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Existing whole-brain models are generally tailored to the modelling of a particular data modality (e.g., fMRI or MEG/EEG). We propose that despite the differing aspects of neural activity each modality captures, they originate from shared network dynamics. Building on the universal principles of self-organising delay-coupled nonlinear systems, we aim to link distinct features of brain activity - captured across modalities - to the dynamics unfolding on a macroscopic structural connectome. To jointly predict connectivity, spatiotemporal and transient features of distinct signal modalities, we consider two large-scale models - the Stuart Landau and Wilson and Cowan models - which generate short-lived 40 Hz oscillations with varying levels of realism. To this end, we measure features of functional connectivity and metastable oscillatory modes (MOMs) in fMRI and MEG signals - and compare them against simulated data. We show that both models can represent MEG functional connectivity (FC), functional connectivity dynamics (FCD) and generate MOMs to a comparable degree. This is achieved by adjusting the global coupling and mean conduction time delay and, in the WC model, through the inclusion of balance between excitation and inhibition. For both models, the omission of delays dramatically decreased the performance. For fMRI, the SL model performed worse for FCD and MOMs, highlighting the importance of balanced dynamics for the emergence of spatiotemporal and transient patterns of ultra-slow dynamics. Notably, optimal working points varied across modalities and no model was able to achieve a correlation with empirical FC higher than 0.4 across modalities for the same set of parameters. Nonetheless, both displayed the emergence of FC patterns that extended beyond the constraints of the anatomical structure. Finally, we show that both models can generate MOMs with empirical-like properties such as size (number of brain regions engaging in a mode) and duration (continuous time interval during which a mode appears). Our results demonstrate the emergence of static and dynamic properties of neural activity at different timescales from networks of delay-coupled oscillators at 40 Hz. Given the higher dependence of simulated FC on the underlying structural connectivity, we suggest that mesoscale heterogeneities in neural circuitry may be critical for the emergence of parallel cross-modal functional networks and should be accounted for in future modelling endeavours., Competing Interests: Declaration of Competing Interest Authors declare that they have no competing interests., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function-and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity-accompanied with adaptation of firing thresholds-is a sufficient neuronal substrate to attain Bayes optimal inference and control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control., (© 2022. The Author(s).)

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., (Copyright © 2021. Published by Elsevier Inc.)

The propagation of epileptic seizure activity in the brain is a widespread pathophysiology that, in principle, should yield to intervention techniques guided by mathematical models of neuronal ensemble dynamics. During a seizure, neural activity will deviate from its current dynamical regime to one in which there are significant signal fluctuations. In silico treatments of neural activity are an important tool for the understanding of how the healthy brain can maintain stability, as well as of how pathology can lead to seizures. The hope is that, contained within the mathematical foundations of such treatments, there lie potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the dynamic causal modelling neuronal state equation generalises to a Fokker-Planck formalism if one extends the framework to model the ways in which activity propagates along the structural connections of neural systems. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity-i.e., by lowering the rate at which neuronal fluctuations disperse to neighbouring regions. We show, for neural systems prone to epileptic seizures, that such a reduction in diffusivity can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror the activity profile of a pathological region in its functionally connected areas. This counter-intuitive method is intended to be used pre-emptively-i.e., in order to mitigate the effects of the seizure, or ideally even prevent it from occurring in the first place. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network prior to seizure onset. Our hope is that this technique can form the basis for future real-time monitoring and intervention devices that are capable of treating epilepsy in a non-invasive manner., Competing Interests: The authors have declared that no competing interests exist.

The moment-to-moment focus of our mind's eye results from a complex interplay of voluntary and involuntary influences on attention. Previous neuroimaging studies suggest that the brain networks of voluntary versus involuntary attention can be segregated into a frontal-versus-parietal or a dorsal-versus-ventral partition-although recent work suggests that the dorsal network may be involved in both bottom-up and top-down attention. Research with nonhuman primates has provided evidence that a key distinction between top-down and bottom-up attention may be the direction of connectivity between frontal and parietal areas. Whereas typical fMRI connectivity analyses cannot disambiguate the direction of connections, dynamic causal modeling (DCM) can model directionality. Using DCM, we provide new evidence that directed connections within the dorsal attention network are differentially modulated for voluntary versus involuntary attention. These results suggest that the intraparietal sulcus exerts a baseline inhibitory effect on the frontal eye fields that is strengthened during exogenous orienting and attenuated during endogenous orienting. Furthermore, the attenuation from endogenous attention occurs even with salient peripheral cues when those cues are known to be counter predictive. Thus, directed connectivity between frontal and parietal regions of the dorsal attention network is highly influenced by the type of attention that is engaged., (© 2019 The Authors. Human Brain Mapping published by Wiley Periodicals, Inc.)

The influence of global BOLD fluctuations on resting state functional connectivity in fMRI data remains a topic of debate, with little consensus. In this study, we assessed the effects of global signal regression (GSR) on effective connectivity within and between resting state networks (RSNs) - as estimated with dynamic causal modelling (DCM) for resting state fMRI (rsfMRI). DCM incorporates a forward (generative) model that quantifies the contribution of different types of noise (including global measurement noise), effective connectivity, and (neuro)vascular processes to functional connectivity measurements. DCM analyses were applied to two different designs; namely, longitudinal and cross-sectional designs. In the modelling of longitudinal designs, we considered four extensive longitudinal resting state fMRI datasets with a total number of 20 subjects. In the analysis of cross-sectional designs, we used rsfMRI data from 361 subjects from the Human Connectome Project. We hypothesized that (1) GSR would have no discernible impact on effective connectivity estimated with DCM, and (2) GSR would be reflected in the parameters representing global measurement noise. Additionally, we performed comparative analyses of information gain with and without GSR. Our results showed negligible to small effects of GSR on effective connectivity within small (separately estimated) RSNs. However, although the effect sizes were small, there was substantial to conclusive evidence for an effect of GSR on connectivity parameters. For between-network connectivity, we found two important effects: the effect of GSR on between-network effective connectivity (averaged over all connections) was negligible to small, while the effect of GSR on individual connections was non-negligible. In the cross-sectional (but not in the longitudinal) data, some connections showed substantial to conclusive evidence for an effect of GSR. Contrary to our expectations, we found either no effect (in the longitudinal designs) or a non-specific (cross-sectional design) effect of GSR on parameters characterising (global) measurement noise. Data without GSR were found to be more informative than data with GSR; however, in small resting state networks the precision of posterior estimates was greater after GSR. In conclusion, GSR is a minor concern in DCM studies; however, quantitative interpretation of between-network connections (as opposed to average between-network connectivity) and noise parameters should be treated with some caution. The Kullback-Leibler divergence of the posterior from the prior (i.e., information gain) - together with the precision of posterior estimates - might offer a useful measure to assess the appropriateness of GSR in resting state fMRI., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2019. Published by Elsevier Inc.)

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., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

Functional and effective connectivity are known to change systematically over time. These changes might be explained by several factors, including intrinsic fluctuations in activity-dependent neuronal coupling and contextual factors, like experimental condition and time. Furthermore, contextual effects may be subject-specific or conserved over subjects. To characterize fluctuations in effective connectivity, we used dynamic causal modelling (DCM) of cross spectral responses over 1- min of electroencephalogram (EEG) recordings during rest, divided into 1-sec windows. We focused on two intrinsic networks: the default mode and the saliency network. DCM was applied to estimate connectivity in each time-window for both networks. Fluctuations in DCM connectivity parameters were assessed using hierarchical parametric empirical Bayes (PEB). Within-subject, between-window effects were modelled with a second-level linear model with temporal basis functions as regressors. This procedure was conducted for every subject separately. Bayesian model reduction was then used to assess which (combination of) temporal basis functions best explain dynamic connectivity over windows. A third (between-subject) level model was used to infer which dynamic connectivity parameters are conserved over subjects. Our results indicate that connectivity fluctuations in the default mode network and to a lesser extent the saliency network comprised both subject-specific components and a common component. For both networks, connections to higher order regions appear to monotonically increase during the 1- min period. These results not only establish the predictive validity of dynamic connectivity estimates - in virtue of detecting systematic changes over subjects - they also suggest a network-specific dissociation in the relative contribution of fluctuations in connectivity that depend upon experimental context. We envisage these procedures could be useful for characterizing brain state transitions that may be explained by their cognitive or neuropathological underpinnings., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

A fundamental question in systems neuroscience is how endogenous neuronal activity self-organizes during particular brain states. Recent neuroimaging studies have demonstrated systematic relationships between resting-state and task-induced functional connectivity (FC). In particular, continuous task studies, such as movie watching, speak to alterations in coupling among cortical regions and enhanced fluctuations in FC compared to the resting-state. This suggests that FC may reflect systematic and large-scale reorganization of functionally integrated responses while subjects are watching movies. In this study, we characterized fluctuations in FC during resting-state and movie-watching conditions. We found that the FC patterns induced systematically by movie-watching can be explained with a single principal component. These condition-specific FC fluctuations overlapped with inter-subject synchronization patterns in occipital and temporal brain regions. However, unlike inter-subject synchronization, condition-specific FC patterns were characterized by increased correlations within frontal brain regions and reduced correlations between frontal-parietal brain regions. We investigated these condition-specific functional variations as a shorter time scale, using time-resolved FC. The time-resolved FC showed condition-specificity over time; notably when subjects watched both the same and different movies. To explain self-organisation of global FC through the alterations in local dynamics, we used a large-scale computational model. We found that condition-specific reorganization of FC could be explained by local changes that engendered changes in FC among higher-order association regions, mainly in frontal and parietal cortices., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Dynamic causal modelling (DCM) for resting state fMRI - namely spectral DCM - is a recently developed and widely adopted method for inferring effective connectivity in intrinsic brain networks. Most applications of spectral DCM have focused on group-averaged connectivity within large-scale intrinsic brain networks; however, the consistency of subject- and session-specific estimates of effective connectivity has not been evaluated. Establishing reliability (within subjects) is crucial for its clinical use; e.g., as a neurophysiological phenotype of disease progression. Effective connectivity during rest is likely to vary due to changes in cognitive, and physiological states. Quantifying these variations may help understand functional brain architectures - and inform clinical applications. In the present study, we investigated the consistency of effective connectivity within and between subjects, as well as potential sources of variability (e.g., hemispheric asymmetry). We also addressed the effects on consistency of standard data processing procedures. DCM analyses were applied to four longitudinal resting state fMRI datasets. Our sample comprised 17 subjects with 589 resting state fMRI sessions in total. These data allowed us to quantify the robustness of connectivity estimates for each subject, and to generalise our conclusions beyond specific data features. We found that subjects showed systematic and reliable patterns of hemispheric asymmetry. When asymmetry was taken into account, subjects showed very similar connectivity patterns. We also found that various processing procedures (e.g. global signal regression and ROI size) had little effect on inference and the reliability of connectivity estimates for the majority of subjects. Finally, Bayesian model reduction significantly increased the consistency of connectivity patterns., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

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., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Context-sensitive and activity-dependent fluctuations in connectivity underlie functional integration in the brain and have been studied widely in terms of synaptic plasticity, learning and condition-specific (e.g., attentional) modulations of synaptic efficacy. This dynamic aspect of brain connectivity has recently attracted a lot of attention in the resting state fMRI community. To explain dynamic functional connectivity in terms of directed effective connectivity among brain regions, we introduce a novel method to identify dynamic effective connectivity using spectral dynamic causal modelling (spDCM). We used parametric empirical Bayes (PEB) to model fluctuations in directed coupling over consecutive windows of resting state fMRI time series. Hierarchical PEB can model random effects on connectivity parameters at the second (between-window) level given connectivity estimates from the first (within-window) level. In this work, we used a discrete cosine transform basis set or eigenvariates (i.e., expression of principal components) to model fluctuations in effective connectivity over windows. We evaluated the ensuing dynamic effective connectivity in terms of the consistency of baseline connectivity within default mode network (DMN), using the resting state fMRI from Human Connectome Project (HCP). To model group-level baseline and dynamic effective connectivity for DMN, we extended the PEB approach by conducting a multilevel PEB analysis of between-session and between-subject group effects. Model comparison clearly spoke to dynamic fluctuations in effective connectivity - and the dynamic functional connectivity these changes explain. Furthermore, baseline effective connectivity was consistent across independent sessions - and notably more consistent than estimates based upon conventional models. This work illustrates the advantage of hierarchical modelling with spDCM, in characterizing the dynamics of effective connectivity., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

Our behavior entails a flexible and context-sensitive interplay between brain areas to integrate information according to goal-directed requirements. However, the neural mechanisms governing the entrainment of functionally specialized brain areas remain poorly understood. In particular, the question arises whether observed changes in the regional activity for different cognitive conditions are explained by modifications of the inputs to the brain or its connectivity? We observe that transitions of fMRI activity between areas convey information about the tasks performed by 19 subjects, watching a movie versus a black screen (rest). We use a model-based framework that explains this spatiotemporal functional connectivity pattern by the local variability for 66 cortical regions and the network effective connectivity between them. We find that, among the estimated model parameters, movie viewing affects to a larger extent the local activity, which we interpret as extrinsic changes related to the increased stimulus load. However, detailed changes in the effective connectivity preserve a balance in the propagating activity and select specific pathways such that high-level brain regions integrate visual and auditory information, in particular boosting the communication between the two brain hemispheres. These findings speak to a dynamic coordination underlying the functional integration in the brain., (Copyright © 2017. Published by Elsevier Inc.)

Although the relationship between resting-state functional connectivity and task-related activity has been addressed, the relationship between task and resting-state directed or effective connectivity - and its behavioral concomitants - remains elusive. We evaluated effective connectivity under an N-back working memory task in 24 participants using stochastic dynamic causal modelling (DCM) of 7 T fMRI data. We repeated the analysis using resting-state data, from the same subjects, to model connectivity among the same brain regions engaged by the N-back task. This allowed us to: (i) examine the relationship between intrinsic (task-independent) effective connectivity during resting (A rest ) and task states (A task ), (ii) cluster phenotypes of task-related changes in effective connectivity (B task ) across participants, (iii) identify edges (B task ) showing high inter-individual effective connectivity differences and (iv) associate reaction times with the similarity between B task and A rest in these edges. We found a strong correlation between A rest and A task over subjects but a marked difference between B task and A rest . We further observed a strong clustering of individuals in terms of B task , which was not apparent in A rest . The task-related effective connectivity B task varied highly in the edges from the parietal to the frontal lobes across individuals, so the three groups were clustered mainly by the effective connectivity within these networks. The similarity between B task and A rest at the edges from the parietal to the frontal lobes was positively correlated with 2-back reaction times. This result implies that a greater change in context-sensitive coupling - from resting-state connectivity - is associated with faster reaction times. In summary, task-dependent connectivity endows resting-state connectivity with a context sensitivity, which predicts the speed of information processing during the N-back task., (Copyright © 2017 Elsevier Inc. All rights reserved.)

An important characteristic of spontaneous brain activity is the anticorrelation between the core default network (cDN) and the dorsal attention network (DAN) and the salience network (SN). This anticorrelation may constitute a key aspect of functional anatomy and is implicated in several brain disorders. We used dynamic causal modeling to assess the hypothesis that a causal hierarchy underlies this anticorrelation structure, using resting-state fMRI of healthy adolescent and young adults (N = 404). Our analysis revealed an asymmetric effective connectivity, such that the regions in the SN and DAN exerted an inhibitory influence on the cDN regions; whereas the cDN exerted an excitatory influence on the SN and DAN regions. The relative strength of efferent versus afferent connections places the SN at the apex of the hierarchy, suggesting that the SN modulates anticorrelated networks with descending hierarchical connections. In short, this study of directed neuronal coupling reveals a causal hierarchical architecture that generates or orchestrates anticorrelation of brain activity. These new findings shed light on functional integration of intrinsic brain networks at rest and speak to future dynamic causal modeling studies of large-scale networks., (© The Author 2017. Published by Oxford University Press.)

