Danielle S. Bassett

Small-World Brain Networks

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.

Hierarchical Organization of Human Cortical Networks in Health and Schizophrenia

The complex organization of connectivity in the human brain is incompletely understood. Recently, topological measures based on graph theory have provided a new approach to quantify large-scale cortical networks. These methods have been applied to anatomical connectivity data on nonhuman species, and cortical networks have been shown to have small-world topology, associated with high local and global efficiency of information transfer. Anatomical networks derived from cortical thickness measurements have shown the same organizational properties of the healthy human brain, consistent with similar results reported in functional networks derived from resting state functional magnetic resonance imaging (MRI) and magnetoencephalographic data. Here we show, using anatomical networks derived from analysis of inter-regional covariation of gray matter volume in MRI data on 259 healthy volunteers, that classical divisions of cortex (multimodal, unimodal, and transmodal) have some distinct topological attributes. Although all cortical divisions shared nonrandom properties of small-worldness and efficient wiring (short mean Euclidean distance between connected regions), the multimodal network had a hierarchical organization, dominated by frontal hubs with low clustering, whereas the transmodal network was assortative. Moreover, in a sample of 203 people with schizophrenia, multimodal network organization was abnormal, as indicated by reduced hierarchy, the loss of frontal and the emergence of nonfrontal hubs, and increased connection distance. We propose that the topological differences between divisions of normal cortex may represent the outcome of different growth processes for multimodal and transmodal networks and that neurodevelopmental abnormalities in schizophrenia specifically impact multimodal cortical organization.

Functional Connectivity and Brain Networks in Schizophrenia

Schizophrenia has often been conceived as a disorder of connectivity between components of large-scale brain networks. We tested this hypothesis by measuring aspects of both functional connectivity and functional network topology derived from resting-state fMRI time series acquired at 72 cerebral regions over 17 min from 15 healthy volunteers (14 male, 1 female) and 12 people diagnosed with schizophrenia (10 male, 2 female). We investigated between-group differences in strength and diversity of functional connectivity in the 0.06–0.125 Hz frequency interval, and some topological properties of undirected graphs constructed from thresholded interregional correlation matrices. In people with schizophrenia, strength of functional connectivity was significantly decreased, whereas diversity of functional connections was increased. Topologically, functional brain networks had reduced clustering and small-worldness, reduced probability of high-degree hubs, and increased robustness in the schizophrenic group. Reduced degree and clustering were locally significant in medial parietal, premotor and cingulate, and right orbitofrontal cortical nodes of functional networks in schizophrenia. Functional connectivity and topological metrics were correlated with each other and with behavioral performance on a verbal fluency task. We conclude that people with schizophrenia tend to have a less strongly integrated, more diverse profile of brain functional connectivity, associated with a less hub-dominated configuration of complex brain functional networks. Alongside these behaviorally disadvantageous differences, however, brain networks in the schizophrenic group also showed a greater robustness to random attack, pointing to a possible benefit of the schizophrenia connectome, if less extremely expressed.

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes—flexibility and selection—must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.

Adaptive reconfiguration of fractal small-world human brain functional networks

Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical δ (low and high), θ, α, β, and γ frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2–37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency γ network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both β and γ networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters.

Brain Graphs: Graphical Models of the Human Brain Connectome

Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

Human Brain Networks in Health and Disease

Purpose of reviewRecent developments in the statistical physics of complex networks have been translated to neuroimaging data in an effort to enhance our understanding of human brain structural and functional networks. This review focuses on studies using graph theoretical measures applied to structural MRI, diffusion MRI, functional MRI, electroencephalography, and magnetoencephalography data. Recent findingsComplex network properties have been identified with some consistency in all modalities of neuroimaging data and over a range of spatial and time scales. Conserved properties include small worldness, high efficiency of information transfer for low wiring cost, modularity, and the existence of network hubs. Structural and functional network metrics have been found to be heritable and to change with normal aging. Clinical studies, principally in Alzheimers disease and schizophrenia, have identified abnormalities of network configuration in patients. Future work will likely involve efforts to synthesize structural and functional networks in integrated models and to explore the interdependence of network configuration and cognitive performance. SummaryGraph theoretical analysis of neuroimaging data is growing rapidly and could potentially provide a relatively simple but powerful quantitative framework to describe and compare whole human brain structural and functional networks under diverse experimental and clinical conditions.

