Information Flow in Networks and the Law of Diminishing Marginal Returns: Evidence from Modeling and Human Electroencephalographic Recordings

We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon.     

Driving and driven architectures of directed small-world human brain functional networks

Recently, increasing attention has been focused on the investigation of the human brain connectome that describes the patterns of structural and functional connectivity networks of the human brain. Many studies of the human connectome have demonstrated that the brain network follows a small-world topology with an intrinsically cohesive modular structure and includes several network hubs in the medial parietal regions. However, most of these studies have only focused on undirected connections between regions in which the directions of information flow are not taken into account. How the brain regions causally influence each other and how the directed network of human brain is topologically organized remain largely unknown. Here, we applied linear multivariate Granger causality analysis (GCA) and graph theoretical approaches to a resting-state functional MRI dataset with a large cohort of young healthy participants (n = 86) to explore connectivity patterns of the population-based whole-brain functional directed network. This directed brain network exhibited prominent small-world properties, which obviously improved previous results of functional MRI studies showing weak small-world properties in the directed brain networks in terms of a kernel-based GCA and individual analysis. This brain network also showed significant modular structures associated with 5 well known subsystems: fronto-parietal, visual, paralimbic/limbic, subcortical and primary systems. Importantly, we identified several driving hubs predominantly located in the components of the attentional network (e.g., the inferior frontal gyrus, supplementary motor area, insula and fusiform gyrus) and several driven hubs predominantly located in the components of the default mode network (e.g., the precuneus, posterior cingulate gyrus, medial prefrontal cortex and inferior parietal lobule). Further split-half analyses indicated that our results were highly reproducible between two independent subgroups. The current study demonstrated the directions of spontaneous information flow and causal influences in the directed brain networks, thus providing new insights into our understanding of human brain functional connectome.     

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.     

Identifying interactions in the time and frequency domains in local and global networks - A Granger Causality Approach

Background  

Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality.     

Detecting effective connectivity in networks of coupled neuronal oscillators

The application of data-driven time series analysis techniques such as Granger causality, partial directed coherence and phase dynamics modeling to estimate effective connectivity in brain networks has recently gained significant prominence in the neuroscience community. While these techniques have been useful in determining causal interactions among different regions of brain networks, a thorough analysis of the comparative accuracy and robustness of these methods in identifying patterns of effective connectivity among brain networks is still lacking. In this paper, we systematically address this issue within the context of simple networks of coupled spiking neurons. Specifically, we develop a method to assess the ability of various effective connectivity measures to accurately determine the true effective connectivity of a given neuronal network. Our method is based on decision tree classifiers which are trained using several time series features that can be observed solely from experimentally recorded data. We show that the classifiers constructed in this work provide a general framework for determining whether a particular effective connectivity measure is likely to produce incorrect results when applied to a dataset.     

On the Inference of Functional Circadian Networks Using Granger Causality

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals.     

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.     

Decoding the different states of visual attention using functional and effective connectivity features in fMRI data

The present paper concentrates on the impact of visual attention task on structure of the brain functional and effective connectivity networks using coherence and Granger causality methods. Since most studies used correlation method and resting-state functional connectivity, the task-based approach was selected for this experiment to boost our knowledge of spatial and feature-based attention. In the present study, the whole brain was divided into 82 sub-regions based on Brodmann areas. The coherence and Granger causality were applied to construct functional and effective connectivity matrices. These matrices were converted into graphs using a threshold, and the graph theory measures were calculated from it including degree and characteristic path length. Visual attention was found to reveal more information during the spatial-based task. The degree was higher while performing a spatial-based task, whereas characteristic path length was lower in the spatial-based task in both functional and effective connectivity. Primary and secondary visual cortex (17 and 18 Brodmann areas) were highly connected to parietal and prefrontal cortex while doing visual attention task. Whole brain connectivity was also calculated in both functional and effective connectivity. Our results reveal that Brodmann areas of 17, 18, 19, 46, 3 and 4 had a significant role proving that somatosensory, parietal and prefrontal regions along with visual cortex were highly connected to other parts of the cortex during the visual attention task. Characteristic path length results indicated an increase in functional connectivity and more functional integration in spatial-based attention compared with feature-based attention. The results of this work can provide useful information about the mechanism of visual attention at the network level.     

