"Dynamic" connectivity in neural systems: theoretical and empirical considerations

Structurally informed models of directed brain connectivity

Understanding how one brain region exerts influence over another in vivo is profoundly constrained by models used to infer or predict directed connectivity. Although such neural interactions rely on the anatomy of the brain, it remains unclear whether, at the macroscale, structural (or anatomical) connectivity provides useful constraints on models of directed connectivity. Here, we review the current state of research on this question, highlighting a key distinction between inference-based effective connectivity and prediction-based directed functional connectivity. We explore the methods via which structural connectivity has been integrated into directed connectivity models: through prior distributions, fixed parameters in state-space models and inputs to structure learning algorithms. Although the evidence suggests that integrating structural connectivity substantially improves directed connectivity models, assessments of reliability and out-of-sample validity are lacking. We conclude this Review with a strategy for future research that addresses current challenges and identifies opportunities for advancing the integration of structural and directed connectivity to ultimately improve understanding of the brain in health and disease.

Violations of the fluctuation-dissipation theorem reveal distinct nonequilibrium dynamics of brain states

The brain is a nonequilibrium system whose dynamics change in different brain states, such as wakefulness and deep sleep. Thermodynamics provides the tools for revealing these nonequilibrium dynamics. We used violations of the fluctuation-dissipation theorem to describe the hierarchy of nonequilibrium dynamics associated with different brain states. Together with a whole-brain model fitted to empirical human neuroimaging data, and deriving the appropriate analytical expressions, we were able to capture the deviation from equilibrium in different brain states that arises from asymmetric interactions and hierarchical organization.

A network-level test of the role of the co-activated default mode network in episodic recall and social cognition

Resting-state network research is extremely influential, yet the functions of many networks remain unknown. In part, this is due to typical (e.g., univariate) analyses independently testing the function of individual regions and not examining the full set of regions that form a network whilst co-activated. Connectivity is dynamic and the function of a region may change based on its current connections. Therefore, determining the function of a network requires assessment at this network-level. Yet popular theories implicating the default mode network (DMN) in episodic memory and social cognition, rest principally upon analyses performed at the level of individual brain regions. Here we use independent component analysis to formally test the role of the DMN in episodic and social processing at the network level. As well as an episodic retrieval task, two independent datasets were employed to assess DMN function across the breadth of social cognition; a person knowledge judgement and a theory of mind task. Each task dataset was separated into networks of co-activated regions. In each, the co-activated DMN, was identified through comparison to an a priori template and its relation to the task model assessed. This co-activated DMN did not show greater activity in episodic or social tasks than high-level baseline conditions. Thus, no evidence was found to support hypotheses that the co-activated DMN is involved in explicit episodic or social tasks at a network-level. The networks associated with these processes are described. Implications for prior univariate findings and the functional significance of the co-activated DMN are considered.

Driving brain state transitions in major depressive disorder through external stimulation

Major depressive disorder (MDD) as a dysfunction of neural circuits and brain networks has been established in modern neuroimaging sciences. However, the brain state transitions between MDD and health through external stimulation remain unclear, which limits translation to clinical contexts and demonstrable clinical utility. We propose a framework of the large-scale whole-brain network model for MDD linking the underlying anatomical connectivity with functional dynamics obtained from diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI). Then, we further explored the optimal brain regions to promote the transition of brain states between MDD and health through external stimulation of the model. Based on the whole-brain model successfully fitting the brain state space in MDD and the health, we demonstrated that the transition from MDD to health is achieved by the excitatory activation of the limbic system and from health to MDD by the inhibitory stimulation of the reward circuit. Our finding provides novel biophysical evidence for the neural mechanism of MDD and its recovery and allows the discovery of new stimulation targets for MDD recovery.

