fig.1). Each branch is comprised of straight cylindrical subsegments whose central lines define the corresponding curvilinear path, s (Fig.2). Given s, we computed all the neurite features as described in Tab.1.

Finally, we computed the general metrics considering the whole set of nodes/edges as described in Tab.1.

Results and Discussion

Morphological features’ reference values. A summary of the features’ typical values is in Tab.2. Besides <Rbranch>s, CVbranch, <μODbranch>s and τbranch, the other features showed wide ranges of values, suggesting high inter-/intra-species variability.

Comparing neuronal and glial morphology. Given the growing interest in differentiating neurons and glia, we also computed mean values across only neuronal and only glial cells, reported in Tab.2. We found that, compared to glia, neurons showed on average larger soma and cell domain and longer branches; smaller branching, branch curvedness, number of primary projections and projections coverage of soma surface; similar values for the remaining features.

We report the morphological features estimated for each cell type and species in Tab.3.

Implications for biophysical modelling. Here we provide a few illustrative examples demonstrating how this study can inform biophysical modelling. Neglecting exchange with the extracellular space, assuming intra-cellular diffusivity D=2.5 μm2/ms and considering a typical single diffusion encoding acquisition with gradient pulse duration/separation δ/Δ and diffusion time td≤60 ms, we can infer from Tab.2 that:

  • Restriction from soma can be significant. Given the low ηsoma, soma can significantly restrict molecular diffusion when (from25) 5Dtd≥Rsoma2, i.e. for td≥4 ms given Rsoma~7.2 μm. This supports previous findings9,12.

  • Restriction from cellular domain is likely negligible. It can only significantly restrict molecular diffusion when 5Dtd≥Rdomain2, i.e. for td≥130 ms given Rdomain≥40 µm, much longer than typical td used;

  • Impact of projections’ curvedness is likely negligible. It can be significant only when (from26) 2DΔ,2Dδ≥(<Rc>s)2, i.e. for Δ,δ≥580 ms given <Rc>s≥55 μm, much longer than typical times used. This supports previous finding12.

  • Impact of projections’ undulation can be significant. Since the estimated <μODbranch>s values match those simulated in14, we conclude that undulations can bias dMRI estimates of projections’ radius also in GM. However, <Rbranch>s~1.6 μm is anyway below the resolution limit of conventional dMRI measurements27.

  • Impact of branching is likely negligible. Given Lbranch~54 μm, the exchange between branches is negligible for td<<Lbranch2/(2D)~580 ms, much longer than typical td used. This supports previous finding10,12.

Limitations. The morphometric approach used can underestimate the soma volume and the branch radius of <20%, and Rc (Fig.2). Future work will address these limitations.

Conclusion

We provided previously unavailable reference values of relevant features of brain-cell morphology, an essential basis to build more sensible biophysical models of dMRI signal in GM. Our results support some of the existing modelling assumptions while challenging others.

Acknowledgements

This work was supported by EPSRC platform grant EP/M020533/1 and the NIHR UCLH Biomedical Research Centre. MP is supported by UKRI Future Leaders Fellowship (MR/T020296/1).

References

1. D. C. Alexander, T. B. Dyrby, M. Nilsson, H. Zhang, Imaging brain microstructure with diffusion MRI: practicality and applications. Nmr Biomed 32, e3841 (2019).

2. I. O. Jelescu, M. Palombo, F. Bagnato, K. G. Schilling, Challenges for biophysical modeling of microstructure. J Neurosci Methods 344, 108861 (2020).

3. D. S. Novikov, E. Fieremans, S. N. Jespersen, V. G. Kiselev, Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. Nmr Biomed 32, e3998 (2019).

4. H. H. Lee 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 224, 1469-1488 (2019).

5. M. Andersson et al., Axon morphology is modulated by the local environment and impacts the non-invasive investigation of its structure-function relationship. bioRxiv preprint doi: https://doi.org/10.1101/2020.05.29.118737 (2020).

6. R. Callaghan, D. C. Alexander, M. Palombo, H. Zhang, ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation. Neuroimage 220, 117107 (2020).

7. M. Kleinnijenhuis, E. Johnson, J. Mollink, S. Jbabdi, K. L. Miller, A semi-automated approach to dense segmentation of 3D white matter electron microscopy. bioRxiv preprint doi: https://doi.org/10.1101/2020.03.19.979393 (2020).

8. M. Palombo et al., New paradigm to assess brain cell morphology by diffusion-weighted MR spectroscopy in vivo. Proc Natl Acad Sci U S A 113, 6671-6676 (2016).

9. M. Palombo et al., SANDI: A compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI. Neuroimage 215, 116835 (2020).

10. A. Ianus, D. C. Alexander, H. Zhang, M. Palombo, Mapping complex cell morphology in the grey matter with double diffusion encoding MRI: a simulation study. arXiv:2009.11778 (2020).

