Dynamic graph metrics: Tutorial, toolbox, and tale

Breastfeeding improves dynamic reorganization of functional connectivity in preterm infants: a temporal brain network study

Substantial evidences have shown the benefits of breastfeeding to infants in terms of better nutrition and neurodevelopmental outcome. However, the relationship between brain development and feeding in preterm infants, who are physiologically and developmentally immature at birth, is only beginning to be quantitatively assessed, coinciding with the recent advent of neuroimaging techniques. In the current work, we studied a sample of 50 preterm infants-born between 29 and 33 weeks (32.20 ± 0.89 weeks) of gestational age, where 30 of them were breastfed and the remaining 20 were formula-fed. Resting-state functional magnetic resonance imaging (fMRI) was recorded around term-equivalent age (40.00 ± 1.31 weeks, range 39-44 weeks) using a 1.5-T scanner under sedation condition. Temporal brain networks were estimated by the correlation of sliding time-window time courses among regions of a predefined atlas. Through our newly introduced temporal efficiency approach, we examined, for the first time, the 3D spatiotemporal architecture of the temporal brain network. We found prominent temporal small-world properties in both groups, suggesting the arrangement of dynamic functional connectivity permits effective coordination of various brain regions for efficient information transfer over time at both local and global levels. More importantly, we showed that breastfed preterm infants exhibited greater temporal global efficiency in comparison with formula-fed preterm infants. Specifically, we found localized elevation of temporal nodal properties in the right temporal gyrus and bilateral caudate. Taken together, these findings provide new evidence to support the notion that breast milk promotes early brain development and cognitive function, which may have neurobiological and public health implications for parents and pediatricians.Breastfeeding has long been recognized to have beneficial effect on early neurodevelopment in infants. However, the influence of breastfeeding on reorganization of functional connectivity in preterm infants are largely unknown. To this end, we utilized our recently developed temporal brain network analysis framework to investigate the dynamic reorganization of brain functional connectivity in preterm infants fed with breast milk. We found that beyond an optimal temporal small-world topology, breastfed preterm infants exhibited improved network efficiency at both global and regional levels in comparisons with those of formula-fed infants. Graphical abstract: Breastfeeding has long been recognized to have beneficial effect on early neurodevelopment in infants. However, the influence of breastfeeding on reorganization of brain functional connectivity in preterm infants are largely unknown. To this end, we utilized our recently developed temporal brain network analysis framework to investigate the dynamic reorganization of functional connectivity in preterm infants fed with breast milk. We found that beyond an optimal temporal small-world topology, breastfed preterm infants exhibited improved network efficiency at both global and regional levels in comparisons with those of formula-fed infants.

Recurrence quantification analysis of dynamic brain networks

Evidence suggests that brain network dynamics are a key determinant of brain function and dysfunction. Here we propose a new framework to assess the dynamics of brain networks based on recurrence analysis. Our framework uses recurrence plots and recurrence quantification analysis to characterize dynamic networks. For resting-state magnetoencephalographic dynamic functional networks (dFNs), we have found that functional networks recur more quickly in people with epilepsy than in healthy controls. This suggests that recurrence of dFNs may be used as a biomarker of epilepsy. For stereo electroencephalography data, we have found that dFNs involved in epileptic seizures emerge before seizure onset, and recurrence analysis allows us to detect seizures. We further observe distinct dFNs before and after seizures, which may inform neurostimulation strategies to prevent seizures. Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders besides epilepsy.

Understanding diaschisis models of attention dysfunction with rTMS

Visual attentive tracking requires a balance of excitation and inhibition across large-scale frontoparietal cortical networks. Using methods borrowed from network science, we characterize the induced changes in network dynamics following low frequency (1 Hz) repetitive transcranial magnetic stimulation (rTMS) as an inhibitory noninvasive brain stimulation protocol delivered over the intraparietal sulcus. When participants engaged in visual tracking, we observed a highly stable network configuration of six distinct communities, each with characteristic properties in node dynamics. Stimulation to parietal cortex had no significant impact on the dynamics of the parietal community, which already exhibited increased flexibility and promiscuity relative to the other communities. The impact of rTMS, however, was apparent distal from the stimulation site in lateral prefrontal cortex. rTMS temporarily induced stronger allegiance within and between nodal motifs (increased recruitment and integration) in dorsolateral and ventrolateral prefrontal cortex, which returned to baseline levels within 15 min. These findings illustrate the distributed nature by which inhibitory rTMS perturbs network communities and is preliminary evidence for downstream cortical interactions when using noninvasive brain stimulation for behavioral augmentations.

