Mikail Rubinov

Complex network measures of brain connectivity: Uses and interpretations

Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis-a new multidisciplinary approach to the study of complex systems-aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets.

Weight-conserving characterization of complex functional brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Important functional network measures include measures of modularity (measures of the goodness with which a network is optimally partitioned into functional subgroups) and measures of centrality (measures of the functional influence of individual brain regions). Characterizations of functional networks are increasing in popularity, but are associated with several important methodological problems. These problems include the inability to characterize densely connected and weighted functional networks, the neglect of degenerate topologically distinct high-modularity partitions of these networks, and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties. In this study we describe a set of methods to overcome these problems. Specifically, we generalize measures of modularity and centrality to fully connected and weighted complex networks, describe the detection of degenerate high-modularity partitions of these networks, and introduce a weighted-connectivity null model of these networks. We illustrate our methods by demonstrating degenerate high-modularity partitions and strong correlations between two complementary measures of centrality in resting-state functional magnetic resonance imaging (MRI) networks from the 1000 Functional Connectomes Project, an open-access repository of resting-state functional MRI datasets. Our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects.

Small-World Properties of Nonlinear Brain Activity in Schizophrenia

A disturbance in the interactions between distributed cortical regions may underlie the cognitive and perceptual dysfunction associated with schizophrenia. In this article, nonlinear measures of cortical interactions and graph‐theoretical metrics of network topography are combined to investigate this schizophrenia “disconnection hypothesis.” This is achieved by analyzing the spatiotemporal structure of resting state scalp EEG data previously acquired from 40 young subjects with a recent first episode of schizophrenia and 40 healthy matched controls. In each subject, a method of mapping the topography of nonlinear interactions between cortical regions was applied to a widely distributed array of these data. The resulting nonlinear correlation matrices were converted to weighted graphs. The path length (a measure of large‐scale network integration), clustering coefficient (a measure of “cliquishness”), and hub structure of these graphs were used as metrics of the underlying brain network activity. The graphs of both groups exhibited high levels of local clustering combined with comparatively short path lengths—features consistent with a “small‐world” topology—as well as the presence of strong, central hubs. The graphs in the schizophrenia group displayed lower clustering and shorter path lengths in comparison to the healthy group. Whilst still “small‐world,” these effects are consistent with a subtle randomization in the underlying network architecture—likely associated with a greater number of links connecting disparate clusters. This randomization may underlie the cognitive disturbances characteristic of schizophrenia. Hum Brain Mapp, 2009.

Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.

A wavelet method for modeling and despiking motion artifacts from resting-state fMRI time series

The impact of in-scanner head movement on functional magnetic resonance imaging (fMRI) signals has long been established as undesirable. These effects have been traditionally corrected by methods such as linear regression of head movement parameters. However, a number of recent independent studies have demonstrated that these techniques are insufficient to remove motion confounds, and that even small movements can spuriously bias estimates of functional connectivity. Here we propose a new data-driven, spatially-adaptive, wavelet-based method for identifying, modeling, and removing non-stationary events in fMRI time series, caused by head movement, without the need for data scrubbing. This method involves the addition of just one extra step, the Wavelet Despike, in standard pre-processing pipelines. With this method, we demonstrate robust removal of a range of different motion artifacts and motion-related biases including distance-dependent connectivity artifacts, at a group and single-subject level, using a range of previously published and new diagnostic measures. The Wavelet Despike is able to accommodate the substantial spatial and temporal heterogeneity of motion artifacts and can consequently remove a range of high and low frequency artifacts from fMRI time series, that may be linearly or non-linearly related to physical movements. Our methods are demonstrated by the analysis of three cohorts of resting-state fMRI data, including two high-motion datasets: a previously published dataset on children (N = 22) and a new dataset on adults with stimulant drug dependence (N = 40). We conclude that there is a real risk of motion-related bias in connectivity analysis of fMRI data, but that this risk is generally manageable, by effective time series denoising strategies designed to attenuate synchronized signal transients induced by abrupt head movements. The Wavelet Despiking software described in this article is freely available for download at www.brainwavelet.org.

Symbiotic relationship between brain structure and dynamics

BackgroundBrain structure and dynamics are interdependent through processes such as activity-dependent neuroplasticity. In this study, we aim to theoretically examine this interdependence in a model of spontaneous cortical activity. To this end, we simulate spontaneous brain dynamics on structural connectivity networks, using coupled nonlinear maps. On slow time scales structural connectivity is gradually adjusted towards the resulting functional patterns via an unsupervised, activity-dependent rewiring rule. The present model has been previously shown to generate cortical-like, modular small-world structural topology from initially random connectivity. We provide further biophysical justification for this model and quantitatively characterize the relationship between structure, function and dynamics that accompanies the ensuing self-organization.ResultsWe show that coupled chaotic dynamics generate ordered and modular functional patterns, even on a random underlying structural connectivity. Consequently, structural connectivity becomes more modular as it rewires towards these functional patterns. Functional networks reflect the underlying structural networks on slow time scales, but significantly less so on faster time scales. In spite of ordered functional topology, structural networks remain robustly interconnected – and therefore small-world – due to the presence of central, inter-modular hub nodes. The noisy dynamics of these hubs enable them to persist despite ongoing rewiring and despite their comparative absence in functional networks.ConclusionOur results outline a theoretical mechanism by which brain dynamics may facilitate neuroanatomical self-organization. We find time scale dependent differences between structural and functional networks. These differences are likely to arise from the distinct dynamics of central structural nodes.