Unifying turbulent dynamics framework distinguishes different brain states

Significant advances have been made by identifying the levels of synchrony of the underlying dynamics of a given brain state. This research has demonstrated that non-conscious dynamics tend to be more synchronous than in conscious states, which are more asynchronous. Here we go beyond this dichotomy to demonstrate that different brain states are underpinned by dissociable spatiotemporal dynamics. We investigated human neuroimaging data from different brain states (resting state, meditation, deep sleep and disorders of consciousness after coma). The model-free approach was based on Kuramoto's turbulence framework using coupled oscillators. This was extended by a measure of the information cascade across spatial scales. Complementarily, the model-based approach used exhaustive in silico perturbations of whole-brain models fitted to these measures. This allowed studying of the information encoding capabilities in given brain states. Overall, this framework demonstrates that elements from turbulence theory provide excellent tools for describing and differentiating between brain states.

Representation Learning for Dynamic Functional Connectivities via Variational Dynamic Graph Latent Variable Models

Latent variable models (LVMs) for neural population spikes have revealed informative low-dimensional dynamics about the neural data and have become powerful tools for analyzing and interpreting neural activity. However, these approaches are unable to determine the neurophysiological meaning of the inferred latent dynamics. On the other hand, emerging evidence suggests that dynamic functional connectivities (DFC) may be responsible for neural activity patterns underlying cognition or behavior. We are interested in studying how DFC are associated with the low-dimensional structure of neural activities. Most existing LVMs are based on a point process and fail to model evolving relationships. In this work, we introduce a dynamic graph as the latent variable and develop a Variational Dynamic Graph Latent Variable Model (VDGLVM), a representation learning model based on the variational information bottleneck framework. VDGLVM utilizes a graph generative model and a graph neural network to capture dynamic communication between nodes that one has no access to from the observed data. The proposed computational model provides guaranteed behavior-decoding performance and improves LVMs by associating the inferred latent dynamics with probable DFC.

Brain States and Transitions: Insights from Computational Neuroscience

Within the field of computational neuroscience there are great expectations of finding new ways to rebalance the complex dynamic system of the human brain through controlled pharmacological or electromagnetic perturbation. Yet many obstacles remain between the ability to accurately predict how and where best to perturb to force a transition from one brain state to another. The foremost challenge is a commonly agreed definition of a given brain state. Recent progress in computational neuroscience has made it possible to robustly define brain states and force transitions between them. Here, we review the state of the art and propose a framework for determining the functional hierarchical organization describing any given brain state. We describe the latest advances in creating sophisticated whole-brain computational models with interacting neuronal and neurotransmitter systems that can be studied fully in silico to predict and design novel pharmacological and electromagnetic interventions to rebalance them in disease.

Bridging the gap between single receptor type activity and whole-brain dynamics

What is the effect of activating a single modulatory neuronal receptor type on entire brain network dynamics? Can such effect be isolated at all? These are important questions because characterizing elementary neuronal processes that influence network activity across the given anatomical backbone is fundamental to guide theories of brain function. Here, we introduce the concept of the cortical 'receptome' taking into account the distribution and densities of expression of different modulatory receptor types across the brain's anatomical connectivity matrix. By modelling whole-brain dynamics in silico, we suggest a bidirectional coupling between modulatory neurotransmission and neuronal connectivity hardware exemplified by the impact of single serotonergic (5-HT) receptor types on cortical dynamics. As experimental support of this concept, we show how optogenetic tools enable specific activation of a single 5-HT receptor type across the cortex as well as in vivo measurement of its distinct effects on cortical processing. Altogether, we demonstrate how the structural neuronal connectivity backbone and its modulation by a single neurotransmitter system allow access to a rich repertoire of different brain states that are fundamental for flexible behaviour. We further propose that irregular receptor expression patterns-genetically predisposed or acquired during a lifetime-may predispose for neuropsychiatric disorders like addiction, depression and anxiety along with distinct changes in brain state. Our long-term vision is that such diseases could be treated through rationally targeted therapeutic interventions of high specificity to eventually recover natural transitions of brain states.

