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This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. [ABSTRACT FROM AUTHOR]

Human faces may signal relevant information and are therefore analysed rapidly and effectively by the brain. However, the precise mechanisms and pathways involved in rapid face processing are unclear. One view posits a role for a subcortical connection between early visual sensory regions and the amygdala, while an alternative account emphasises cortical mediation. To adjudicate between these functional architectures, we recorded magnetoencephalographic (MEG) evoked fields in human subjects to presentation of faces with varying emotional valence. Early brain activity was better explained by dynamic causal models containing a direct subcortical connection to the amygdala irrespective of emotional modulation. At longer latencies, models without a subcortical connection had comparable evidence. Hence, our results support the hypothesis that a subcortical pathway to the amygdala plays a role in rapid sensory processing of faces, in particular during early stimulus processing. This finding contributes to an understanding of the amygdala as a behavioural relevance detector. [ABSTRACT FROM AUTHOR]

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally, we show that this problem can be finessed by deriving spectral causality measures from Volterra kernels, estimated using dynamic causal modelling. [ABSTRACT FROM AUTHOR]

This paper examines intrinsic brain networks in light of recent developments in the characterisation of resting state fMRI timeseries -- and simulations of neuronal fluctuations based upon the connectome. Its particular focus is on patterns or modes of distributed activity that underlie functional connectivity. We first demonstrate that the eigenmodes of functional connectivity - or covariance among regions or nodes - are the same as the eigenmodes of the underlying effective connectivity, provided we limit ourselves to symmetrical connections. This symmetry constraint is motivated by appealing to proximity graphs based upon multidimensional scaling. Crucially, the principal modes of functional connectivity correspond to the dynamically unstable modes of effective connectivity that decay slowly and show long term memory. Technically, these modes have small negative Lyapunov exponents that approach zero from below. Interestingly, the superposition of modes - whose exponents are sampled from a power law distribution - produces classical 1/f (scale free) spectra. We conjecture that the emergence of dynamical instability - that underlies intrinsic brain networks - is inevitable in any system that is separated from external states by a Markov blanket. This conjecture appeals to a free energy formulation of nonequilibrium steady-state dynamics. The common theme that emerges from these theoretical considerations is that endogenous fluctuations are dominated by a small number of dynamically unstable modes. We use this as the basis of a dynamic causal model (DCM) of resting state fluctuations -- as measured in terms of their complex cross spectra. In this model, effective connectivity is parameterised in terms of eigenmodes and their Lyapunov exponents -- that can also be interpreted as locations in a multidimensional scaling space. Model inversion provides not only estimates of edges or connectivity but also the topography and dimensionality of the underlying scaling space. Here, we focus on conceptual issues with simulated fMRI data and provide an illustrative application using an empirical multi-region timeseries. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we address the problem of using dynamic causal modelling (DCM) to estimate the coupling parameters (effective connectivity) of large models with many regions. This is a potentially important problem because meaningful graph theoretic analyses of effective connectivity rest upon the statistics of the connections (edges). This calls for characterisations of networks with an appreciable number of regions (nodes). The problem here is that the number of coupling parameters grows quadratically with the number of nodes—leading to severe conditional dependencies among their estimates and a computational load that quickly becomes unsustainable. Here, we describe a simple solution, in which we use functional connectivity to provide prior constraints that bound the effective number of free parameters. In brief, we assume that priors over connections between individual nodes can be replaced by priors over connections between modes (patterns over nodes). By using a small number of modes, we can reduce the dimensionality of the problem in an informed way. The modes we use are the principal components or eigenvectors of the functional connectivity matrix. However, this approach begs the question of how many modes to use. This question can be addressed using Bayesian model comparison to optimise the number of modes. We imagine that this form of prior – over the extrinsic (endogenous) connections in large DCMs – may be useful for people interested in applying graph theory to distributed networks in the brain or to characterise connectivity beyond the subgraphs normally examined in DCM. [Copyright &y& Elsevier]

