Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization—axonal growth. Emulating the chemoaffinity-guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective. Author Summary Generative models of the human connectome provide insight into principles driving brain network development. However, current models do not capture axonal outgrowth, which is crucial to the formation of neural circuits. We develop a novel generative connectome model featuring dynamic axonal outgrowth, revealing the contribution of microscopic axonal guidance to the network topology and axonal geometry of macroscopic connectomes. Simple axonal outgrowth rules representing continuous chemoaffinity gradients are shown to generate complex, brain-like topologies and realistic axonal fascicle architectures. Our model is sufficiently sensitive to capture subtle interindividual differences in axonal outgrowth between healthy adults. Our results are significant because they reveal core principles that may give rise to both complex brain networks and brain-like axonal bundles, unifying neurogenesis across scales.

Author Summary We study a dense sampling dataset of one brain ( N = 1) imaged across two complete menstrual cycles (60 scan sessions). We identify network states—high-amplitude patterns of time-varying connectivity that reoccur across scan sessions—and show that the frequency with which states occur is linked to endogenous fluctuations in follicle-stimulating and luteinizing hormones. We further show that the weights of scan-specific and whole-brain co-fluctuation patterns are broadly associated with hormone fluctuations. Abstract Many studies have shown that the human endocrine system modulates brain function, reporting associations between fluctuations in hormone concentrations and brain connectivity. However, how hormonal fluctuations impact fast changes in brain network organization over short timescales remains unknown. Here, we leverage a recently proposed framework for modeling co-fluctuations between the activity of pairs of brain regions at a framewise timescale. In previous studies we showed that time points corresponding to high-amplitude co-fluctuations disproportionately contributed to the time-averaged functional connectivity pattern and that these co-fluctuation patterns could be clustered into a low-dimensional set of recurring “states.” Here, we assessed the relationship between these network states and quotidian variation in hormone concentrations. Specifically, we were interested in whether the frequency with which network states occurred was related to hormone concentration. We addressed this question using a dense-sampling dataset ( N = 1 brain). In this dataset, a single individual was sampled over the course of two endocrine states: a natural menstrual cycle and while the subject underwent selective progesterone suppression via oral hormonal contraceptives. During each cycle, the subject underwent 30 daily resting-state fMRI scans and blood draws. Our analysis of the imaging data revealed two repeating network states. We found that the frequency with which state 1 occurred in scan sessions was significantly correlated with follicle-stimulating and luteinizing hormone concentrations. We also constructed representative networks for each scan session using only “event frames”—those time points when an event was determined to have occurred. We found that the weights of specific subsets of functional connections were robustly correlated with fluctuations in the concentration of not only luteinizing and follicle-stimulating hormones, but also progesterone and estradiol.

A rapidly emerging application of network neuroscience in neuroimaging studies has provided useful tools to understand individual differences in intrinsic brain function by mapping spontaneous brain activity, namely intrinsic functional network neuroscience (ifNN). However, the variability of methodologies applied across the ifNN studies—with respect to node definition, edge construction, and graph measurements—makes it difficult to directly compare findings and also challenging for end users to select the optimal strategies for mapping individual differences in brain networks. Here, we aim to provide a benchmark for best ifNN practices by systematically comparing the measurement reliability of individual differences under different ifNN analytical strategies using the test-retest design of the Human Connectome Project. The results uncovered four essential principles to guide ifNN studies: (1) use a whole brain parcellation to define network nodes, including subcortical and cerebellar regions; (2) construct functional networks using spontaneous brain activity in multiple slow bands; and (3) optimize topological economy of networks at individual level; and (4) characterize information flow with specific metrics of integration and segregation. We built an interactive online resource of reliability assessments for future ifNN ( https://ibraindata.com/research/ifNN ). Author Summary It is an essential mission for neuroscience to understand the individual differences in brain function. Graph or network theory offer novel methods of network neuroscience to address such a challenge. This article documents optimal strategies on the test-retest reliability of measuring individual differences in intrinsic brain networks of spontaneous activity. The analytical pipelines are identified to optimize for highly reliable, individualized network measurements. These pipelines optimize network metrics for high interindividual variances and low inner-individual variances by defining network nodes with whole-brain parcellations, deriving the connectivity with spontaneous high-frequency slow-band oscillations, constructing brain graphs with topology-based methods for edge filtering, and favoring multilevel or multimodal metrics. These psychometric findings are critical for translating the functional network neuroscience into clinical or other personalized practices requiring neuroimaging markers.