Frontal-temporal functional connectivity of EEG signal by standardized permutation mutual information during anesthesia

Quantifying brain dynamics during anesthesia is an important challenge for understanding the neurophysiological mechanisms of anesthetic drug effect. Several single channel Electroencephalogram (EEG) indices have been proposed for monitoring anesthetic drug effect. The most commonly used single channel commercial index is the Bispectral index (BIS). However, this monitor has shown some drawbacks. In this study, a nonlinear functional connectivity measure named Standardized Permutation Mutual Information (SPMI) is proposed to describe communication between two-channel EEG signals at frontal and temporal brain regions during a controlled propofol-induced anesthesia and recovery design from eight subjects. The SPMI index has higher correlation with estimated propofol effect-site concentration and has better ability to distinguish three anesthetic states of patient than the other functional connectivity indexes (cross-correlation, coherence, phase analysis) and also the BIS index. Moreover, the SPMI index has a faster reaction to the effect of drug concentration, less variability at the consciousness state and better robustness to noise than BIS.

Dynamics of large-scale electrophysiological networks: A technical review

For several years it has been argued that neural synchronisation is crucial for cognition. The idea that synchronised temporal patterns between different neural groups carries information above and beyond the isolated activity of these groups has inspired a shift in focus in the field of functional neuroimaging. Specifically, investigation into the activation elicited within certain regions by some stimulus or task has, in part, given way to analysis of patterns of co-activation or functional connectivity between distal regions. Recently, the functional connectivity community has been looking beyond the assumptions of stationarity that earlier work was based on, and has introduced methods to incorporate temporal dynamics into the analysis of connectivity. In particular, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)), which provides direct measurement of whole-brain activity and rich temporal information, offers an exceptional window into such (potentially fast) brain dynamics. In this review, we discuss challenges, solutions, and a collection of analysis tools that have been developed in recent years to facilitate the investigation of dynamic functional connectivity using these imaging modalities. Further, we discuss the applications of these approaches in the study of cognition and neuropsychiatric disorders. Finally, we review some existing developments that, by using realistic computational models, pursue a deeper understanding of the underlying causes of non-stationary connectivity.

Putting the "dynamic" back into dynamic functional connectivity

The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term "dynamic functional connectivity" implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arises under different configurations of local dynamics and intersystem coupling: We show how they generate time series data with nonlinear and/or nonstationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity, and flexibility. The code for simulating these dynamics is available in a freeware software platform, the Brain Dynamics Toolbox.

Anticorrelations between Active Brain Regions: An Agent-Based Model Simulation Study

Anticorrelations among brain areas observed in fMRI acquisitions under resting state are not endowed with a well-defined set of characters. Some evidence points to a possible physiological role for them, and simulation models showed that it is appropriate to explore such an issue. A large-scale brain representation was considered, implementing an agent-based brain-inspired model (ABBM) incorporating the SER (susceptible-excited-refractory) cyclic mechanism of state change. The experimental data used for validation included 30 selected functional images of healthy controls from the 1000 Functional Connectomes Classic collection. To study how different fractions of positive and negative connectivities could modulate the model efficiency, the correlation coefficient was systematically used to check the goodness-of-fit of empirical data by simulations under different combinations of parameters. The results show that a small fraction of positive connectivity is necessary to match at best the empirical data. Similarly, a goodness-of-fit improvement was observed upon addition of negative links to an initial pattern of only-positive connections, indicating a significant information intrinsic to negative links. As a general conclusion, anticorrelations showed that it is crucial to improve the performance of our simulation and, since these cannot be assimilated to noise, should be always considered in order to refine any brain functional model.

The graphical brain: Belief propagation and active inference

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference-and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium.

AUTHOR SUMMARY

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference-and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain.

