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Chaos / Volume 18 / Issue 1 / FOCUS ISSUE: MIXED MODE OSCILLATIONS: EXPERIMENT, COMPUTATION, AND ANALYSIS

Chaos 18, 015115 (2008); http://dx.doi.org/10.1063/1.2900015 (14 pages)

Rhythms of the brain: An examination of mixed mode oscillation approaches to the analysis of neurophysiological data

Irina Erchova1 and David J. McGonigle2

1Institute for Adaptive and Neural Computation, School of Informatics and Centre of Neuroscience Research, University of Edinburgh, 5 Forrest Hill Road, Edinburgh EH1 2QL, United Kingdom
2Schools of Psychology and Biosciences, Cardiff University, Tower Building, Park Place, Cardiff CF10 3AT, United Kingdom

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(Received 6 March 2007; accepted 29 February 2008; published online 27 March 2008)

In the nervous system many behaviorally relevant dynamical processes are characterized by episodes of complex oscillatory states, whose periodicity may be expressed over multiple temporal and spatial scales. In at least some of these instances the variability in oscillatory amplitude and frequency can be explained in terms of deterministic dynamics, rather than being purely noise-driven. Recently interest has increased in studying the application of mixed-mode oscillations (MMOs) to neurophysiological data. MMOs are complex periodic waveforms where each period is comprised of several maxima and minima of different amplitudes. While MMOs might be expected to occur in brain kinetics, only a few examples have been identified thus far. In this article, we review recent theoretical and experimental findings on brain oscillatory rhythms in relation to MMOs, focusing on examples at the single neuron level but also briefly touching on possible instances of the phenomenon across local and global brain networks.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE SPATIAL SCALE OF BRAIN OSCILLATIONS
    1. Invasive techniques: Single cells and small networks
    2. Noninvasive techniques: Local networks and between-area dynamics
  3. SINGLE NEURONS AND LOCAL NETWORK OSCILLATIONS IN THE PERIPHERAL NERVOUS SYSTEM
    1. The discovery of neural oscillators
    2. “True” pacemakers and other oscillators
    3. Single neurons and oscillating networks
  4. MATHEMATICAL MODELING OF AN ISOLATED NEURON
    1. Approaches to modeling: An overview
      1. Conductance-based models
      2. Reduced models
      3. Simplified models
    2. Low-dimensional models
      1. Modeling oscillatory behavior
  5. MODELS DISPLAYING SUBTHRESHOLD OSCILLATIONS AND MIXED-MODE OSCILLATIONS: THE CASE OF STELLATE CELLS WITHIN THE ENTORHINAL CORTEX
    1. Extended model
    2. Point neuron models
    3. Subthreshold oscillatory regimes
    4. Reduced stellate cell models
    5. Return to the multicompartmental neuron
    6. Spoiling the party: Integrating noise and models?
  6. WHY STUDY IRREGULAR OSCILLATIONS IN ISOLATED NEURONS?
  7. SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

bioelectric phenomena, brain, neurophysiology

PACS

  • 87.19.ln

    Oscillations and resonance

  • 87.19.lp

    Pattern formation: activity and anatomic

  • 87.19.ld

    Electrodynamics in the nervous system

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2900015
OpenURL
Portland State University Library

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    V. A. Makarov, V. I. Nekorkin, and M. G. Velarde, “Spiking behavior in a noise-driven system combining oscillatory and excitatory properties,” Phys. Rev. Lett. 86, 3431 (2001).

    M. J. Chacron, B. Lindner, and A. Longtin, “Noise shaping by interval correlations increases information transfer,” Phys. Rev. Lett. 92, 080601 (2004).

    C. B. Muratov and E. Vanden-Eijnden, “Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle,” Chaos 18, 015111 (2008)CHAOEH000018000001015111000001.

    N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, “Generalized synchronization of chaos in directionally coupled chaotic systems,” Phys. Rev. E 51, 980 (1995).


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