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Coarse-grained event tree analysis for quantifying Hodgkin-Huxley neuronal network dynamics.

Yi Sun1, Aaditya V Rangan, Douglas Zhou

  • 1Statistical and Applied Mathematical Sciences Institute, 19 T.W. Alexander Drive, P.O. Box 14006, Research Triangle Park, NC 27709, USA. yisun@samsi.info

Journal of Computational Neuroscience
|May 21, 2011
PubMed
Summary

Event tree analysis effectively distinguishes neuronal network dynamics by analyzing spiking sequences. This method validates an efficient library-based approach for simulating Hodgkin-Huxley networks with larger time steps.

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Area of Science:

  • Computational neuroscience
  • Complex systems analysis

Background:

  • Hodgkin-Huxley (HH) neuronal networks are fundamental models of neural activity.
  • Analyzing the complex dynamics of these networks, especially their responses to subtle input variations, remains challenging.

Purpose of the Study:

  • To introduce and validate an event tree analysis for studying HH neuronal network dynamics.
  • To demonstrate the efficacy of this analysis in discriminating between different network dynamical regimes.
  • To assess the statistical accuracy and efficiency of a library-based numerical method for HH network simulations.

Main Methods:

  • Coarse-grained projection of spatial-temporal sequences of physiological observables (e.g., neuron spiking) onto event trees and event chains.
  • Statistical analysis of event chains to capture higher-order statistics of network dynamics.

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  • Application of event tree analysis to evaluate results from a library-based numerical method that uses pre-computed neuronal trajectories.

    • Main Results:

    • Event tree analysis effectively captures network dynamics and robustly distinguishes small differences in input stimuli.
    • The library-based numerical method allows for significantly larger time steps (one order of magnitude) with comparable statistical accuracy (average firing rate, power spectra) to traditional solvers.
    • Numerical simulations analyzed via event trees confirm the high-order statistical similarity between the library method and regular solvers.

    Conclusions:

    • Event tree analysis provides a powerful tool for understanding and discriminating the dynamics of neuronal networks.
    • The library-based numerical method offers a computationally efficient alternative for simulating HH networks without sacrificing statistical fidelity.
    • Combining event tree analysis with efficient numerical methods enhances the study of large-scale neuronal network behavior.