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Network neuroscience applied to epilepsy holds promise to map pathological networks, localize seizure generators, and inform targeted interventions to control seizures. However, incomplete sampling of the epileptic brain because of sparse placement of intracranial electrodes may affect model results. In this study, we evaluate the sensitivity of several published network measures to incomplete spatial sampling and propose an algorithm using network subsampling to determine confidence in model results. We retrospectively evaluated intracranial EEG data from 28 patients implanted with grid, strip, and depth electrodes during evaluation for epilepsy surgery. We recalculated global and local network metrics after randomly and systematically removing subsets of intracranial EEG electrode contacts. We found that sensitivity to incomplete sampling varied significantly across network metrics. This sensitivity was largely independent of whether seizure onset zone contacts were targeted or spared from removal. We present an algorithm using random subsampling to compute patient-specific confidence intervals for network localizations. Our findings highlight the difference in robustness between commonly used network metrics and provide tools to assess confidence in intracranial network localization. We present these techniques as an important step toward translating personalized network models of seizures into rigorous, quantitative approaches to invasive therapy.

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.

Summary: Large-scale interactions among multiple brain regions manifest as bursts of activations called neuronal avalanches, which reconfigure according to the task at hand and, hence, might constitute natural candidates to design brain-computer interfaces (BCIs). To test this hypothesis, we used source-reconstructed magneto/electroencephalography during resting state and a motor imagery task performed within a BCI protocol. To track the probability that an avalanche would spread across any two regions, we built an avalanche transition matrix (ATM) and demonstrated that the edges whose transition probabilities significantly differed between conditions hinged selectively on premotor regions in all subjects. Furthermore, we showed that the topology of the ATMs allows task-decoding above the current gold standard. Hence, our results suggest that neuronal avalanches might capture interpretable differences between tasks that can be used to inform brain-computer interfaces.

Cluster synchronization is of great importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as neurological disorders in the brain. Therefore, it is crucial to restore normal system functions by stabilizing the appropriate cluster synchronization patterns. Most existing studies focus on designing controllers based on state measurements to achieve system stabilization. However, in many real-world scenarios, measuring system states in real time, such as neuronal activity in the brain, poses significant challenges, rendering the stabilization of such systems difficult. To overcome this challenge, in this article, we employ an open-loop control strategy, vibrational control, which does not require any state measurements. We establish some sufficient conditions under which vibrational inputs stabilize cluster synchronization. Further, we provide a tractable approach to design vibrational control. Finally, numerical experiments are conducted to demonstrate our theoretical findings.

Cross-frequency phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. It has been widely observed in the brain and linked to various brain functions. In this paper, we show that Stuart-Landau oscillators coupled in a nonlinear fashion can give rise to PAC in two commonly accepted architectures, namely, (1) a high-frequency neural oscillation driven by an external low-frequency input and (2) two interacting local oscillations with distinct, locally generated frequencies. We characterize the parameters that affect PAC behavior, thus providing insight on this phenomenon observed in neuronal networks. Inspired by some empirical studies, we further present an interconnection structure for brain regions wherein cross-region interactions are established only by low-frequency oscillations. We then demonstrate that low-frequency phase synchrony can integrate high-frequency activities regulated by local PAC and control the direction of information flow between distant regions.

Scientific research is often thought of as being conducted by individuals and small teams striving for disciplinary advances. Yet as a whole, this endeavor more closely resembles a complex and integrated system of people, papers, and ideas. Studies of co-authorship and citation networks have revealed important structural properties of researchers and articles, but currently the structure of scientific ideas themselves is not well understood. In this study, we posit that topic networks may be a useful framework for revealing the nature of conceptual relationships. Using this framework, we map the landscape of interconnected research topics covered in the multidisciplinary journal PNAS since 2000, constructing networks in which nodes represent topics of study and edges give the extent to which topics occur in the same papers. The network displays small-world architecture, characterized by regions of dense local connectivity with sparse connectivity between them. In this network, dense local connectivity additionally gives rise to distinct clusters of related topics. Yet notably, these clusters tend not to align with assigned article classifications, and instead contain topics from various disciplines. Using a temporal graph, we find that small-worldness has increased over time, suggesting growing efficiency and integration of ideas. Finally, we define two measures of interdisciplinarity, one of which is found to be positively associated with PNAS's impact factor. Broadly, this work suggests that complex and dynamic patterns of knowledge emerge from scientific research, and that structures reflecting intellectual integration may be beneficial for obtaining scientific insight.

Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph's hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain's structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.

Despite mounting evidence that human learners are sensitive to community structure underpinning temporal sequences, this phenomenon has been studied using an extremely narrow set of network ensembles. The extent to which behavioral signatures of learning are robust to changes in community size and number is the focus of the present work. Here we present adult participants with a continuous stream of novel objects generated by a random walk along graphs of 1, 2, 3, 4, or 6 communities comprised of N = 24, 12, 8, 6, and 4 nodes, respectively. Nodes of the graph correspond to a unique object and edges correspond to their immediate succession in the stream. In short, we find that previously observed processing costs associated with community boundaries persist across an array of graph architectures. These results indicate that statistical learning mechanisms can flexibly accommodate variation in community structure during visual event segmentation.

Delay discounting is a measure of impulsive choice relevant in adolescence as it predicts many real-life outcomes, including obesity and academic achievement. However, resting-state functional networks underlying individual differences in delay discounting during youth remain incompletely described. Here we investigate the association between multivariate patterns of functional connectivity and individual differences in impulsive choice in a large sample of children, adolescents, and adults. A total of 293 participants (9–23 years) completed a delay discounting task and underwent 3T resting-state fMRI. A connectome-wide analysis using multivariate distance-based matrix regression was used to examine whole-brain relationships between delay discounting and functional connectivity. These analyses revealed that individual differences in delay discounting were associated with patterns of connectivity emanating from the left dorsal prefrontal cortex, a default mode network hub. Greater delay discounting was associated with greater functional connectivity between the dorsal prefrontal cortex and other default mode network regions, but reduced connectivity with regions in the dorsal and ventral attention networks. These results suggest delay discounting in children, adolescents, and adults is associated with individual differences in relationships both within the default mode network and between the default mode and networks involved in attentional and cognitive control.

Studies of brain network development typically focus on a single scale. Here, the authors derived personalized functional networks across scales, and find that network development systematically adheres to and strengthens hierarchical cortical organization.

Sukhvir Wright et al. present a NMDAR antibody-induced model of encephalitis in rats and use in vitro, in vivo, and in silico electrophysiology to examine alterations in neural circuit behavior. Their results suggest that reduction of NMDARs leads to increased excitability and seizure activity, and highlights the potential use of receptor-specific treatments in antibody-mediated seizures and epilepsy.

Abstract Recent advances in neuroscience have enabled the exploration of brain structure at the level of individual synaptic connections. These connectomics datasets continue to grow in size and complexity; methods to search for and identify interesting graph patterns offer a promising approach to quickly reduce data dimensionality and enable discovery. These graphs are often too large to be analyzed manually, presenting significant barriers to searching for structure and testing hypotheses. We combine graph database and analysis libraries with an easy-to-use neuroscience grammar suitable for rapidly constructing queries and searching for subgraphs and patterns of interest. Our approach abstracts many of the computer science and graph theory challenges associated with nanoscale brain network analysis and allows scientists to quickly conduct research at scale. We demonstrate the utility of these tools by searching for motifs on simulated data and real public connectomics datasets, and we share simple and complex structures relevant to the neuroscience community. We contextualize our findings and provide case studies and software to motivate future neuroscience exploration.

Working memory requires the brain to switch between cognitive states and activity patterns. Here, the authors show that the steering of these neural network dynamics is influenced by dopamine D1- and D2-receptor function and altered in schizophrenia.

