Consistent spectral predictors for dynamic causal models of steady-state responses
Open accessAbstract
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 (~2-100 Hz) 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.
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The Hodgkin-Huxley equation is a concrete instantiation of the function f(x) governing neuronal dynamics and can be extended to include neurotransmitter systems.
“This detailed equation is a concrete instantiation of the function f(x) governing neuronal dynamics, and can be easily extended to include a range of neurotransmitter systems (for example, adding calcium channels and a voltage gate to model NMDA (24);).”
From Predictive coding and neurocomputational psychiatry: a mechanistic framework for understanding mental disorders (2026) · cites this paper as [24]
The Conductance-Based Neuronal Ensemble Model section describes equations of neuronal dynamics as a flow f(x,u) and extends its conductance equation to include voltage-gated NMDA currents. But it identifies the underlying model as Morris–Lecar, not Hodgkin–Huxley, and does not describe adding calcium channels to model NMDA. (LLM, conf=0.88)
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“Z-axis: Neuromodulatory gain control (in fl uence of neurotransmitters like NMDA on precision).”
Influential
- Authors
- Moran, R. J., Stephan, K. E., Dolan, R. J., & Friston, K. J.
- Affiliations
- Wellcome Centre for Human Neuroimaging (GB)
- Corresponding author
- Moran, Rosalyn J.
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2011-04
- Volume
- 55
- Issue
- 4
- Pages
- 1694-1708
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC3093618
- OpenAlex
- W2043037283
- Cited by
- 75
- References
- 76
- Citations by year
- 2026: 5 · 2025: 4 · 2024: 4 · 2023: 4 · 2022: 1 · 2021: 4 · 2020: 6 · 2019: 8 · 2018: 9 · 2017: 4 · 2016: 2 · 2015: 10 · 2014: 6 · 2013: 3 · 2012: 2
- FWCI
- 2.27
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- NeuroImage (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, other-oa)
- UCL Discovery (University College London) (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- Research Portal (King's College London) (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Bristol Research (University of Bristol) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Wellcome Trust
- Max Planck Award
- NEUROCHOICE
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
- Keywords
- dynamic causal modeling, steady-state response, power spectrum, mean-field model, neural mass model, Fokker-Planck equation, bifurcation, phase transitions, center manifold theory, linear stability analysis, NMDA receptor, model inversion
- MeSH terms
- Action Potentials, Animals, Brain, Computer Simulation, Humans, Models, Neurological, Nerve Net
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