Abnormal static and dynamic functional connectivity of resting-state fMRI in multiple system atrophy

In order to explore the topological alterations in functional brain networks between multiple system atrophy (MSA) patients and healthy controls (HC), a new joint analysis method of static and dynamic functional connectivity (FC) is proposed in this paper. Twenty-four MSA patients and twenty HCs were enrolled in this study. We constructed static and dynamic brain networks from resting-state fMRI data and calculated four graph theory attributes. Statistical comparisons and correlation analysis were carried out for static and dynamic FC separately before combining both cases. We found decreased local efficiency (LE) and weighted degree (WD) in cerebellum from both static and dynamic graph attributes. For static FC alone, we identified increased betweenness centrality (BC) at left dorsolateral prefrontal cortex, left Cerebellum_Crus9 and decreased WD at Vermis_6. For dynamic FC alone, decreased BC, clustering coefficients and LE at several cortical regions and cerebellum were identified. All the features had significant correlation with total UMSARS scores. Receiver operating characteristic analysis showed that dynamic features had the highest area under the curve value. Our work not only added new evidence for the underlying neurobiology and disrupted dynamic disconnection syndrome of MSA, but also proved the possibility of disease diagnosis and progression tracking using rs-fMRI.

Robust dynamic community detection with applications to human brain functional networks

While current technology permits inference of dynamic brain networks over long time periods at high temporal resolution, the detailed structure of dynamic network communities during human seizures remains poorly understood. We introduce a new methodology that addresses critical aspects unique to the analysis of dynamic functional networks inferred from noisy data. We propose a dynamic plex percolation method (DPPM) that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time. We show in simulation that DPPM outperforms existing methods in accurately capturing certain stereotypical dynamic community behaviors in noisy situations. We then illustrate the ability of this method to track dynamic community organization during human seizures, using invasive brain voltage recordings at seizure onset. We conjecture that application of this method will yield new targets for surgical treatment of epilepsy, and more generally could provide new insights in other network neuroscience applications.

Understanding how brain networks evolve in time remains a challenge, with the potential for significant impact to human health and disease. Here, the authors introduce a new methodology to track dynamic functional networks that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time.

Dynamic Reconfiguration, Fragmentation, and Integration of Whole-Brain Modular Structure across Depths of Unconsciousness

General anesthetics are routinely used to induce unconsciousness, and much is known about their effects on receptor function and single neuron activity. Much less is known about how these local effects are manifest at the whole-brain level nor how they influence network dynamics, especially past the point of induced unconsciousness. Using resting-state functional magnetic resonance imaging (fMRI) with nonhuman primates, we investigated the dose-dependent effects of anesthesia on whole-brain temporal modular structure, following loss of consciousness. We found that higher isoflurane dose was associated with an increase in both the number and isolation of whole-brain modules, as well as an increase in the uncoordinated movement of brain regions between those modules. Conversely, we found that higher dose was associated with a decrease in the cohesive movement of brain regions between modules, as well as a decrease in the proportion of modules in which brain regions participated. Moreover, higher dose was associated with a decrease in the overall integrity of networks derived from the temporal modules, with the exception of a single, sensory-motor network. Together, these findings suggest that anesthesia-induced unconsciousness results from the hierarchical fragmentation of dynamic whole-brain network structure, leading to the discoordination of temporal interactions between cortical modules.

Altered resting-state dynamic functional brain networks in major depressive disorder: Findings from the REST-meta-MDD consortium

BACKGROUND

Major depressive disorder (MDD) is known to be characterized by altered brain functional connectivity (FC) patterns. However, whether and how the features of dynamic FC would change in patients with MDD are unclear. In this study, we aimed to characterize dynamic FC in MDD using a large multi-site sample and a novel dynamic network-based approach.