Abstract: This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity. This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series. The implicit adjacency matrix specifies the form of the network (e.g., cyclic or acyclic) and its graph-theoretical attributes (e.g., degree distribution). The scheme is illustrated using functional magnetic resonance imaging (fMRI) time series to discover functional brain networks. Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies. Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs. Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations. The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks. The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions. We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies. [Copyright &y& Elsevier]

Abstract: We describe the use of spatial and temporal constraints in dynamic causal modelling (DCM) of magneto- and electroencephalography (M/EEG) data. DCM for M/EEG is based on a spatiotemporal, generative model of electromagnetic brain activity. The temporal dynamics are described by neural-mass models of equivalent current dipole (ECD) sources and their spatial expression is modelled by parameterized lead-field functions. Often, in classical ECD models, symmetry constraints are used to model homologous pairs of dipoles in both hemispheres. These constraints are motivated by assumptions about symmetric activation of bilateral sensory sources. In classical approaches, these constraints are ‘hard’; i.e. the parameters of homologous dipoles are shared. Here, in the context of DCM, we illustrate the use of informed Bayesian priors to implement ‘soft’ symmetry constraints that are expressed in the posterior estimates only when supported by the data. Critically, with DCM one can deploy symmetry constraints in either the temporal or spatial components of the model. This enables one to test for symmetry in temporal (neural-mass) parameters in the presence of non-symmetric spatial expressions of homologous sources (and vice versa). Furthermore, we demonstrate that Bayesian model comparison can be used to identify the best models among a range of symmetric and non-symmetric variants. Our main finding is that the use of ‘soft’ symmetry priors is recommended for evoked responses to bilateral sensory input. We illustrate the use of symmetry constraints in DCM on synthetic and real EEG data. [Copyright &y& Elsevier]

Metastability is a key source of itinerant dynamics in the brain; namely, spontaneous spatiotemporal reorganization of neuronal activity. This itinerancy has been the focus of numerous dynamic functional connectivity (DFC) analyses – developed to characterize the formation and dissolution of distributed functional patterns over time, using resting state fMRI. However, aside from technical and practical controversies, these approaches cannot recover the neuronal mechanisms that underwrite itinerant (e.g., metastable) dynamics—due to their descriptive, model-free nature. We argue that effective connectivity (EC) analyses are more apt for investigating the neuronal basis of metastability. To this end, we appeal to biologically-grounded models (i.e., dynamic causal modelling, DCM) and dynamical systems theory (i.e., heteroclinic sequential dynamics) to create a probabilistic, generative model of haemodynamic fluctuations. This model generates trajectories in the parametric space of EC modes (i.e., states of connectivity) that characterize functional brain architectures. In brief, it extends an established spectral DCM, to generate functional connectivity data features that change over time. This foundational paper tries to establish the model's face validity by simulating non-stationary fMRI time series and recovering key model parameters (i.e., transition probabilities among connectivity states and the parametric nature of these states) using variational Bayes. These data are further characterized using Bayesian model comparison (within and between subjects). Finally, we consider practical issues that attend applications and extensions of this scheme. Importantly, the scheme operates within a generic Bayesian framework – that can be adapted to study metastability and itinerant dynamics in any non-stationary time series. [ABSTRACT FROM AUTHOR]

Abstract: In this note, we describe a variant of dynamic causal modelling for evoked responses as measured with electroencephalography or magnetoencephalography (EEG and MEG). We depart from equivalent current dipole formulations of DCM, and extend it to provide spatiotemporal source estimates that are spatially distributed. The spatial model is based upon neural-field equations that model neuronal activity on the cortical manifold. We approximate this description of electrocortical activity with a set of local standing-waves that are coupled though their temporal dynamics. The ensuing distributed DCM models source as a mixture of overlapping patches on the cortical mesh. Time-varying activity in this mixture, caused by activity in other sources and exogenous inputs, is propagated through appropriate lead-field or gain-matrices to generate observed sensor data. This spatial model has three key advantages. First, it is more appropriate than equivalent current dipole models, when real source activity is distributed locally within a cortical area. Second, the spatial degrees of freedom of the model can be specified and therefore optimised using model selection. Finally, the model is linear in the spatial parameters, which finesses model inversion. Here, we describe the distributed spatial model and present a comparative evaluation with conventional equivalent current dipole (ECD) models of auditory processing, as measured with EEG. [Copyright &y& Elsevier]