11. M. B. Hansen, S. N. Jespersen, L. A. Leigland, C. D. Kroenke, Using diffusion anisotropy to characterize neuronal morphology in gray matter: the orientation distribution of axons and dendrites in the NeuroMorpho.org database. Front Integr Neurosci 7, 31 (2013).

12. J. L. Olesen, S. N. Jespersen (2020) Stick power law scaling in neurons withstands realistic curvature and branching. in International Society for Magnetic Resonance in Medicine Annual Meeting.

13. M. Nilsson, J. Latt, F. Stahlberg, D. van Westen, H. Hagslatt, The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study. Nmr Biomed 25, 795-805 (2012).

14. J. Brabec, S. Lasic, M. Nilsson, Time-dependent diffusion in undulating thin fibers: Impact on axon diameter estimation. Nmr Biomed 33, e4187 (2020).

15. D. S. Novikov, V. G. Kiselev, Surface-to-volume ratio with oscillating gradients. J Magn Reson 210, 141-145 (2011).

16. H. H. Lee, A. Papaioannou, S. L. Kim, D. S. Novikov, E. Fieremans, A time-dependent diffusion MRI signature of axon caliber variations and beading. Commun Biol 3, 354 (2020).

17. D. S. Novikov, J. H. Jensen, J. A. Helpern, E. Fieremans, Revealing mesoscopic structural universality with diffusion. P Natl Acad Sci USA 111, 5088-5093 (2014).

18. M. Palombo, C. Ligneul, J. Valette, Modeling diffusion of intracellular metabolites in the mouse brain up to very high diffusion-weighting: Diffusion in long fibers (almost) accounts for non-monoexponential attenuation. Magnet Reson Med 77, 343-350 (2017).

19. H. Cuntz, F. Forstner, A. Borst, M. Hausser, One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application. Plos Comput Biol 6 (2010).

20. https://www.blender.org.

21. G. Peyre (2020) Toolbox Graph (https://www.mathworks.com/matlabcentral/fileexchange/5355-toolbox-graph),. (MATLAB Central File Exchange. Retrieved December 15, 2020.).

22. M. Palombo, D. C. Alexander, H. Zhang, A generative model of realistic brain cells with application to numerical simulation of the diffusion-weighted MR signal. Neuroimage 188, 391-402 (2019).

23. J. J. Garcia-Cantero, J. P. Brito, S. Mata, S. Bayona, L. Pastor, NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement. Front Neuroinform 11, 38 (2017).

24. I. Velasco et al., Neuronize v2: Bridging the Gap Between Existing Proprietary Tools to Optimize Neuroscientific Workflows. Front Neuroanat 14, 585793 (2020).

25. P. T. Callaghan, Principles of nuclear magnetic resonance microscopy (Clarendon Press ; Oxford University Press, 1991).

26. E. Ozarslan, C. Yolcu, M. Herberthson, H. Knutsson, C. F. Westin, Influence of the size and curvedness of neural projections on the orientationally averaged diffusion MR signal. Front Phys 6(2018).

27. M. Nilsson, S. Lasic, I. Drobnjak, D. Topgaard, C. F. Westin, Resolution limit of cylinder diameter estimation by diffusion MRI: The impact of gradient waveform and orientation dispersion. Nmr Biomed10.1002/nbm.3711 (2017).

Figures

Fig.1 An example of SWC file and how it relates to the cellular geometry. The SWC file defines a set of labelled nodes connected by edges characterizing the three-dimensional structure of each cell. We highlight the structural elements used to estimate the morphological features, as described in the Methods. Note that the first node in the SWC file is the so called ‘root’. It often coincides with the soma's centre and it is used to compute metrics such as BO, which starts at 0 at the root and increases after every branch point (more details in Methods).

Fig.2 Illustration of the morphological features investigated for an exemplar cell. We estimated general features of the whole structure and separated soma from neurites, processing them individually to estimate a set of other relevant features (see Methods). Additionally, we display the Gaussian curvature of the soma surface to show that it is a non-spherical geometry (always positive but not constant). A limitation of the current approach (and the majority of existing tools23,24) is the slightly inaccurate definition of the soma surface, as shown in the top right corner (arrows).

Tab.1 Definition of the 13 morphological features estimated.

Tab.2 Reference values for all the morphological features of neuronal and glial cells. The ranges and mean values obtained from the whole dataset investigated (N = 3,448) are reported, together with mean values for only neurons and glia. The ‘≥’ and ‘≤’ are used when the estimated value of the corresponding feature may be slightly (on average <20%) under- or over-estimated, respectively, given the known limitations of the approach used (e.g., see Fig.2).

Tab.3 Summary of the 13 morphological features computed for each species and cell type. N is the number of cellular structures investigated with complete information about the neurite structure; same information for soma in brackets. The reported values are mean±s.d. over the corresponding sample. The ‘≥’ and ‘≤’ are used when the estimated value of the corresponding feature may be slightly (on average <20%) under- or over-estimated, respectively, given the known limitations of the approach used (e.g., see Fig.2). n.a. = not available.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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