Author Summary Edge time series decompose functional connectivity into its framewise contributions. Previous studies have focused on high-amplitude frames (time points when the global co-fluctuation amplitude takes on its largest value), including their cluster structure. Less is known about middle- and low-amplitude co-fluctuations. Here, we address those questions directly, using data from two dense sampling studies. We group peak co-fluctuations of all magnitudes into hierarchical clusters based on their pairwise concordance. At a coarse scale, we find evidence of three large clusters that engage all brain systems. At finer scales clusters dissolve, yielding refined patterns of co-fluctuations involving specific sets of brain systems. We also find an increase in global co-fluctuation amplitude with hierarchical scale. Finally, we comment on the amount of data needed to estimate co-fluctuation pattern clusters. Abstract Edge time series decompose functional connectivity into its framewise contributions. Previous studies have focused on characterizing the properties of high-amplitude frames (time points when the global co-fluctuation amplitude takes on its largest value), including their cluster structure. Less is known about middle- and low-amplitude co-fluctuations (peaks in co-fluctuation time series but of lower amplitude). Here, we directly address those questions, using data from two dense-sampling studies: the MyConnectome project and Midnight Scan Club. We develop a hierarchical clustering algorithm to group peak co-fluctuations of all magnitudes into nested and multiscale clusters based on their pairwise concordance. At a coarse scale, we find evidence of three large clusters that, collectively, engage virtually all canonical brain systems. At finer scales, however, each cluster is dissolved, giving way to increasingly refined patterns of co-fluctuations involving specific sets of brain systems. We also find an increase in global co-fluctuation magnitude with hierarchical scale. Finally, we comment on the amount of data needed to estimate co-fluctuation pattern clusters and implications for brain-behavior studies. Collectively, the findings reported here fill several gaps in current knowledge concerning the heterogeneity and richness of co-fluctuation patterns as estimated with edge time series while providing some practical guidance for future studies.

Consciousness and cognition are an increasing focus of theoretical and experimental research in neuroscience, leveraging the methods and tools of brain dynamics and connectivity. This Focus Feature brings together a collection of articles that examine the various roles of brain networks in computational and dynamic models, and in studies of physiological and neuroimaging processes that underpin and enable behavioral and cognitive function.

Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relationships, including connectivity and similarity among nodes. Adopting a specific definition of edges can fundamentally alter how we analyze and interpret a brain network. Furthermore, edges can associate into collectives and higher order arrangements, describe time series, and form edge communities that provide insights into brain network topology complementary to the traditional node-centric perspective. Focusing on the edges, and the higher order or dynamic information they can provide, discloses previously underappreciated aspects of structural and functional network organization.

Functional connectivity (FC) describes the statistical dependence between neuronal populations or brain regions in resting-state fMRI studies and is commonly estimated as the Pearson correlation of time courses. Clustering or community detection reveals densely coupled sets of regions constituting resting-state networks or functional systems. These systems manifest most clearly when FC is sampled over longer epochs but appear to fluctuate on shorter timescales. Here, we propose a new approach to reveal temporal fluctuations in neuronal time series. Unwrapping FC signal correlations yields pairwise co-fluctuation time series, one for each node pair or edge, and allows tracking of fine-scale dynamics across the network. Co-fluctuations partition the network, at each time step, into exactly two communities. Sampled over time, the overlay of these bipartitions, a binary decomposition of the original time series, very closely approximates functional connectivity. Bipartitions exhibit characteristic spatiotemporal patterns that are reproducible across participants and imaging runs, capture individual differences, and disclose fine-scale temporal expression of functional systems. Our findings document that functional systems appear transiently and intermittently, and that FC results from the overlay of many variable instances of system expression. Potential applications of this decomposition of functional connectivity into a set of binary patterns are discussed. Author Summary Numerous studies of functional connectivity have revealed densely coupled sets of brain regions corresponding to resting-state networks or functional systems. Prior work suggests that functional connectivity fluctuates over time. Here, we extend those studies by suggesting that functional connectivity can be decomposed into a set of momentary network states, with each one partitioning the network into exactly two clusters or communities. We show that these bipartitions exhibit characteristic spatiotemporal patterns that are reproducible across participants and imaging runs, and can capture individual differences. Our decomposition approach discloses fine-scale dynamics of functional systems, and reveals that functional systems coalesce and dissolve at different times and on fast timescales. Numerous applications and extensions of the approach are discussed.

