Biological Cybernetics

, Volume 73, Issue 2, pp 129–137 | Cite as

Synchrony measures for biological neural networks

  • Paul F. Pinsky
  • John Rinzel
Original Papers

Abstract

Synchronous firing of a population of neurons has been observed in many experimental preparations; in addition, various mathematical neural network models have been shown, analytically or numerically, to contain stable synchronous solutions. In order to assess the level of synchrony of a particular network over some time interval, quantitative measures of synchrony are needed. We develop here various synchrony measures which utilize only the spike times of the neurons; these measures are applicable in both experimental situations and in computer models. Using a mathematical model of the CA3 region of the hippocampus, we evaluate these synchrony measures and compare them with pictorial representations of network activity. We illustrate how synchrony is lost and synchrony measures change as heterogeneity amongst cells increases. Theoretical expected values of the synchrony measures for different categories of network solutions are derived and compared with results of simulations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Christiansen B, Levinsen M (1993) Collective phenomena in large populations of globally coupled relaxation oscillators. Phys Rev E 48:743–756CrossRefGoogle Scholar
  2. Daido H (1987) Scaling behavior at the onset of mutual entrainment in a population of interacting oscillators. J Phys A Math Gen 20:L629-L636CrossRefGoogle Scholar
  3. Golomb D, Rinzel J (1993) Dynamics of globally coupled conductance-based inhibitory neurons with heterogeneity. Phys Rev E 48:4810–4814CrossRefGoogle Scholar
  4. Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons. Physica D 72:259–282CrossRefGoogle Scholar
  5. Hale J (1969) Ordinary differential equations. Krieger Publishing, Malabar, Fl.Google Scholar
  6. Kuramoto Y (1984) Chemical oscillations, waves and turbulence. Springer, Berlin Heidelberg New YorkGoogle Scholar
  7. Pinsky P (1994a) Synchrony and clustering in an excitatory neural network with intrinsic relaxation kinetics. Siam J Appl Math 55:220–241CrossRefGoogle Scholar
  8. Pinsky P (1994b) Mathematical models of hippocampal neurons and neural networks: exploiting multiple time scales. Ph.D thesis, Univ of MD, College ParkGoogle Scholar
  9. Pinsky P, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J Comput Neurosci 1:39–60CrossRefPubMedGoogle Scholar
  10. Schwartzkroin P, Prince R (1978) Penicillin induced epileptiform activity in the hippocampal in-vitro preparation. Ann Neurol 1:463–469CrossRefGoogle Scholar
  11. Strogatz S, Mirollo R (1991) Stability of incoherence in a population of coupled oscillators. J Stat Phys 63:613–636CrossRefGoogle Scholar
  12. Traub R, Wong R, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophysiol 66:635–649PubMedGoogle Scholar
  13. Traub R, Miles R, Jefferys J (1993) Synaptic and intrinsic conductances shape picrotoxin-induced synchronized afterdischarges in the guinea-pig hippocampal slice. J Physiol (Lond) 93:525–547Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Paul F. Pinsky
    • 1
    • 2
  • John Rinzel
    • 1
  1. 1.Mathematical Research BranchNIDDK, National Institutes of HealthBethesdaUSA
  2. 2.Applied Mathematics, University of MarylandCollege ParkUSA

Personalised recommendations