Altered intrinsic and extrinsic connectivity in schizophrenia

Schizophrenia is a disorder characterized by functional dysconnectivity among distributed brain regions. However, it is unclear how causal influences among large-scale brain networks are disrupted in schizophrenia. In this study, we used dynamic causal modeling (DCM) to assess the hypothesis that there is aberrant directed (effective) connectivity within and between three key large-scale brain networks (the dorsal attention network, the salience network and the default mode network) in schizophrenia during a working memory task. Functional MRI data during an n-back task from 40 patients with schizophrenia and 62 healthy controls were analyzed. Using hierarchical modeling of between-subject effects in DCM with Parametric Empirical Bayes, we found that intrinsic (within-region) and extrinsic (between-region) effective connectivity involving prefrontal regions were abnormal in schizophrenia. Specifically, in patients (i) inhibitory self-connections in prefrontal regions of the dorsal attention network were decreased across task conditions; (ii) extrinsic connectivity between regions of the default mode network was increased; specifically, from posterior cingulate cortex to the medial prefrontal cortex; (iii) between-network extrinsic connections involving the prefrontal cortex were altered; (iv) connections within networks and between networks were correlated with the severity of clinical symptoms and impaired cognition beyond working memory. In short, this study revealed the predominance of reduced synaptic efficacy of prefrontal efferents and afferents in the pathophysiology of schizophrenia.

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A first use of hierarchical modeling of effective connectivity to characterize large-scale networks in schizophrenia.

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Intrinsic and extrinsic effective connectivity involving prefrontal regions were abnormal in schizophrenia.

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Diagnostic connections could predict the severity of clinical symptoms and cognition in schizophrenia.

Large-scale DCMs for resting-state fMRI

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

Bayesian switching factor analysis for estimating time-varying functional connectivity in fMRI

There is growing interest in understanding the dynamical properties of functional interactions between distributed brain regions. However, robust estimation of temporal dynamics from functional magnetic resonance imaging (fMRI) data remains challenging due to limitations in extant multivariate methods for modeling time-varying functional interactions between multiple brain areas. Here, we develop a Bayesian generative model for fMRI time-series within the framework of hidden Markov models (HMMs). The model is a dynamic variant of the static factor analysis model (Ghahramani and Beal, 2000). We refer to this model as Bayesian switching factor analysis (BSFA) as it integrates factor analysis into a generative HMM in a unified Bayesian framework. In BSFA, brain dynamic functional networks are represented by latent states which are learnt from the data. Crucially, BSFA is a generative model which estimates the temporal evolution of brain states and transition probabilities between states as a function of time. An attractive feature of BSFA is the automatic determination of the number of latent states via Bayesian model selection arising from penalization of excessively complex models. Key features of BSFA are validated using extensive simulations on carefully designed synthetic data. We further validate BSFA using fingerprint analysis of multisession resting-state fMRI data from the Human Connectome Project (HCP). Our results show that modeling temporal dependencies in the generative model of BSFA results in improved fingerprinting of individual participants. Finally, we apply BSFA to elucidate the dynamic functional organization of the salience, central-executive, and default mode networks-three core neurocognitive systems with central role in cognitive and affective information processing (Menon, 2011). Across two HCP sessions, we demonstrate a high level of dynamic interactions between these networks and determine that the salience network has the highest temporal flexibility among the three networks. Our proposed methods provide a novel and powerful generative model for investigating dynamic brain connectivity.

Neural decoding of visual stimuli varies with fluctuations in global network efficiency

Functional magnetic resonance imaging (fMRI) studies have shown that neural activity fluctuates spontaneously between different states of global synchronization over a timescale of several seconds. Such fluctuations generate transient states of high and low correlation across distributed cortical areas. It has been hypothesized that such fluctuations in global efficiency might alter patterns of activity in local neuronal populations elicited by changes in incoming sensory stimuli. To test this prediction, we used a linear decoder to discriminate patterns of neural activity elicited by face and motion stimuli presented periodically while participants underwent time-resolved fMRI. As predicted, decoding was reliably higher during states of high global efficiency than during states of low efficiency, and this difference was evident across both visual and nonvisual cortical regions. The results indicate that slow fluctuations in global network efficiency are associated with variations in the pattern of activity across widespread cortical regions responsible for representing distinct categories of visual stimulus. More broadly, the findings highlight the importance of understanding the impact of global fluctuations in functional connectivity on specialized, stimulus driven neural processes. Hum Brain Mapp 38:3069-3080, 2017. © 2017 Wiley Periodicals, Inc.

Neural Microstates Govern Perception of Auditory Input without Rhythmic Structure

Human perception fluctuates with the phase of neural oscillations in the presence of environmental rhythmic structure by which neural oscillations become entrained. However, in the absence of predictability afforded by rhythmic structure, we hypothesize that the neural dynamical states associated with optimal psychophysical performance are more complex than what has been described previously for rhythmic stimuli. The current electroencephalography study characterized the brain dynamics associated with optimal detection of gaps embedded in narrow-band acoustic noise stimuli lacking low-frequency rhythmic structure. Optimal gap detection was associated with three spectrotemporally distinct delta-governed neural microstates. Individual microstates were characterized by unique instantaneous combinations of neural phase in the delta, theta, and alpha frequency bands. Critically, gap detection was not predictable from local fluctuations in stimulus acoustics. The current results suggest that, in the absence of rhythmic structure to entrain neural oscillations, good performance hinges on complex neural states that vary from moment to moment. Significance statement: Our ability to hear faint sounds fluctuates together with slow brain activity that synchronizes with environmental rhythms. However, it is so far not known how brain activity at different time scales might interact to influence perception when there is no rhythm with which brain activity can synchronize. Here, we used electroencephalography to measure brain activity while participants listened for short silences that interrupted ongoing noise. We examined brain activity in three different frequency bands: delta, theta, and alpha. Participants' ability to detect gaps depended on different numbers of frequency bands--sometimes one, sometimes two, and sometimes three--at different times. Changes in the number of frequency bands that predict perception are a hallmark of a complex neural system.

Temporal expectations and neural amplitude fluctuations in auditory cortex interactively influence perception

Alignment of neural oscillations with temporally regular input allows listeners to generate temporal expectations. However, it remains unclear how behavior is governed in the context of temporal variability: What role do temporal expectations play, and how do they interact with the strength of neural oscillatory activity? Here, human participants detected near-threshold targets in temporally variable acoustic sequences. Temporal expectation strength was estimated using an oscillator model and pre-target neural amplitudes in auditory cortex were extracted from magnetoencephalography signals. Temporal expectations modulated target-detection performance, however, only when neural delta-band amplitudes were large. Thus, slow neural oscillations act to gate influences of temporal expectation on perception. Furthermore, slow amplitude fluctuations governed linear and quadratic influences of auditory alpha-band activity on performance. By fusing a model of temporal expectation with neural oscillatory dynamics, the current findings show that human perception in temporally variable contexts relies on complex interactions between multiple neural frequency bands.

Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously--elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow timescales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding 'feeder' cortical regions shows unstable, rapidly fluctuating dynamics likely to be crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems-resonance pairs-promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.

Construct validation of a DCM for resting state fMRI

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.

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This paper provides construct validation of spectral DCM against stochastic DCM.

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Spectral DCM is shown to be more accurate than stochastic DCM in terms of root mean square error.

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Spectral DCM is shown to be more sensitive at identifying group differences.

LORETA EEG phase reset of the default mode network

Objectives: The purpose of this study was to explore phase reset of 3-dimensional current sources in Brodmann areas located in the human default mode network (DMN) using Low Resolution Electromagnetic Tomography (LORETA) of the human electroencephalogram (EEG).

Methods: The EEG was recorded from 19 scalp locations from 70 healthy normal subjects ranging in age from 13 to 20 years. A time point by time point computation of LORETA current sources were computed for 14 Brodmann areas comprising the DMN in the delta frequency band. The Hilbert transform of the LORETA time series was used to compute the instantaneous phase differences between all pairs of Brodmann areas. Phase shift and lock durations were calculated based on the 1st and 2nd derivatives of the time series of phase differences.

Results: Phase shift duration exhibited three discrete modes at approximately: (1) 25 ms, (2) 50 ms, and (3) 65 ms. Phase lock duration present primarily at: (1) 300–350 ms and (2) 350–450 ms. Phase shift and lock durations were inversely related and exhibited an exponential change with distance between Brodmann areas.

Conclusions: The results are explained by local neural packing density of network hubs and an exponential decrease in connections with distance from a hub. The results are consistent with a discrete temporal model of brain function where anatomical hubs behave like a “shutter” that opens and closes at specific durations as nodes of a network giving rise to temporarily phase locked clusters of neurons for specific durations.

Genomic instantiation of consciousness in neurons through a biophoton field theory

A theoretical framework is developed based on the premise that brains evolved into sufficiently complex adaptive systems capable of instantiating genomic consciousness through self-awareness and complex interactions that recognize qualitatively the controlling factors of biological processes. Furthermore, our hypothesis assumes that the collective interactions in neurons yield macroergic effects, which can produce sufficiently strong electric energy fields for electronic excitations to take place on the surface of endogenous structures via alpha-helical integral proteins as electro-solitons. Specifically the process of radiative relaxation of the electro-solitons allows for the transfer of energy via interactions with deoxyribonucleic acid (DNA) molecules to induce conformational changes in DNA molecules producing an ultra weak non-thermal spontaneous emission of coherent biophotons through a quantum effect. The instantiation of coherent biophotons confined in spaces of DNA molecules guides the biophoton field to be instantaneously conducted along the axonal and neuronal arbors and in-between neurons and throughout the cerebral cortex (cortico-thalamic system) and subcortical areas (e.g., midbrain and hindbrain). Thus providing an informational character of the electric coherence of the brain - referred to as quantum coherence. The biophoton field is realized as a conscious field upon the re-absorption of biophotons by exciplex states of DNA molecules. Such quantum phenomenon brings about self-awareness and enables objectivity to have access to subjectivity in the unconscious. As such, subjective experiences can be recalled to consciousness as subjective conscious experiences or qualia through co-operative interactions between exciplex states of DNA molecules and biophotons leading to metabolic activity and energy transfer across proteins as a result of protein-ligand binding during protein-protein communication. The biophoton field as a conscious field is attributable to the resultant effect of specifying qualia from the metabolic energy field that is transported in macromolecular proteins throughout specific networks of neurons that are constantly transforming into more stable associable representations as molecular solitons. The metastability of subjective experiences based on resonant dynamics occurs when bottom-up patterns of neocortical excitatory activity are matched with top-down expectations as adaptive dynamic pressures. These dynamics of on-going activity patterns influenced by the environment and selected as the preferred subjective experience in terms of a functional field through functional interactions and biological laws are realized as subjectivity and actualized through functional integration as qualia. It is concluded that interactionism and not information processing is the key in understanding how consciousness bridges the explanatory gap between subjective experiences and their neural correlates in the transcendental brain.

Time-resolved resting-state brain networks

Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using high-resolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and fronto-parietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.

On nodes and modes in resting state fMRI

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.

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This paper presents a formal characterisation of [eigen] modes in resting state fMRI.

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It relates these to dynamical instabilities in neuronal (inferential) processing.

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It uses the equivalence between eigenmodes of functional and effective connectivity for dynamical causal modelling.

A DCM for resting state fMRI

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.

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This paper describes an efficient estimation of resting state connectivity.

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The scheme is based on fitting observed complex fMRI cross spectra.

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This spectral DCM grandfathers functional connectivity and Granger causality.

Complexity of spontaneous brain activity in mental disorders

Recent reports of functional and anatomical studies have provided evidence that aberrant neural connectivity lies at the heart of many mental disorders. Information related to neural networks has elucidated the nonlinear dynamical complexity in brain signals over a range of temporal scales. The recent advent of nonlinear analytic methods, which have served for the quantitative description of the brain signal complexity, has provided new insights into aberrant neural connectivity in many mental disorders. Although many studies have underpinned aberrant neural connectivity, findings related to complexity behavior are still inconsistent. This inconsistency might result from (i) heterogeneity in mental disorders, (ii) analytical issues, (iii) interference of typical development and aging. First, most mental disorders are heterogeneous in their clinical feature or intrinsic pathological mechanisms. Second, neurophysiologic output signals from complex brain connectivity might be characterized with multiple time scales or frequencies. Finally, age-related brain complexity changes must be considered when investigating pathological brain because typical brain complexity is not constant across generations. Future systematic studies addressing these issues will greatly expand our knowledge of neural connections and dynamics related to mental disorders.

