  Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden
(latent) neuronal states, based on measurements of brain activity. Since its
introduction in 2003 for functional magnetic resonance imaging data, DCM has
been extended to electrophysiological data, and several variants have been
developed. Their biophysically motivated formulations make these models
promising candidates for providing a mechanistic understanding of human brain
dynamics, both in health and disease. However, due to their complexity and
reliance on concepts from several fields, fully understanding the mathematical
and conceptual basis behind certain variants of DCM can be challenging. At the
same time, a solid theoretical knowledge of the models is crucial to avoid
pitfalls in the application of these models and interpretation of their
results. In this paper, we focus on one of the most advanced formulations of
DCM, i.e. conductance-based DCM for cross-spectral densities, whose components
are described across multiple technical papers. The aim of the present article
is to provide an accessible exposition of the mathematical background, together
with an illustration of the model's behavior. To this end, we include
step-by-step derivations of the model equations, point to important aspects in
the software implementation of those models, and use simulations to provide an
intuitive understanding of the type of responses that can be generated and the
role that specific parameters play in the model. Furthermore, all code utilized
for our simulations is made publicly available alongside the manuscript to
allow readers an easy hands-on experience with conductance-based DCM.
