Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain''s network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.     

Modeling fluctuations in default-mode brain network using a spiking neural network

Recently, numerous attempts have been made to understand the dynamic behavior of complex brain systems using neural network models. The fluctuations in blood-oxygen-level-dependent (BOLD) brain signals at less than 0.1 Hz have been observed by functional magnetic resonance imaging (fMRI) for subjects in a resting state. This phenomenon is referred to as a "default-mode brain network." In this study, we model the default-mode brain network by functionally connecting neural communities composed of spiking neurons in a complex network. Through computational simulations of the model, including transmission delays and complex connectivity, the network dynamics of the neural system and its behavior are discussed. The results show that the power spectrum of the modeled fluctuations in the neuron firing patterns is consistent with the default-mode brain network's BOLD signals when transmission delays, a characteristic property of the brain, have finite values in a given range.     

Noise during rest enables the exploration of the brain's dynamic repertoire

Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1–100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space–time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.     

Decoding lifespan changes of the human brain using resting-state functional connectivity MRI

The development of large-scale functional brain networks is a complex, lifelong process that can be investigated using resting-state functional connectivity MRI (rs-fcMRI). In this study, we aimed to decode the developmental dynamics of the whole-brain functional network in seven decades (8-79 years) of the human lifespan. We first used parametric curve fitting to examine linear and nonlinear age effect on the resting human brain, and then combined manifold learning and support vector machine methods to predict individuals' "brain ages" from rs-fcMRI data. We found that age-related changes in interregional functional connectivity exhibited spatially and temporally specific patterns. During brain development from childhood to senescence, functional connections tended to linearly increase in the emotion system and decrease in the sensorimotor system; while quadratic trajectories were observed in functional connections related to higher-order cognitive functions. The complex patterns of age effect on the whole-brain functional network could be effectively represented by a low-dimensional, nonlinear manifold embedded in the functional connectivity space, which uncovered the inherent structure of brain maturation and aging. Regression of manifold coordinates with age further showed that the manifold representation extracted sufficient information from rs-fcMRI data to make prediction about individual brains' functional development levels. Our study not only gives insights into the neural substrates that underlie behavioral and cognitive changes over age, but also provides a possible way to quantitatively describe the typical and atypical developmental progression of human brain function using rs-fcMRI.     

The development of a noisy brain

Early in life, brain development carries with it a large number of structural changes that impact the functional interactions of distributed neuronal networks. Such changes enhance information processing capacity, moving the brain from a deterministic system to one that is more stochastic. The evidence from empirical studies with EEG and functional MRI suggests that this stochastic property is a result of an increased number of possible functional network configurations for a given situation. This is captured in the variability of endogenous and evoked responses or "brain noise ". In empirical data from infants and children, brain noise increases with maturation and correlates positively with stable behavior and accuracy. The noise increase is best explained through increased noise from network level interactions with a concomitant decrease of local noise. In old adults, brain noise continues to change, although the pattern of changes is not as global as in early development. The relation between high brain noise and stable behavior is maintained, but the relationships differ by region, suggesting changes in local dynamics that then impact potential network configurations. These data, when considered in concert with our extant modeling work, suggest that maturational changes in brain noise represent the enhancement offunctional network potential--the brain's dynamic repertoire.     

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.     

Cortical network dynamics with time delays reveals functional connectivity in the resting brain

In absence of all goal-directed behavior, a characteristic network of cortical regions involving prefrontal and cingulate cortices consistently shows temporally coherent fluctuations. The origin of these fluctuations is unknown, but has been hypothesized to be of stochastic nature. In the present paper we test the hypothesis that time delays in the network dynamics play a crucial role in the generation of these fluctuations. By tuning the propagation velocity in a network based on primate connectivity, we scale the time delays and demonstrate the emergence of the resting state networks for biophysically realistic parameters.     