Graph analysis of the human connectome: promise, progress, and pitfalls

The human brain is a complex, interconnected network par excellence. Accurate and informative mapping of this human connectome has become a central goal of neuroscience. At the heart of this endeavor is the notion that brain connectivity can be abstracted to a graph of nodes, representing neural elements (e.g., neurons, brain regions), linked by edges, representing some measure of structural, functional or causal interaction between nodes. Such a representation brings connectomic data into the realm of graph theory, affording a rich repertoire of mathematical tools and concepts that can be used to characterize diverse anatomical and dynamical properties of brain networks. Although this approach has tremendous potential - and has seen rapid uptake in the neuroimaging community - it also has a number of pitfalls and unresolved challenges which can, if not approached with due caution, undermine the explanatory potential of the endeavor. We review these pitfalls, the prevailing solutions to overcome them, and the challenges at the forefront of the field.

Analysing connectivity with Granger causality and dynamic causal modelling

This review considers state-of-the-art analyses of functional integration in neuronal macrocircuits. We focus on detecting and estimating directed connectivity in neuronal networks using Granger causality (GC) and dynamic causal modelling (DCM). These approaches are considered in the context of functional segregation and integration and--within functional integration--the distinction between functional and effective connectivity. We review recent developments that have enjoyed a rapid uptake in the discovery and quantification of functional brain architectures. GC and DCM have distinct and complementary ambitions that are usefully considered in relation to the detection of functional connectivity and the identification of models of effective connectivity. We highlight the basic ideas upon which they are grounded, provide a comparative evaluation and point to some outstanding issues.

Perception and self-organized instability

This paper considers state-dependent dynamics that mediate perception in the brain. In particular, it considers the formal basis of self-organized instabilities that enable perceptual transitions during Bayes-optimal perception. The basic phenomena we consider are perceptual transitions that lead to conscious ignition (Dehaene and Changeux, 2011) and how they depend on dynamical instabilities that underlie chaotic itinerancy (Breakspear, 2001; Tsuda, 2001) and self-organized criticality (Beggs and Plenz, 2003; Plenz and Thiagarajan, 2007; Shew et al., 2011). Our approach is based on a dynamical formulation of perception as approximate Bayesian inference, in terms of variational free energy minimization. This formulation suggests that perception has an inherent tendency to induce dynamical instabilities (critical slowing) that enable the brain to respond sensitively to sensory perturbations. We briefly review the dynamics of perception, in terms of generalized Bayesian filtering and free energy minimization, present a formal conjecture about self-organized instability and then test this conjecture, using neuronal (numerical) simulations of perceptual categorization.

Surface EEG shows that functional segregation via phase coupling contributes to the neural substrate of mental calculations

Multichannel EEG traces from healthy subjects are used to investigate the brain's self-organisation tendencies during two different mental arithmetic tasks. By making a comparison with a control-state in the form of a classification problem, we can detect and quantify the changes in coordinated brain activity in terms of functional connectivity. The interactions are quantified at the level of EEG sensors through descriptors that differ over the nature of functional dependencies sought (linear vs. nonlinear) and over the specific form of the measures employed (amplitude/phase covariation). Functional connectivity graphs (FCGs) are analysed with a novel clustering algorithm, and the resulting segregations enter an appropriate discriminant function. The magnitude of the contrast function depends on the frequency-band (θ, α(1), α(2), β and γ) and the neural synchrony descriptor. We first show that the maximal-contrast corresponds to a phase coupling descriptor and then identify the corresponding spatial patterns that represent best the task-induced changes for each frequency band. The principal finding of this study is that, during mental calculations, phase synchrony plays a crucial role in the segregation into distinct functional domains, and this segregation is the most prominent feature of the brain's self-organisation as this is reflected in sensor space.