METHODS

Resting-state functional magnetic resonance imaging (fMRI) data were acquired from a total of 460 MDD patients and 473 healthy controls, as a part of the REST-meta-MDD consortium. Resting-state dynamic functional brain networks were constructed for each subject by a sliding-window approach. Multiple spatio-temporal features of dynamic brain networks, including temporal variability, temporal clustering and temporal efficiency, were then compared between patients and healthy subjects at both global and local levels.

RESULTS

The group of MDD patients showed significantly higher temporal variability, lower temporal correlation coefficient (indicating decreased temporal clustering) and shorter characteristic temporal path length (indicating increased temporal efficiency) compared with healthy controls (corrected p < 3.14×10-3). Corresponding local changes in MDD were mainly found in the default-mode, sensorimotor and subcortical areas. Measures of temporal variability and characteristic temporal path length were significantly correlated with depression severity in patients (corrected p < 0.05). Moreover, the observed between-group differences were robustly present in both first-episode, drug-naïve (FEDN) and non-FEDN patients.

CONCLUSIONS

Our findings suggest that excessive temporal variations of brain FC, reflecting abnormal communications between large-scale bran networks over time, may underlie the neuropathology of MDD.

Using Low-Dimensional Manifolds to Map Relationships Between Dynamic Brain Networks

As the field of dynamic brain networks continues to expand, new methods are needed to allow for optimal handling and understanding of this explosion in data. We propose here a novel approach that embeds dynamic brain networks onto a two-dimensional (2D) manifold based on similarities and differences in network organization. Each brain network is represented as a single point on the low dimensional manifold with networks of similar topology being located in close proximity. The rich spatio-temporal information has great potential for visualization, analysis, and interpretation of dynamic brain networks. The fact that each network is represented by a single point makes it possible to switch between the low-dimensional space and the full connectivity of any given brain network. Thus, networks in a specific region of the low-dimensional space can be examined to identify network features, such as the location of brain network hubs or the interconnectivity between brain circuits. In this proof-of-concept manuscript, we show that these low dimensional manifolds contain meaningful information, as they were able to successfully discriminate between cognitive tasks and study populations. This work provides evidence that embedding dynamic brain networks onto low dimensional manifolds has the potential to help us better visualize and understand dynamic brain networks with the hope of gaining a deeper understanding of normal and abnormal brain dynamics.

Stability of spontaneous, correlated activity in mouse auditory cortex

Neural systems can be modeled as complex networks in which neural elements are represented as nodes linked to one another through structural or functional connections. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system’s topological organization and to better understand its function. Here, we used two-photon calcium imaging to record spontaneous activity from the same set of cells in mouse auditory cortex over the course of several weeks. We reconstruct functional networks in which cells are linked to one another by edges weighted according to the correlation of their fluorescence traces. We show that the networks exhibit modular structure across multiple topological scales and that these multi-scale modules unfold as part of a hierarchy. We also show that, on average, network architecture becomes increasingly dissimilar over time, with similarity decaying monotonically with the distance (in time) between sessions. Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery. Our work indicates a framework for studying spontaneous activity measured by two-photon calcium imaging using computational methods and graphical models from network science. The methods are flexible and easily extended to additional datasets, opening the possibility of studying cellular level network organization of neural systems and how that organization is modulated by stimuli or altered in models of disease.

Neurons coordinate their activity with one another, forming networks that help support adaptive, flexible behavior. Still, little is known about the organization of these networks at the cellular scale and their stability over time. Here, we reconstruct networks from calcium imaging data recorded in mouse primary auditory cortex. We show that these networks exhibit spatially constrained, hierarchical modular structure, which may facilitate specialized information processing. However, we show that connection weights and modular structure are also variable over time, changing on a timescale of days and adopting novel network configurations. Despite this, a small subset of neurons maintain their connections to one another and preserve their modular organization across time, forming a stable temporal core surrounded by a flexible periphery. These findings represent a conceptual bridge linking network analyses of macroscale and cellular-level neuroimaging data. They also represent a complementary approach to existing circuits- and systems-based interrogation of nervous system function, opening the door for deeper and more targeted analysis in the future.