Functional Brain Networks: Random, “Small World” or Deterministic?

Lately the problem of connectivity in brain networks is being approached frequently by graph theoretical analysis. In several publications based on bivariate estimators of relations between EEG channels authors reported random or “small world” structure of networks. The results of these works often have no relation to other evidence based on imaging, inverse solutions methods, physiological and anatomical data. Herein we try to find reasons for this discrepancy. We point out that EEG signals are very much interdependent, thus bivariate measures applied to them may produce many spurious connections. In fact, they may outnumber the true connections. Giving all connections equal weights, as it is usual in the framework of graph theoretical analysis, further enhances these spurious links. In effect, close to random and disorganized patterns of connections emerge. On the other hand, multivariate connectivity estimators, which are free of the artificial links, show specific, well determined patterns, which are in a very good agreement with other evidence. The modular structure of brain networks may be identified by multivariate estimators based on Granger causality and formalism of assortative mixing. In this way, the strength of coupling may be evaluated quantitatively. During working memory task, by means of multivariate Directed Transfer Function, it was demonstrated that the modules characterized by strong internal bonds exchange the information by weaker connections.     

Dynamical correlation patterns and corresponding community structure in neural spontaneous activity at criticality

It has been considered that the state in the vicinity of a critical point, which is the point between ordered and disordered states, can underlie and facilitate information processing of the brain in various aspects. In this research, we numerically study the influence of criticality on one aspect of brain information processing, i.e., the community structure, which is an important characteristic of complex networks. We examine community structure of the functional connectivity in simulated brain spontaneous activity, which is based on dynamical correlations between neural activity patterns at different positions. The brain spontaneous activity is simulated by a neural field model whose parameter covers subcritical, critical, and supercritical regions. Then, the corresponding dynamical correlation patterns and community structure are compared. In the critical region, we found some distinctive properties, namely high correlation and correlation switching, high modularity and a low number of modules, high stability of the dynamical functional connectivity, and moderate flexibility of the community structure across temporal scales. We also discuss how these characteristics might improve information processing of the brain.     

Intra- and Inter-Frequency Brain Network Structure in Health and Schizophrenia

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands (, , , and ). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency and band networks as well as in the - cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.     

Measuring Granger Causality between cortical regions from voxelwise fMRI BOLD signals with LASSO

Functional brain network studies using the Blood Oxygen-Level Dependent (BOLD) signal from functional Magnetic Resonance Imaging (fMRI) are becoming increasingly prevalent in research on the neural basis of human cognition. An important problem in functional brain network analysis is to understand directed functional interactions between brain regions during cognitive performance. This problem has important implications for understanding top-down influences from frontal and parietal control regions to visual occipital cortex in visuospatial attention, the goal motivating the present study. A common approach to measuring directed functional interactions between two brain regions is to first create nodal signals by averaging the BOLD signals of all the voxels in each region, and to then measure directed functional interactions between the nodal signals. Another approach, that avoids averaging, is to measure directed functional interactions between all pairwise combinations of voxels in the two regions. Here we employ an alternative approach that avoids the drawbacks of both averaging and pairwise voxel measures. In this approach, we first use the Least Absolute Shrinkage Selection Operator (LASSO) to pre-select voxels for analysis, then compute a Multivariate Vector AutoRegressive (MVAR) model from the time series of the selected voxels, and finally compute summary Granger Causality (GC) statistics from the model to represent directed interregional interactions. We demonstrate the effectiveness of this approach on both simulated and empirical fMRI data. We also show that averaging regional BOLD activity to create a nodal signal may lead to biased GC estimation of directed interregional interactions. The approach presented here makes it feasible to compute GC between brain regions without the need for averaging. Our results suggest that in the analysis of functional brain networks, careful consideration must be given to the way that network nodes and edges are defined because those definitions may have important implications for the validity of the analysis.     

