Dynamic causal modeling: Difference between revisions

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== Motivation ==

DCM was developed for (and is applied principally to) estimating the coupling among brain regions and how that coupling is influenced by experimental changes (e.g., time or context). The basic idea is to construct reasonably realistic models of interacting brain regions or nodes. These models are then supplemented with a forward model of how the hidden states of each nodebrain region (e.g., neuronal activity) map tocauses measured responses. This enables the best model and its parameters (i.e., effective connectivity) to be identified from observed data. [[Bayesian model comparison]] is used to select the best model in terms of its evidence, which can then be characterised in terms of its parameters. This enables one to test hypotheses about how nodes communicate; e.g., whether activity in a given neuronal population modulates the coupling between other populations, in a task-specific fashion.

== Procedure ==

DCMExperiments studiesusing DCM typically involve the following stages:

# FormulatingFormulate specific hypotheses and conductingconduct a anneuroimaging experiment to test those hypotheses.

# Preparing the acquired data for modelling (such as selecting relevant data features and removing confounds from the data).

# SpecifyingSpecify one or more forward models (DCMs) of how the data were caused.

# ComparingFit the evidencemodel(s) forto thesethe models,data orto takingdetermine thetheir evidence orand parameters to the group level for testing hypotheses.

# Compare the evidence for the models using Bayesian Model Comparison, at the single-subject or group level, and inspect the parameters of the model(s).

Each of these steps is briefly reviewed below.

Dynamic Causal Models (DCMs) are nonlinear state-space models in continuous time that model the dynamics of hidden states in the nodes of a probabilistic graphical model, where conditional dependencies are parameterised in terms of directed effective connectivity. Unlike [[Bayesian network|Bayesian Networks]] the networks used in DCM can be cyclic, and unlike [[Structural equation modeling|Structural Equation modelling]] and [[Granger causality]], DCM does not depend on the theory of Martingales, i.e., it does not assume that random fluctuations' are serially uncorrelated.

=== Experimental design ===

In functional neuroimaging, theexperiments dataare maytypically betask-based functionalor magnetic[[Resting resonancestate imaging (fMRI)|resting measurementsstate]]. orIn electrophysiologicaltask-based (e.g.designs, in magnetoencephalography or electroencephalography; MEG/EEG). Brainbrain responses are evoked by known deterministic inputs (experimentally controlled stimuli) that embody designed changes in sensory stimulation or cognitive set. These experimental or exogenous variables can change hidden states in one of two ways. First, they can elicit responses through direct influences on specific network nodes. This would be appropriate, for example, in modelling sensory evoked responses in the early visual cortex. The second class of inputs exerts their effects vicariously, through a modulation of the coupling among nodes, for example, the influence of attention on the processing of sensory information. The hidden states cover any neurophysiological or biophysical variables needed to form observed outputs. These outputs are measured (hemodynamic or electromagnetic) responses over the sensors considered. Bayesian inversion furnishes the marginal likelihood (evidence) of the model and the posterior distribution of its parameters (e.g., neuronal coupling strengths). The evidence is used for Bayesian model selection (BMS) to disambiguate between competing models, while the posterior distribution of the parameters is used to characterise the model selected.Typic

=== Preprocessing ===

=== Model specification ===

Dynamic Causal Models (DCMs) are nonlinear state-space models in continuous time that model the dynamics of hidden states in the nodes of a probabilistic graphical model, where conditional dependencies are parameterised in terms of directed effective connectivity. Unlike [[Bayesian network|Bayesian Networks]] the networks used in DCMDCMs can be cyclic, and unlike [[Structural equation modeling|Structural Equation modelling]] and [[Granger causality]], DCM does not depend on the theory of Martingales, i.e., it does not assume that random fluctuations' are serially uncorrelated.

=== Estimation ===

Bayesian inversion furnishes the marginal likelihood (evidence) of the model and the posterior distribution of its parameters (e.g., neuronal coupling strengths). The evidence is used for Bayesian model selection (BMS) to disambiguate between competing models, while the posterior distribution of the parameters is used to characterise the model selected.

=== Model comparison ===

In functional neuroimaging, the data may be functional magnetic resonance imaging (fMRI) measurements or electrophysiological (e.g., in magnetoencephalography or electroencephalography; MEG/EEG). Brain responses are evoked by known deterministic inputs (experimentally controlled stimuli) that embody designed changes in sensory stimulation or cognitive set. These experimental or exogenous variables can change hidden states in one of two ways. First, they can elicit responses through direct influences on specific network nodes. This would be appropriate, for example, in modelling sensory evoked responses in the early visual cortex. The second class of inputs exerts their effects vicariously, through a modulation of the coupling among nodes, for example, the influence of attention on the processing of sensory information. The hidden states cover any neurophysiological or biophysical variables needed to form observed outputs. These outputs are measured (hemodynamic or electromagnetic) responses over the sensors considered. Bayesian inversion furnishes the marginal likelihood (evidence) of the model and the posterior distribution of its parameters (e.g., neuronal coupling strengths). The evidence is used for Bayesian model selection (BMS) to disambiguate between competing models, while the posterior distribution of the parameters is used to characterise the model selected.

== DCM for fMRI ==