Psychological resilience negatively correlates with resting-state brain network flexibility in young healthy adults: a dynamic functional magnetic resonance imaging study

Background

Psychological resilience is an important personality trait whose decrease is associated with many common psychiatric disorders, but the neural mechanisms underlying it remain largely unclear. In this study, we aimed to explore the neural correlates of psychological resilience in healthy adults by investigating its relationship with functional brain network flexibility, a fundamental dynamic feature of brain network defined by switching frequency of its modular community structures.

Methods

Resting-state functional magnetic resonance imaging (fMRI) scans were acquired from 41 healthy adults, whose psychological resilience was quantified by the Connor-Davidson Resilience Scale (CD-RISC). Dynamic functional brain network was constructed for each subject, whose flexibility was calculated at all the global, subnetwork and region-of-interest (ROI) levels. After that, the associations between CD-RISC score and brain network flexibility were assessed at all levels by partial correlations controlling for age, sex, education and head motion. Correlation was also tested between the CD-RISC score and modularity of conventional static brain network for comparative purposes.

Results

The CD-RISC score was significant negatively correlated with the brain network flexibility at global level (r=-0.533, P=0.001), and with flexibility of the visual subnetwork at subnetwork level (r=-0.576, corrected P=0.002). Moreover, significant (corrected P<0.05) or trends for (corrected P<0.10) negative correlations were found between the CD-RISC score and flexibilities of a number of visual and default-mode areas at ROI level. Meanwhile, the modularity of static brain network did not reveal significant correlation with CD-RISC score (P>0.05).

Conclusions

Our results suggest that excessive fluctuations of the functional brain community structures during rest may be indicative of a lower psychological resilience, and the visual and default-mode systems may play crucial roles in such relationship. These findings may provide important implications for improving our understanding of the psychological resilience.

Negatively Linking Connector Networks in Cognitive Control of Affective Pictures

Cognitive control of emotions depends on intermodular long-distance communications. However, negative connections between connector hubs are removed by traditional hard-thresholding approach in graph-theoretical research. Using soft-thresholding approach to reserve negative links, we explore time-varying features of connector hubs in intermodular communications during cognitive control of affective pictures. We develop a novel approach to sparse functional networks and construct negatively linking connector networks for positive, negative, and neutral pictures. We find that consisting of flexible hubs, the frontoparietal system dynamically top–down inhibits neural activities through negative connections from the salience subnetwork and visual processing area. Moreover, the shared connectors form functional backbones that dynamically reconfigure according to differently-valenced pictures in order to coordinate both stability and flexibility of cognitive connector networks. These results reveal the necessity of conserving negative links between intermodular communications in chronnectome research and deepen the understanding of how connector networks dynamically evolute during cognitive control of affective processing.

COGTIPS: a double-blind randomized active controlled trial protocol to study the effect of home-based, online cognitive training on cognition and brain networks in Parkinson's disease

Background

Cognitive dysfunction is highly prevalent in Parkinson’s disease (PD) and a large proportion of patients eventually develops PD-related dementia. Currently, no effective treatment is available. Cognitive training is effective in relieving cognitive dysfunctions in several –neurodegenerative– diseases, and earlier small-scale trials have shown positive results for PD. In this randomized controlled trial, we assess the efficacy of online home-based cognitive training, its long-term effects, as well as the underlying neural correlates in a large group of PD patients.

Methods

In this double-blind randomized controlled trial we will include 140 non-demented patients with idiopathic PD that experience significant subjective cognitive complaints. Participants will be randomized into a cognitive training group and an active control group. In both groups, participants will individually perform an online home-based intervention for eight weeks, three times a week during 45 min. The cognitive training consists of thirteen games that focus on executive functions, attention and processing speed with an adaptive difficulty. The active control comprises three games that keep participants cognitively engaged without a training component. Participants will be subjected to extensive neuropsychological assessments at baseline and after the intervention, and at six months, one year and two years of follow-up. A subset of participants (40 in each treatment condition) will undergo structural and functional magnetic resonance imaging. The primary outcome of this study is the performance on the Tower of London task. Secondary outcomes are objective and subjective cognitive functioning, conversion to PD-related mild cognitive impairment or dementia, functional and structural connectivity and network topological indices measured with magnetic resonance imaging. None of the outcome measures are part of the cognitive training program. Data will be analyzed using multivariate mixed-model analyses and odds ratios.