Abstract Psychopathology is rooted in neurodevelopment. However, clinical and biological heterogeneity, together with a focus on case-control approaches, have made it difficult to link dimensions of psychopathology to abnormalities of neurodevelopment. Here, using the Philadelphia Neurodevelopmental Cohort, we built normative models of cortical volume and tested whether deviations from these models better predicted psychiatric symptoms compared to raw cortical volume. Specifically, drawing on the p-factor hypothesis, we distilled 117 clinical symptom measures into six orthogonal psychopathology dimensions: overall psychopathology, anxious-misery, externalizing disorders, fear, positive psychosis symptoms, and negative psychosis symptoms. We found that multivariate patterns of deviations yielded improved out-of-sample prediction of psychopathology dimensions compared to multivariate patterns of raw cortical volume. We also found that correlations between overall psychopathology and deviations in ventromedial prefrontal, inferior temporal, and dorsal anterior cingulate cortices were stronger than those observed for specific dimensions of psychopathology (e.g., anxious-misery). Notably, these same regions are consistently implicated in a range of putatively distinct disorders. Finally, we performed conventional case-control comparisons of deviations in a group of individuals with depression and a group with attention-deficit hyperactivity disorder (ADHD). We observed spatially overlapping effects between these groups that diminished when controlling for overall psychopathology. Together, our results suggest that modeling cortical brain features as deviations from normative neurodevelopment improves prediction of psychiatric symptoms in out-of-sample testing, and that p-factor models of psychopathology may assist in separating biomarkers that are disorder-general from those that are disorder-specific.

Controlling the behavior of a complex network usually requires a knowledge of the network dynamics. Baggio et al. propose a data-driven framework to control a complex dynamical network, effective for non-complete or random datasets, which is of relevance for power grids and neural networks.

Ashourvan et al. apply a pairwise maximum entropy model to intracranial EEG data from epileptic patients to infer structure-function relationships. Their results indicate that the pairwise MEM model provides insight into the structural connectivity of the brain and how it gives rise to activity patterns.

[This corrects the article DOI: 10.1371/journal.pcbi.1007360.].

Driscoll, Rosch et al. design transparent graphene-based surface probes to achieve simultaneous electrophysiological recording and calcium imaging of epileptic seizures in mice. This method could be used to investigate circuit dynamics during seizure onset and evolution with high temporal and spatial resolution.

AbstractRecent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

AbstractThe human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step toward the ability to manipulate the brain’s large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain’s diverse mesoscale structure supports transient communication dynamics.

AbstractAn overarching goal of neuroscience research is to understand how heterogeneous neuronal ensembles cohere into networks of coordinated activity to support cognition. To investigate how local activity harmonizes with global signals, we measured electroencephalography (EEG) while single pulses of transcranial magnetic stimulation (TMS) perturbed occipital and parietal cortices. We estimate the rapid network reconfigurations in dynamic network communities within specific frequency bands of the EEG, and characterize two distinct features of network reconfiguration, flexibility and allegiance, among spatially distributed neural sources following TMS. Using distance from the stimulation site to infer local and global effects, we find that alpha activity (8–12 Hz) reflects concurrent local and global effects on network dynamics. Pairwise allegiance of brain regions to communities on average increased near the stimulation site, whereas TMS-induced changes to flexibility were generally invariant to distance and stimulation site. In contrast, communities within the beta (13–20 Hz) band demonstrated a high level of spatial specificity, particularly within a cluster comprising paracentral areas. Together, these results suggest that focal magnetic neurostimulation to distinct cortical sites can help identify both local and global effects on brain network dynamics, and highlight fundamental differences in the manifestation of network reconfigurations within alpha and beta frequency bands.

Working memory is a critical component of executive function that allows people to complete complex tasks in the moment. Here, the authors show that this ability is underpinned by two newly defined brain networks.

Humans can easily uncover abstract associations. Here, the authors propose that higher-order associations arise from natural errors in learning and memory. They suggest that mental errors influence the humans’ representation of the world in significant and predictable ways.

Working memory training reshapes the brain functional network reorganization. Here, the authors demonstrate an increase of the whole-brain network segregation during the n-back task, accompanied by alterations in dynamic communication between the default mode system and task-positive systems.

Adaptive adjustments in learning dynamics are accompanied by dynamic changes in a pattern of whole-brain functional connectivity characterized by integration between fronto-parietal and other networks. These dynamic functional connectivity changes also track individual differences in learning.