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. 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.

Progress in scientific disciplines is accompanied by standardization of terminology. Network neuroscience, at the level of macroscale organization of the brain, is beginning to confront the challenges associated with developing a taxonomy of its fundamental explanatory constructs. The Workgroup for HArmonized Taxonomy of NETworks (WHATNET) was formed in 2020 as an Organization for Human Brain Mapping (OHBM)–endorsed best practices committee to provide recommendations on points of consensus, identify open questions, and highlight areas of ongoing debate in the service of moving the field toward standardized reporting of network neuroscience results. The committee conducted a survey to catalog current practices in large-scale brain network nomenclature. A few well-known network names (e.g., default mode network) dominated responses to the survey, and a number of illuminating points of disagreement emerged. We summarize survey results and provide initial considerations and recommendations from the workgroup. This perspective piece includes a selective review of challenges to this enterprise, including (1) network scale, resolution, and hierarchies; (2) interindividual variability of networks; (3) dynamics and nonstationarity of networks; (4) consideration of network affiliations of subcortical structures; and (5) consideration of multimodal information. We close with minimal reporting guidelines for the cognitive and network neuroscience communities to adopt.

The brain’s structural connectivity supports the propagation of electrical impulses, manifesting as patterns of coactivation, termed functional connectivity. Functional connectivity emerges from the underlying sparse structural connections, particularly through polysynaptic communication. As a result, functional connections between brain regions without direct structural links are numerous, but their organization is not completely understood. Here we investigate the organization of functional connections without direct structural links. We develop a simple, data-driven method to benchmark functional connections with respect to their underlying structural and geometric embedding. We then use this method to reweigh and reexpress functional connectivity. We find evidence of unexpectedly strong functional connectivity among distal brain regions and within the default mode network. We also find unexpectedly strong functional connectivity at the apex of the unimodal-transmodal hierarchy. Our results suggest that both phenomena—functional modules and functional hierarchies—emerge from functional interactions that transcend the underlying structure and geometry. These findings also potentially explain recent reports that structural and functional connectivity gradually diverge in transmodal cortex. Collectively, we show how structural connectivity and geometry can be used as a natural frame of reference with which to study functional connectivity patterns in the brain. Author Summary The structural connectivity of the brain supports interregional signaling, manifesting as highly organized patterns of functional connectivity. Importantly, structural and functional connectivity are fundamentally constrained by the spatial embedding of brain regions, such that proximal regions are more likely to exhibit stronger connectivity. Here we develop a simple method that uses robust relationships between geometry, structure, and function as the baseline to reweigh and reexpress functional connectivity. We use the method to identify functional connections that are greater than expected given their structural and geometric embedding. We then show that the arrangement of these connections systematically follows the functional modules and the putative unimodal-transmodal hierarchy of the brain. Collectively, our findings demonstrate highly organized patterns of polysynaptic functional connections that support the emergence of canonical features of functional connectivity networks, including modules and hierarchies.

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.

Network science has begun to reveal the fundamental principles by which large-scale brain networks are organized, including geometric constraints, a balance between segregative and integrative features, and functionally flexible brain areas. However, it remains unknown whether whole-brain networks imaged at the cellular level are organized according to similar principles. Here, we analyze whole-brain functional networks reconstructed from calcium imaging data recorded in larval zebrafish. Our analyses reveal that functional connections are distance-dependent and that networks exhibit hierarchical modular structure and hubs that span module boundaries. We go on to show that spontaneous network structure places constraints on stimulus-evoked reconfigurations of connections and that networks are highly consistent across individuals. Our analyses reveal basic organizing principles of whole-brain functional brain networks at the mesoscale. Our overarching methodological framework provides a blueprint for studying correlated activity at the cellular level using a low-dimensional network representation. Our work forms a conceptual bridge between macro- and mesoscale network neuroscience and opens myriad paths for future studies to investigate network structure of nervous systems at the cellular level. Author Summary Little is known about the principles by which mesoscale functional networks are organized and whether they parallel the features of macroscale networks. Here, we used network science methods to investigate the architecture of functional connectivity in zebrafish larvae. We find that its architectural features are remarkably similar to that of macroscale functional brain networks, with connection weights exhibiting clear distance-dependence, evidence of multiscale and hierarchical community structure, high participation hub regions, and flexible reconfiguration across a range of tasks.

