Typology of nonlinear activity waves in a layered neural continuum

Paul Koch, Gerry Leisman

Research output: Contribution to journalArticlepeer-review

Abstract

Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).

Original languageEnglish
Pages (from-to)381-405
Number of pages25
JournalInternational Journal of Neuroscience
Volume116
Issue number4
StatePublished - Apr 2006

Bibliographical note

Funding Information:
Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular Received 17 February 2005. This work was supported, in part, by a grant-in-aid from the Foundation for Cognitive Neuroscience to the second author. Address correspondence to Dr. Gerry Leisman, The Dr. Ted Carrick Institute for Clinical Ergonomics, Rehabilitation and Applied Neuroscience, 1700 Union Blvd., Bay Shore, NY 11706, USA. E-mail: drgersh@yahoo.com

Keywords

  • Cognition
  • Continuum theory
  • Neural networks
  • Nonlinear theory
  • Wave growth

ASJC Scopus subject areas

  • General Neuroscience

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