Despite substantial recent progress, our understanding of the principles and mechanisms underlying complex brain function and cognition remains incomplete. Network neuroscience proposes to tackle ...these enduring challenges. Approaching brain structure and function from an explicitly integrative perspective, network neuroscience pursues new ways to map, record, analyze and model the elements and interactions of neurobiological systems. Two parallel trends drive the approach: the availability of new empirical tools to create comprehensive maps and record dynamic patterns among molecules, neurons, brain areas and social systems; and the theoretical framework and computational tools of modern network science. The convergence of empirical and computational advances opens new frontiers of scientific inquiry, including network dynamics, manipulation and control of brain networks, and integration of network processes across spatiotemporal domains. We review emerging trends in network neuroscience and attempt to chart a path toward a better understanding of the brain as a multiscale networked system.
Many functional network properties of the human brain have been identified during rest and task states, yet it remains unclear how the two relate. We identified a whole-brain network architecture ...present across dozens of task states that was highly similar to the resting-state network architecture. The most frequent functional connectivity strengths across tasks closely matched the strengths observed at rest, suggesting this is an “intrinsic,” standard architecture of functional brain organization. Furthermore, a set of small but consistent changes common across tasks suggests the existence of a task-general network architecture distinguishing task states from rest. These results indicate the brain’s functional network architecture during task performance is shaped primarily by an intrinsic network architecture that is also present during rest, and secondarily by evoked task-general and task-specific network changes. This establishes a strong relationship between resting-state functional connectivity and task-evoked functional connectivity—areas of neuroscientific inquiry typically considered separately.
•There is an “intrinsic” functional network architecture present across many tasks•The intrinsic architecture is highly similar to the resting-state architecture•Tasks modify the intrinsic architecture to produce “evoked” network architectures•Task-evoked changes common across tasks form a task-general network architecture
Cole et al. identify a whole-brain functional network architecture in humans that is intrinsic, as it is present across rest and dozens of tasks. Only small network modifications were observed, but many were consistent, composing a task-general evoked network architecture.
Small-World Brain Networks Revisited Bassett, Danielle S.; Bullmore, Edward T.
Neuroscientist,
10/2017, Volume:
23, Issue:
5
Book Review, Journal Article
Peer reviewed
Open access
It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of ...complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.
Two’s company, three (or more) is a simplex Giusti, Chad; Ghrist, Robert; Bassett, Danielle S.
Journal of Computational Neuroscience,
08/2016, Volume:
41, Issue:
1
Journal Article, Book Review
Peer reviewed
Open access
The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying ...assumption: that the quintessential unit of interest in a brain is a dyad – two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of
simplicial complexes
: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.
Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, ...so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.
Brain areas’ functional repertoires are shaped by their incoming and outgoing structural connections. In empirically measured networks, most connections are short, reflecting spatial and energetic ...constraints. Nonetheless, a small number of connections span long distances, consistent with the notion that the functionality of these connections must outweigh their cost. While the precise function of long-distance connections is unknown, the leading hypothesis is that they act to reduce the topological distance between brain areas and increase the efficiency of interareal communication. However, this hypothesis implies a nonspecificity of long-distance connections that we contend is unlikely. Instead, we propose that long-distance connections serve to diversify brain areas’ inputs and outputs, thereby promoting complex dynamics. Through analysis of five weighted interareal network datasets, we show that long-distance connections play only minor roles in reducing average interareal topological distance. In contrast, areas’ long-distance and short-range neighbors exhibit marked differences in their connectivity profiles, suggesting that long-distance connections enhance dissimilarity between areal inputs and outputs. Next, we show that—in isolation—areas’ long-distance connectivity profiles exhibit nonrandom levels of similarity, suggesting that the communication pathways formed by long connections exhibit redundancies that may serve to promote robustness. Finally, we use a linearization of Wilson–Cowan dynamics to simulate the covariance structure of neural activity and show that in the absence of long-distance connections a common measure of functional diversity decreases. Collectively, our findings suggest that long-distance connections are necessary for supporting diverse and complex brain dynamics.
Stimulation-Based Control of Dynamic Brain Networks Muldoon, Sarah Feldt; Pasqualetti, Fabio; Gu, Shi ...
PLOS computational biology/PLoS computational biology,
09/2016, Volume:
12, Issue:
9
Journal Article
Peer reviewed
Open access
The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain ...stimulation as a form of neuromodulation, much remains unknown about the network-level impact of these focal perturbations. To study the system wide impact of regional stimulation, we employ a data-driven computational model of nonlinear brain dynamics to systematically explore the effects of targeted stimulation. Validating predictions from network control theory, we uncover the relationship between regional controllability and the focal versus global impact of stimulation, and we relate these findings to differences in the underlying network architecture. Finally, by mapping brain regions to cognitive systems, we observe that the default mode system imparts large global change despite being highly constrained by structural connectivity. This work forms an important step towards the development of personalized stimulation protocols for medical treatment or performance enhancement.
Multi-scale brain networks Betzel, Richard F.; Bassett, Danielle S.
NeuroImage,
10/2017, Volume:
160
Journal Article
Peer reviewed
Open access
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 from human neuroimaging, we hope that this account will offer an accessible guide to any neuroscientist aiming to measure, characterize, and understand the full richness of the brain's multiscale network structure—irrespective of species, imaging modality, or spatial resolution.
•The human brain can be represented as a multi-scale network.•Characterizing the architecture of multi-scale networks requires new tools.•We review promising multilayer tools from network science.
Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network ...dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks.
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