Population dynamics under the Laplace assumption

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • André C. Marreiros - , University College London (Author)
  • Stefan J. Kiebel - , University College London (Author)
  • Jean Daunizeau - , University College London (Author)
  • Lee M. Harrison - , University College London (Author)
  • Karl J. Friston - , University College London (Author)

Abstract

In this paper, we describe a generic approach to modelling dynamics in neuronal populations. This approach models a full density on the states of neuronal populations but finesses this high-dimensional problem by re-formulating density dynamics in terms of ordinary differential equations on the sufficient statistics of the densities considered (c.f., the method of moments). The particular form for the population density we adopt is a Gaussian density (c.f., the Laplace assumption). This means population dynamics are described by equations governing the evolution of the population's mean and covariance. We derive these equations from the Fokker-Planck formalism and illustrate their application to a conductance-based model of neuronal exchanges. One interesting aspect of this formulation is that we can uncouple the mean and covariance to furnish a neural-mass model, which rests only on the populations mean. This enables us to compare equivalent mean-field and neural-mass models of the same populations and evaluate, quantitatively, the contribution of population variance to the expected dynamics. The mean-field model presented here will form the basis of a dynamic causal model of observed electromagnetic signals in future work.

Details

Original languageEnglish
Pages (from-to)701-714
Number of pages14
JournalNeuroImage
Volume44
Issue number3
Publication statusPublished - 1 Feb 2009
Peer-reviewedYes
Externally publishedYes

External IDs

PubMed 19013532

Keywords

ASJC Scopus subject areas

Keywords

  • Laplace assumption, Mean-field, Modelling, Neural-mass models, Neuronal, Nonlinear

Library keywords