In this article, we present an open source neuroinformatics platform for exploring, analyzing, and validating distilled graphical representations of high-dimensional neuroimaging data extracted using topological data analysis (TDA). TDA techniques like Mapper have been recently applied to examine the brain’s dynamical organization during ongoing cognition without averaging data in space, in time, or across participants at the outset. Such TDA-based approaches mark an important deviation from standard neuroimaging analyses by distilling complex high-dimensional neuroimaging data into simple—yet neurophysiologically valid and behaviorally relevant—representations that can be interactively explored at the single-participant level. To facilitate wider use of such techniques within neuroimaging and general neuroscience communities, our work provides several tools for visualizing, interacting with, and grounding TDA-generated graphical representations in neurophysiology. Through Python-based Jupyter notebooks and open datasets, we provide a platform to assess and visualize different intermittent stages of Mapper and examine the influence of Mapper parameters on the generated representations. We hope this platform could enable researchers and clinicians alike to explore topological representations of neuroimaging data and generate biological insights underlying complex mental disorders. Author Summary To develop biologically grounded psychiatric diagnosis, researchers and clinicians need tools for distilling complex high-dimensional neuroimaging data into simple yet interactive and clinically relevant representations. Further, for translational outcomes, these representations should be conceivable at the single-participant level. Topological data analysis techniques such as Mapper allow generation of these representations. Here, we introduce a set of tools that can facilitate wider acceptance of Mapper within the neuroscience community and provide a series of easy-to-follow steps for visualizing Mapper-generated graphical representations. We provide detailed examples to reveal the “under-the-hood” workings of Mapper.

Connectomics is an integral part of network neuroscience. The field has undergone rapid expansion over recent years and increasingly involves a blend of experimental and computational approaches to brain connectivity. This Focus Feature on “New Trends in Connectomics” aims to track the progress of the field and its many applications across different neurobiological systems and species.

The intricate connectivity patterns of neural circuits support a wide repertoire of communication processes and functional interactions. Here we systematically investigate how neural signaling is constrained by anatomical connectivity in the mesoscale Drosophila (fruit fly) brain network. We use a spreading model that describes how local perturbations, such as external stimuli, trigger global signaling cascades that spread through the network. Through a series of simple biological scenarios we demonstrate that anatomical embedding potentiates sensory-motor integration. We find that signal spreading is faster from nodes associated with sensory transduction (sensors) to nodes associated with motor output (effectors). Signal propagation was accelerated if sensor nodes were activated simultaneously, suggesting a topologically mediated synergy among sensors. In addition, the organization of the network increases the likelihood of convergence of multiple cascades towards effector nodes, thereby facilitating integration prior to motor output. Moreover, effector nodes tend to coactivate more frequently than other pairs of nodes, suggesting an anatomically enhanced coordination of motor output. Altogether, our results show that the organization of the mesoscale Drosophila connectome imparts privileged, behaviorally relevant communication patterns among sensors and effectors, shaping their capacity to collectively integrate information. Author Summary The complex network spanned by neurons and their axonal projections promotes a diverse set of functions. In the present report, we study how the topological organization of the fruit fly brain supports sensory-motor integration. Using a simple communication model, we demonstrate that the topology of this network allows efficient coordination among sensory and motor neurons. Our results suggest that brain network organization may profoundly shape the functional repertoire of this simple organism.

Understanding the brain represents one of the most profound and pressing scientific challenges of the 21st century. As brain data have increased in volume and complexity, the tools and methods of network science have become indispensable for mapping and modeling brain structure and function, for bridging scales of organization, and for integrating across empirical and computational methodologies. The creation of a new journal, Network Neuroscience , will contribute to guiding this emerging and interdisciplinary field in new directions.

This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity . This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.