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Modeling distributed axonal delays in mean-field brain dynamics.

J A Roberts1, P A Robinson

  • 1School of Physics, University of Sydney, and Brain Dynamics Centre, Westmead Millenium Institute, Westmead Hospital, Westmead, New South Wales 2145, Australia. jamesr@physics.usyd.edu.au

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary

Distributed delays in neuronal networks act as filters, affecting signal propagation and electroencephalogram (EEG) power spectra. Thalamocortical delay width significantly impacts the EEG spectrum by imposing a frequency cutoff.

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Area of Science:

  • Computational Neuroscience
  • Systems Neuroscience
  • Biophysics

Background:

  • Neuronal conduction delays are typically modeled as single discrete values.
  • This simplification overlooks the impact of distributed delays on signal propagation.

Purpose of the Study:

  • To investigate the effects of distributed conduction delays on signal propagation.
  • To analyze the influence of distributed thalamocortical and corticothalamic delays on electroencephalogram (EEG) power spectra.
  • To evaluate approximations of delay distributions using discrete delays.

Main Methods:

  • Incorporation of distributed thalamocortical and corticothalamic delays into a physiologically based mean-field model of the cortex and thalamus.
  • Analysis of the power spectrum sensitivity to delay distribution width and mean.

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  • Comparison of approximations using single discrete delays and pairs of discrete delays.

    • Main Results:

    • Distributed delays act as linear filters, introducing a frequency cutoff inversely proportional to delay width.
    • The EEG power spectrum is highly sensitive to the width of the thalamocortical delay distribution.
    • Spectral peak positions in the resting EEG are mainly determined by the delay distribution mean.
    • Increased delay distribution width enhances the stability of fixed-point solutions.
    • A single discrete delay approximates a distribution below a cutoff frequency, requiring parameter adjustment.
    • A pair of discrete delays can approximate a distribution without parameter adjustment.
    • Low-order differential equations effectively approximate delay distributions with large fractional widths.

    Conclusions:

    • Distributed delays significantly influence neuronal signal propagation and EEG spectral characteristics.
    • Thalamocortical pathway delays are critical determinants of EEG spectral damping.
    • Approximations of delay distributions using discrete delays are feasible under specific conditions, offering insights into network dynamics.