Abstract: Dynamic causal modelling is an approach to characterising evoked responses as measured by magneto/electroencephalography (M/EEG). A dynamic causal model (DCM) is a spatiotemporal, generative network model for event-related fields/responses (ERP/ERF) data. Using Bayesian model inversion, one can compute the posterior distributions of the DCM’s physiological parameters and its marginal likelihood for model comparison. Model comparison can be used to test mechanistic hypotheses about how electrophysiological data were generated. In this work, we look at the relative importance of changes in intrinsic (within source) and extrinsic (between sources) connections in generating mismatch responses. In short, we introduce the modulation of intrinsic connectivity to the DCM framework. This is useful for testing hypotheses about adaptation of neuronal responses to local influences, in relation to influences that are mediated by long-range extrinsic connections (forward, backward, and lateral) from other sources. We illustrate this extension using synthetic data and empirical data from an oddball ERP experiment. [Copyright &y& Elsevier]

• We developed neurochemistry-enriched dynamic causal model of resting-state MEG data using MRS measurements of neurotransmitter concentrations. • Neurotransmitter levels, place prior constraints on synaptic connectivity, in the biologically informed model of MEG data. • Comparing evidence of group DCMs using Bayesian model selection procedure reveal synaptic connections that are likely to be informed by MRS data. We present a hierarchical empirical Bayesian framework for testing hypotheses about neurotransmitters' concertation as empirical prior for synaptic physiology using ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography data (MEG). A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of individuals' neurophysiological observations. At the second level, individuals' 7T-MRS estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the group-wise evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction (BMR), parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare alternative model evidence of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the subset of synaptic connections that are influenced by individual differences in neurotransmitter levels, as measured by 7T-MRS. We demonstrate the method using resting-state MEG (i.e., task-free recording) and 7T-MRS data from healthy adults. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. Using within-subject split-sampling of the MEG dataset (i.e., validation by means of a held-out dataset), we show that model comparison for hypothesis testing can be highly reliable. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to reveal the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions. [ABSTRACT FROM AUTHOR]

Abstract Parkinson's disease (PD) is a neurodegenerative condition in which aberrant oscillatory synchronization of neuronal activity at beta frequencies (15–35 Hz) across the cortico-basal ganglia-thalamocortical circuit is associated with debilitating motor symptoms, such as bradykinesia and rigidity. Mounting evidence suggests that the magnitude of beta synchrony in the parkinsonian state fluctuates over time, but the mechanisms by which thalamocortical circuitry regulates the dynamic properties of cortical beta in PD are poorly understood. Using the recently developed generic Dynamic Causal Modelling (DCM) framework, we recursively optimized a set of plausible models of the thalamocortical circuit (n = 144) to infer the neural mechanisms that best explain the transitions between low and high beta power states observed in recordings of field potentials made in the motor cortex of anesthetized Parkinsonian rats. Bayesian model comparison suggests that upregulation of cortical rhythmic activity in the beta-frequency band results from changes in the coupling strength both between and within the thalamus and motor cortex. Specifically, our model indicates that high levels of cortical beta synchrony are mainly achieved by a delayed (extrinsic) input from thalamic relay cells to deep pyramidal cells and a fast (intrinsic) input from middle pyramidal cells to superficial pyramidal cells. From a clinical perspective, our study provides insights into potential therapeutic strategies that could be utilized to modulate the network mechanisms responsible for the enhancement of cortical beta in PD. Specifically, we speculate that cortical stimulation aimed to reduce the enhanced excitatory inputs to either the superficial or deep pyramidal cells could be a potential non-invasive therapeutic strategy for PD. Highlights • Coupling changes within and between circuit nodes lead to cortical beta enhancement. • Input propagation delays play a crucial role in the up-regulation of cortical beta. • Beta power could be modulated by altering lamina specific inputs. [ABSTRACT FROM AUTHOR]

