Dynamic causal modeling: Difference between revisions

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Dynamic Causal Modelling (DCM) is a methodology and software framework for specifying models of neural dynamics, estimating their parameters and comparing their evidence. It enables hypotheses to be tested about the interaction of neural populations (effective connectivity) to be inferred fromusing functional neuroimaging data e.g., [[functional magnetic resonance imaging]] (fMRI), [[magnetoencephalography]] (MEG) or [[electroencephalography]]; (EEG).

== Motivation ==

The aim of dynamic causal modeling (DCM) is used to infer the causal architecture of coupled nonlinear dynamical systems, usingby Bayesianspecifying modelmodels comparisonof procedurehow thatthe restsdata onwere generated and comparing modelsthe of[[Marginal howlikelihood|evidence]] datafor weredifferent generatedmodels. Dynamic causalCausal modelsModels (DCMs) are formulated in terms of nonlinear state-space models in continuous time andthat 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 graphsnetworks 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.

DCM was developed for (and applied principally to) estimating 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 (cortical) regions or nodes. These models are then supplemented with a forward model of how the hidden states of each node (e.g., neuronal activity) map to measured responses. This enables the best model and its parameters (i.e., effective connectivity) to be identified from observed data. The [[Bayesian model comparison]] is used to select the best model in terms of its evidence (inference on model-space), which can then be characterised in terms of its parameters (inference on parameter-space). 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.

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.