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The Default Mode Network (DMN) is a brain system that mediates internal modes of cognitive activity, showing higher neural activation when one is at rest. Nowadays, there is a lot of interest in assessing functional interactions between its key regions, but in the majority of studies only association of Blood-oxygen-level dependent (BOLD) activation patterns is measured, so it is impossible to identify causal influences. There are some studies of causal interactions (i.e., effective connectivity), however often with inconsistent results. The aim of the current work is to find a stable pattern of connectivity between four DMN key regions: the medial prefrontal cortex (mPFC), the posterior cingulate cortex (PCC), left and right intraparietal cortex (LIPC and RIPC). For this purpose functional magnetic resonance imaging (fMRI) data from 30 healthy subjects (1000 time points from each one) was acquired and spectral dynamic causal modeling (DCM) on a resting-state fMRI data was performed. The endogenous brain fluctuations were explicitly modeled by Discrete Cosine Set at the low frequency band of 0.0078-0.1 Hz. The best model at the group level is the one where connections from both bilateral IPC to mPFC and PCC are significant and symmetrical in strength (p < 0.05). Connections between mPFC and PCC are bidirectional, significant in the group and weaker than connections originating from bilateral IPC. In general, all connections from LIPC/RIPC to other DMN regions are much stronger. One can assume that these regions have a driving role within the DMN. Our results replicate some data from earlier works on effective connectivity within the DMN as well as provide new insights on internal DMN relationships and brain's functioning at resting state.

Abstract To study social sequence learning, earlier functional magnetic resonance imaging (fMRI) studies investigated the neural correlates of a novel Belief Serial Reaction Time task in which participants learned sequences of beliefs held by protagonists. The results demonstrated the involvement of the mentalizing network in the posterior cerebellum and cerebral areas (e.g. temporoparietal junction, precuneus and temporal pole) during implicit and explicit social sequence learning. However, little is known about the neural functional interaction between these areas during this task. Dynamic causal modeling analyses for both implicit and explicit belief sequence learning revealed that the posterior cerebellar Crus I & II were effectively connected to cerebral mentalizing areas, especially the bilateral temporoparietal junction, via closed loops (i.e. bidirectional functional connections that initiate and terminate at the same cerebellar and cerebral areas). There were more closed loops during implicit than explicit learning, which may indicate that the posterior cerebellum may be more involved in implicitly learning sequential social information. Our analysis supports the general view that the posterior cerebellum receives incoming signals from critical mentalizing areas in the cerebrum to identify sequences of social actions and then sends signals back to the same cortical mentalizing areas to better prepare for others’ social actions and one’s responses to it.

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. •We describe a novel scheme for inverting non-linear models (e.g. DCMs) within subjects and linear models at the group level•We demonstrate this scheme is more robust to violations of the (commonly used) Laplace assumption than the standard approach•We validate the approach using a simulated mismatch negativity study of schizophrenia•We demonstrate the application of this scheme to classification and prediction of group membership

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.

This technical note introduces a dynamic causal model (DCM) for resting state fMRI time series based upon observed functional connectivity—as measured by the cross spectra among different brain regions. This DCM is based upon a deterministic model that generates predicted crossed spectra from a biophysically plausible model of coupled neuronal fluctuations in a distributed neuronal network or graph. Effectively, the resulting scheme finds the best effective connectivity among hidden neuronal states that explains the observed functional connectivity among haemodynamic responses. This is because the cross spectra contain all the information about (second order) statistical dependencies among regional dynamics. In this note, we focus on describing the model, its relationship to existing measures of directed and undirected functional connectivity and establishing its face validity using simulations. In subsequent papers, we will evaluate its construct validity in relation to stochastic DCM and its predictive validity in Parkinson's and Huntington's disease. •This paper describes an efficient estimation of resting state connectivity.•The scheme is based on fitting observed complex fMRI cross spectra.•This spectral DCM grandfathers functional connectivity and Granger causality.

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.

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.

Recently, there has been a lot of interest in characterising the connectivity of resting state brain networks. Most of the literature uses functional connectivity to examine these intrinsic brain networks. Functional connectivity has well documented limitations because of its inherent inability to identify causal interactions. Dynamic causal modelling (DCM) is a framework that allows for the identification of the causal (directed) connections among neuronal systems — known as effective connectivity. This technical note addresses the validity of a recently proposed DCM for resting state fMRI – as measured in terms of their complex cross spectral density – referred to as spectral DCM. Spectral DCM differs from (the alternative) stochastic DCM by parameterising neuronal fluctuations using scale free (i.e., power law) forms, rendering the stochastic model of neuronal activity deterministic. Spectral DCM not only furnishes an efficient estimation of model parameters but also enables the detection of group differences in effective connectivity, the form and amplitude of the neuronal fluctuations or both. We compare and contrast spectral and stochastic DCM models with endogenous fluctuations or state noise on hidden states. We used simulated data to first establish the face validity of both schemes and show that they can recover the model (and its parameters) that generated the data. We then used Monte Carlo simulations to assess the accuracy of both schemes in terms of their root mean square error. We also simulated group differences and compared the ability of spectral and stochastic DCMs to identify these differences. We show that spectral DCM was not only more accurate but also more sensitive to group differences. Finally, we performed a comparative evaluation using real resting state fMRI data (from an open access resource) to study the functional integration within default mode network using spectral and stochastic DCMs. •This paper provides construct validation of spectral DCM against stochastic DCM.•Spectral DCM is shown to be more accurate than stochastic DCM in terms of root mean square error.•Spectral DCM is shown to be more sensitive at identifying group differences.

Obsessive-compulsive disorder (OCD) is a chronic mental illness characterized by abnormal functional connectivity among distributed brain regions. Previous studies have primarily focused on undirected functional connectivity and rarely reported from network perspective. To better understand between or within-network connectivities of OCD, effective connectivity (EC) of a large-scale network is assessed by spectral dynamic causal modeling with eight key regions of interests from default mode (DMN), salience (SN), frontoparietal (FPN) and cerebellum networks, based on large sample size including 100 OCD patients and 120 healthy controls (HCs). Parametric empirical Bayes (PEB) framework was used to identify the difference between the two groups. We further analyzed the relationship between connections and Yale-Brown Obsessive Compulsive Scale (Y-BOCS). OCD and HCs shared some similarities of inter- and intra-network patterns in the resting state. Relative to HCs, patients showed increased ECs from left anterior insula (LAI) to medial prefrontal cortex, right anterior insula (RAI) to left dorsolateral prefrontal cortex (L-DLPFC), right dorsolateral prefrontal cortex (R-DLPFC) to cerebellum anterior lobe (CA), CA to posterior cingulate cortex (PCC) and to anterior cingulate cortex (ACC). Moreover, weaker from LAI to L-DLPFC, RAI to ACC, and the self-connection of R-DLPFC. Connections from ACC to CA and from L-DLPFC to PCC were positively correlated with compulsion and obsession scores ( = 0.209, = 0.037; = 0.199, = 0.047, uncorrected). Our study revealed dysregulation among DMN, SN, FPN, and cerebellum in OCD, emphasizing the role of these four networks in achieving top-down control for goal-directed behavior. There existed a top-down disruption among these networks, constituting the pathophysiological and clinical basis.

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several instantiations of this (epidemic) model to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity—and the exchange of people between regions—and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium.