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 variables--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：我们以教学方式介绍频谱动态因果建模（Spectral DCM）——一种用于从无创神经影像数据推断有效连接的贝叶斯状态空间建模方法。频谱DCM是目前静息态功能磁共振成像分析中应用最广泛的DCM变体。我们的目标是向状态空间建模和频谱数据分析领域专业知识有限的读者解释其技术基础。特别关注跨频谱密度这一特性，该特性是频谱DCM最显著的特征，且与通过（零延迟）皮尔逊相关系数测量的功能连接密切相关。事实上，频谱DCM估计的模型参数正是能最佳重现所有变量间所有时间延迟（包括通常被解释为功能连接的零延迟相关）的互相关关系的参数。我们从模型方程推导出功能连接矩阵，并展示改变单个有效连接参数如何影响所有成对相关。更复杂的是，呈现最大功能连接变化的脑区对不一定与呈现最大有效连接变化的脑区对重合。我们讨论了相关影响，并最后对频谱DCM的假设与局限性进行了全面总结。