Neuronal avalanches: Where temporal complexity and criticality meet

  • Mohammad Dehghani-Habibabadi
  • Marzieh Zare
  • Farhad Shahbazi
  • Javad Usefie-Mafahim
  • Paolo Grigolini
Regular Article

Abstract.

The model of the current paper is an extension of a previous publication, wherein we have used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was a manifestation of supercriticality rather than criticality. Here, however, we show that the continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity, and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may be a numerical artifact originated by the discrete description of the model which may imply a slow numerical convergence of the avalanche distribution compared to temporal complexity.

Graphical abstract

Keywords

Living systems: Structure and Function 

References

  1. 1.
    J. Laherrè, D. Sornette, Eur. Phys. J. B 2, 525 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    B.J. He, J.M. Zempel, A.Z. Snyder, M.E. Raichle, Neuron 66, 353 (2010)CrossRefGoogle Scholar
  3. 3.
    J.M. Beggs, D. Plenz, J. Neurosci. 23, 11167 (2003)Google Scholar
  4. 4.
    N. Friedman, S. Ito, B.A.W. Brinkman, M. Shimono, R.E. Lee De Ville, K. Dahmen, J. Beggs, T. Butler, Phys. Rev. Lett. 108, 208102 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    W.L. Shew, H. Yang, T. Petermann, R. Roy, D. Plenz, J. Neurosci. 29, 15595 (2009)CrossRefGoogle Scholar
  6. 6.
    H. Yang, W.L. Shew, R. Roy, D. Plenz, J. Neurosci. 32, 1061 (2012)CrossRefGoogle Scholar
  7. 7.
    E.D. Gireesh, D. Plenz, Proc. Natl. Acad. Sci. U.S.A. 105, 7576 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    G. Hahn, T. Petermann, M.N. Havenith, S. Yu, W. Singer, D. Plenz, D. Nikolic, J. Neurophysiol. 104, 3312 (2010)CrossRefGoogle Scholar
  9. 9.
    V. Priesemann, Front. Syst. Neurosci. 8, 108 (2014)CrossRefGoogle Scholar
  10. 10.
    T. Petermann, T.C. Thiagarajan, M.A. Lebedev, M.A. Nicolelis, D.R. Chialvo, D. Plenz, Proc. Natl. Acad. Sci. U.S.A. 106, 15921 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)ADSCrossRefGoogle Scholar
  12. 12.
    J.A. Bonachela, S. de Franciscis, J.J. Torres, M.A. Munoz, J. Stat. Mech. 2010, P02015 (2010)CrossRefGoogle Scholar
  13. 13.
    P. Moretti, M.A. Munoz, Nat. Commun. 4, 2521 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    F. Lombardi, H.J. Herrmann, D. Plenz, L. de Arcangelis, Front. Syst. Neurosci. 8, 204 (2014)CrossRefGoogle Scholar
  15. 15.
    F. Lombardi, H.J. Herrmann, C. Perrone-Capano, D. Plenz, L. de Arcangelis, Phys. Rev. Lett. 108, 228703 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    J.M. Beggs, N. Timme, Front. Physiol. 3, 163 (2012)CrossRefGoogle Scholar
  17. 17.
    J.E.S. Socolar, S.A. Kauffman, Phys. Rev. Lett. 90, 068702 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    N. Bertschinger, T. Natschlger, Neural Comput. 16, 1413 (2004)CrossRefGoogle Scholar
  19. 19.
    P. Rämö, S. Kauffman, J. Kesseli, O. Yli-Harja, Physica D: Nonlinear Phenomena 227, 100 (2007)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    K.T.T. Tanaka, T. Aoyagi, Neural Comput. 21, 1038 (2009)MathSciNetCrossRefGoogle Scholar
  21. 21.
    D.R. Chialvo, Nat. Phys. 6, 744 (2010)CrossRefGoogle Scholar
  22. 22.
    W.L. Shew, H. Yang, S. Yu, R. Roy, D. Plenz, J. Neurosci. 31, 55 (2011)CrossRefGoogle Scholar
  23. 23.
    O. Kinouchi, M. Copelli, Nat. Phys. 2, 348 (2006)CrossRefGoogle Scholar
  24. 24.
    C. Bédard, H. Kroger, A. Destexhe, Phys. Rev. Lett. 97, 118102 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    V. Priesemann, M. Munk, M. Wibral, BMC Neurosci. 10, 40 (2009)CrossRefGoogle Scholar
  26. 26.
    M.E.J. Newman, Contemp. Phys. 46, 323 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    J. Touboul, A. Destexhe, PLoS One 5, 14 (2010)CrossRefGoogle Scholar
  28. 28.
    N. Dehghani, C. Bédard, S.S. Cash, E. Halgren, A. Destexhe, J. Comput. Neurosci. 29, 405 (2010)CrossRefGoogle Scholar
  29. 29.
    M. Zare, P. Grigolini, Chaos, Solitons Fractals 55, 80 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    M. Zare, P. Grigolini, Phys. Rev. E 86, 051918 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    J. Usefie-Mafahim, D. Lambert, M. Zare, P. Grigolini, New J. Phys. 17, 015003 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    N. Dehghani, N.G. Hatsopoulos, Z.D. Haga, R.A. Parker, B. Greger, E. Halgren, A. Destexhe, Front. Physiol. 3, 302 (2012)CrossRefGoogle Scholar
  33. 33.
    James P. Sethna, Karin A. Dahmen, Christopher R. Myers, Nature 410, 242 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    A. Politi, S. Luccioli, Dynamics of networks of leaky-integrate-and-fire neurons, in Network Science, edited by E. Estrada, M. Fox, D.J. Higham, G.-L. Oppo (Springer, Berlin, 2010) pp. 217--242Google Scholar
  35. 35.
    R.E. Mirollo, S.H. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990)MathSciNetCrossRefGoogle Scholar
  36. 36.
    K. Christensen, N.R. Moloney, Complexity and Criticality, Vol. 1 (Imperial College Press, London, 2005)Google Scholar
  37. 37.
    R. Failla, M. Ignaccolo, P. Grigolini, A. Schwettmann, Phys. Rev. E 70, 010101 (2004)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Mohammad Dehghani-Habibabadi
    • 1
  • Marzieh Zare
    • 2
  • Farhad Shahbazi
    • 1
    • 3
  • Javad Usefie-Mafahim
    • 4
  • Paolo Grigolini
    • 5
  1. 1.Department of PhysicsIsfahan University of TechnologyIsfahanIran
  2. 2.School of Computer ScienceInstitute for Research in Fundamental Sciences (IPM)TehranIran
  3. 3.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  4. 4.Department of PhysicsShahid Beheshti UniversityTehranIran
  5. 5.Center for Nonlinear ScienceUniversity of North TexasDentonUSA

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