Skip to main content
SpringerLink
Log in

Avalanche Dynamics and Correlations in Neural Systems

  • Chapter
  • First Online:
The Functional Role of Critical Dynamics in Neural Systems

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 11))

Abstract

The existence of power law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression of a system acting close to a critical point. This chapter focuses on temporal correlations and avalanche dynamics in the spontaneous activity of cortex slice cultures and in the resting fMRI BOLD signal. Long-range correlations are investigated by means of the scaling of power spectra and of Detrended Fluctuations Analysis. The existence of 1 / f decay in the power spectrum, as well as of power-law scaling in the root mean square fluctuation function for the appropriate balance of excitation and inhibition suggests that long-range temporal correlations are distinctive of “healthy brains”. The corresponding temporal organization of neuronal avalanches can be dissected by analyzing the distribution of inter-event times between successive events. In rat cortex slice cultures this distribution exhibits a non-monotonic behavior, not usually found in other natural processes. Numerical simulations provide evidences that this behavior is a consequence of the alternation between states of high and low activity, leading to a dynamic balance between excitation and inhibition that tunes the system at criticality. In this scenario, inter-times show a peculiar relation with avalanche sizes, resulting in a hierarchical structure of avalanche sequences. Large avalanches correspond to low-frequency oscillations, and trigger cascades of smaller ones that are part of higher frequency rhythms. The self-regulated balance of excitation and inhibition observed in cultures is confirmed at larger scales, i.e. on fMRI data from resting brain activity, and appears to be closely related to critical features of avalanche activity, which could play an important role in learning and other functional performance of neuronal systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Beggs, J.M., Plenz, D.: J. Neurosci. 23, 11167 (2003)

    Article  CAS  Google Scholar 

  2. Beggs, J.M., Plenz, D.: J. Neurosci. 24, 5216 (2004)

    Article  CAS  Google Scholar 

  3. Gireesh, E.D., Plenz, D.: Proc. Natl. Acad. Sci. USA 105, 7576–7581 (2008)

    Article  CAS  Google Scholar 

  4. Petermann, T., Thiagarajan, T.C., Lebedev, M.A., Nicolelis, M.A.L., Chialvo, D.R., Plenz, D.: Proc. Natl. Acad. Sci. USA 106, 15921–15926 (2009)

    Article  CAS  Google Scholar 

  5. Mazzoni, A., Broccard, F.D., Garcia-Perez, E., Bonifazi, P., Ruaro, M.E., Torre, V.: PLoS One 2(5), e439, 1–12 (2007). https://doi.org/10.1371/journal.pone.0000439

    Article  Google Scholar 

  6. Pasquale, V., Massobrio, P., Bologna, L.L., Chiappalone, M., Martinoia, S.: Neuroscience 153, 1354–1369 (2008)

    Article  CAS  Google Scholar 

  7. Shriki, O., Alstott, J., Carver, F., Holroyd, T., Hanson, R.N.A., Smith, M.L., Coppola, R., Bullmore, E., Plenz, D.: J. Neurosci. 33, 7079–7090 (2013)

    Article  CAS  Google Scholar 

  8. Zapperi, S., Lauritsen, K.B., Stanley, E.: Phys. Rev. Lett. 75, 4071 (1995)

    Article  CAS  Google Scholar 

  9. Michiels van Kessenich, L., de Arcangelis, L., Herrmann, H.J.: Sci. Rep. 6, 32071 (2016)

    Article  CAS  Google Scholar 

  10. de Arcangelis, L., Herrmann, H.J.: Proc. Natl. Acad. Sci. USA 107, 39773981 (2009)

    Google Scholar 

  11. Capano, V., Herrmann, H.J., de Arcangelis, L.: Sci. Rep. 5, 9895 (2015)

    Article  Google Scholar 

  12. de Arcangelis, L., Godano, C., Grasso, J.R., Lippiello, E.: Phys. Rep. 628, 1–91 (2016)

    Article  Google Scholar 

  13. Poil, S., Hardstone, R., Mansvelder, H.D., Linkenkaer-Hansen, K.: J. Neurosci. 32, 98179823 (2012)

    Article  Google Scholar 

  14. Lombardi, F., Herrmann, H.J., Plenz, D., de Arcangelis, L.: Front. Syst. Neurosci. 8, 204 (2014)

    Article  Google Scholar 

  15. Pathria, R.K.: Statistical Mechanics. Pergamon Press, Oxford (1972)

    Chapter  Google Scholar 

  16. Novikov, E., Novikov, A., Shannahoff-Khalsa, D., Schwartz, B., Wright, J.: Phys. Rev. E 56, R2387 (1997)

    Article  CAS  Google Scholar 

  17. Bedard, C., Kröger, H., Destexhe, A.: Phys. Rev. Lett. 97, 118102 (2006)

    Article  CAS  Google Scholar 

  18. Dehghani, N., Bedard, C., Cash, S.S., Halgren, E., Destexhe, A.: J. Comput. Neurosci. 21, 405–421 (2010)

    Article  Google Scholar 

  19. Pritchard, W.: Int. J. Neurosci. 66, 119–129 (1992)

    Article  CAS  Google Scholar 

  20. Zarahn, E., Aguirre, G.K., Esposito, M.D.: Neuroimage 5, 179 (1997)

    Article  CAS  Google Scholar 

  21. He, B.J., Zempel, J.M., Snyder, A.Z., Raichle, M.E.: Neuron 66, 353–369 (2014)

    Google Scholar 

  22. de Arcangelis, L., Perrone-Capano, C., Herrmann, H.J.: Phys. Rev. Lett. 96, 028107 (2006)