Adult cortex is organized into distributed functional communities. Yet, little is known about community architecture of children’s brains. Here, we uncovered the community structure of cortex in childhood using fMRI data from 670 children aged 9–11 years (48% female, replication sample n=544, 56% female) from the Adolescent Brain and Cognitive Development study. We first applied a data-driven community detection approach to cluster cortical regions into communities, then employed a generative model-based approach called the weighted stochastic block model to further probe community interactions. Children showed similar community structure to adults, as defined by Yeo and colleagues in 2011, in early-developing sensory and motor communities, but differences emerged in transmodal areas. Children have more cortical territory in the limbic community, which is involved in emotion processing, than adults. Regions in association cortex interact more flexibly across communities, creating uncertainty for the model-based assignment algorithm, and perhaps reflecting cortical boundaries that are not yet solidified. Uncertainty was highest for cingulo-opercular areas involved in flexible deployment of cognitive control. Activation and deactivation patterns during a working memory task showed that both the data-driven approach and a set of adult communities statistically capture functional organization in middle childhood. Collectively, our findings suggest that community boundaries are not solidified by middle childhood.

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal’s external drivers and shines a light on the likely external sources contributing to the BOLD signal’s non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain’s time-varying functional dynamics.

Resting-state blood-oxygen-level-dependent (BOLD) signal acquired through functional magnetic resonance imaging is a proxy of neural activity and a key mechanism for assessing neurological conditions. Therefore, practical tools to filter out artefacts that can compromise the assessment are required. On the one hand, a variety of tailored methods to preprocess the data to deal with identified sources of noise (e.g., head motion, heart beating, and breathing, just to mention a few) are in place. But, on the other hand, there might be unknown sources of unstructured noise present in the data. Therefore, to mitigate the effects of such unstructured noises, we propose a model-based filter that explores the statistical properties of the underlying signal (i.e., long-term memory). Specifically, we consider autoregressive fractional integrative process filters. Remarkably, we provide evidence that such processes can model the signals at different regions of interest to attain stationarity. Furthermore, we use a principled analysis where a ground-truth signal with statistical properties similar to the BOLD signal under the injection of noise is retrieved using the proposed filters. Next, we considered preprocessed (i.e., the identified sources of noise removed) resting-state BOLD data of 98 subjects from the Human Connectome Project. Our results demonstrate that the proposed filters decrease the power in the higher frequencies. However, unlike the low-pass filters, the proposed filters do not remove all high-frequency information, instead they preserve process-related higher frequency information. Additionally, we considered four different metrics (power spectrum, functional connectivity using the Pearson's correlation, coherence, and eigenbrains) to infer the impact of such filter. We provided evidence that whereas the first three keep most of the features of interest from a neuroscience perspective unchanged, the latter exhibits some variations that could be due to the sporadic activity filtered out.

Resting-state blood-oxygen-level-dependent (BOLD) signal acquired through functional magnetic resonance imaging is a proxy of neural activity and a key mechanism for assessing neurological conditions. Therefore, practical tools to filter out artefacts that can compromise the assessment are required. On the one hand, a variety of tailored methods to preprocess the data to deal with identified sources of noise (e.g., head motion, heart beating, and breathing, just to mention a few) are in place. But, on the other hand, there might be unknown sources of unstructured noise present in the data. Therefore, to mitigate the effects of such unstructured noises, we propose a model-based filter that explores the statistical properties of the underlying signal (i.e., long-term memory). Specifically, we consider autoregressive fractional integrative process filters. Remarkably, we provide evidence that such processes can model the signals at different regions of interest to attain stationarity. Furthermore, we use a principled analysis where a ground-truth signal with statistical properties similar to the BOLD signal under the injection of noise is retrieved using the proposed filters. Next, we considered preprocessed (i.e., the identified sources of noise removed) resting-state BOLD data of 98 subjects from the Human Connectome Project. Our results demonstrate that the proposed filters decrease the power in the higher frequencies. However, unlike the low-pass filters, the proposed filters do not remove all high-frequency information, instead they preserve process-related higher frequency information. Additionally, we considered four different metrics (power spectrum, functional connectivity using the Pearson’s correlation, coherence, and eigenbrains) to infer the impact of such filter. We provided evidence that whereas the first three keep most of the features of interest from a neuroscience perspective unchanged, the latter exhibits some variations that could be due to the sporadic activity filtered out.