BOLD Granger Causality Reflects Vascular Anatomy

A number of studies have tried to exploit subtle phase differences in BOLD time series to resolve the order of sequential activation of brain regions, or more generally the ability of signal in one region to predict subsequent signal in another region. More recently, such lag-based measures have been applied to investigate directed functional connectivity, although this application has been controversial. We attempted to use large publicly available datasets (FCON 1000, ADHD 200, Human Connectome Project) to determine whether consistent spatial patterns of Granger Causality are observed in typical fMRI data. For BOLD datasets from 1,240 typically developing subjects ages 7–40, we measured Granger causality between time series for every pair of 7,266 spherical ROIs covering the gray matter and 264 seed ROIs at hubs of the brain’s functional network architecture. Granger causality estimates were strongly reproducible for connections in a test and replication sample (n=620 subjects for each group), as well as in data from a single subject scanned repeatedly, both during resting and passive video viewing. The same effect was even stronger in high temporal resolution fMRI data from the Human Connectome Project, and was observed independently in data collected during performance of 7 task paradigms. The spatial distribution of Granger causality reflected vascular anatomy with a progression from Granger causality sources, in Circle of Willis arterial inflow distributions, to sinks, near large venous vascular structures such as dural venous sinuses and at the periphery of the brain. Attempts to resolve BOLD phase differences with Granger causality should consider the possibility of reproducible vascular confounds, a problem that is independent of the known regional variability of the hemodynamic response.     

Spatially constrained adaptive rewiring in cortical networks creates spatially modular small world architectures

A modular small-world topology in functional and anatomical networks of the cortex is eminently suitable as an information processing architecture. This structure was shown in model studies to arise adaptively; it emerges through rewiring of network connections according to patterns of synchrony in ongoing oscillatory neural activity. However, in order to improve the applicability of such models to the cortex, spatial characteristics of cortical connectivity need to be respected, which were previously neglected. For this purpose we consider networks endowed with a metric by embedding them into a physical space. We provide an adaptive rewiring model with a spatial distance function and a corresponding spatially local rewiring bias. The spatially constrained adaptive rewiring principle is able to steer the evolving network topology to small world status, even more consistently so than without spatial constraints. Locally biased adaptive rewiring results in a spatial layout of the connectivity structure, in which topologically segregated modules correspond to spatially segregated regions, and these regions are linked by long-range connections. The principle of locally biased adaptive rewiring, thus, may explain both the topological connectivity structure and spatial distribution of connections between neuronal units in a large-scale cortical architecture.     

The research of constructing dynamic cognition model based on brain network

Estimating the functional interactions and connections between brain regions to corresponding process in cognitive, behavioral and psychiatric domains is a central pursuit for understanding the human connectome. Few studies have examined the effects of dynamic evolution on cognitive processing and brain activation using brain network model in scalp electroencephalography (EEG) data. Aim of this study was to investigate the brain functional connectivity and construct dynamic programing model from EEG data and to evaluate a possible correlation between topological characteristics of the brain connectivity and cognitive evolution processing. Here, functional connectivity between brain regions is defined as the statistical dependence between EEG signals in different brain areas and is typically determined by calculating the relationship between regional time series using wavelet coherence. We present an accelerated dynamic programing algorithm to construct dynamic cognitive model that we found that spatially distributed regions coherence connection difference, the topologic characteristics with which they can transfer information, producing temporary network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time after variation audio stimulation, dynamic programing model gives the dynamic evolution processing at different time and frequency. In this paper, by applying a new construct approach to understand whole brain network dynamics, firstly, brain network is constructed by wavelet coherence, secondly, different time active brain regions are selected by network topological characteristics and minimum spanning tree. Finally, dynamic evolution model is constructed to understand cognitive process by dynamic programing algorithm, this model is applied to the auditory experiment, results showed that, quantitatively, more correlation was observed after variation audio stimulation, the EEG function connection dynamic evolution model on cognitive processing is feasible with wavelet coherence EEG recording.     

