Header

UZH-Logo

Maintenance Infos

Consistent spectral predictors for dynamic causal models of steady-state responses


Moran, Rosalyn J; Stephan, Klaas E; Dolan, Raymond J; Friston, Karl J (2011). Consistent spectral predictors for dynamic causal models of steady-state responses. NeuroImage, 55(4):1694-1708.

Abstract

Dynamic causal modelling (DCM) for steady-state responses (SSR) is a framework for inferring the mechanisms that underlie observed electrophysiological spectra, using biologically plausible generative models of neuronal dynamics. In this paper, we examine the dynamic repertoires of nonlinear conductance-based neural population models and propose a generative model of their power spectra. Our model comprises an ensemble of interconnected excitatory and inhibitory cells, where synaptic currents are mediated by fast, glutamatergic and GABAergic receptors and slower voltage-gated NMDA receptors. We explore two formulations of how hidden neuronal states (depolarisation and conductances) interact: through their mean and variance (mean-field model) or through their mean alone (neural-mass model). Both rest on a nonlinear Fokker-Planck description of population dynamics, which can exhibit bifurcations (phase transitions). We first characterise these phase transitions numerically: by varying critical model parameters, we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics (~2-100Hz) of real electrophysiological data. We then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis. This predictor is based on sampling the system's Jacobian over the orbits of hidden neuronal states. This predictor behaves consistently and smoothly in the region of phase transitions, which permits the use of gradient descent methods for model inversion. We demonstrate this by inverting generative models (DCMs) of SSRs, using simulated data that entails phase transitions.

Abstract

Dynamic causal modelling (DCM) for steady-state responses (SSR) is a framework for inferring the mechanisms that underlie observed electrophysiological spectra, using biologically plausible generative models of neuronal dynamics. In this paper, we examine the dynamic repertoires of nonlinear conductance-based neural population models and propose a generative model of their power spectra. Our model comprises an ensemble of interconnected excitatory and inhibitory cells, where synaptic currents are mediated by fast, glutamatergic and GABAergic receptors and slower voltage-gated NMDA receptors. We explore two formulations of how hidden neuronal states (depolarisation and conductances) interact: through their mean and variance (mean-field model) or through their mean alone (neural-mass model). Both rest on a nonlinear Fokker-Planck description of population dynamics, which can exhibit bifurcations (phase transitions). We first characterise these phase transitions numerically: by varying critical model parameters, we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics (~2-100Hz) of real electrophysiological data. We then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis. This predictor is based on sampling the system's Jacobian over the orbits of hidden neuronal states. This predictor behaves consistently and smoothly in the region of phase transitions, which permits the use of gradient descent methods for model inversion. We demonstrate this by inverting generative models (DCMs) of SSRs, using simulated data that entails phase transitions.

Statistics

Citations

21 citations in Web of Science®
23 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

65 downloads since deposited on 07 Apr 2011
18 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Special Collections > SystemsX.ch
Special Collections > SystemsX.ch > Research, Technology and Development Projects > Neurochoice
08 University Research Priority Programs > Foundations of Human Social Behavior: Altruism and Egoism
Dewey Decimal Classification:570 Life sciences; biology
170 Ethics
330 Economics
Language:English
Date:2011
Deposited On:07 Apr 2011 11:28
Last Modified:03 Aug 2017 15:29
Publisher:Elsevier
ISSN:1053-8119
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.neuroimage.2011.01.012
PubMed ID:21238593

Download

Preview Icon on Download
Preview
Content: Accepted Version
Filetype: PDF
Size: 1MB
View at publisher