We present a didactic introduction to spectral Dynamic Causal Modelling (DCM), a Bayesian state-space modelling approach used to infer effective connectivity from non-invasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modelling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements--at all time lags--including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

翻译：本文对频谱动态因果建模（Spectral DCM）进行教学式导论。频谱动态因果建模是一种贝叶斯状态空间建模方法，用于从无创神经影像数据中推断有效连接。目前，频谱DCM是静息态功能磁共振成像分析中应用最广泛的DCM变体。本文旨在向缺乏状态空间建模和频谱数据分析经验的研究人员阐释其技术基础。我们将重点关注交叉谱密度——这是频谱DCM最显著的特征，且与通过（零滞后）皮尔逊相关测量的功能连接密切相关。事实上，频谱DCM估计的模型参数能最佳地再现所有测量值之间所有时间滞后的互相关（包括通常被解释为功能连接的零滞后相关）。我们从模型方程中推导出功能连接矩阵，并展示单个有效连接参数的改变如何影响所有成对相关。更为复杂的是，功能连接变化最大的脑区对与有效连接变化最大的脑区对未必重合。我们讨论这些含义，并最终全面总结频谱DCM的假设与局限性。