Many analysis methods exist to extract graphs of functional connectivity from neuronal networks. Confidence in the results is limited because, (i) different methods give different results, (ii) parameter setting directly influences the final result, and (iii) systematic evaluation of the results is not always performed. Here, we introduce MULAN (MULtiple method ANalysis), which assumes an ensemble based approach combining multiple analysis methods and fuzzy logic to extract graphs with the most probable structure. In order to reduce the dependency on parameter settings, we determine the best set of parameters using a genetic algorithm on simulated datasets, whose temporal structure is similar to the experimental one. After a validation step, the selected set of parameters is used to analyze experimental data. The final step cross-validates experimental subsets of data and provides a direct estimate of the most likely graph and our confidence in the proposed connectivity. A systematic evaluation validates our strategy against empirical stereotactic electroencephalography (SEEG) and functional magnetic resonance imaging (fMRI) data., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)

Working memory (WM) impairment is regarded as a core aspect of schizophrenia. However, the neural mechanisms behind this cognitive deficit remain unclear. The connectivity of a frontoparietal network is known to be important for subserving WM. Using functional magnetic resonance imaging, the current study investigated whether WM-dependent modulation of effective connectivity in this network is affected in a group of first-episode schizophrenia (FES) patients compared with similarly performing healthy participants during a verbal n-back task. Dynamic causal modeling (DCM) of the coupling between regions (left inferior frontal gyrus (IFG), left inferior parietal lobe (IPL), and primary visual area) identified in a psychophysiological interaction (PPI) analysis was performed to characterize effective connectivity during the n-back task. The PPI analysis revealed that the connectivity between the left IFG and left IPL was modulated by WM and that this modulation was reduced in FES patients. The subsequent DCM analysis confirmed this modulation by WM and found evidence that FES patients had reduced forward connectivity from IPL to IFG. These findings provide evidence for impaired WM modulation of frontoparietal effective connectivity in the early phase of schizophrenia, even with intact WM performance, suggesting a failure of context-sensitive coupling in the schizophrenic brain., (© The Author 2017. Published by Oxford University Press.)

The "dysconnection hypothesis" of psychosis suggests that a disruption of functional integration underlies cognitive deficits and clinical symptoms. Impairments in the P300 potential are well documented in psychosis. Intrinsic (self-)connectivity in a frontoparietal cortical hierarchy during a P300 experiment was investigated. Dynamic Causal Modeling was used to estimate how evoked activity results from the dynamics of coupled neural populations and how neural coupling changes with the experimental factors. Twenty-four patients with psychotic disorder, twenty-four unaffected relatives, and twenty-five controls underwent EEG recordings during an auditory oddball paradigm. Sixteen frontoparietal network models (including primary auditory, superior parietal, and superior frontal sources) were analyzed and an optimal model of neural coupling, explaining diagnosis and genetic risk effects, as well as their interactions with task condition were identified. The winning model included changes in connectivity at all three hierarchical levels. Patients showed decreased self-inhibition-that is, increased cortical excitability-in left superior frontal gyrus across task conditions, compared with unaffected participants. Relatives had similar increases in excitability in left superior frontal and right superior parietal sources, and a reversal of the normal synaptic gain changes in response to targets relative to standard tones. It was confirmed that both subjects with psychotic disorder and their relatives show a context-independent loss of synaptic gain control at the highest hierarchy levels. The relatives also showed abnormal gain modulation responses to task-relevant stimuli. These may be caused by NMDA-receptor and/or GABAergic pathologies that change the excitability of superficial pyramidal cells and may be a potential biological marker for psychosis. Hum Brain Mapp 38:3262-3276, 2017. © 2017 Wiley Periodicals, Inc., (© 2017 Wiley Periodicals, Inc.)

Brain activity derives from intrinsic dynamics (due to neurophysiology and anatomical connectivity) in concert with stochastic effects that arise from sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random fluctuations can be studied with stochastic dynamic models (SDMs). This article, Part II of a two-part series, reviews applications of SDMs to large-scale neural systems in health and disease. Stochastic models have already elucidated a number of pathophysiological phenomena, such as epilepsy and hypoxic ischemic encephalopathy, although their use in biological psychiatry remains rather nascent. Emerging research in this field includes phenomenological models of mood fluctuations in bipolar disorder and biophysical models of functional imaging data in psychotic and affective disorders. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior., (Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.)

Biological phenomena arise through interactions between an organism's intrinsic dynamics and stochastic forces-random fluctuations due to external inputs, thermal energy, or other exogenous influences. Dynamic processes in the brain derive from neurophysiology and anatomical connectivity; stochastic effects arise through sensory fluctuations, brainstem discharges, and random microscopic states such as thermal noise. The dynamic evolution of systems composed of both dynamic and random effects can be studied with stochastic dynamic models (SDMs). This article, Part I of a two-part series, offers a primer of SDMs and their application to large-scale neural systems in health and disease. The companion article, Part II, reviews the application of SDMs to brain disorders. SDMs generate a distribution of dynamic states, which (we argue) represent ideal candidates for modeling how the brain represents states of the world. When augmented with variational methods for model inversion, SDMs represent a powerful means of inferring neuronal dynamics from functional neuroimaging data in health and disease. Together with deeper theoretical considerations, this work suggests that SDMs will play a unique and influential role in computational psychiatry, unifying empirical observations with models of perception and behavior., (Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved.)

Unlabelled: Integrating costs and benefits is crucial for optimal decision-making. Although much is known about decisions that involve outcome-related costs (e.g., delay, risk), many of our choices are attached to actions and require an evaluation of the associated motor costs. Yet how the brain incorporates motor costs into choices remains largely unclear. We used human fMRI during choices involving monetary reward and physical effort to identify brain regions that serve as a choice comparator for effort-reward trade-offs. By independently varying both options' effort and reward levels, we were able to identify the neural signature of a comparator mechanism. A network involving supplementary motor area and the caudal portion of dorsal anterior cingulate cortex encoded the difference in reward (positively) and effort levels (negatively) between chosen and unchosen choice options. We next modeled effort-discounted subjective values using a novel behavioral model. This revealed that the same network of regions involving dorsal anterior cingulate cortex and supplementary motor area encoded the difference between the chosen and unchosen options' subjective values, and that activity was best described using a concave model of effort-discounting. In addition, this signal reflected how precisely value determined participants' choices. By contrast, separate signals in supplementary motor area and ventromedial prefrontal cortex correlated with participants' tendency to avoid effort and seek reward, respectively. This suggests that the critical neural signature of decision-making for choices involving motor costs is found in human cingulate cortex and not ventromedial prefrontal cortex as typically reported for outcome-based choice. Furthermore, distinct frontal circuits seem to drive behavior toward reward maximization and effort minimization., Significance Statement: The neural processes that govern the trade-off between expected benefits and motor costs remain largely unknown. This is striking because energetic requirements play an integral role in our day-to-day choices and instrumental behavior, and a diminished willingness to exert effort is a characteristic feature of a range of neurological disorders. We use a new behavioral characterization of how humans trade off reward maximization with effort minimization to examine the neural signatures that underpin such choices, using BOLD MRI neuroimaging data. We find the critical neural signature of decision-making, a signal that reflects the comparison of value between choice options, in human cingulate cortex, whereas two distinct brain circuits drive behavior toward reward maximization or effort minimization., (Copyright © 2016 Klein-Flügge et al.)

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity - and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Oscillatory activity in the beta range, in human primary motor cortex (M1), shows interesting dynamics that are tied to behaviour and change systematically in disease. To investigate the pathophysiology underlying these changes, we must first understand how changes in beta activity are caused in healthy subjects. We therefore adapted a canonical (repeatable) microcircuit model used in dynamic causal modelling (DCM) previously used to model induced responses in visual cortex. We adapted this model to accommodate cytoarchitectural differences between visual and motor cortex. Using biologically plausible connections, we used Bayesian model selection to identify the best model of measured MEG data from 11 young healthy participants, performing a simple handgrip task. We found that the canonical M1 model had substantially more model evidence than the generic canonical microcircuit model when explaining measured MEG data. The canonical M1 model reproduced measured dynamics in humans at rest, in a manner consistent with equivalent studies performed in mice. Furthermore, the changes in excitability (self-inhibition) necessary to explain beta suppression during handgrip were consistent with the attenuation of sensory precision implied by predictive coding. These results establish the face validity of a model that can be used to explore the laminar interactions that underlie beta-oscillatory dynamics in humans in vivo. Our canonical M1 model may be useful for characterising the synaptic mechanisms that mediate pathophysiological beta dynamics associated with movement disorders, such as stroke or Parkinson's disease., (Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.)

Individual differences in cognitive efficiency, particularly in relation to working memory (WM), have been associated both with personality dimensions that reflect enduring regularities in brain configuration, and with short-term neural plasticity, that reflects task-related changes in brain connectivity. To elucidate the relationship of these two divergent mechanisms, we tested the hypothesis that personality dimensions, which reflect enduring aspects of brain configuration, inform about the neurobiological framework within which short-term, task-related plasticity, as measured by effective connectivity, can be facilitated or constrained. As WM consistently engages the dorsolateral prefrontal (DLPFC), parietal (PAR), and anterior cingulate cortex (ACC), we specified a WM network model with bidirectional, ipsilateral, and contralateral connections between these regions from a functional magnetic resonance imaging dataset obtained from 40 healthy adults while performing the 3-back WM task. Task-related effective connectivity changes within this network were estimated using Dynamic Causal Modelling. Personality was evaluated along the major dimensions of Neuroticism, Extraversion, Openness to Experience, Agreeableness, and Conscientiousness. Only two dimensions were relevant to task-dependent effective connectivity. Neuroticism and Conscientiousness respectively constrained and facilitated neuroplastic responses within the WM network. These results suggest individual differences in cognitive efficiency arise from the interplay between enduring and short-term plasticity in brain configuration., (© 2015 Wiley Periodicals, Inc.)