The brain is a complex, multiscale dynamical system composed of many interacting regions. Knowledge of the spatiotemporal organization of these interactions is critical for establishing a solid understanding of the brain’s functional architecture and the relationship between neural dynamics and cognition in health and disease. The possibility of studying these dynamics through careful analysis of neuroimaging data has catalyzed substantial interest in methods that estimate time-resolved fluctuations in functional connectivity (often referred to as “dynamic” or time-varying functional connectivity; TVFC). At the same time, debates have emerged regarding the application of TVFC analyses to resting fMRI data, and about the statistical validity, physiological origins, and cognitive and behavioral relevance of resting TVFC. These and other unresolved issues complicate interpretation of resting TVFC findings and limit the insights that can be gained from this promising new research area. This article brings together scientists with a variety of perspectives on resting TVFC to review the current literature in light of these issues. We introduce core concepts, define key terms, summarize controversies and open questions, and present a forward-looking perspective on how resting TVFC analyses can be rigorously and productively applied to investigate a wide range of questions in cognitive and systems neuroscience.

Author Summary Sparse structural connectivity data from many subjects can be succinctly represented using appropriate averaging procedures. We show, however, that several popular procedures for doing so generate group-averaged networks with statistics that are dissimilar from the subject-level networks they are intended to represent. These dissimilarities, we argue, arise from the over- and underexpression of short-range and long-distance connections, respectively, in the group-averaged matrix. We present a distance-dependent thresholding procedure that preserves connection length distributions and consequently better matches subject-level networks and their statistics. These findings inform data-driven exploratory analyses of connectomes. Abstract Large-scale structural brain networks encode white matter connectivity patterns among distributed brain areas. These connection patterns are believed to support cognitive processes and, when compromised, can lead to neurocognitive deficits and maladaptive behavior. A powerful approach for studying the organizing principles of brain networks is to construct group-representative networks from multisubject cohorts. Doing so amplifies signal to noise ratios and provides a clearer picture of brain network organization. Here, we show that current approaches for generating sparse group-representative networks overestimate the proportion of short-range connections present in a network and, as a result, fail to match subject-level networks along a wide range of network statistics. We present an alternative approach that preserves the connection-length distribution of individual subjects. We have used this method in previous papers to generate group-representative networks, though to date its performance has not been appropriately benchmarked and compared against other methods. As a result of this simple modification, the networks generated using this approach successfully recapitulate subject-level properties, outperforming similar approaches by better preserving features that promote integrative brain function rather than segregative. The method developed here holds promise for future studies investigating basic organizational principles and features of large-scale structural brain networks.

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.

AUTHOR SUMMARY The human brain is characterized by a complex pattern of anatomical wiring, in the form of white-matter tracts that link large volumes of neural tissue. The organization of this pattern is likely driven by many factors, including evolutionary adaptability, robustness to perturbations, and a separation of the timescales necessary to produce a diverse repertoire of neural dynamics. In this study, we sought to disentangle two such factors—the drive to decrease the cost of wiring, and the putative drive to increase the efficiency of the network topology—and we explored the impacts of these factors on the brain’s modular organization. The contributions of this work include a new algorithmic approach to community detection and novel insights into the role of modules in human brain function. Abstract Brain networks are expected to be modular. However, existing techniques for estimating a network’s modules make it difficult to assess the influence of organizational principles such as wiring cost reduction on the detected modules. Here we present a modification of an existing module detection algorithm that allowed us to focus on connections that are unexpected under a cost-reduction wiring rule and to identify modules from among these connections. We applied this technique to anatomical brain networks and showed that the modules we detected differ from those detected using the standard technique. We demonstrated that these novel modules are spatially distributed, exhibit unique functional fingerprints, and overlap considerably with rich clubs, giving rise to an alternative and complementary interpretation of the functional roles of specific brain regions. Finally, we demonstrated that, using the modified module detection approach, we can detect modules in a developmental dataset that track normative patterns of maturation. Collectively, these findings support the hypothesis that brain networks are composed of modules and provide additional insight into the function of those modules.