Abstract We present a technical development in the dynamic causal modelling of electrophysiological responses that combines qualitatively different neural mass models within a single network. This affords the option to couple various cortical and subcortical nodes that differ in their form and dynamics. Moreover, it enables users to implement new neural mass models in a straightforward and standardized way. This generic framework hence supports flexibility and facilitates the exploration of increasingly plausible models. We illustrate this by coupling a basal ganglia-thalamus model to a (previously validated) cortical model developed specifically for motor cortex. The ensuing DCM is used to infer pathways that contribute to the suppression of beta oscillations induced by dopaminergic medication in patients with Parkinson's disease. Experimental recordings were obtained from deep brain stimulation electrodes (implanted in the subthalamic nucleus) and simultaneous magnetoencephalography. In line with previous studies, our results indicate a reduction of synaptic efficacy within the circuit between the subthalamic nucleus and external pallidum, as well as reduced efficacy in connections of the hyperdirect and indirect pathway leading to this circuit. This work forms the foundation for a range of modelling studies of the synaptic mechanisms (and pathophysiology) underlying event-related potentials and cross-spectral densities. Highlights • We present a generic framework that affords a flexible implementation of DCM. • Different cortical and subcortical nodes can now be combined within a network. • User specified modulatory effects on intrinsic connections are accommodated. • We used a cortical-basal ganglia DCM to study beta oscillations in Parkinsonism. • Dopamine reduces synaptic efficacy within hyper and indirect pathways. [ABSTRACT FROM AUTHOR]

This paper shows that it is possible to estimate the subjective precision (inverse variance) of Bayesian beliefs during oculomotor pursuit. Subjects viewed a sinusoidal target, with or without random fluctuations in its motion. Eye trajectories and magnetoencephalographic (MEG) data were recorded concurrently. The target was periodically occluded, such that its reappearance caused a visual evoked response field (ERF). Dynamic causal modelling (DCM) was used to fit models of eye trajectories and the ERFs. The DCM for pursuit was based on predictive coding and active inference, and predicts subjects' eye movements based on their (subjective) Bayesian beliefs about target (and eye) motion. The precisions of these hierarchical beliefs can be inferred from behavioural (pursuit) data. The DCM for MEG data used an established biophysical model of neuronal activity that includes parameters for the gain of superficial pyramidal cells, which is thought to encode precision at the neuronal level. Previous studies (using DCM of pursuit data) suggest that noisy target motion increases subjective precision at the sensory level: i.e., subjects attend more to the target's sensory attributes. We compared (noisy motion-induced) changes in the synaptic gain based on the modelling of MEG data to changes in subjective precision estimated using the pursuit data. We demonstrate that imprecise target motion increases the gain of superficial pyramidal cells in V1 (across subjects). Furthermore, increases in sensory precision – inferred by our behavioural DCM – correlate with the increase in gain in V1, across subjects. This is a step towards a fully integrated model of brain computations, cortical responses and behaviour that may provide a useful clinical tool in conditions like schizophrenia. [ABSTRACT FROM AUTHOR]