Microglia in development: linking brain wiring to brain environment

Microglia are enigmatic non-neuronal cells that infiltrate and take up residence in the brain during development and are thought to perform a surveillance function. An established literature has documented how microglia are activated by pathogenic stimuli and how they contribute to and resolve injuries to the brain. However, much less work has been aimed at understanding their function in the uninjured brain. A series of recent in vivo imaging studies shows that microglia in their resting state are highly motile and actively survey their neuronal surroundings. Furthermore, new data suggest that microglia in their resting state are able to phagocytose unwanted synapses and in this way contribute to synaptic pruning and maturation during development. Coupled with their exquisite sensitivity to pathogenic stimuli, these data suggest that microglia form a link that couples changes in brain environment to changes in brain wiring. Here we discuss this hypothesis and propose a model for the role of microglia during development in sculpting brain connectivity.     

Nested structure acquired through simple evolutionary process

Nested structure, which is non-random, controls cooperation dynamics and biodiversity in plant-animal mutualistic networks. This structural pattern has been explained in a static (non-growth) network models. However, evolutionary processes might also influence the formation of such a structural pattern. We thereby propose an evolving network model for plant-animal interactions and show that non-random patterns such as nested structure and heterogeneous connectivity are both qualitatively and quantitatively predicted through simple evolutionary processes. This finding implies that network models can be simplified by considering evolutionary processes, and also that another explanation exists for the emergence of non-random patterns and might provide more comprehensible insights into the formation of plant-animal mutualistic networks from the evolutionary perspective.     

Disrupted functional brain connectivity in partial epilepsy: a resting-state fMRI study

Examining the spontaneous activity to understand the neural mechanism of brain disorder is a focus in recent resting-state fMRI. In the current study, to investigate the alteration of brain functional connectivity in partial epilepsy in a systematical way, two levels of analyses (functional connectivity analysis within resting state networks (RSNs) and functional network connectivity (FNC) analysis) were carried out on resting-state fMRI data acquired from the 30 participants including 14 healthy controls(HC) and 16 partial epilepsy patients. According to the etiology, all patients are subdivided into temporal lobe epilepsy group (TLE, included 7 patients) and mixed partial epilepsy group (MPE, 9 patients). Using group independent component analysis, eight RSNs were identified, and selected to evaluate functional connectivity and FNC between groups. Compared with the controls, decreased functional connectivity within all RSNs was found in both TLE and MPE. However, dissociating patterns were observed within the 8 RSNs between two patient groups, i.e, compared with TLE, we found decreased functional connectivity in 5 RSNs increased functional connectivity in 1 RSN, and no difference in the other 2 RSNs in MPE. Furthermore, the hierarchical disconnections of FNC was found in two patient groups, in which the intra-system connections were preserved for all three subsystems while the lost connections were confined to intersystem connections in patients with partial epilepsy. These findings may suggest that decreased resting state functional connectivity and disconnection of FNC are two remarkable characteristics of partial epilepsy. The selective impairment of FNC implicated that it is unsuitable to understand the partial epilepsy only from global or local perspective. We presumed that studying epilepsy in the multi-perspective based on RSNs may be a valuable means to assess the functional changes corresponding to specific RSN and may contribute to the understanding of the neuro-pathophysiological mechanism of epilepsy.     

Role of structural inhomogeneities in resting-state brain dynamics

Brain imaging methods allow a non-invasive assessment of both structural and functional connectivity. However, the mechanism of how functional connectivity arises in a structured network of interacting neural populations is as yet poorly understood. Here we use a modeling approach to explore the way in which functional correlations arise from underlying structural connections taking into account inhomogeneities in the interactions between the brain regions of interest. The local dynamics of a neural population is assumed to be of phase-oscillator type. The considered structural connectivity patterns describe long-range anatomical connections between interacting neural elements. We find a dependence of the simulated functional connectivity patterns on the parameters governing the dynamics. We calculate graph-theoretic measures of the functional network topology obtained from numerical simulations. The effect of structural inhomogeneities in the coupling term on the observed network state is quantified by examining the relation between simulated and empirical functional connectivity. Importantly, we show that simulated and empirical functional connectivity agree for a narrow range of coupling strengths. We conclude that identification of functional connectivity during rest requires an analysis of the network dynamics.     