The superior temporal sulcus (STS) in the human and monkey is sensitive to the motion of complex forms such as facial and bodily actions. We used functional magnetic resonance imaging (fMRI) to explore network-level explanations for how the form and motion information in dynamic facial expressions might be combined in the human STS. Ventral occipitotemporal areas selective for facial form were localized in occipital and fusiform face areas (OFA and FFA), and motion sensitivity was localized in the more dorsal temporal area V5. We then tested various connectivity models that modeled communication between the ventral form and dorsal motion pathways. We show that facial form information modulated transmission of motion information from V5 to the STS, and that this face-selective modulation likely originated in OFA. This finding shows that form-selective motion sensitivity in the STS can be explained in terms of modulation of gain control on information flow in the motion pathway, and provides a substantial constraint for theories of the perception of faces and biological motion., (© The Author 2014. Published by Oxford University Press.)

This paper considers neuronal architectures from a computational perspective and asks what aspects of neuroanatomy and neurophysiology can be disclosed by the nature of neuronal computations? In particular, we extend current formulations of the brain as an organ of inference--based upon hierarchical predictive coding--and consider how these inferences are orchestrated. In other words, what would the brain require to dynamically coordinate and contextualize its message passing to optimize its computational goals? The answer that emerges rests on the delicate (modulatory) gain control of neuronal populations that select and coordinate (prediction error) signals that ascend cortical hierarchies. This is important because it speaks to a hierarchical anatomy of extrinsic (between region) connections that form two distinct classes, namely a class of driving (first-order) connections that are concerned with encoding the content of neuronal representations and a class of modulatory (second-order) connections that establish context-in the form of the salience or precision ascribed to content. We explore the implications of this distinction from a formal perspective (using simulations of feature-ground segregation) and consider the neurobiological substrates of the ensuing precision-engineered dynamics, with a special focus on the pulvinar and attention.

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., (Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.)

Reward outcome signalling in the sensory cortex is held as important for linking stimuli to their consequences and for modulating perceptual learning in response to incentives. Evidence for reward outcome signalling has been found in sensory regions including the visual, auditory and somatosensory cortices across a range of different paradigms, but it is unknown whether the population of neurons signalling rewarding outcomes are the same as those processing predictive stimuli. We addressed this question using a multivariate analysis of high-resolution functional magnetic resonance imaging (fMRI), in a task where subjects were engaged in instrumental learning with visual predictive cues and auditory signalled reward feedback. We found evidence that outcome signals in sensory regions localise to the same areas involved in stimulus processing. These outcome signals are non-specific and we show that the neuronal populations involved in stimulus representation are not their exclusive target, in keeping with theoretical models of value learning. Thus, our results reveal one likely mechanism through which rewarding outcomes are linked to predictive sensory stimuli, a link that may be key for both reward and perceptual learning., (© 2013.)

The agranular architecture of motor cortex lacks a functional interpretation. Here, we consider a 'predictive coding' account of this unique feature based on asymmetries in hierarchical cortical connections. In sensory cortex, layer 4 (the granular layer) is the target of ascending pathways. We theorise that the operation of predictive coding in the motor system (a process termed 'active inference') provides a principled rationale for the apparent recession of the ascending pathway in motor cortex. The extension of this theory to interlaminar circuitry also accounts for a sub-class of 'mirror neuron' in motor cortex--whose activity is suppressed when observing an action--explaining how predictive coding can gate hierarchical processing to switch between perception and action., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.

Spontaneous fluctuations in resting state activity can change in response to experience-dependent plasticity and learning. Visual learning is fast and can be elicited in an MRI scanner. Here, we showed that a random dot motion coherence task can be learned within one training session. While the task activated primarily visual and parietal brain areas, learning related changes in neural activity were observed in the hippocampus. Crucially, even this rapid learning affected resting state dynamics both immediately after the learning and 24h later. Specifically, the hippocampus changed its coupling with the striatum, in a way that was best explained as a consolidation of early learning related changes. Our findings suggest that long-lasting changes in neuronal coupling are accompanied by changes in resting state activity., (Copyright © 2013 Elsevier Inc. All rights reserved.)

The descending projections from motor cortex share many features with top-down or backward connections in visual cortex; for example, corticospinal projections originate in infragranular layers, are highly divergent and (along with descending cortico-cortical projections) target cells expressing NMDA receptors. This is somewhat paradoxical because backward modulatory characteristics would not be expected of driving motor command signals. We resolve this apparent paradox using a functional characterisation of the motor system based on Helmholtz's ideas about perception; namely, that perception is inference on the causes of visual sensations. We explain behaviour in terms of inference on the causes of proprioceptive sensations. This explanation appeals to active inference, in which higher cortical levels send descending proprioceptive predictions, rather than motor commands. This process mirrors perceptual inference in sensory cortex, where descending connections convey predictions, while ascending connections convey prediction errors. The anatomical substrate of this recurrent message passing is a hierarchical system consisting of functionally asymmetric driving (ascending) and modulatory (descending) connections: an arrangement that we show is almost exactly recapitulated in the motor system, in terms of its laminar, topographic and physiological characteristics. This perspective casts classical motor reflexes as minimising prediction errors and may provide a principled explanation for why motor cortex is agranular.

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 © 2012 Elsevier Inc. All rights reserved.)

