, Volume 1, Issue 1, pp 65–80 | Cite as

A percolation approach to neural morphometry and connectivity

  • Luciano da Fontoura Costa
  • Edson Tadeu Monteiro Manoel
Original Article


This article addresses the issues of neural shape characterization and analysis from the perspective of one of the main roles played by neural shapes, namely, connectivity. This study is oriented toward the geometry at the individual cell level and involves the use of the percolation concept from statistical mechanics, which is reviewed in an accessible fashion. The characterization of the neural cell geometry with respect to connectivity is performed in terms of critical percolation probability obtained experimentally while considering several types of geometrical interactions between cells, therefore directly expressing the potential for connections defined by each situation. Two basic situations are considered: dendrite-dendrite and dendrite-axon interactions. The obtained results corroborate the potential of the critical percolation probability as a valuable resource for characterizing, classifying, and analyzing the morphology of neural cells.

Index Entries

Connectivity neuromorphometry percolation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arbib, M. (1998) The Handbook of Brain Theory and Neural Networks. The MIT Press Cambridge, MA.Google Scholar
  2. Ascoli, G. A., ed. (2002) Computational Neuroanatomy: Principles and Methods, Humana Press, Totowa, NJ.Google Scholar
  3. Ascoli, G. A., Krichmar, J. L., Nasuto, S. J., and Senft, S. L. (2001) Generation, description and storage of dendritic morphological data. Philosophical Transactions of the Royal Society, Series-B 356(1412): 1131–1145.CrossRefGoogle Scholar
  4. Bianchi, A. G. C., dos Santos, M. F., Hamassaki-Britto, D. E., and Costa, L. F. (2002) Inferring Shape Evolution. Pattern Recognition Letters (Accepted).Google Scholar
  5. Cajal, S. R. (1989) Recollections of my life. The MIT Press, Cambridge, MA.Google Scholar
  6. Cesar R. M. Jr., and Costa, L. F. (1997a) Application and Assessment of Multiscale Bending Energy for Morphometric Characterization of Neural Cells. Review of Scientific Instruments 68(5),:2177–2186.CrossRefGoogle Scholar
  7. Cesar R. M. Jr., and Costa, L. F. (1997b) Computer-Vision-Based Extraction of Neural Dendrograms. J Neurosci Meth 93:121–131.CrossRefGoogle Scholar
  8. Chklovskii, D. B. (2000) Optimal Size of Dendritic and Axonal Arbors in a Topographic Projection. J Neurophysiol 83: 2113–2119.PubMedGoogle Scholar
  9. Coelho, R. C., di Gesu, V., Bosco, G. L., Tanaka, J. S., and Valenti, C. (2002) Shape-Based features for cat ganglion retinal cells classification. Journal of Real-Time Imaging Accepted.Google Scholar
  10. Costa, L. F. (1995) Computer vision-based morphometric characterization of neural cells. Review of Scientific Instruments 66(7): 3770–3773.CrossRefGoogle Scholar
  11. Costa, L. F. (2000) Robust skeletonization through exact Euclidean distance transform and its application to neuromorphometry. Real Time Imaging 6: 415–431.CrossRefGoogle Scholar
  12. Costa, L. F. (2001) On neural shape and function. In: Proceedings of the First World Congress on Neuroinformatics, Vienna University of Technology, Vienna, Austria. pp. 397–410.Google Scholar
  13. Costa, L. F. and Cesar R. M. Jr., (2001) Shape Analysis and Classification. CRC Press Boca Raton, FL.Google Scholar
  14. Costa, L. F. and Velte, T. J. (1999) Automatic Characterization and Classification of Ganglion Cells From the Salamander Retina. J Comp Neurol. 404: 33–51.CrossRefGoogle Scholar
  15. Dam, A. M. (1978) The density of neurons in the human hipocampus. J Neuropath Appl Neurobiol 5: 249–264.CrossRefGoogle Scholar
  16. Duijnhouwer, J., Remme, M. W. H., van Ooyen, A., and van Pelt J. (2001) Influence of dendritic topology on firing patterns in model neurons. Neurocomputing 38–40: 183–189.CrossRefGoogle Scholar