    Article  Google Scholar 

  23. Pellegrini, G.L., de Arcangelis, L., Herrmann, H.J., Perrone-Capano, C.: Phys. Rev. E 76, 016107 (2007)

    Article  Google Scholar 

  24. Lombardi, F., Herrmann, H.J., de Arcangelis, L.: Chaos 27, 047402 (2017)

    Article  CAS  Google Scholar 

  25. Jensen, H.J.: Self-organized criticality: emergent complex behavior in physical and biological systems. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  26. Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Phys. Rev. Lett. 94, 018102 (2005)

    Article  Google Scholar 

  27. Roerig, B., Chen, B.: Cereb. Cortex 12, 187–198 (2002)

    Article  CAS  Google Scholar 

  28. Song, S., Sjstrm, P.J., Reigl, M., Nelson, S., Chklovskii, D.B.: PLoS Biol. 3, e68 (2005)

    Article  Google Scholar 

  29. Buzsaki, G., Draguhn, A.: Science 304, 1926–1929 (2004)

    Article  CAS  Google Scholar 

  30. Kuntz, M., Sethna, J.: Phys. Rev. B 62, 17 (2000)

    Article  Google Scholar 

  31. Rios, P.D.L., Zhang, Y.C.: Phys. Rev. Lett. 82, 472 (1999)

    Article  Google Scholar 

  32. Utsu, T.: International Handbook of Earthquake and Engineering Seismology, vol. 81A, p. 719. Elsevier, Amsterdam (2002)

    Book  Google Scholar 

  33. Corral, A.: Phys. Rev. Lett. 92, 108501 (2004)

    Google Scholar 

  34. Lombardi, F., Herrmann, H.J., Perrone-Capano, C., Plenz, D., de Arcangelis, L.: Phys. Rev. Lett. 108, 228703 (2012)

    Article  CAS  Google Scholar 

  35. Wilson, C.: Scholarpedia 3, 1410 (2008)

    Article  Google Scholar 

  36. Timofeev, I., Grenier, F., Bazhenov, M., Sejnowski, T.J., Steriade, M.: Cereb. Cortex 10, 1185–1199 (2000)

    Article  CAS  Google Scholar 

  37. Timofeev, I., Grenier, F., Steriade, M.: Proc. Natl. Acad. Sci. USA 98, 1924–1929 (2001)

    Article  CAS  Google Scholar 

  38. Thompson, S.M., Haas, H.L., Ghwiler, B.H.: J. Physiol. 451, 347–363 (1992)

    Google Scholar 

  39. Cossart, R., Aronov, D., Yuste, R.: Nature 423, 283–288 (2003)

    Article  CAS  Google Scholar 

  40. Mendoza, M., Kaydul, A., de Arcangelis, L., Andrade, Jr., J.S., Herrmann, H.J.: Nat. Commun. 5, 5035 (2014)

    Google Scholar 

  41. Lombardi, F., Herrmann, H.J., Plenz, D., de Arcangelis, L.: Sci. Rep. 24690 (2016)

    Google Scholar 

  42. Lombardi, F., de Arcangelis, L.: Eur. Phys. J. Spec. Top. 223, 2119–2130 (2014)

    Article  Google Scholar 

  43. Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., Goldberger, A.L.: Phys. Rev. E 49, 1685 (1994)

    Article  CAS  Google Scholar 

  44. Hu, K., Ivanov, P.C., Chen, Z., Carpena, P., Stanley, H.E.: Phys. Rev. E 64, 011114 (2001)

    Google Scholar 

  45. Chen, Z., Ivanov, P.C., Hu, K., Stanley, H.E.: Phys. Rev. E 65, 041107 (2002)

    Google Scholar 

  46. Lippiello, E., de Arcangelis, L., Godano, C.: Phys. Rev. Lett. 100, 038501 (2008)

    Article  CAS  Google Scholar 

  47. Lombardi, F., Chialvo, D.R., Herrmann, H.J., de Arcangelis, L.: Chaos Solitons Fractals 55, 102 (2013)

    Article  Google Scholar 

  48. Gao, Richard, Peterson, Erik J., Voytek, Bradley: Neuroimage 158, 70–78 (2017)

    Article  Google Scholar 

  49. Shew, W., Yang, H., Petermann, T., Roy, R., Plenz, D.: J. Neurosci. 29, 15595–15600 (2009)

    Article  CAS  Google Scholar 

  50. Scarpetta, S., de Candia, A.: Front. Syst. Neurosci. 8, 88 (2014)

    Article  Google Scholar 

  51. He, B.J., Zempel, J.M., Snyder, A.Z., Raichle, M.E.: Neuron 66, 353–369 (2010)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, MA, USA

    Fabrizio Lombardi

  2. Institute of Computational Physics for Engineering Materials, IfB, ETH Zürich, Zürich, Switzerland

    Hans J. Herrmann

  3. Department of Engineering, University of Campania “Luigi Vanvitelli”, INFN sez. Napoli Gr. Coll., Salerno, Aversa (CE), Italy

    Lucilla de Arcangelis

Authors
  1. Fabrizio Lombardi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans J. Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lucilla de Arcangelis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lucilla de Arcangelis .

Editor information

Editors and Affiliations

  1. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Nergis Tomen

  2. Institute of Perception, Action and Behaviour, University of Edinburgh, Edinburgh, UK

    J. Michael Herrmann

  3. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Udo Ernst

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lombardi, F., Herrmann, H.J., de Arcangelis, L. (2019). Avalanche Dynamics and Correlations in Neural Systems. In: Tomen, N., Herrmann, J., Ernst, U. (eds) The Functional Role of Critical Dynamics in Neural Systems . Springer Series on Bio- and Neurosystems, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-20965-0_1

Download citation

Publish with us

Policies and ethics

Search

Navigation