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal's external drivers and shines a light on the likely external sources contributing to the BOLD signal's non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain's time-varying functional dynamics.

Functional connectivity (FC) networks are typically inferred from resting-state fMRI data using the Pearson correlation between BOLD time series from pairs of brain regions. However, alternative methods of estimating functional connectivity have not been systematically tested for their sensitivity or robustness to head motion artifact. Here, we evaluate the sensitivity of eight different functional connectivity measures to motion artifact using resting-state data from the Human Connectome Project. We report that FC estimated using full correlation has a relatively high residual distance-dependent relationship with motion compared to partial correlation, coherence, and information theory-based measures, even after implementing rigorous methods for motion artifact mitigation. This disadvantage of full correlation, however, may be offset by higher test-retest reliability, fingerprinting accuracy, and system identifiability. FC estimated by partial correlation offers the best of both worlds, with low sensitivity to motion artifact and intermediate system identifiability, with the caveat of low test-retest reliability and fingerprinting accuracy. We highlight spatial differences in the sub-networks affected by motion with different FC metrics. Further, we report that intra-network edges in the default mode and retrosplenial temporal sub-networks are highly correlated with motion in all FC methods. Our findings indicate that the method of estimating functional connectivity is an important consideration in resting-state fMRI studies and must be chosen carefully based on the parameters of the study.

There is growing interest in how neuromodulators shape brain networks. Recent neuroimaging studies provide evidence that brainstem arousal systems, such as the locus coeruleus-norepinephrine system (LC-NE), influence functional connectivity and brain network topology, suggesting they have a role in flexibly reconfiguring brain networks in order to adapt behavior and cognition to environmental demands. To date, however, the relationship between brainstem arousal systems and functional connectivity has not been assessed within the context of a task with an established relationship between arousal and behavior, with most prior studies relying on incidental variations in arousal or pharmacological manipulation and static brain networks constructed over long periods of time. These factors have likely contributed to a heterogeneity of effects across studies. To address these issues, we took advantage of the association between LC-NE-linked arousal and exploration to probe the relationships between exploratory choice, arousal—as measured indirectly via pupil diameter—and brain network dynamics. Exploration in a bandit task was associated with a shift toward fewer, more weakly connected modules that were more segregated in terms of connectivity and topology but more integrated with respect to the diversity of cognitive systems represented in each module. Functional connectivity strength decreased, and changes in connectivity were correlated with changes in pupil diameter, in line with the hypothesis that brainstem arousal systems influence the dynamic reorganization of brain networks. More broadly, we argue that carefully aligning dynamic network analyses with task designs can increase the temporal resolution at which behaviorally- and cognitively-relevant modulations can be identified, and offer these results as a proof of concept of this approach.

Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems. For the network neuroscientist, this exposition aims to communicate both the mathematics and the advantages of using tools from applied topology for the study of neural systems. Using data from the mouse connectome, electrical and chemical synapses in C. elegans, and chromatin interaction data, we offer example computations and applications to further demonstrate the power of topological data analysis in neuroscience. Finally, we expose the reader to novel developments in applied topology and relate these developments to current questions and methodological difficulties in network neuroscience.

Chronically implantable neurostimulation devices are becoming a clinically viable option for treating patients with neurological disease and psychiatric disorders. Neurostimulation offers the ability to probe and manipulate distributed networks of interacting brain areas in dysfunctional circuits. Here, we use tools from network control theory to examine the dynamic reconfiguration of functionally interacting neuronal ensembles during targeted neurostimulation of cortical and subcortical brain structures. By integrating multimodal intracranial recordings and diffusion-weighted imaging from patients with drug-resistant epilepsy, we test hypothesized structural and functional rules that predict altered patterns of synchronized local field potentials. We demonstrate the ability to predictably reconfigure functional interactions depending on stimulation strength and location. Stimulation of areas with structurally weak connections largely modulates the functional hubness of downstream areas and concurrently propels the brain towards more difficult-to-reach dynamical states. By using focal perturbations to bridge large-scale structure, function, and markers of behavior, our findings suggest that stimulation may be tuned to influence different scales of network interactions driving cognition. Brain stimulation devices capable of perturbing the physiological state of neural systems are rapidly gaining popularity for their potential to treat neurological and psychiatric disease. A root problem is that underlying dysfunction spans a large-scale network of brain regions, requiring the ability to control the complex interactions between multiple brain areas. Here, we use tools from network control theory to examine the dynamic reconfiguration of functionally interacting neuronal ensembles during targeted neurostimulation of cortical and subcortical brain structures. We demonstrate the ability to predictably reconfigure patterns of interactions between functional brain areas by modulating the strength and location of stimulation. Our findings have high significance for designing stimulation protocols capable of modulating distributed neural circuits in the human brain.

