The Effect of Host Morphology on Network Characteristics and Thermodynamical Properties of Ising Model Defined on the Network of Human Pyramidal Neurons

  • Renato Aparecido Pimentel da Silva
  • Matheus Palhares Viana
  • Luciano da Fontoura Costa
Part of the Communications in Computer and Information Science book series (CCIS, volume 116)


The question about the effect of the host (node) morphology on complex network characteristics and properties of dynamical processes defined on networks is addressed. The complex networks are formed by hosts represented by realistic neural cells of complex morphology. The neural cells of different types are randomly placed on a 3-dimensional cubic domain. The connections between nodes established according to overlaps between different nearest-neighbor hosts significantly depend on the host morphology and thus are also random. The influence of host morphology on the following network characteristics has been studied: edge density, clustering coefficient, giant component size, global efficiency, degree entropy, and assortative mixing. The zero-field Ising model has been used as a prototype model to study the effect of the host morphology on dynamical processes defined on the networks of hosts which can be in two states. The mean magnetization, internal energy and spin-cluster size as function of temperature have been numerically studied for several networks composed of hosts of different morphology.


Ising Model Neuronal Network Edge Density Morphometric Measurement Giant Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson, K., Bones, B., Robinson, B., Hass, C., Lee, H., Ford, K., Roberts, T.A., Jacobs, B.: The morphology of supragranular pyramidal neurons in the human insular cortex: a quantitative Golgi study. Cereb. Cortex 19(9), 2131–2144 (2009)CrossRefGoogle Scholar
  2. 2.
    Ascoli, G.A.: Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat. Rev. Neurosci. 7, 318–324 (2006)CrossRefGoogle Scholar
  3. 3.
    Ascoli, G.A., Scorcioni, R.: Neuron and Network Modeling. In: Zaborszky, L., Wouterlood, F.G., Lanciego, J.L. (eds.) Neuroanatomical Tract-Tracing, vol. 3, pp. 604–630. Springer, New York (2006)CrossRefGoogle Scholar
  4. 4.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)CrossRefGoogle Scholar
  6. 6.
    da Costa, L.F., Manoel, E.T.M.: A percolation approach to neural morphometry and connectivity. Neuroinform. 1 (1), 65–80 (2003)CrossRefGoogle Scholar
  7. 7.
    da Costa, L.F., Coelho, R.C.: Growth-driven percolations: the dynamics of connectivity in neuronal systems. Eur. Phys. J. B 47, 571–581 (2005)CrossRefGoogle Scholar
  8. 8.
    da Costa, L.F., Rodrigues, F.A., Travieso, G., Boas, P.R.V.: Characterization of complex networks: a survey of measurements. Adv. Phys. 56 (1), 167–242 (2007)CrossRefGoogle Scholar
  9. 9.
    Eberhard, J.P., Wanner, A., Wittum, G.: NeuGen: A tool for the generation of realistic morphology of cortical neurons and neuronal networks in 3D. Neurocomputing 70(1-3), 327–342 (2006)CrossRefGoogle Scholar
  10. 10.
    Gleeson, P., Steuber, V., Silver, R.: Neuroconstruct: a tool for modeling networks of neurons in 3D space. Neuron. 54, 219–235 (2007)CrossRefGoogle Scholar
  11. 11.
    Hayes, T.L., Lewis, D.A.: Magnopyramidal neurons in the anterior motor speech region. Dendritic features and interhemispheric comparisons. Arch. Neurol. 53(12), 1277–1283 (1996)CrossRefGoogle Scholar
  12. 12.
    Jacobs, B., Schall, M., Prather, M., Kapler, E., Driscoll, L., Baca, S., Jacobs, J., Ford, K., Wainwright, M., Treml, M.: Regional dendritic and spine variation in human cerebral cortex: a quantitative Golgi study. Cereb. Cortex 11(6), 558–571 (2001)CrossRefGoogle Scholar
  13. 13.
    Koene, R.A., Tijms, B., van Hees, P., Postma, F., Ridder, A., Ramakers, G.J.A., van Pelt, J., van Ooyen, A.: NETMORPH: A framework for the stochastic generation of large scale neuronal networks with realistic neuron morphologies. Neuroinform. 7, 195–210 (2009)CrossRefGoogle Scholar
  14. 14.
    Lago-Fernández, L.F., Huerta, R., Corbacho, F., Sigüenza, J.A.: Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett. 84, 2758–2761 (2000)CrossRefGoogle Scholar
  15. 15.
    Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001)CrossRefGoogle Scholar
  16. 16.
    Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)CrossRefGoogle Scholar
  17. 17.
    Wang, B., Tang, H., Guo, C., Xiu, Z.: Entropy optimization of scale-free networks’ robustness to random failures. Phys. A 363(2), 591–596 (2005)CrossRefGoogle Scholar
  18. 18.
    Watson, K.K., Jones, T.K., Allman, J.M.: Dendritic architecture of the von Economo neurons. Neurosci. 141(3), 1107–1112 (2006)CrossRefGoogle Scholar
  19. 19.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  20. 20.
    White, J.G., Southgate, E., Thomson, J.N., Brenner, S.: The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. Lond. B 314, 1–340 (1986)CrossRefGoogle Scholar
  21. 21.
    Yu, S., Huang, D., Singer, W., Nikolic, D.: A small world of neuronal synchrony. Cereb. Cortex 18, 2891–2901 (2008)CrossRefGoogle Scholar
  22. 22.
    Zubler, F., Douglas, R.: A framework for modeling the growth and development of neurons and networks. Front. Comput. Neurosci. (2009), doi: 10.3389/neuro.10.025.2009Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Renato Aparecido Pimentel da Silva
    • 1
  • Matheus Palhares Viana
    • 1
  • Luciano da Fontoura Costa
    • 1
    • 2
  1. 1.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrazil
  2. 2.Instituto Nacional de Ciência e Tecnologia para Sistemas ComplexosCentro Brasileiro de Pesquisa FísicaRio de JaneiroBrazil

Personalised recommendations