Parkinson's disease is a common and debilitating condition, caused by aberrant activity in a complex basal ganglia-thalamocortical circuit. Therapeutic advances rely on characterising interactions in this circuit. However, recording electrophysiological responses over the entire circuit is impractical. Dynamic causal modelling offers large-scale models of predictive value based on a limited or partial sampling of complex networks. Using dynamic causal modelling, we determined the network changes underlying the pathological excess of beta oscillations that characterise the Parkinsonian state. We modelled data from five patients undergoing surgery for deep brain stimulation of more than one target. We found that connections to and from the subthalamic nucleus were strengthened and promoted beta synchrony, in the untreated compared to the treated Parkinsonian state. Dynamic causal modelling was able to replicate the effects of lesioning this nucleus and may provide a new means of directing the search for therapeutic targets., (Copyright © 2012 Elsevier Inc. All rights reserved.)

In Kilner et al. [Kilner, J.M., Kiebel, S.J., Friston, K.J., 2005. Applications of random field theory to electrophysiology. Neurosci. Lett. 374, 174-178.] we described a fairly general analysis of induced responses-in electromagnetic brain signals-using the summary statistic approach and statistical parametric mapping. This involves localising induced responses-in peristimulus time and frequency-by testing for effects in time-frequency images that summarise the response of each subject to each trial type. Conventionally, these time-frequency summaries are estimated using post-hoc averaging of epoched data. However, post-hoc averaging of this sort fails when the induced responses overlap or when there are multiple response components that have variable timing within each trial (for example stimulus and response components associated with different reaction times). In these situations, it is advantageous to estimate response components using a convolution model of the sort that is standard in the analysis of fMRI time series. In this paper, we describe one such approach, based upon ordinary least squares deconvolution of induced responses to input functions encoding the onset of different components within each trial. There are a number of fundamental advantages to this approach: for example; (i) one can disambiguate induced responses to stimulus onsets and variably timed responses; (ii) one can test for the modulation of induced responses-over peristimulus time and frequency-by parametric experimental factors and (iii) one can gracefully handle confounds-such as slow drifts in power-by including them in the model. In what follows, we consider optimal forms for convolution models of induced responses, in terms of impulse response basis function sets and illustrate the utility of deconvolution estimators using simulated and real MEG data., (Copyright © 2012 Elsevier Inc. All rights reserved.)

This Perspective considers the influential notion of a canonical (cortical) microcircuit in light of recent theories about neuronal processing. Specifically, we conciliate quantitative studies of microcircuitry and the functional logic of neuronal computations. We revisit the established idea that message passing among hierarchical cortical areas implements a form of Bayesian inference-paying careful attention to the implications for intrinsic connections among neuronal populations. By deriving canonical forms for these computations, one can associate specific neuronal populations with specific computational roles. This analysis discloses a remarkable correspondence between the microcircuitry of the cortical column and the connectivity implied by predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries between feedforward and feedback connections and the characteristic frequencies over which they operate., (Copyright © 2012 Elsevier Inc. All rights reserved.)

Estimating the precision or uncertainty associated with sensory signals is an important part of perception. Based on a previous computational model, we tested the hypothesis that increasing visual contrast increased the precision encoded in early visual areas by the gain or excitability of superficial pyramidal cells. This hypothesis was investigated using electroencephalography and dynamic causal modelling (DCM); a biologically constrained modelling of the cortical processes underlying EEG activity. Source localisation identified the electromagnetic sources of visually evoked responses and DCM was used to characterise the coupling among these sources. Bayesian model selection was used to select the most likely connectivity pattern and contrast-dependent changes in connectivity. As predicted, the model with the highest evidence entailed increased superficial pyramidal cell gain in higher-contrast trials. As predicted theoretically, contrast-dependent increases were reduced at higher levels of the hierarchy. These results demonstrate that increased signal-to-noise ratio in sensory signals produce (or are represented by) increased superficial pyramidal cell gain, and that synaptic parameters encoding statistical properties like sensory precision can be quantified using EEG and dynamic causal modelling., (Copyright © 2012 Elsevier Inc. All rights reserved.)

The articles in this special issue provide a rich and thoughtful perspective on the brain as an inference machine. They illuminate key aspects of the internal or generative models the brain might use for perception. Furthermore, they explore the implications for a sense of agency and the nature of false inference in neuropsychiatric syndromes. In this review, I try to gather together some of the themes that emerge in this special issue and use them to illustrate how far one can take the notion of predictive coding in understanding behaviour and agency., (Copyright © 2011 Elsevier B.V. All rights reserved.)

The role of dopamine in behaviour and decision-making is often cast in terms of reinforcement learning and optimal decision theory. Here, we present an alternative view that frames the physiology of dopamine in terms of Bayes-optimal behaviour. In this account, dopamine controls the precision or salience of (external or internal) cues that engender action. In other words, dopamine balances bottom-up sensory information and top-down prior beliefs when making hierarchical inferences (predictions) about cues that have affordance. In this paper, we focus on the consequences of changing tonic levels of dopamine firing using simulations of cued sequential movements. Crucially, the predictions driving movements are based upon a hierarchical generative model that infers the context in which movements are made. This means that we can confuse agents by changing the context (order) in which cues are presented. These simulations provide a (Bayes-optimal) model of contextual uncertainty and set switching that can be quantified in terms of behavioural and electrophysiological responses. Furthermore, one can simulate dopaminergic lesions (by changing the precision of prediction errors) to produce pathological behaviours that are reminiscent of those seen in neurological disorders such as Parkinson's disease. We use these simulations to demonstrate how a single functional role for dopamine at the synaptic level can manifest in different ways at the behavioural level., (© 2012 Friston et al.)

