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We present a didactic introduction to spectral Dynamic Causal Modelling(DCM), a Bayesian state-space modelling approach used to infer effectiveconnectivity from non-invasive neuroimaging data. Spectral DCM is currently themost widely applied DCM variant for resting-state functional MRI analysis. Ouraim is to explain its technical foundations to an audience with limitedexpertise in state-space modelling and spectral data analysis. Particularattention will be paid to cross-spectral density, which is the most distinctivefeature of spectral DCM and is closely related to functional connectivity, asmeasured by (zero-lag) Pearson correlations. In fact, the model parametersestimated by spectral DCM are those that best reproduce the cross-correlationsbetween all measurements--at all time lags--including the zero-lag correlationsthat are usually interpreted as functional connectivity. We derive thefunctional connectivity matrix from the model equations and show how changing asingle effective connectivity parameter can affect all pairwise correlations.To complicate matters, the pairs of brain regions showing the largest changesin functional connectivity do not necessarily coincide with those presentingthe largest changes in effective connectivity. We discuss the implications andconclude with a comprehensive summary of the assumptions and limitations ofspectral DCM.

Spectral Dynamic Causal Modelling: A Didactic Introduction and its Relationship with Functional Connectivity