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Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden(latent) neuronal states, based on measurements of brain activity. Since itsintroduction in 2003 for functional magnetic resonance imaging data, DCM hasbeen extended to electrophysiological data, and several variants have beendeveloped. Their biophysically motivated formulations make these modelspromising candidates for providing a mechanistic understanding of human braindynamics, both in health and disease. However, due to their complexity andreliance on concepts from several fields, fully understanding the mathematicaland conceptual basis behind certain variants of DCM can be challenging. At thesame time, a solid theoretical knowledge of the models is crucial to avoidpitfalls in the application of these models and interpretation of theirresults. In this paper, we focus on one of the most advanced formulations ofDCM, i.e. conductance-based DCM for cross-spectral densities, whose componentsare described across multiple technical papers. The aim of the present articleis to provide an accessible exposition of the mathematical background, togetherwith an illustration of the model's behavior. To this end, we includestep-by-step derivations of the model equations, point to important aspects inthe software implementation of those models, and use simulations to provide anintuitive understanding of the type of responses that can be generated and therole that specific parameters play in the model. Furthermore, all code utilizedfor our simulations is made publicly available alongside the manuscript toallow readers an easy hands-on experience with conductance-based DCM.

Conductance-based Dynamic Causal Modeling: A mathematical review of its application to cross-power spectral densities