A mathematical perspective on edge-centric brain functional connectivity

Edge-centric connectome-genetic markers of bridging factor to comorbidity between depression and anxiety

Depression-anxiety comorbidity is commonly attributed to the occurrence of specific symptoms bridging the two disorders. However, the significant heterogeneity of most bridging symptoms presents challenges for psychopathological interpretation and clinical applicability. Here, we conceptually established a common bridging factor (cb factor) to characterize a general structure of these bridging symptoms, analogous to the general psychopathological p factor. We identified a cb factor from 12 bridging symptoms in depression-anxiety comorbidity network. Moreover, this cb factor could be predicted using edge-centric connectomes with robust generalizability, and was characterized by connectome patterns in attention and frontoparietal networks. In an independent twin cohort, we found that these patterns were moderately heritable, and identified their genetic connectome-transcriptional markers that were associated with the neurobiological enrichment of vasculature and cerebellar development, particularly during late-childhood-to-young-adulthood periods. Our findings revealed a general factor of bridging symptoms and its neurobiological architectures, which enriched neurogenetic understanding of depression-anxiety comorbidity.

Functional network modules overlap and are linked to interindividual connectome differences during human brain development

The modular structure of functional connectomes in the human brain undergoes substantial reorganization during development. However, previous studies have implicitly assumed that each region participates in one single module, ignoring the potential spatial overlap between modules. How the overlapping functional modules develop and whether this development is related to gray and white matter features remain unknown. Using longitudinal multimodal structural, functional, and diffusion MRI data from 305 children (aged 6 to 14 years), we investigated the maturation of overlapping modules of functional networks and further revealed their structural associations. An edge-centric network model was used to identify the overlapping modules, and the nodal overlap in module affiliations was quantified using the entropy measure. We showed a regionally heterogeneous spatial topography of the overlapping extent of brain nodes in module affiliations in children, with higher entropy (i.e., more module involvement) in the ventral attention, somatomotor, and subcortical regions and lower entropy (i.e., less module involvement) in the visual and default-mode regions. The overlapping modules developed in a linear, spatially dissociable manner, with decreased entropy (i.e., decreased module involvement) in the dorsomedial prefrontal cortex, ventral prefrontal cortex, and putamen and increased entropy (i.e., increased module involvement) in the parietal lobules and lateral prefrontal cortex. The overlapping modular patterns captured individual brain maturity as characterized by chronological age and were predicted by integrating gray matter morphology and white matter microstructural properties. Our findings highlight the maturation of overlapping functional modules and their structural substrates, thereby advancing our understanding of the principles of connectome development.

Lack of evidence for predictive utility from resting state fMRI data for individual exposure-based cognitive behavioral therapy outcomes: A machine learning study in two large multi-site samples in anxiety disorders

Data-based predictions of individual Cognitive Behavioral Therapy (CBT) treatment response are a fundamental step towards precision medicine. Past studies demonstrated only moderate prediction accuracy (i.e. ability to discriminate between responders and non-responders of a given treatment) when using clinical routine data such as demographic and questionnaire data, while neuroimaging data achieved superior prediction accuracy. However, these studies may be considerably biased due to very limited sample sizes and bias-prone methodology. Adequately powered and cross-validated samples are a prerequisite to evaluate predictive performance and to identify the most promising predictors. We therefore analyzed resting state functional magnet resonance imaging (rs-fMRI) data from two large clinical trials to test whether functional neuroimaging data continues to provide good prediction accuracy in much larger samples. Data came from two distinct German multicenter studies on exposure-based CBT for anxiety disorders, the Protect-AD and SpiderVR studies. We separately and independently preprocessed baseline rs-fMRI data from n = 220 patients (Protect-AD) and n = 190 patients (SpiderVR) and extracted a variety of features, including ROI-to-ROI and edge-functional connectivity, sliding-windows, and graph measures. Including these features in sophisticated machine learning pipelines, we found that predictions of individual outcomes never significantly differed from chance level, even when conducting a range of exploratory post-hoc analyses. Moreover, resting state data never provided prediction accuracy beyond the sociodemographic and clinical data. The analyses were independent of each other in terms of selecting methods to process resting state data for prediction input as well as in the used parameters of the machine learning pipelines, corroborating the external validity of the results. These similar findings in two independent studies, analyzed separately, urge caution regarding the interpretation of promising prediction results based on neuroimaging data from small samples and emphasizes that some of the prediction accuracies from previous studies may result from overestimation due to homogeneous data and weak cross-validation schemes. The promise of resting-state neuroimaging data to play an important role in the prediction of CBT treatment outcomes in patients with anxiety disorders remains yet to be delivered.