Discussion

This study is a large-scale cognitive training study in PD patients that evaluates the efficacy in relieving cognitive dysfunction, and the underlying mechanisms. The strengths of this study are the large sample size, the long follow-up period and the use of neuroimaging in a large subsample. The study is expected to have a low attrition and a high compliance rate given the home-based and easily-accessible intervention in both conditions.

Trial registration

ClinicalTrials.gov ID NCT02920632. Registered September 30, 2016.

Electronic supplementary material

The online version of this article (10.1186/s12883-019-1403-6) contains supplementary material, which is available to authorized users.

Extraction of Time-Varying Spatiotemporal Networks Using Parameter-Tuned Constrained IVA

Dynamic functional connectivity analysis is an effective way to capture the networks that are functionally associated and continuously changing over the scanning period. However, these methods mostly analyze the dynamic associations across the activation patterns of the spatial networks while assuming that the spatial networks are stationary. Hence, a model that allows for the variability in both domains and reduces the assumptions imposed on the data provides an effective way for extracting spatiotemporal networks. Independent vector analysis (IVA) is a joint blind source separation technique that allows for estimation of spatial and temporal features while successfully preserving variability. However, its performance is affected for higher number of datasets. Hence, we develop an effective two-stage method to extract time-varying spatial and temporal features using IVA, mitigating the problems with higher number of datasets while preserving the variability across subjects and time. The first stage is used to extract reference signals using group-independent component analysis (GICA) that are used in a parameter-tuned constrained IVA framework to estimate time-varying representations of these signals by preserving the variability through tuning the constraint parameter. This approach effectively captures variability across time from a large-scale resting-state fMRI data acquired from healthy controls and patients with schizophrenia and identifies more functionally relevant connections that are significantly different among healthy controls and patients with schizophrenia, compared with the widely used GICA method alone.

Applications of dynamic functional connectivity to pain and its modulation

Since early work attempting to characterize the brain's role in pain, it has been clear that pain is not generated by a specific brain region, but rather by coordinated activity across a network of brain regions, the "neuromatrix." The advent of noninvasive whole-brain neuroimaging, including functional magnetic resonance imaging, has provided insight on coordinated activity in the pain neuromatrix and how correlations in activity between regions, referred to as "functional connectivity," contribute to pain and its modulation. Initial functional connectivity investigations assumed interregion connectivity remained stable over time, and measured variability across individuals. However, new dynamic functional connectivity (dFC) methods allow researchers to measure how connectivity changes over time within individuals, permitting insights on the dynamic reorganization of the pain neuromatrix in humans. We review how dFC methods have been applied to pain, and insights afforded on how brain connectivity varies across time, either spontaneously or as a function of psychological states, cognitive demands, or the external environment. Specifically, we review psychophysiological interaction, dynamic causal modeling, state-based dynamic community structure, and sliding-window analyses and their use in human functional neuroimaging of acute pain, chronic pain, and pain modulation. We also discuss promising uses of dFC analyses for the investigation of chronic pain conditions and predicting pain treatment efficacy and the relationship between state- and trait-based pain measures. Throughout this review, we provide information regarding the advantages and shortcomings of each approach, and highlight potential future applications of these methodologies for better understanding the brain processes associated with pain.

Temporal information gathering process for node ranking in time-varying networks

Many systems are dynamic and time-varying in the real world. Discovering the vital nodes in temporal networks is more challenging than that in static networks. In this study, we proposed a temporal information gathering (TIG) process for temporal networks. The TIG-process, as a node's importance metric, can be used to do the node ranking. As a framework, the TIG-process can be applied to explore the impact of temporal information on the significance of the nodes. The key point of the TIG-process is that nodes' importance relies on the importance of its neighborhood. There are four variables: temporal information gathering depth n, temporal distance matrix D, initial information c, and weighting function f. We observed that the TIG-process can degenerate to classic metrics by a proper combination of these four variables. Furthermore, the fastest arrival distance based TIG-process ( fad-tig) is performed optimally in quantifying nodes' efficiency and nodes' spreading influence. Moreover, for the fad-tig process, we can find an optimal gathering depth n that makes the TIG-process perform optimally when n is small.

