Richard Betzel

The development of new technologies for mapping structural and functional brain connectivity has led to the creation of comprehensive network maps of neuronal circuits and systems. The architecture of these brain networks can be examined and analyzed with a large variety of graph theory tools. Methods for detecting modules, or network communities, are of particular interest because they uncover major building blocks or subnetworks that are particularly densely connected, often corresponding to specialized functional components. A large number of methods for community detection have become available and are now widely applied in network neuroscience. This article first surveys a number of these methods, with an emphasis on their advantages and shortcomings; then it summarizes major findings on the existence of modules in both structural and functional brain networks and briefly considers their …

At rest, the brain's sensorimotor and higher cognitive systems engage in organized patterns of correlated activity forming resting-state networks. An important empirical question is how functional connectivity and structural connectivity within and between resting-state networks change with age. In this study we use network modeling techniques to identify significant changes in network organization across the human lifespan. The results of this study demonstrate that whole-brain functional and structural connectivity both exhibit reorganization with age. On average, functional connections within resting-state networks weaken in magnitude while connections between resting-state networks tend to increase. These changes can be localized to a small subset of functional connections that exhibit systematic changes across the lifespan. Collectively, changes in functional connectivity are also manifest at a system-wide …

The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures—search information and path transitivity—which account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of …

The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its alteration in disease or injury. Traditional tools and approaches to study this architecture have largely focused on single scales—of topology, time, and space. Expanding beyond this narrow view, we focus this review on pertinent questions and novel methodological advances for the multi-scale brain. We separate our exposition into content related to multi-scale topological structure, multi-scale temporal structure, and multi-scale spatial structure. In each case, we recount empirical evidence for such structures, survey network-based methodological approaches to reveal these structures, and outline current frontiers and open questions. Although predominantly peppered with examples …

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features …

Increasingly detailed data on the network topology of neural circuits create a need for theoretical principles that explain how these networks shape neural communication. Here we use a model of cascade spreading to reveal architectural features of human brain networks that facilitate spreading. Using an anatomical brain network derived from high-resolution diffusion spectrum imaging (DSI), we investigate scenarios where perturbations initiated at seed nodes result in global cascades that interact either cooperatively or competitively. We find that hub regions and a backbone of pathways facilitate early spreading, while the shortest path structure of the connectome enables cooperative effects, accelerating the spread of cascades. Finally, competing cascades become integrated by converging on polysensory associative areas. These findings show that the organizational principles of brain networks shape global …

We investigate the relationship of resting-state fMRI functional connectivity estimated over long periods of time with time-varying functional connectivity estimated over shorter time intervals. We show that using Pearson's correlation to estimate functional connectivity implies that the range of fluctuations of functional connections over short time-scales is subject to statistical constraints imposed by their connectivity strength over longer scales. We present a method for estimating time-varying functional connectivity that is designed to mitigate this issue and allows us to identify episodes where functional connections are unexpectedly strong or weak. We apply this method to data recorded from N = 80 participants, and show that the number of unexpectedly strong/weak connections fluctuates over time, and that these variations coincide with intermittent periods of high and low modularity in time-varying functional …

To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain’s network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions’ weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input …

The dynamics of spontaneous fluctuations in neural activity are shaped by underlying patterns of anatomical connectivity. While numerous studies have demonstrated edge-wise correspondence between structural and functional connections, much less is known about how large-scale coherent functional network patterns emerge from the topology of structural networks. In the present study, we deploy a multivariate statistical technique, partial least squares, to investigate the association between spatially extended structural networks and functional networks. We find multiple statistically robust patterns, reflecting reliable combinations of structural and functional subnetworks that are optimally associated with one another. Importantly, these patterns generally do not show a one-to-one correspondence between structural and functional edges, but are instead distributed and heterogeneous, with many functional …

Intrinsically driven neural activity generated at rest exhibits complex spatiotemporal dynamics characterized by patterns of synchronization across distant brain regions. Mounting evidence suggests that these patterns exhibit fluctuations and nonstationarity at multiple time scales. Resting-state EEG recordings were examined in 12 young adults for changes in synchronization patterns on a fast time scale in the range of tens to hundreds of milliseconds. Results revealed that EEG dynamics continuously underwent rapid transitions between intermittently stable states. Numerous approximate recurrences of states were observed within single recording epochs, across different epochs separated by longer times, and between participants. For broadband (4-30 Hz) data, a majority of states could be grouped into three families, suggesting the existence of a limited repertoire of core states that is continually revisited and shared across participants. Our results document the existence of fast synchronization dynamics iterating amongst a small set of core networks in the resting brain, complementing earlier findings of nonstationary dynamics in electromagnetic recordings and transient EEG microstates.

The human brain is organized into large-scale functional modules that have been shown to evolve in childhood and adolescence. However, it remains unknown whether the underlying white matter architecture is similarly refined during development, potentially allowing for improvements in executive function. In a sample of 882 participants (ages 8–22) who underwent diffusion imaging as part of the Philadelphia Neurodevelopmental Cohort, we demonstrate that structural network modules become more segregated with age, with weaker connections between modules and stronger connections within modules. Evolving modular topology facilitates global network efficiency and is driven by age-related strengthening of hub edges present both within and between modules. Critically, both modular segregation and network efficiency are associated with enhanced executive performance and mediate the improvement …

The human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. Past studies have often used single-scale modularity measures in order to infer the connectome's community structure, possibly overlooking interesting structure at other organizational scales. In this report, we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure. Comparing the community structure to observed resting-state functional connectivity revealed communities across a broad range of scales that were closely related to functional connectivity. This result suggests a mapping between communities in structural networks, models of influence-spreading and diffusion, and brain function. It further …

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying …

Connectomics has enhanced our understanding of neurocognitive development and decline by the integration of network sciences into studies across different stages of the human life span. However, these studies commonly occurred independently, missing the opportunity to test integrated models of the dynamical brain organization across the entire life span. In this review article, we survey empirical findings in life-span connectomics and propose a generative framework for computationally modeling the connectome over the human life span. This framework highlights initial findings that across the life span, the human connectome gradually shifts from an ‘anatomically driven’ organization to one that is more ‘topological’. Finally, we consider recent advances that are promising to provide an integrative and systems perspective of human brain plasticity as well as underscore the pitfalls and challenges.

Encoding brain regions and their connections as a network of nodes and edges captures many of the possible paths along which information can be transmitted as humans process and perform complex behaviors. Because cognitive processes involve large, distributed networks of brain areas, principled examinations of multi-node routes within larger connection patterns can offer fundamental insights into the complexities of brain function. Here, we investigate both densely connected groups of nodes that could perform local computations as well as larger patterns of interactions that would allow for parallel processing. Finding such structures necessitates that we move from considering exclusively pairwise interactions to capturing higher order relations, concepts naturally expressed in the language of algebraic topology. These tools can be used to study mesoscale network structures that arise from the …