Abstract: Mesial temporal lobe epilepsy (mTLE) is the most prevalent form of focal epilepsy, and hippocampal sclerosis (HS) is considered the most frequent associated pathological finding. Recent connectivity studies have shown that abnormalities, either structural or functional, are not confined to the affected hippocampus, but can be found in other connected structures within the same hemisphere, or even in the contralesional hemisphere. Despite the role of hippocampus in memory functions, most of these studies have explored network properties at resting state, and in some cases compared connectivity values with neuropsychological memory scores. Here, we measured magnetoencephalographic responses during verbal working memory (WM) encoding in left mTLE patients and controls, and compared their effective connectivity within a frontotemporal network using dynamic causal modelling. Bayesian model comparison indicated that the best model included bilateral, forward and backward connections, linking inferior temporal cortex (ITC), inferior frontal cortex (IFC), and the medial temporal lobe (MTL). Test for differences in effective connectivity revealed that patients exhibited decreased ipsilesional MTL-ITC backward connectivity, and increased bidirectional IFC-MTL connectivity in the contralesional hemisphere. Critically, a negative correlation was observed between these changes in patients, with decreases in ipsilesional coupling among temporal sources associated with increases contralesional frontotemporal interactions. Furthermore, contralesional frontotemporal interactions were inversely related to task performance and level of education. The results demonstrate that unilateral sclerosis induced local and remote changes in the dynamic organization of a distributed network supporting verbal WM. Crucially, pre-(peri) morbid factors (educational level) were reflected in both cognitive performance and (putative) compensatory changes in physiological coupling. [Copyright &y& Elsevier]

Abstract: Functional integration in the brain rests on anatomical connectivity (the presence of axonal connections) and effective connectivity (the causal influences mediated by these connections). The deployment of anatomical connections provides important constraints on effective connectivity, but does not fully determine it, because synaptic connections can be expressed functionally in a dynamic and context-dependent fashion. Although it is generally assumed that anatomical connectivity data is important to guide the construction of neurobiologically realistic models of effective connectivity; the degree to which these models actually profit from anatomical constraints has not yet been formally investigated. Here, we use diffusion weighted imaging and probabilistic tractography to specify anatomically informed priors for dynamic causal models (DCMs) of fMRI data. We constructed 64 alternative DCMs, which embodied different mappings between the probability of an anatomical connection and the prior variance of the corresponding of effective connectivity, and fitted them to empirical fMRI data from 12 healthy subjects. Using Bayesian model selection, we show that the best model is one in which anatomical probability increases the prior variance of effective connectivity parameters in a nonlinear and monotonic (sigmoidal) fashion. This means that the higher the likelihood that a given connection exists anatomically, the larger one should set the prior variance of the corresponding coupling parameter; hence making it easier for the parameter to deviate from zero and represent a strong effective connection. To our knowledge, this study provides the first formal evidence that probabilistic knowledge of anatomical connectivity can improve models of functional integration. [Copyright &y& Elsevier]

Abstract: Bayesian model selection (BMS) is a powerful method for determining the most likely among a set of competing hypotheses about the mechanisms that generated observed data. BMS has recently found widespread application in neuroimaging, particularly in the context of dynamic causal modelling (DCM). However, so far, combining BMS results from several subjects has relied on simple (fixed effects) metrics, e.g. the group Bayes factor (GBF), that do not account for group heterogeneity or outliers. In this paper, we compare the GBF with two random effects methods for BMS at the between-subject or group level. These methods provide inference on model-space using a classical and Bayesian perspective respectively. First, a classical (frequentist) approach uses the log model evidence as a subject-specific summary statistic. This enables one to use analysis of variance to test for differences in log-evidences over models, relative to inter-subject differences. We then consider the same problem in Bayesian terms and describe a novel hierarchical model, which is optimised to furnish a probability density on the models themselves. This new variational Bayes method rests on treating the model as a random variable and estimating the parameters of a Dirichlet distribution which describes the probabilities for all models considered. These probabilities then define a multinomial distribution over model space, allowing one to compute how likely it is that a specific model generated the data of a randomly chosen subject as well as the exceedance probability of one model being more likely than any other model. Using empirical and synthetic data, we show that optimising a conditional density of the model probabilities, given the log-evidences for each model over subjects, is more informative and appropriate than both the GBF and frequentist tests of the log-evidences. In particular, we found that the hierarchical Bayesian approach is considerably more robust than either of the other approaches in the presence of outliers. We expect that this new random effects method will prove useful for a wide range of group studies, not only in the context of DCM, but also for other modelling endeavours, e.g. comparing different source reconstruction methods for EEG/MEG or selecting among competing computational models of learning and decision-making. [Copyright &y& Elsevier]

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]

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]

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]