Fledgling pathoconnectomics of psychiatric disorders

Pathoconnectomics, the mapping of abnormal brain networks, is a popular current framework for the study of brain dysfunction in psychiatric disorders. In this review we evaluate the conceptual foundations of this framework, describe the construction and analysis of empirical models of brain networks or connectomes, and summarize recent reports of the large-scale whole-brain connectome organization of two candidate brain-network disorders, schizophrenia and autism. We consider the evidence for the abnormal brain-network nature of psychiatric disorders and find it inconclusive. For instance, although there is some evidence for more random whole-brain network organization in schizophrenia and autism, future studies need to determine if these and other observed brain-network abnormalities represent sufficient phenotypes of psychiatric disorders, in order to validate pathoconnectomics as a scientific and clinical framework.

Dynamic Change of Global and Local Information Processing in Propofol-Induced Loss and Recovery of Consciousness

Whether unique to humans or not, consciousness is a central aspect of our experience of the world. The neural fingerprint of this experience, however, remains one of the least understood aspects of the human brain. In this paper we employ graph-theoretic measures and support vector machine classification to assess, in 12 healthy volunteers, the dynamic reconfiguration of functional connectivity during wakefulness, propofol-induced sedation and loss of consciousness, and the recovery of wakefulness. Our main findings, based on resting-state fMRI, are three-fold. First, we find that propofol-induced anesthesia does not bear differently on long-range versus short-range connections. Second, our multi-stage design dissociated an initial phase of thalamo-cortical and cortico-cortical hyperconnectivity, present during sedation, from a phase of cortico-cortical hypoconnectivity, apparent during loss of consciousness. Finally, we show that while clustering is increased during loss of consciousness, as recently suggested, it also remains significantly elevated during wakefulness recovery. Conversely, the characteristic path length of brain networks (i.e., the average functional distance between any two regions of the brain) appears significantly increased only during loss of consciousness, marking a decrease of global information-processing efficiency uniquely associated with unconsciousness. These findings suggest that propofol-induced loss of consciousness is mainly tied to cortico-cortical and not thalamo-cortical mechanisms, and that decreased efficiency of information flow is the main feature differentiating the conscious from the unconscious brain.

State and Trait Components of Functional Connectivity: Individual Differences Vary with Mental State

Resting-state functional connectivity, as measured by functional magnetic resonance imaging (fMRI), is often treated as a trait, used, for example, to draw inferences about individual differences in cognitive function, or differences between healthy or diseased populations. However, functional connectivity can also depend on the individuals mental state. In the present study, we examined the relative contribution of state and trait components in shaping an individuals functional architecture. We used fMRI data from a large, population-based human sample (N = 587, age 18–88 years), as part of the Cambridge Centre for Aging and Neuroscience (Cam-CAN), which were collected in three mental states: resting, performing a sensorimotor task, and watching a movie. Whereas previous studies have shown commonalities across mental states in the average functional connectivity across individuals, we focused on the effects of states on the pattern of individual differences in functional connectivity. We found that state effects were as important as trait effects in shaping individual functional connectivity patterns, each explaining an approximately equal amount of variance. This was true when we looked at aging, as one specific dimension of individual differences, as well as when we looked at generic aspects of individual variation. These results show that individual differences in functional connectivity consist of state-dependent aspects, as well as more stable, trait-like characteristics. Studying individual differences in functional connectivity across a wider range of mental states will therefore provide a more complete picture of the mechanisms underlying factors such as cognitive ability, aging, and disease. SIGNIFICANCE STATEMENT The brains functional architecture is remarkably similar across different individuals and across different mental states, which is why many studies use functional connectivity as a trait measure. Despite these trait-like aspects, functional connectivity varies over time and with changes in cognitive state. We measured connectivity in three different states to quantify the size of the trait-like component of functional connectivity, compared with the state-dependent component. Our results show that studying individual differences within one state (such as resting) uncovers only part of the relevant individual differences in brain function, and that the study of functional connectivity under multiple mental states is essential to disentangle connectivity differences that are transient versus those that represent more stable, trait-like characteristics of an individual.

Wiring cost and topological participation of the mouse brain connectome

Significance We analyzed a large dataset of tract tracing experiments to investigate the topological and spatial properties of the mouse brain connectome. We found expensive, topologically integrative hub nodes, which could not be explained by global minimization of wiring cost alone. These “high-participation” hubs mediated communication between functionally specialized and anatomically localized network modules and were associated with high expression of genes involved in cognitive and behavioral processes. We propose that the mouse brain network is selected by simultaneous competitive pressures for wiring-cost minimization and hub-mediated information exchange between network modules. High-participation hubs are expensive but central to global integration of information and, thus, essential for adaptive “higher order” brain functions. Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of “wiring cost” explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.