  17. Falcao, A. X., Costa, L. F., and da Cunha, B.S. (2002) Multiscale Skeletons by image foresting transform and its application to neuromorphometry. Pattern Recognition 35(7): 1571–1582.CrossRefGoogle Scholar
  18. Fuxe, K. and Agnati, A. F. (1991) Volume transmission in the brain: novel mechanisms for neural transmission. Raven Perss, New York, NY.Google Scholar
  19. Haydon, P. G. and Drapeau, P. (1995) From contact to connection: early events during synaptogenesis. Trends Neurosci 18: 196–201.PubMedCrossRefGoogle Scholar
  20. Koch, C. and Segev, I. (1998) Methods in Neuronal Modeling: From Ions to Networks. The MIT Press, Cambridge, MA.Google Scholar
  21. Krichmar, J. L., Nasuto, S. J., Scorcioni, R., Washington S.D., and Ascoli, G.A. (2002) Effects of dendritic morphology on CA3 pyramidal cell electrophysiology: a simulation study. Brain Res 941: 11–28.PubMedCrossRefGoogle Scholar
  22. Mainen, Z. F. and Sejnowski, T. J. (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382(6589): 363–366.PubMedCrossRefGoogle Scholar
  23. Montague, P. R. and Friedlander, M. J. (1991) Morphogenesis and territorial coverage by isolated mammalian retinal ganglion cells. J Neurosci 11(5): 1440–1457.PubMedGoogle Scholar
  24. Murre, J. M. J. and Sturdy, D. P. F. (1996) The connectivity of the brain: multi-level quantitative analysis. Biol Cybernet 73: 529–545.Google Scholar
  25. Nasuto, S. J., Krichmar, J. L., and Ascoli, G. A. (2001) A computational study of the relationship between neuronal morphology and electrophysiology in an Alzheimer’s Disease model. Neurocomputing 38–40: 1477–1487.CrossRefGoogle Scholar
  26. van Ooyen, A., Willshaw, D. J., and Ramakers, G. (2000) Influence of Dendritic Morphology on Axonal Competition. Neurocomputing 32: 255–260.CrossRefGoogle Scholar
  27. van Ooyen, A., Pakdaman, K., Houweling, A.R., van Pelt, J., and Vibert, J. F. (2001) Network connectivity changes through activity-dependent neurite outgrowth. Neural Proc Lett 3: 123–130.CrossRefGoogle Scholar
  28. van Pelt, J., van Ooyen, A., and Uylings, H. B. M. (2001) Network connectivity changes through activity-dependent neurite outgrowth. Anat Embryol 204: 255–265.PubMedCrossRefGoogle Scholar
  29. Ramakers, G. J. A., Winter, J., Hogland, T. M., Lequin, M. B., van Hulten, P., van Pelt, J., and Pool C. W. (1998) Depolarization stimulates lamellipodia formation and axonal but not dendritical branching in cultured rat cerebral cortex neurons. Dev Brain Res 108(1–2): 205–216.CrossRefGoogle Scholar
  30. Sholl, D. A. (1953) Dendritic organization in the neurons of the visual and motor cortices of the cat. J Anat 87: 387–406.PubMedGoogle Scholar
  31. Stauffer, D. and Aharony, A. (1994) Introduction to Percolation Theory. Taylor Francis, Bristol, PA.Google Scholar
  32. Stepanyants, A., Hof, P. R., and Chklovskii, D. B. (2002) Geometry and structural plasticity of synaptic connectivity. Neuron 34(2): 275–288.PubMedCrossRefGoogle Scholar
  33. Szigeti, C., Fulop, Z., and Gulya, K. (2002) Branching-pattern analysis of the dendritic arborization in the thalamic nuclei of the rat brain. Acta Biologica Hungarica 53: 177–186.PubMedCrossRefGoogle Scholar
  34. Toris, C. B., Eiesland, J. L., and Miller, R. F. (1995) Morphology of ganglion cells in the neotenous tiger salamander retina. J Comp Neurol 352: 535–559.PubMedCrossRefGoogle Scholar
  35. Vetter, P., Roth, A., and Hausser, M. (2001) Propagation of action potentials in dendrites depends on dendritic morphology. J Neurophysiol 85(2): 926–937.PubMedGoogle Scholar
  36. Wassle, H., Boycott, B. B., and Illing, R. B. (1981) Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc Royal Soc Lond. B 212: 177–195.CrossRefGoogle Scholar
  37. Xia, W. and Thorpe, M. F. (1988) Percolation properties of random ellipses. Physical Review A 38(5): 2650–2656.PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press Inc 2003

Authors and Affiliations

  • Luciano da Fontoura Costa
    • 1
  • Edson Tadeu Monteiro Manoel
    • 1
  1. 1.Cybernetic Vision Research GroupIFSC-USPSão CarlosBrazil

Personalised recommendations