Dynamic causal modeling (DCM) is a generic Bayesian framework for inferring hidden neuronal states from measurements of brain activity. It provides posterior estimates of neurobiologically interpretable quantities such as the effective strength of synaptic connections among neuronal populations and their context-dependent modulation. DCM is increasingly used in the analysis of a wide range of neuroimaging and electrophysiological data. Given the relative complexity of DCM, compared to conventional analysis techniques, a good knowledge of its theoretical foundations is needed to avoid pitfalls in its application and interpretation of results. By providing good practice recommendations for DCM, in the form of ten simple rules, we hope that this article serves as a helpful tutorial for the growing community of DCM users.

In Bayesian brain theories, hierarchically related prediction errors (PEs) play a central role for predicting sensory inputs and inferring their underlying causes, e.g., the probabilistic structure of the environment and its volatility. Notably, PEs at different hierarchical levels may be encoded by different neuromodulatory transmitters. Here, we tested this possibility in computational fMRI studies of audio-visual learning. Using a hierarchical Bayesian model, we found that low-level PEs about visual stimulus outcome were reflected by widespread activity in visual and supramodal areas but also in the midbrain. In contrast, high-level PEs about stimulus probabilities were encoded by the basal forebrain. These findings were replicated in two groups of healthy volunteers. While our fMRI measures do not reveal the exact neuron types activated in midbrain and basal forebrain, they suggest a dichotomy between neuromodulatory systems, linking dopamine to low-level PEs about stimulus outcome and acetylcholine to more abstract PEs about stimulus probabilities.

Models of effective connectivity characterize the influence that neuronal populations exert over each other. Additionally, some approaches, for example Dynamic Causal Modelling (DCM) and variants of Structural Equation Modelling, describe how effective connectivity is modulated by experimental manipulations. Mathematically, both are based on bilinear equations, where the bilinear term models the effect of experimental manipulations on neuronal interactions. The bilinear framework, however, precludes an important aspect of neuronal interactions that has been established with invasive electrophysiological recording studies; i.e., how the connection between two neuronal units is enabled or gated by activity in other units. These gating processes are critical for controlling the gain of neuronal populations and are mediated through interactions between synaptic inputs (e.g. by means of voltage-sensitive ion channels). They represent a key mechanism for various neurobiological processes, including top-down (e.g. attentional) modulation, learning and neuromodulation. This paper presents a nonlinear extension of DCM that models such processes (to second order) at the neuronal population level. In this way, the modulation of network interactions can be assigned to an explicit neuronal population. We present simulations and empirical results that demonstrate the validity and usefulness of this model. Analyses of synthetic data showed that nonlinear and bilinear mechanisms can be distinguished by our extended DCM. When applying the model to empirical fMRI data from a blocked attention to motion paradigm, we found that attentioninduced increases in V5 responses could be best explained as a gating of the V1→V5 connection by activity in posterior parietal cortex. Furthermore, we analysed fMRI data from an event-related binocular rivalry paradigm and found that interactions amongst percept-selective visual areas were modulated by activity in the middle frontal gyrus. In both practical examples, Bayesian model selection favoured the nonlinear models over corresponding bilinear ones.