Using large-scale neural models to interpret connectivity measures of cortico-cortical dynamics at millisecond temporal resolution

Over the last two decades numerous functional imaging studies have shown that higher order cognitive functions are crucially dependent on the formation of distributed, large-scale neuronal assemblies (neurocognitive networks), often for very short durations. This has fueled the development of a vast number of functional connectivity measures that attempt to capture the spatiotemporal evolution of neurocognitive networks. Unfortunately, interpreting the neural basis of goal directed behavior using connectivity measures on neuroimaging data are highly dependent on the assumptions underlying the development of the measure, the nature of the task, and the modality of the neuroimaging technique that was used. This paper has two main purposes. The first is to provide an overview of some of the different measures of functional/effective connectivity that deal with high temporal resolution neuroimaging data. We will include some results that come from a recent approach that we have developed to identify the formation and extinction of task-specific, large-scale neuronal assemblies from electrophysiological recordings at a ms-by-ms temporal resolution. The second purpose of this paper is to indicate how to partially validate the interpretations drawn from this (or any other) connectivity technique by using simulated data from large-scale, neurobiologically realistic models. Specifically, we applied our recently developed method to realistic simulations of MEG data during a delayed match-to-sample (DMS) task condition and a passive viewing of stimuli condition using a large-scale neural model of the ventral visual processing pathway. Simulated MEG data using simple head models were generated from sources placed in V1, V4, IT, and prefrontal cortex (PFC) for the passive viewing condition. The results show how closely the conclusions obtained from the functional connectivity method match with what actually occurred at the neuronal network level.

Network discovery with DCM

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.

Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy: a MEG study

To describe the spatial and temporal profiles of connectivity networks and sources preceding generalized spike-and-wave discharges (SWDs) in human absence epilepsy. Nonlinear associations of MEG signals and cluster indices obtained within the framework of graph theory were determined, while source localization in the frequency domain was performed in the low frequency bands with dynamic imaging of coherent sources. The results were projected on a three-dimensional surface rendering of the brain using a semi-realistic head model and MRI images obtained for each of the five patients studied. An increase in clustering and a decrease in path length preceding SWD onset and a rhythmic pattern of increasing and decreasing connectivity were seen during SWDs. Beamforming showed a consistent appearance of a low frequency frontal cortical source prior to the first generalized spikes. This source was preceded by a low frequency occipital source. The changes in the connectivity networks with the onset of SWDs suggest a pathologically predisposed state towards synchronous seizure networks with increasing connectivity from interictal to preictal and ictal state, while the occipital and frontal low frequency early preictal sources demonstrate that SWDs are not suddenly arising but gradually build up in a dynamic network.

Analyzing effective connectivity with functional magnetic resonance imaging

Functional neuroimaging techniques are used widely in cognitive neuroscience to investigate aspects of functional specialization and functional integration in the human brain. Functional integration can be characterized in two ways, functional connectivity and effective connectivity. While functional connectivity describes statistical dependencies between data, effective connectivity rests on a mechanistic model of the causal effects that generated the data. This review addresses the conceptual and methodological basis of established techniques for characterizing effective connectivity using functional magnetic resonance imaging (fMRI) data. In particular, we focus on dynamic causal modeling (DCM) of fMRI data and emphasize the importance of model selection procedures and nonlinear mechanisms for context-dependent changes in connection strengths. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Nonlinear connectivity by Granger causality

The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger causality. While DCM models nonlinear couplings, Granger causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality. We show the application of the proposed approach on EEG signals and fMRI data.

A comparative study of pattern synchronization detection between neural signals using different cross-entropy measures

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz-Lorenz, Rossler-Rossler, Rossler-Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.

Network dynamics of the epileptic brain at rest

Baseline neurodynamics are believed to play an important role in normal brain function. A potentially intrinsic property of the brain is the weak coupling between networks at rest, which enables it to be flexible, adapt, process novel stimuli, and learn. Brain regions become differentially coordinated in response to cognitive task and behavior demands and external stimuli. However, abnormally synchronized resting brain networks may also be associated with different pathologies. We investigated baseline network dynamics in the epileptic brain using information theoretic parameters to quantify coupling and directionality of information flow between different cortical regions. We estimated relative entropy, conditional mutual information and a related measure of directional coupling, from EEGs of patients with epilepsy and healthy subjects. At rest, the healthy brain appears to be characterized by low and non-directional network coupling, whereas the epileptic brain appears to be transiently and directionally synchronized.

Ten simple rules for dynamic causal modeling

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