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This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i.e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. The preliminary first level (subject specific) DCM for fMRI analysis is covered in a companion paper. Here, we detail group-level analysis procedures that are suitable for use with data from any neuroimaging modality. This paper is accompanied by an example dataset, together with step-by-step instructions demonstrating how to reproduce the analyses. • This guide walks through a group effective connectivity study using DCM and PEB. • It explains recently developed tools for hierarchical Bayesian modelling. • The appendices clarify the technical detail of the PEB framework and its priors. • An accompanying dataset is provided with step-by-step analysis instructions. [ABSTRACT FROM AUTHOR]

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity. [ABSTRACT FROM AUTHOR]

• Repeated face images cause decreased fMRI signal in early visual cortex (EVC), occipital face area (OFA), and fusiform face area (FFA). • The repetition suppression (RS) effect can be explained by the modulation of connectivity between EVC and OFA/FFA. • The between-region modulation supports synchronization and predictive coding theories of RS. • Face perception modulates nearly all within- and between-region connectivity, including direct connections from EVC to FFA. Stimulus repetition normally causes reduced neural activity in brain regions that process that stimulus. Some theories claim that this "repetition suppression" reflects local mechanisms such as neuronal fatigue or sharpening within a region, whereas other theories claim that it results from changed connectivity between regions, following changes in synchrony or top-down predictions. In this study, we applied dynamic causal modeling (DCM) on a public fMRI dataset involving repeated presentations of faces and scrambled faces to test whether repetition affected local (self-connections) and/or between-region connectivity in left and right early visual cortex (EVC), occipital face area (OFA) and fusiform face area (FFA). Face "perception" (faces versus scrambled faces) modulated nearly all connections, within and between regions, including direct connections from EVC to FFA, supporting a non-hierarchical view of face processing. Face "recognition" (familiar versus unfamiliar faces) modulated connections between EVC and OFA/FFA, particularly in the left hemisphere. Most importantly, immediate and delayed repetition of stimuli were also best captured by modulations of connections between EVC and OFA/FFA, but not self-connections of OFA/FFA, consistent with synchronization or predictive coding theories, though also possibly reflecting local mechanisms like synaptic depression. [ABSTRACT FROM AUTHOR]

This paper asks whether integrating multimodal EEG and fMRI data offers a better characterisation of functional brain architectures than either modality alone. This evaluation rests upon a dynamic causal model that generates both EEG and fMRI data from the same neuronal dynamics. We introduce the use of Bayesian fusion to provide informative (empirical) neuronal priors – derived from dynamic causal modelling (DCM) of EEG data – for subsequent DCM of fMRI data. To illustrate this procedure, we generated synthetic EEG and fMRI timeseries for a mismatch negativity (or auditory oddball) paradigm, using biologically plausible model parameters (i.e., posterior expectations from a DCM of empirical, open access, EEG data). Using model inversion, we found that Bayesian fusion provided a substantial improvement in marginal likelihood or model evidence, indicating a more efficient estimation of model parameters, in relation to inverting fMRI data alone. We quantified the benefits of multimodal fusion with the information gain pertaining to neuronal and haemodynamic parameters – as measured by the Kullback-Leibler divergence between their prior and posterior densities. Remarkably, this analysis suggested that EEG data can improve estimates of haemodynamic parameters; thereby furnishing proof-of-principle that Bayesian fusion of EEG and fMRI is necessary to resolve conditional dependencies between neuronal and haemodynamic estimators. These results suggest that Bayesian fusion may offer a useful approach that exploits the complementary temporal (EEG) and spatial (fMRI) precision of different data modalities. We envisage the procedure could be applied to any multimodal dataset that can be explained by a DCM with a common neuronal parameterisation. • Multimodal DCM shows how the same neuronal activity causes multiple measurements. • Bayesian fusion of EEG/fMRI resolves conditional dependencies between parameters. • Information gain quantifies the added benefits of multimodal Bayesian fusion. [ABSTRACT FROM AUTHOR]

This paper revisits the dynamic causal modelling of fMRI timeseries by replacing the usual (Taylor) approximation to neuronal dynamics with a neural mass model of the canonical microcircuit. This provides a generative or dynamic causal model of laminar specific responses that can generate haemodynamic and electrophysiological measurements. In principle, this allows the fusion of haemodynamic and (event related or induced) electrophysiological responses. Furthermore, it enables Bayesian model comparison of competing hypotheses about physiologically plausible synaptic effects; for example, does attentional modulation act on superficial or deep pyramidal cells – or both? In this technical note, we describe the resulting dynamic causal model and provide an illustrative application to the attention to visual motion dataset used in previous papers. Our focus here is on how to answer long-standing questions in fMRI; for example, do haemodynamic responses reflect extrinsic (afferent) input from distant cortical regions, or do they reflect intrinsic (recurrent) neuronal activity? To what extent do inhibitory interneurons contribute to neurovascular coupling? What is the relationship between haemodynamic responses and the frequency of induced neuronal activity? This paper does not pretend to answer these questions; rather it shows how they can be addressed using neural mass models of fMRI timeseries. • This paper describes a DCM for fMRI based on neural mass models and canonical microcircuits. • This enables the (Bayesian) fusion of EEG and fMRI data. • That encompasses the formal modelling of neurovascular coupling. • Offers a surprising insight into the relationship between haemodynamic and electrophysiological responses. [ABSTRACT FROM AUTHOR]

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain – using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison – asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software. • A method is introduced for Bayesian fusion of M/EEG and BOLD fMRI data using dynamic causal modelling. • The key novel contribution is the introduction of neural drive functions, which link models of the two modalities. • Bayesian model comparison is used to select plausible hypotheses about the function of neurovascular coupling. [ABSTRACT FROM AUTHOR]