Digital phenotyping for psychiatry: Accommodating data and theory with network science methodologies

Digital phenotyping is the moment-by-moment quantification of our interactions with digital devices. With appropriate tools, digital phenotyping data afford unprecedented insight into our transactions with the world and hold promise for developing novel signatures of psychopathology that will aid in diagnosis, prognosis, and treatment selection of psychiatric disorders. In this review, we highlight empirical work merging digital phenotyping data, and particularly experience-sampling data collected via smartphone, with network theories of psychopathology and network science methodologies. The intensive, longitudinal, and multivariate data collected through digital phenotyping designs provide the necessary foundation for the application of network science methodologies to parsimoniously test network theories of psychopathology emphasizing causal interactions among psychiatric symptoms, as well as other phenotypes, across time.

Evaluation of confound regression strategies for the mitigation of micromovement artifact in studies of dynamic resting-state functional connectivity and multilayer network modularity

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 and Symptoms of Parkinson's Disease: A Resting-State fMRI Study

Research has shown that dynamic functional connectivity (dFC) in Parkinson’s disease (PD) is associated with better attention performance and with motor symptom severity. In the current study, we aimed to investigate dFC of both the default mode network (DMN) and the frontoparietal network (FPN) as neural correlates of cognitive functioning in patients with PD. Additionally, we investigated pain and motor problems as symptoms of PD in relation to dFC. Twenty-four PD patients and 27 healthy controls participated in this study. Memory and executive functioning were assessed with neuropsychological tests. Pain was assessed with the Numeric Rating Scale (NRS); motor symptom severity was assessed with the Unified Parkinson’s Disease Rating Scale (UPDRS). All subjects underwent resting-state functional magnetic resonance imaging (fMRI), from which dFC was defined by calculating the variability of functional connectivity over a number of sliding windows within each scan. dFC of both the DMN and FPN with the rest of the brain was calculated. Patients performed worse on tests of visuospatial memory, verbal memory and working memory. No difference existed between groups regarding dFC of the DMN nor the FPN with the rest of the brain. A positive correlation existed between dFC of the DMN and visuospatial memory. Our results suggest that dynamics during the resting state are a neural correlate of visuospatial memory in PD patients. Furthermore, we suggest that brain dynamics of the DMN, as measured with dFC, could be a phenomenon specifically linked to cognitive functioning in PD, but not to other symptoms.

Modeling and interpreting mesoscale network dynamics

Recent advances in brain imaging techniques, measurement approaches, and storage capacities have provided an unprecedented supply of high temporal resolution neural data. These data present a remarkable opportunity to gain a mechanistic understanding not just of circuit structure, but also of circuit dynamics, and its role in cognition and disease. Such understanding necessitates a description of the raw observations, and a delineation of computational models and mathematical theories that accurately capture fundamental principles behind the observations. Here we review recent advances in a range of modeling approaches that embrace the temporally-evolving interconnected structure of the brain and summarize that structure in a dynamic graph. We describe recent efforts to model dynamic patterns of connectivity, dynamic patterns of activity, and patterns of activity atop connectivity. In the context of these models, we review important considerations in statistical testing, including parametric and non-parametric approaches. Finally, we offer thoughts on careful and accurate interpretation of dynamic graph architecture, and outline important future directions for method development.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Knowledge gaps in the early growth of semantic feature networks

Understanding language learning, and more general knowledge acquisition, requires characterization of inherently qualitative structures. Recent work has applied network science to this task by creating semantic feature networks, in which words correspond to nodes and connections to shared features, then characterizing the structure of strongly inter-related groups of words. However, the importance of sparse portions of the semantic network - knowledge gaps - remains unexplored. Using applied topology we query the prevalence of knowledge gaps, which we propose manifest as cavities within the growing semantic feature network of toddlers. We detect topological cavities of multiple dimensions and find that despite word order variation, global organization remains similar. We also show that nodal network measures correlate with filling cavities better than basic lexical properties. Finally, we discuss the importance of semantic feature network topology in language learning and speculate that the progression through knowledge gaps may be a robust feature of knowledge acquisition.