Higher-order functional connectivity analysis of resting-state functional magnetic resonance imaging data using multivariate cumulants

Blood-level oxygenation-dependent (BOLD) functional magnetic resonance imaging (fMRI) is the most common modality to study functional connectivity in the human brain. Most research to date has focused on connectivity between pairs of brain regions. However, attention has recently turned towards connectivity involving more than two regions, that is, higher-order connectivity. It is not yet clear how higher-order connectivity can best be quantified. The measures that are currently in use cannot distinguish between pairwise (i.e., second-order) and higher-order connectivity. We show that genuine higher-order connectivity can be quantified by using multivariate cumulants. We explore the use of multivariate cumulants for quantifying higher-order connectivity and the performance of block bootstrapping for statistical inference. In particular, we formulate a generative model for fMRI signals exhibiting higher-order connectivity and use it to assess bias, standard errors, and detection probabilities. Application to resting-state fMRI data from the Human Connectome Project demonstrates that spontaneous fMRI signals are organized into higher-order networks that are distinct from second-order resting-state networks. Application to a clinical cohort of patients with multiple sclerosis further demonstrates that cumulants can be used to classify disease groups and explain behavioral variability. Hence, we present a novel framework to reliably estimate genuine higher-order connectivity in fMRI data which can be used for constructing hyperedges, and finally, which can readily be applied to fMRI data from populations with neuropsychiatric disease or cognitive neuroscientific experiments.

Spectral dynamic causal modeling: A didactic introduction and its relationship with functional connectivity

We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modeling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements-at all time lags-including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

Modular subgraphs in large-scale connectomes underpin spontaneous co-fluctuation events in mouse and human brains

Previous studies have adopted an edge-centric framework to study fine-scale network dynamics in human fMRI. To date, however, no studies have applied this framework to data collected from model organisms. Here, we analyze structural and functional imaging data from lightly anesthetized mice through an edge-centric lens. We find evidence of "bursty" dynamics and events - brief periods of high-amplitude network connectivity. Further, we show that on a per-frame basis events best explain static FC and can be divided into a series of hierarchically-related clusters. The co-fluctuation patterns associated with each cluster centroid link distinct anatomical areas and largely adhere to the boundaries of algorithmically detected functional brain systems. We then investigate the anatomical connectivity undergirding high-amplitude co-fluctuation patterns. We find that events induce modular bipartitions of the anatomical network of inter-areal axonal projections. Finally, we replicate these same findings in a human imaging dataset. In summary, this report recapitulates in a model organism many of the same phenomena observed in previously edge-centric analyses of human imaging data. However, unlike human subjects, the murine nervous system is amenable to invasive experimental perturbations. Thus, this study sets the stage for future investigation into the causal origins of fine-scale brain dynamics and high-amplitude co-fluctuations. Moreover, the cross-species consistency of the reported findings enhances the likelihood of future translation.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Static and dynamic fMRI-derived functional connectomes represent largely similar information

Functional connectivity (FC) of blood oxygen level-dependent (BOLD) fMRI time series can be estimated using methods that differ in sensitivity to the temporal order of time points (static vs. dynamic) and the number of regions considered in estimating a single edge (bivariate vs. multivariate). Previous research suggests that dynamic FC explains variability in FC fluctuations and behavior beyond static FC. Our aim was to systematically compare methods on both dimensions. We compared five FC methods: Pearson's/full correlation (static, bivariate), lagged correlation (dynamic, bivariate), partial correlation (static, multivariate), and multivariate AR model with and without self-connections (dynamic, multivariate). We compared these methods by (i) assessing similarities between FC matrices, (ii) by comparing node centrality measures, and (iii) by comparing the patterns of brain-behavior associations. Although FC estimates did not differ as a function of sensitivity to temporal order, we observed differences between the multivariate and bivariate FC methods. The dynamic FC estimates were highly correlated with the static FC estimates, especially when comparing group-level FC matrices. Similarly, there were high correlations between the patterns of brain-behavior associations obtained using the dynamic and static FC methods. We conclude that the dynamic FC estimates represent information largely similar to that of the static FC.