Emerging concepts for the dynamical organization of resting-state activity in the brain

A broad body of experimental work has demonstrated that apparently spontaneous brain activity is not random. At the level of large-scale neural systems, as measured with functional MRI (fMRI), this ongoing activity reflects the organization of a series of highly coherent functional networks. These so-called resting-state networks (RSNs) closely relate to the underlying anatomical connectivity but cannot be understood in those terms alone. Here we review three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs. We propose that the formation and dissolution of resting-state patterns reflects the exploration of possible functional network configurations around a stable anatomical skeleton.     

Altered Resting State Brain Dynamics in Temporal Lobe Epilepsy Can Be Observed in Spectral Power,Functional Connectivity and Graph Theory Metrics

Despite a wealth of EEG epilepsy data that accumulated for over half a century, our ability to understand brain dynamics associated with epilepsy remains limited. Using EEG data from 15 controls and 9 left temporal lobe epilepsy (LTLE) patients, in this study we characterize how the dynamics of the healthy brain differ from the “dynamically balanced” state of the brain of epilepsy patients treated with anti-epileptic drugs in the context of resting state. We show that such differences can be observed in band power, synchronization and network measures, as well as deviations from the small world network (SWN) architecture of the healthy brain. The θ (4–7 Hz) and high α (10–13 Hz) bands showed the biggest deviations from healthy controls across various measures. In particular, patients demonstrated significantly higher power and synchronization than controls in the θ band, but lower synchronization and power in the high α band. Furthermore, differences between controls and patients in graph theory metrics revealed deviations from a SWN architecture. In the θ band epilepsy patients showed deviations toward an orderly network, while in the high α band they deviated toward a random network. These findings show that, despite the focal nature of LTLE, the epileptic brain differs in its global network characteristics from the healthy brain. To our knowledge, this is the only study to encompass power, connectivity and graph theory metrics to investigate the reorganization of resting state functional networks in LTLE patients.     

Emergence of Slow-Switching Assemblies in Structured Neuronal Networks

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.     

Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac).

The need to integrate massively increasing amounts of data on the mammalian brain has driven several ambitious neuroscientific database projects that were started during the last decade. Databasing the brain's anatomical connectivity as delivered by tracing studies is of particular importance as these data characterize fundamental structural constraints of the complex and poorly understood functional interactions between the components of real neural systems. Previous connectivity databases have been crucial for analysing anatomical brain circuitry in various species and have opened exciting new ways to interpret functional data, both from electrophysiological and from functional imaging studies. The eventual impact and success of connectivity databases, however, will require the resolution of several methodological problems that currently limit their use. These problems comprise four main points: (i) objective representation of coordinate-free, parcellation-based data, (ii) assessment of the reliability and precision of individual data, especially in the presence of contradictory reports, (iii) data mining and integration of large sets of partially redundant and contradictory data, and (iv) automatic and reproducible transformation of data between incongruent brain maps. Here, we present the specific implementation of the 'collation of connectivity data on the macaque brain' (CoCoMac) database (http://www.cocomac.org). The design of this database addresses the methodological challenges listed above, and focuses on experimental and computational neuroscientists' needs to flexibly analyse and process the large amount of published experimental data from tracing studies. In this article, we explain step-by-step the conceptual rationale and methodology of CoCoMac and demonstrate its practical use by an analysis of connectivity in the prefrontal cortex.     

Functional network organization of the human brain

Real-world complex systems may be mathematically modeled as graphs, revealing properties of the system. Here we study graphs of functional brain organization in healthy adults using resting state functional connectivity MRI. We propose two novel brain-wide graphs, one of 264 putative functional areas, the other a modification of voxelwise networks that eliminates potentially artificial short-distance relationships. These graphs contain many subgraphs in good agreement with known functional brain systems. Other subgraphs lack established functional identities; we suggest possible functional characteristics for these subgraphs. Further, graph measures of the areal network indicate that the default mode subgraph shares network properties with sensory and motor subgraphs: it is internally integrated but isolated from other subgraphs, much like a "processing" system. The modified voxelwise graph also reveals spatial motifs in the patterning of systems across the cortex.     