The Role of Magnetoencephalography in the Early Stages of Alzheimer's Disease

The ever increasing proportion of aged people in modern societies is leading to a substantial increase in the number of people affected by dementia, and Alzheimer’s Disease (AD) in particular, which is the most common cause for dementia. Throughout the course of the last decades several different compounds have been tested to stop or slow disease progression with limited success, which is giving rise to a strong interest toward the early stages of the disease. Alzheimer’s disease has an extended an insidious preclinical stage in which brain pathology accumulates slowly until clinical symptoms are observable in prodromal stages and in dementia. For this reason, the scientific community is focusing into investigating early signs of AD which could lead to the development of validated biomarkers. While some CSF and PET biomarkers have already been introduced in the clinical practice, the use of non-invasive measures of brain function as early biomarkers is still under investigation. However, the electrophysiological mechanisms and the early functional alterations underlying preclinical Alzheimer’s Disease is still scarcely studied. This work aims to briefly review the most relevant findings in the field of electrophysiological brain changes as measured by magnetoencephalography (MEG). MEG has proven its utility in some clinical areas. However, although its clinical relevance in dementia is still limited, a growing number of studies highlighted its sensitivity in these preclinical stages. Studies focusing on different analytical approaches will be reviewed. Furthermore, their potential applications to establish early diagnosis and determine subsequent progression to dementia are discussed.

Network Approaches to Understand Individual Differences in Brain Connectivity: Opportunities for Personality Neuroscience

Over the past decade, advances in the interdisciplinary field of network science have provided a framework for understanding the intrinsic structure and function of human brain networks. A particularly fruitful area of this work has focused on patterns of functional connectivity derived from non-invasive neuroimaging techniques such as functional magnetic resonance imaging (fMRI). An important subset of these efforts has bridged the computational approaches of network science with the rich empirical data and biological hypotheses of neuroscience, and this research has begun to identify features of brain networks that explain individual differences in social, emotional, and cognitive functioning. The most common approach estimates connections assuming a single configuration of edges that is stable across the experimental session. In the literature, this is referred to as a static network approach, and researchers measure static brain networks while a subject is either at rest or performing a cognitively demanding task. Research on social and emotional functioning has primarily focused on linking static brain networks with individual differences, but recent advances have extended this work to examine temporal fluctuations in dynamic brain networks. Mounting evidence suggests that both the strength and flexibility of time-evolving brain networks influence individual differences in executive function, attention, working memory, and learning. In this review, we first examine the current evidence for brain networks involved in cognitive functioning. Then we review some preliminary evidence linking static network properties to individual differences in social and emotional functioning. We then discuss the applicability of emerging dynamic network methods for examining individual differences in social and emotional functioning. We close with an outline of important frontiers at the intersection between network science and neuroscience that will enhance our understanding of the neurobiological underpinnings of social behavior.

Putting the "dynamic" back into dynamic functional connectivity

The study of fluctuations in time-resolved functional connectivity is a topic of substantial current interest. As the term "dynamic functional connectivity" implies, such fluctuations are believed to arise from dynamics in the neuronal systems generating these signals. While considerable activity currently attends to methodological and statistical issues regarding dynamic functional connectivity, less attention has been paid toward its candidate causes. Here, we review candidate scenarios for dynamic (functional) connectivity that arise in dynamical systems with two or more subsystems; generalized synchronization, itinerancy (a form of metastability), and multistability. Each of these scenarios arises under different configurations of local dynamics and intersystem coupling: We show how they generate time series data with nonlinear and/or nonstationary multivariate statistics. The key issue is that time series generated by coupled nonlinear systems contain a richer temporal structure than matched multivariate (linear) stochastic processes. In turn, this temporal structure yields many of the phenomena proposed as important to large-scale communication and computation in the brain, such as phase-amplitude coupling, complexity, and flexibility. The code for simulating these dynamics is available in a freeware software platform, the Brain Dynamics Toolbox.

