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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
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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.

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.