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Neurophysiology

, Volume 40, Issue 4, pp 310–315 | Cite as

Neuronal Morphology: Shape Characteristics and Models

Proceedings of the International School “Problems of Experimental, Clinical, and Theoretical Neurosciences” (Dnepropetrovsk, Ukraine, May 2–4, 2008)
  • A. SchierwagenEmail author
Article

This paper is focused on quantification (morphometry) and modeling of neuronal morphological complexity. First, computer-aided methods for reconstruction, processing, and analysis of raw morphological data are reviewed. Then, topological and metrical measures are touched upon. Fractal measures (together with the extension of multiscale fractal dimension) are presented more explicitly. Models of neuronal arborizations are differentiated between reconstruction models and growth models (stochastic or mechanistic). The growth model approach is discussed in more detail. The methods presented are applied to several types of neurons and shown to have considerable discriminative power. Recent developments stress the importance of these methods for optimizing virtual neuronal trees in view of functional characteristics of the neurons.

Keywords

neuronal morphology neuromorphometry fractal analyses growth models 

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References

  1. 1.
    S. Ramon y Cajal, Histologie du systéme nerveux de l’ homme et des vertébrés, Vol. 1. Maloine, Paris (1909).Google Scholar
  2. 2.
    A. Schierwagen and R. Grantyn, “Quantitative morphological analysis of deep superior colliculus neurons stained intracellularly with HRP in the cat,” J. Hirnforsch., 27, 611–623 (1986).PubMedGoogle Scholar
  3. 3.
    A. Schierwagen, “Growth, structure and dynamics of real neurons: model studies and experimental results,” Biomed. Biochim. Acta, 49, 709–722 (1990).PubMedGoogle Scholar
  4. 4.
    A. van Ooyen (ed.), Modeling Neural Development, MIT Press, Cambridge MA (2003).Google Scholar
  5. 5.
    G. Ascoli (ed.), Computational Neuroanatomy, Principles and Methods, Humana Press, Totawa, NJ (2002).Google Scholar
  6. 6.
    R. C. Cannon, “Structure editing and conversion with cvapp (2000).” Available from: http://www.compneuro.org/CDROM/nmorph/usage.html.
  7. 7.
    J. van Pelt, H. B. M. Uylings, R. W. H. Verwer, et al., “Tree asymmetry – a sensitive and practical measure for binary topological trees,” Bull. Math. Biol., 54, 759–784 (1992).PubMedCrossRefGoogle Scholar
  8. 8.
    D. A. Sholl, “Dendritic organization in the neurons of the visual cortices of the cat,” J. Anat., 87, 387-406 (1953).PubMedGoogle Scholar
  9. 9.
    B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman and Co., San Francisco (1983).Google Scholar
  10. 10.
    A. Schierwagen, “Dendritic branching patterns,” in: Chaos in Biological System, H. Degn, A. V. Holden, and L. F. Olsen (eds.), Plenum Press, New York, London (1987), pp. 191–193.Google Scholar
  11. 11.
    A. Schierwagen, “Scale-invariant diffusive growth: A dissipative principle relating neuronal form to function,” in: Organizational Constraints on the Dynamics of Evolution, J. Maynard-Smith and G. Vida (eds.), Manchester Univ. Press, Manchester (1990), pp. 167–189.Google Scholar
  12. 12.
    P. Meakin, “A new model for biological pattern formation,” J. Theor. Biol., 118, 101–113 (1986).PubMedCrossRefGoogle Scholar
  13. 13.
    E. Fernandez and H. F. Jelinek, “Use of fractal theory in neuroscience: methods, advantages and potential problems,” Methods, 24, 309–321 (2001).PubMedCrossRefGoogle Scholar
  14. 14.
    H. F. Jelinek, G. N. Elston, and B. Zietsch, “Fractal analysis: pitfalls and revelations in neuroscience,” in: Fractals in Biology and Medicine, Vol. IV, G. A. Losa, D. Merlini, T. F. Nonnenmacher, and E. R. Weibel (eds.), Birkhäuser, Basel (2005), pp. 85–94.CrossRefGoogle Scholar
  15. 15.
    L. Costa, E. Manoel, F. Faucereau, et al., “A shape analysis framework for neuromorphometry,” Network: Comput. Neural Syst., 13, 283–310 (2002).CrossRefGoogle Scholar
  16. 16.
    A. Schierwagen, L. F. Costa, A. Alpar, et al., “Neuromorphological phenotyping in transgenic mice: a multiscale fractal analysis,” in: Mathematical Modeling of Biological Systems, Vol. II, A. Deutsch, R. Bravo de la Parra, R. de Boer, et al., (eds.), Birkhäuser, Boston, 2007, pp. 191–199.Google Scholar
  17. 17.
    A. Schierwagen and J. van Pelt, “Shaping neuronal dendrites: Interplay of topological and metrical parameters,” J. Biol. Syst., 3, 1193–1200 (1995).CrossRefGoogle Scholar
  18. 18.
    J. van Pelt and A. Schierwagen, “Morphological analysis and modeling of neuronal dendrites,” Math. Biosci., 188, Nos. 1/2, 147–155 (2004).PubMedGoogle Scholar
  19. 19.
    R. E. Burke, W. B. Marks, and B. Ulfhake, “A parsimonious description of motoneuron dendritic morphology using computer simulation,” J. Neurosci., 12, 2403–2416 (1992).PubMedGoogle Scholar
  20. 20.
    A. Lindenmayer, “Mathematical models for cellular interaction in development,” J. Theor. Biol., 18, 280–315 (1968).PubMedCrossRefGoogle Scholar
  21. 21.
    B. Torben-Nielsen, K. Tuyls, and E. Postma, “EvOL-neuron: Neuronal morphology generation,” Neurocomputing, doi: 10.1016/j.neucom.2007.02.016 (2007).
  22. 22.
    J. van Pelt, A. Schierwagen, and H. B. M. Uylings, “Modeling dendritic complexity of deep layer superior colliculus neurons,” Neurocomputing, 38/40, Nos. 1/4, 403–408 (2001).CrossRefGoogle Scholar
  23. 23.
    F. Caserta, H. E. Stanley, W. Eldred, et al., “Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape,” Phys. Rev. Lett., 64, 95–98 (1990).PubMedCrossRefGoogle Scholar
  24. 24.
    A. Luczak, “Spatial embedding of neuronal trees modeled by diffusive growth,” J. Neurosci. Meth., 157, 132–141 (2006).CrossRefGoogle Scholar
  25. 25.
    K. M. Stiefel and T. J. Sejnowski, “Mapping functions onto neuronal morphology,” J. Neurophysiol., 98, 513–526 (2007).PubMedCrossRefGoogle Scholar
  26. 26.
    A. Schierwagen, “Brain organization and computation,” in: IWINAC 2007, Part I: Bio-Inspired Modeling of Cognitive Tasks, LNCS 4527, J. Mira and J. R. Alvarez (eds.), Springer Verlag, Berlin (2007), pp. 31–40.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute for Computer ScienceUniversity of LeipzigLeipzigGermany

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