The perception of facial affect engages a distributed cortical network. We used functional magnetic resonance imaging and dynamic causal modeling to characterize effective connectivity during explicit (conscious) categorization of affective stimuli in the human brain. Specifically, we examined the modulation of connectivity from posterior regions of the face-processing network to the lateral ventral prefrontal cortex (VPFC) during affective categorization and we tested for a potential role of the amygdala (AMG) in mediating this modulation. We found that explicit processing of facial affect led to prominent modulation (increase) in the effective connectivity from the inferior occipital gyrus (IOG) to the VPFC, while there was less evidence for modulation of the afferent connections from fusiform gyrus and AMG to VPFC. More specifically, the forward connection from IOG to the VPFC exhibited a selective increase under anger (as opposed to fear or sadness). Furthermore, Bayesian model comparison suggested that the modulation of afferent connections to the VPFC was mediated directly by facial affect, as opposed to an indirect modulation mediated by the AMG. Our results thus suggest that affective information is conveyed to the VPFC along multiple parallel pathways and that AMG activity is not sufficient to account for the gating of information transfer to the VPFC during explicit emotional processing.

This is the final paper in a Comments and Controversies series dedicated to "The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution". We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener-Akaike-Granger-Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Cortico-basal ganglia-thalamocortical circuits are severely disrupted by the dopamine depletion of Parkinson's disease (PD), leading to pathologically exaggerated beta oscillations. Abnormal rhythms, found in several circuit nodes are correlated with movement impairments but their neural basis remains unclear. Here, we used dynamic causal modelling (DCM) and the 6-hydroxydopamine-lesioned rat model of PD to examine the effective connectivity underlying these spectral abnormalities. We acquired auto-spectral and cross-spectral measures of beta oscillations (10-35 Hz) from local field potential recordings made simultaneously in the frontal cortex, striatum, external globus pallidus (GPe) and subthalamic nucleus (STN), and used these data to optimise neurobiologically plausible models. Chronic dopamine depletion reorganised the cortico-basal ganglia-thalamocortical circuit, with increased effective connectivity in the pathway from cortex to STN and decreased connectivity from STN to GPe. Moreover, a contribution analysis of the Parkinsonian circuit distinguished between pathogenic and compensatory processes and revealed how effective connectivity along the indirect pathway acquired a strategic importance that underpins beta oscillations. In modelling excessive beta synchrony in PD, these findings provide a novel perspective on how altered connectivity in basal ganglia-thalamocortical circuits reflects a balance between pathogenesis and compensation, and predicts potential new therapeutic targets to overcome dysfunctional oscillations.

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 © 2011 Elsevier Inc. All rights reserved.)

Dynamic causal modelling (DCM) for steady-state responses (SSR) is a framework for inferring the mechanisms that underlie observed electrophysiological spectra, using biologically plausible generative models of neuronal dynamics. In this paper, we examine the dynamic repertoires of nonlinear conductance-based neural population models and propose a generative model of their power spectra. Our model comprises an ensemble of interconnected excitatory and inhibitory cells, where synaptic currents are mediated by fast, glutamatergic and GABAergic receptors and slower voltage-gated NMDA receptors. We explore two formulations of how hidden neuronal states (depolarisation and conductances) interact: through their mean and variance (mean-field model) or through their mean alone (neural-mass model). Both rest on a nonlinear Fokker-Planck description of population dynamics, which can exhibit bifurcations (phase transitions). We first characterise these phase transitions numerically: by varying critical model parameters, we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics (~2-100 Hz) of real electrophysiological data. We then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis. This predictor is based on sampling the system's Jacobian over the orbits of hidden neuronal states. This predictor behaves consistently and smoothly in the region of phase transitions, which permits the use of gradient descent methods for model inversion. We demonstrate this by inverting generative models (DCMs) of SSRs, using simulated data that entails phase transitions., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.

The synchronous discharge of neuronal assemblies is thought to facilitate communication between areas within distributed networks in the human brain. This oscillatory activity is especially interesting, given the pathological modulation of specific frequencies in diseases affecting the motor system. Many studies investigating oscillatory activity have focused on same frequency, or linear, coupling between areas of a network. In this study, our aim was to establish a functional architecture in the human motor system responsible for induced responses as measured in normal subjects with magnetoencephalography. Specifically, we looked for evidence for additional nonlinear (between-frequency) coupling among neuronal sources and, in particular, whether nonlinearities were found predominantly in connections within areas (intrinsic), between areas (extrinsic) or both. We modeled the event-related modulation of spectral responses during a simple hand-grip using dynamic casual modeling. We compared models with and without nonlinear connections under conditions of symmetric and asymmetric interhemispheric connectivity. Bayesian model comparison suggested that the task-dependent motor network was asymmetric during right hand movements. Furthermore, it revealed very strong evidence for nonlinear coupling between sources in this distributed network, but interactions among frequencies within a source appeared linear in nature. Our results provide empirical evidence for nonlinear coupling among distributed neuronal sources in the motor system and that these play an important role in modulating spectral responses under normal conditions.