A validated network of effective amygdala connectivity

Regulatory interactions with the amygdala are thought to be critical for emotional processing in the extended limbic system. Structural equation modeling (path analysis) is a widely used method to quantify interactions among brain regions based on connectivity models, but is often limited by lack of precise anatomical and functional constraints. To address this issue, we developed an automated elaborative path analysis procedure guided by known anatomical connectivity in the macaque. We applied this technique to a large human fMRI data set acquired during perceptual processing of angry or fearful facial stimuli. The derived models were inferentially validated using a bootstrapping split-half approach in pairs of 500 independent groups. Significant paths across the groups were used to form a rigorously validated and consistent path model. We confirm and extend previous observations of amygdala regulation by an extended prefrontal network encompassing cingulate, orbitofrontal, insular, and dorsolateral prefrontal cortex, as well as strong interactions between amygdala and parahippocampal gyrus. This validated model can be used to study neurocognitive correlates as well as genotype or disease-related alterations of functional interactions in the limbic system.

Cognitive fitness of cost-efficient brain functional networks

The human brains capacity for cognitive function is thought to depend on coordinated activity in sparsely connected, complex networks organized over many scales of space and time. Recent work has demonstrated that human brain networks constructed from neuroimaging data have economical small-world properties that confer high efficiency of information processing at relatively low connection cost. However, it has been unclear how the architecture of complex brain networks functioning at different frequencies can be related to behavioral performance on cognitive tasks. Here, we show that impaired accuracy of working memory could be related to suboptimal cost efficiency of brain functional networks operating in the classical β frequency band, 15–30 Hz. We analyzed brain functional networks derived from magnetoencephalography data recorded during working-memory task performance in 29 healthy volunteers and 28 people with schizophrenia. Networks functioning at higher frequencies had greater global cost efficiency than low-frequency networks in both groups. Superior task performance was positively correlated with global cost efficiency of the β-band network and specifically with cost efficiency of nodes in left lateral parietal and frontal areas. These results are consistent with biophysical models highlighting the importance of β-band oscillations for long-distance functional connections in brain networks and with pathophysiological models of schizophrenia as a dysconnection syndrome. More generally, they echo the saying that “less is more”: The information processing performance of a network can be enhanced by a sparse or low-cost configuration with disproportionately high efficiency.

Conserved and variable architecture of human white matter connectivity

Whole-brain network analysis of diffusion imaging tractography data is an important new tool for quantification of differential connectivity patterns across individuals and between groups. Here we investigate both the conservation of network architectural properties across methodological variation and the reproducibility of individual architecture across multiple scanning sessions. Diffusion spectrum imaging (DSI) and diffusion tensor imaging (DTI) data were both acquired in triplicate from a cohort of healthy young adults. Deterministic tractography was performed on each dataset and inter-regional connectivity matrices were then derived by applying each of three widely used whole-brain parcellation schemes over a range of spatial resolutions. Across acquisitions and preprocessing streams, anatomical brain networks were found to be sparsely connected, hierarchical, and assortative. They also displayed signatures of topo-physical interdependence such as Rentian scaling. Basic connectivity properties and several graph metrics consistently displayed high reproducibility and low variability in both DSI and DTI networks. The relative increased sensitivity of DSI to complex fiber configurations was evident in increased tract counts and network density compared with DTI. In combination, this pattern of results shows that network analysis of human white matter connectivity provides sensitive and temporally stable topological and physical estimates of individual cortical structure across multiple spatial scales.