Abstract We apply recent innovations in network science to analyze how correlations of stock returns evolve over time. To illustrate these techniques we study the returns of 30 industry stock portfolios from 1927 to 2014. We calculate Pearson correlation matrices for each year, and apply multilayer network tools to these correlation matrices to uncover mesoscale architecture in the form of communities. These communities are easily interpretable as groups of industries with highly correlated stock returns. We observe that the flexibility, or the likelihood of industries to switch communities, exhibits a statistically significant increase after 1970, and that the communities evolve in ways consistent with changes in the structure of the U.S. economy. We find that these patterns are not explained by changes in average pairwise correlations or industry market betas. These results therefore underscore the potential for using multilayer network tools to study time-varying correlations of financial assets.

Dynamic functional connectivity reflects the spatiotemporal organization of spontaneous brain activity in health and disease. Dynamic functional connectivity may be susceptible to artifacts induced by participant motion. This report provides a systematic evaluation of 12 commonly used participant-level confound regression strategies designed to mitigate the effects of micromovements in a sample of 393 youths (ages 8–22 years). Each strategy was evaluated according to a number of benchmarks, including (a) the residual association between participant motion and edge dispersion, (b) distance-dependent effects of motion on edge dispersion, (c) the degree to which functional subnetworks could be identified by multilayer modularity maximization, and (d) measures of module reconfiguration, including node flexibility and node promiscuity. Results indicate variability in the effectiveness of the evaluated pipelines across benchmarks. Methods that included global signal regression were the most consistently effective de-noising strategies. Dynamic functional connectivity reflects the spatiotemporal organization of spontaneous brain activity in health and disease, but it can be susceptible to motion artifacts. Here we provide a systematic evaluation of 12 commonly used participant-level confound regression strategies designed to mitigate the effects of micromovements in a sample of 393 youths (ages 8–22 years). Each strategy was evaluated according to the residual association between participant motion and edge dispersion, distance-dependent effects of motion on edge dispersion, the degree to which functional subnetworks could be identified by multilayer modularity maximization, and measures of module reconfiguration, including node flexibility and node promiscuity. Results indicate variability in the effectiveness of the evaluated pipelines across benchmarks. Methods that included global signal regression were the most consistently effective de-noising strategies.

Alterations in the structural connectome of schizophrenia patients have been widely characterized, but the mechanisms remain largely unknown. Generative network models have recently been introduced as a tool to test the biological underpinnings of altered brain network formation. We evaluated different generative network models in healthy controls (n=152), schizophrenia patients (n=66), and their unaffected first-degree relatives (n=32), and we identified spatial and topological factors contributing to network formation. We further investigated how these factors relate to cognition and to polygenic risk for schizophrenia. Our data show that among the four tested classes of generative network models, structural brain networks were optimally accounted for by a two-factor model combining spatial constraints and topological neighborhood structure. The same wiring model explained brain network formation across study groups. However, relatives and schizophrenia patients exhibited significantly lower spatial constraints and lower topological facilitation compared to healthy controls. Further exploratory analyses point to potential associations of the model parameter reflecting spatial constraints with the polygenic risk for schizophrenia and cognitive performance. Our results identify spatial constraints and local topological structure as two interrelated mechanisms contributing to regular brain network formation as well as altered connectomes in schizophrenia and healthy individuals at familial risk for schizophrenia. On an exploratory level, our data further point to the potential relevance of spatial constraints for the genetic risk for schizophrenia and general cognitive functioning, thereby encouraging future studies in following up on these observations to gain further insights into the biological basis and behavioral relevance of model parameters.