Living on the edge: network neuroscience beyond nodes

Network neuroscience has emphasized the connectional properties of neural elements - cells, populations, and regions. This has come at the expense of the anatomical and functional connections that link these elements to one another. A new perspective - namely one that emphasizes 'edges' - may prove fruitful in addressing outstanding questions in network neuroscience. We highlight one recently proposed 'edge-centric' method and review its current applications, merits, and limitations. We also seek to establish conceptual and mathematical links between this method and previously proposed approaches in the network science and neuroimaging literature. We conclude by presenting several avenues for future work to extend and refine existing edge-centric analysis.

A new causal centrality measure reveals the prominent role of subcortical structures in the causal architecture of the extended default mode network

Network representation has been an incredibly useful concept for understanding the behavior of complex systems in social sciences, biology, neuroscience, and beyond. Network science is mathematically founded on graph theory, where nodal importance is gauged using measures of centrality. Notably, recent work suggests that the topological centrality of a node should not be over-interpreted as its dynamical or causal importance in the network. Hence, identifying the influential nodes in dynamic causal models (DCM) remains an open question. This paper introduces causal centrality for DCM, a dynamics-sensitive and causally-founded centrality measure based on the notion of intervention in graphical models. Operationally, this measure simplifies to an identifiable expression using Bayesian model reduction. As a proof of concept, the average DCM of the extended default mode network (eDMN) was computed in 74 healthy subjects. Next, causal centralities of different regions were computed for this causal graph, and compared against several graph-theoretical centralities. The results showed that the subcortical structures of the eDMN were more causally central than the cortical regions, even though the graph-theoretical centralities unanimously favored the latter. Importantly, model comparison revealed that only the pattern of causal centrality was causally relevant. These results are consistent with the crucial role of the subcortical structures in the neuromodulatory systems of the brain, and highlight their contribution to the organization of large-scale networks. Potential applications of causal centrality-to study causal models of other neurotypical and pathological functional networks-are discussed, and some future lines of research are outlined.

High-amplitude network co-fluctuations linked to variation in hormone concentrations over the menstrual cycle

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

Hierarchical organization of spontaneous co-fluctuations in densely sampled individuals using fMRI

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

A low dimensional embedding of brain dynamics enhances diagnostic accuracy and behavioral prediction in stroke

Large-scale brain networks reveal structural connections as well as functional synchronization between distinct regions of the brain. The latter, referred to as functional connectivity (FC), can be derived from neuroimaging techniques such as functional magnetic resonance imaging (fMRI). FC studies have shown that brain networks are severely disrupted by stroke. However, since FC data are usually large and high-dimensional, extracting clinically useful information from this vast amount of data is still a great challenge, and our understanding of the functional consequences of stroke remains limited. Here, we propose a dimensionality reduction approach to simplify the analysis of this complex neural data. By using autoencoders, we find a low-dimensional representation encoding the fMRI data which preserves the typical FC anomalies known to be present in stroke patients. By employing the latent representations emerging from the autoencoders, we enhanced patients' diagnostics and severity classification. Furthermore, we showed how low-dimensional representation increased the accuracy of recovery prediction.

Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data

Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.

Intermediately synchronised brain states optimise trade-off between subject specificity and predictive capacity

Functional connectivity (FC) refers to the statistical dependencies between activity of distinct brain areas. To study temporal fluctuations in FC within the duration of a functional magnetic resonance imaging (fMRI) scanning session, researchers have proposed the computation of an edge time series (ETS) and their derivatives. Evidence suggests that FC is driven by a few time points of high-amplitude co-fluctuation (HACF) in the ETS, which may also contribute disproportionately to interindividual differences. However, it remains unclear to what degree different time points actually contribute to brain-behaviour associations. Here, we systematically evaluate this question by assessing the predictive utility of FC estimates at different levels of co-fluctuation using machine learning (ML) approaches. We demonstrate that time points of lower and intermediate co-fluctuation levels provide overall highest subject specificity as well as highest predictive capacity of individual-level phenotypes.