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.     

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.     

基于听觉刺激的意识障碍患者脑功能连通性研究

目的 目前对意识障碍（DOC）患者的分级评估仍是相关领域的重点和难点。因效性网络可以通过时间序列间的因果关系直观地反映信息传递方向,帮助人们更好地理解患者大脑不同区域之间的信息交互作用。本文结合脑电图和因效性网络探讨听觉刺激下无反应觉醒综合征（VS）患者与最低意识状态（MCS）患者的脑功能连通性差异。方法 共纳入23例DOC患者,采集并分析唤名刺激下的脑电信号,通过多元格兰杰因果方法构建脑功能网络,利用脑网络节点度、聚类系数、全局效率以及因果流向性等参量从脑区之间协同工作的角度对比研究听觉刺激下不同意识水平患者的网络特征。结果 唤名刺激下MCS患者的脑功能连通性强于VS患者,且呈现出因果流向差异,MCS与VS患者四个脑区的信息传递方向均不相同。结论 唤名听觉刺激下MCS患者的信息传递能力强于VS患者;与VS患者相比MCS患者为因果源的电极通道数增多,对其他脑区的信息输出增多。本研究可为DOC患者意识水平的分级评估提供一定的理论依据。     

Multimodal functional network connectivity: an EEG-fMRI fusion in network space

EEG and fMRI recordings measure the functional activity of multiple coherent networks distributed in the cerebral cortex. Identifying network interaction from the complementary neuroelectric and hemodynamic signals may help to explain the complex relationships between different brain regions. In this paper, multimodal functional network connectivity (mFNC) is proposed for the fusion of EEG and fMRI in network space. First, functional networks (FNs) are extracted using spatial independent component analysis (ICA) in each modality separately. Then the interactions among FNs in each modality are explored by Granger causality analysis (GCA). Finally, fMRI FNs are matched to EEG FNs in the spatial domain using network-based source imaging (NESOI). Investigations of both synthetic and real data demonstrate that mFNC has the potential to reveal the underlying neural networks of each modality separately and in their combination. With mFNC, comprehensive relationships among FNs might be unveiled for the deep exploration of neural activities and metabolic responses in a specific task or neurological state.     

Recursive cluster elimination based support vector machine for disease state prediction using resting state functional and effective brain connectivity

Background

Brain state classification has been accomplished using features such as voxel intensities, derived from functional magnetic resonance imaging (fMRI) data, as inputs to efficient classifiers such as support vector machines (SVM) and is based on the spatial localization model of brain function. With the advent of the connectionist model of brain function, features from brain networks may provide increased discriminatory power for brain state classification.

Methodology/Principal Findings

In this study, we introduce a novel framework where in both functional connectivity (FC) based on instantaneous temporal correlation and effective connectivity (EC) based on causal influence in brain networks are used as features in an SVM classifier. In order to derive those features, we adopt a novel approach recently introduced by us called correlation-purged Granger causality (CPGC) in order to obtain both FC and EC from fMRI data simultaneously without the instantaneous correlation contaminating Granger causality. In addition, statistical learning is accelerated and performance accuracy is enhanced by combining recursive cluster elimination (RCE) algorithm with the SVM classifier. We demonstrate the efficacy of the CPGC-based RCE-SVM approach using a specific instance of brain state classification exemplified by disease state prediction. Accordingly, we show that this approach is capable of predicting with 90.3% accuracy whether any given human subject was prenatally exposed to cocaine or not, even when no significant behavioral differences were found between exposed and healthy subjects.

Conclusions/Significance

The framework adopted in this work is quite general in nature with prenatal cocaine exposure being only an illustrative example of the power of this approach. In any brain state classification approach using neuroimaging data, including the directional connectivity information may prove to be a performance enhancer. When brain state classification is used for disease state prediction, our approach may aid the clinicians in performing more accurate diagnosis of diseases in situations where in non-neuroimaging biomarkers may be unable to perform differential diagnosis with certainty.