We used a virtual lesion DTI fiber tracking approach with healthy subject DTI data and simulated periventricular white matter (PVWM) lesion masks to predict the sequence of connectivity changes associated with progressive PVWM ischemia. We found that the optic radiations, inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, corpus callosum, temporopontine tract and fornix were affected in early simulated ischemic injury, and that the connectivity of subcortical, cerebellar, and visual regions were significantly disrupted with increasing simulated lesion severity. The results of this study provide insights into the spatial-temporal changes of the brain structural connectome under progressive PVWM ischemia. The virtual lesion approach provides a meaningful proxy to the spatial-temporal changes of the brain's structural connectome and can be used to further characterize the cognitive sequelae of progressive PVWM ischemia in both normal aging and dementia.

At the macroscale, the brain operates as a network of interconnected neuronal populations, which display coordinated rhythmic dynamics that support interareal communication. Understanding how stimulation of different brain areas impacts such activity is important for gaining basic insights into brain function and for further developing therapeutic neurmodulation. However, the complexity of brain structure and dynamics hinders predictions regarding the downstream effects of focal stimulation. More specifically, little is known about how the collective oscillatory regime of brain network activity-in concert with network structure-affects the outcomes of perturbations. Here, we combine human connectome data and biophysical modeling to begin filling these gaps. By tuning parameters that control collective system dynamics, we identify distinct states of simulated brain activity and investigate how the distributed effects of stimulation manifest at different dynamical working points. When baseline oscillations are weak, the stimulated area exhibits enhanced power and frequency, and due to network interactions, activity in this excited frequency band propagates to nearby regions. Notably, beyond these linear effects, we further find that focal stimulation causes more distributed modifications to interareal coherence in a band containing regions' baseline oscillation frequencies. Importantly, depending on the dynamical state of the system, these broadband effects can be better predicted by functional rather than structural connectivity, emphasizing a complex interplay between anatomical organization, dynamics, and response to perturbation. In contrast, when the network operates in a regime of strong regional oscillations, stimulation causes only slight shifts in power and frequency, and structural connectivity becomes most predictive of stimulation-induced changes in network activity patterns. In sum, this work builds upon and extends previous computational studies investigating the impacts of stimulation, and underscores the fact that both the stimulation site, and, crucially, the regime of brain network dynamics, can influence the network-wide responses to local perturbations.

The 21st century marks the emergence of “big data” with a rapid increase in the availability of datasets with multiple measurements. In neuroscience, brain-imaging datasets are more commonly accompanied by dozens or hundreds of phenotypic subject descriptors on the behavioral, neural, and genomic level. The complexity of such “big data” repositories offer new opportunities and pose new challenges for systems neuroscience. Canonical correlation analysis (CCA) is a prototypical family of methods that is useful in identifying the links between variable sets from different modalities. Importantly, CCA is well suited to describing relationships across multiple sets of data, such as in recently available big biomedical datasets. Our primer discusses the rationale, promises, and pitfalls of CCA.

Diffusion weighted imaging (DWI) has advanced our understanding of brain microstructure evolution over development. Recently, the use of multi-shell diffusion imaging sequences has coincided with advances in modeling the diffusion signal, such as Neurite Orientation Dispersion and Density Imaging (NODDI) and Laplacian-regularized Mean Apparent Propagator MRI (MAPL). However, the relative utility of recently-developed diffusion models for understanding brain maturation remains sparsely investigated. Additionally, despite evidence that motion artifact is a major confound for studies of development, the vulnerability of metrics derived from contemporary models to in-scanner motion has not been described. Accordingly, in a sample of 120 youth and young adults (ages 12–30) we evaluated metrics derived from diffusion tensor imaging (DTI), NODDI, and MAPL for associations with age and in-scanner head motion at multiple scales. Specifically, we examined mean white matter values, white matter tracts, white matter voxels, and connections in structural brain networks. Our results revealed that multi-shell diffusion imaging data can be leveraged to robustly characterize neurodevelopment, and demonstrate stronger age effects than equivalent single-shell data. Additionally, MAPL-derived metrics were less sensitive to the confounding effects of head motion. Our findings suggest that multi-shell imaging data and contemporary modeling techniques confer important advantages for studies of neurodevelopment.