Tracking Neuronal Connectivity from Electric Brain Signals to Predict Performance

The human brain is a complex container of interconnected networks. Network neuroscience is a recent venture aiming to explore the connection matrix built from the human brain or human “Connectome.” Network-based algorithms provide parameters that define global organization of the brain; when they are applied to electroencephalographic (EEG) signals network, configuration and excitability can be monitored in millisecond time frames, providing remarkable information on their instantaneous efficacy also for a given task’s performance via online evaluation of the underlying instantaneous networks before, during, and after the task. Here we provide an updated summary on the connectome analysis for the prediction of performance via the study of task-related dynamics of brain network organization from EEG signals.

Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.

From Maps to Multi-dimensional Network Mechanisms of Mental Disorders

The development of advanced neuroimaging techniques and their deployment in large cohorts has enabled an assessment of functional and structural brain network architecture at an unprecedented level of detail. Across many temporal and spatial scales, network neuroscience has emerged as a central focus of intellectual efforts, seeking meaningful descriptions of brain networks and explanatory sets of network features that underlie circuit function in health and dysfunction in disease. However, the tools of network science commonly deployed provide insight into brain function at a fundamentally descriptive level, often failing to identify (patho-)physiological mechanisms that link system-level phenomena to the multiple hierarchies of brain function. Here we describe recently developed techniques stemming from advances in complex systems and network science that have the potential to overcome this limitation, thereby contributing mechanistic insights into neuroanatomy, functional dynamics, and pathology. Finally, we build on the Research Domain Criteria framework, highlighting the notion that mental illnesses can be conceptualized as dysfunctions of neural circuitry present across conventional diagnostic boundaries, to sketch how network-based methods can be combined with pharmacological, intermediate phenotype, genetic, and magnetic stimulation studies to probe mechanisms of psychopathology.

The persuasion network is modulated by drug-use risk and predicts anti-drug message effectiveness

While a persuasion network has been proposed, little is known about how network connections between brain regions contribute to attitude change. Two possible mechanisms have been advanced. One hypothesis predicts that attitude change results from increased connectivity between structures implicated in affective and executive processing in response to increases in argument strength. A second functional perspective suggests that highly arousing messages reduce connectivity between structures implicated in the encoding of sensory information, which disrupts message processing and thereby inhibits attitude change. However, persuasion is a multi-determined construct that results from both message features and audience characteristics. Therefore, persuasive messages should lead to specific functional connectivity patterns among a priori defined structures within the persuasion network. The present study exposed 28 subjects to anti-drug public service announcements where arousal, argument strength, and subject drug-use risk were systematically varied. Psychophysiological interaction analyses provide support for the affective-executive hypothesis but not for the encoding-disruption hypothesis. Secondary analyses show that video-level connectivity patterns among structures within the persuasion network predict audience responses in independent samples (one college-aged, one nationally representative). We propose that persuasion neuroscience research is best advanced by considering network-level effects while accounting for interactions between message features and target audience characteristics.

Generative models for network neuroscience: prospects and promise

Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and identifying principles with which to understand them. Within this discipline, one particularly powerful approach is network generative modelling, in which wiring rules are algorithmically implemented to produce synthetic network architectures with the same properties as observed in empirical network data. Successful models can highlight the principles by which a network is organized and potentially uncover the mechanisms by which it grows and develops. Here, we review the prospects and promise of generative models for network neuroscience. We begin with a primer on network generative models, with a discussion of compressibility and predictability, and utility in intuiting mechanisms, followed by a short history on their use in network science, broadly. We then discuss generative models in practice and application, paying particular attention to the critical need for cross-validation. Next, we review generative models of biological neural networks, both at the cellular and large-scale level, and across a variety of species including Caenorhabditis elegans, Drosophila, mouse, rat, cat, macaque and human. We offer a careful treatment of a few relevant distinctions, including differences between generative models and null models, sufficiency and redundancy, inferring and claiming mechanism, and functional and structural connectivity. We close with a discussion of future directions, outlining exciting frontiers both in empirical data collection efforts as well as in method and theory development that, together, further the utility of the generative network modelling approach for network neuroscience.