Evaluating the effective connectivity of resting state networks using conditional Granger causality

The human brain has been documented to be spatially organized in a finite set of specific coherent patterns, namely resting state networks (RSNs). The interactions among RSNs, being potentially dynamic and directional, may not be adequately captured by simple correlation or anticorrelation. In order to evaluate the possible effective connectivity within those RSNs, we applied a conditional Granger causality analysis (CGCA) to the RSNs retrieved by independent component analysis (ICA) from resting state functional magnetic resonance imaging (fMRI) data. Our analysis provided evidence for specific causal influences among the detected RSNs: default-mode, dorsal attention, core, central-executive, self-referential, somatosensory, visual, and auditory networks. In particular, we identified that self-referential and default-mode networks (DMNs) play distinct and crucial roles in the human brain functional architecture. Specifically, the former RSN exerted the strongest causal influence over the other RSNs, revealing a top-down modulation of self-referential mental activity (SRN) over sensory and cognitive processing. In quite contrast, the latter RSN was profoundly affected by the other RSNs, which may underlie an integration of information from primary function and higher level cognition networks, consistent with previous task-related studies. Overall, our results revealed the causal influences among these RSNs at different processing levels, and supplied information for a deeper understanding of the brain network dynamics.     

Altered Functional Connectivity between Emotional and Cognitive Resting State Networks in Euthymic Bipolar I Disorder Patients

Bipolar disorder is characterized by a functional imbalance between hyperactive ventral/limbic areas and hypoactive dorsal/cognitive brain regions potentially contributing to affective and cognitive symptoms. Resting-state studies in bipolar disorder have identified abnormal functional connectivity between these brain regions. However, most of these studies used a seed-based approach, thus restricting the number of regions that were analyzed. Using data-driven approaches, researchers identified resting state networks whose spatial maps overlap with frontolimbic areas such as the default mode network, the frontoparietal networks, the salient network, and the meso/paralimbic network. These networks are specifically engaged during affective and cognitive tasks and preliminary evidence suggests that functional connectivity within and between some of these networks is impaired in bipolar disorder. The present study used independent component analysis and functional network connectivity approaches to investigate functional connectivity within and between these resting state networks in bipolar disorder. We compared 30 euthymic bipolar I disorder patients and 35 age- and gender-matched healthy controls. Inter-network connectivity analysis revealed increased functional connectivity between the meso/paralimbic and the right frontoparietal network in bipolar disorder. This abnormal connectivity pattern did not correlate with variables related to the clinical course of the disease. The present finding may reflect abnormal integration of affective and cognitive information in ventral-emotional and dorsal-cognitive networks in euthymic bipolar patients. Furthermore, the results provide novel insights into the role of the meso/paralimbic network in bipolar disorder.     

Non-stationarity in the "resting brain's" modular architecture

Task-free functional magnetic resonance imaging (TF-fMRI) has great potential for advancing the understanding and treatment of neurologic illness. However, as with all measures of neural activity, variability is a hallmark of intrinsic connectivity networks (ICNs) identified by TF-fMRI. This variability has hampered efforts to define a robust metric of connectivity suitable as a biomarker for neurologic illness. We hypothesized that some of this variability rather than representing noise in the measurement process, is related to a fundamental feature of connectivity within ICNs, which is their non-stationary nature. To test this hypothesis, we used a large (n = 892) population-based sample of older subjects to construct a well characterized atlas of 68 functional regions, which were categorized based on independent component analysis network of origin, anatomical locations, and a functional meta-analysis. These regions were then used to construct dynamic graphical representations of brain connectivity within a sliding time window for each subject. This allowed us to demonstrate the non-stationary nature of the brain's modular organization and assign each region to a "meta-modular" group. Using this grouping, we then compared dwell time in strong sub-network configurations of the default mode network (DMN) between 28 subjects with Alzheimer's dementia and 56 cognitively normal elderly subjects matched 1:2 on age, gender, and education. We found that differences in connectivity we and others have previously observed in Alzheimer's disease can be explained by differences in dwell time in DMN sub-network configurations, rather than steady state connectivity magnitude. DMN dwell time in specific modular configurations may also underlie the TF-fMRI findings that have been described in mild cognitive impairment and cognitively normal subjects who are at risk for Alzheimer's dementia.     

Broadband Criticality of Human Brain Network Synchronization

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.