Coordinated brain activity reflects underlying cognitive processes and can be modeled as a network of inter-regional functional connections. The most costly connections in the network are long-distance correlations that, in the absence of underlying structural connections, are maintained by sustained energetic inputs. Here, we present a spatial modeling approach that amplifies contributions made by long-distance functional connections to whole-brain network architecture, while simultaneously suppressing contributions made by short-range connections. We use this method to characterize the long-distance architecture of functional networks and to identify aspects of community and hub structure that are driven by long-distance correlations and that, we argue, are of greater functional significance. We find that based only on patterns of long-distance connectivity, primary sensory cortices occupy increasingly central positions and appear more “hub-like”. Additionally, we show that the community structure of long-distance connections spans multiple topological levels and differs from the community structure detected in networks that include both short-range and long-distance connections. In summary, these findings highlight the complex relationship between the brain’s physical layout and its functional architecture. The results presented here inform future analyses of community structure and network hubs in health, across development, and in the case of neuropsychiatric disorders.

Most humans have the good fortune to live their lives embedded in richly structured social groups. Yet, it remains unclear how humans acquire knowledge about these social structures to successfully navigate social relationships. Here we address this knowledge gap with an interdisciplinary neuroimaging study drawing on recent advances in network science and statistical learning. Specifically, we collected BOLD MRI data while participants learned the community structure of both social and non-social networks, in order to examine whether the learning of these two types of networks was differentially associated with functional brain network topology. We found that participants learned the community structure of the networks, as evidenced by a slower reaction time when a trial moved between communities than when a trial moved within a community. Learning the community structure of social networks was also characterized by significantly greater functional connectivity of the hippocampus and temporoparietal junction when transitioning between communities than when transitioning within a community. Furthermore, temporoparietal regions of the default mode were more strongly connected to hippocampus, somatomotor, and visual regions for social networks than for non-social networks. Collectively, our results identify neurophysiological underpinnings of social versus non-social network learning, extending our knowledge about the impact of social context on learning processes. More broadly, this work offers an empirical approach to study the learning of social network structures, which could be fruitfully extended to other participant populations, various graph architectures, and a diversity of social contexts in future studies.

Brain-computer interfaces (BCIs) have been largely developed to allow communication, control, and neurofeedback in human beings. Despite their great potential, BCIs perform inconsistently across individuals and the neural processes that enable humans to achieve good control remain poorly understood. To address this question, we performed simultaneous high-density electroencephalographic (EEG) and magnetoencephalographic (MEG) recordings in a motor imagery-based BCI training involving a group of healthy subjects. After reconstructing the signals at the cortical level, we showed that the reinforcement of motor-related activity during the BCI skill acquisition is paralleled by a progressive disconnection of associative areas which were not directly targeted during the experiments. Notably, these network connectivity changes reflected growing automaticity associated with BCI performance and predicted future learning rate. Altogether, our findings provide new insights into the large-scale cortical organizational mechanisms underlying BCI learning, which have implications for the improvement of this technology in a broad range of real-life applications.

Executive function develops during adolescence, yet it remains unknown how structural brain networks mature to facilitate activation of the fronto-parietal system, which is critical for executive function. In a sample of 946 human youths (ages 8-23y) who completed diffusion imaging, we capitalized upon recent advances in linear dynamical network control theory to calculate the energetic cost necessary to activate the fronto-parietal system through the control of multiple brain regions given existing structural network topology. We found that the energy required to activate the fronto-parietal system declined with development, and the pattern of regional energetic cost predicts unseen individuals’ brain maturity. Finally, energetic requirements of the cingulate cortex were negatively correlated with executive performance, and partially mediated the development of executive performance with age. Our results reveal a mechanism by which structural networks develop during adolescence to reduce the theoretical energetic costs of transitions to activation states necessary for executive function.