Brain fingerprint is based on the aperiodic, scale-free, neuronal activity

Subject differentiation bears the possibility to individualize brain analyses. However, the nature of the processes generating subject-specific features remains unknown. Most of the current literature uses techniques that assume stationarity (e.g., Pearson's correlation), which might fail to capture the non-linear nature of brain activity. We hypothesize that non-linear perturbations (defined as neuronal avalanches in the context of critical dynamics) spread across the brain and carry subject-specific information, contributing the most to differentiability. To test this hypothesis, we compute the avalanche transition matrix (ATM) from source-reconstructed magnetoencephalographic data, as to characterize subject-specific fast dynamics. We perform differentiability analysis based on the ATMs, and compare the performance to that obtained using Pearson's correlation (which assumes stationarity). We demonstrate that selecting the moments and places where neuronal avalanches spread improves differentiation (P < 0.0001, permutation testing), despite the fact that most of the data (i.e., the linear part) are discarded. Our results show that the non-linear part of the brain signals carries most of the subject-specific information, thereby clarifying the nature of the processes that underlie individual differentiation. Borrowing from statistical mechanics, we provide a principled way to link emergent large-scale personalized activations to non-observable, microscopic processes.

Edge-centric functional network predicts risk propensity in economic decision-making: evidence from a resting-state fMRI study

Despite node-centric studies revealing an association between resting-state functional connectivity and individual risk propensity, the prediction of future risk decisions remains undetermined. Herein, we applied a recently emerging edge-centric method, the edge community similarity network (ECSN), to alternatively describe the community structure of resting-state brain activity and to probe its contribution to predicting risk propensity during gambling. Results demonstrated that inter-individual variability of risk decisions correlates with the inter-subnetwork couplings spanning the visual network (VN) and default mode network (DMN), cingulo-opercular task control network, and sensory/somatomotor hand network (SSHN). Particularly, participants who have higher community similarity of these subnetworks during the resting state tend to choose riskier and higher yielding bets. And in contrast to low-risk propensity participants, those who behave high-risky show stronger couplings spanning the VN and SSHN/DMN. Eventually, based on the resting-state ECSN properties, the risk rate during the gambling task is effectively predicted by the multivariable linear regression model at the individual level. These findings provide new insights into the neural substrates of the inter-individual variability in risk propensity and new neuroimaging metrics to predict individual risk decisions in advance.

Multivariate information theory uncovers synergistic subsystems of the human cerebral cortex

One of the most well-established tools for modeling the brain is the functional connectivity network, which is constructed from pairs of interacting brain regions. While powerful, the network model is limited by the restriction that only pairwise dependencies are considered and potentially higher-order structures are missed. Here, we explore how multivariate information theory reveals higher-order dependencies in the human brain. We begin with a mathematical analysis of the O-information, showing analytically and numerically how it is related to previously established information theoretic measures of complexity. We then apply the O-information to brain data, showing that synergistic subsystems are widespread in the human brain. Highly synergistic subsystems typically sit between canonical functional networks, and may serve an integrative role. We then use simulated annealing to find maximally synergistic subsystems, finding that such systems typically comprise ≈10 brain regions, recruited from multiple canonical brain systems. Though ubiquitous, highly synergistic subsystems are invisible when considering pairwise functional connectivity, suggesting that higher-order dependencies form a kind of shadow structure that has been unrecognized by established network-based analyses. We assert that higher-order interactions in the brain represent an under-explored space that, accessible with tools of multivariate information theory, may offer novel scientific insights.

Dynamical interactions reconfigure the gradient of cortical timescales

The functional organization of the brain is usually presented with a back-to-front gradient of timescales, reflecting regional specialization with sensory areas (back) processing information faster than associative areas (front), which perform information integration. However, cognitive processes require not only local information processing but also coordinated activity across regions. Using magnetoencephalography recordings, we find that the functional connectivity at the edge level (between two regions) is also characterized by a back-to-front gradient of timescales following that of the regional gradient. Unexpectedly, we demonstrate a reverse front-to-back gradient when nonlocal interactions are prominent. Thus, the timescales are dynamic and can switch between back-to-front and front-to-back patterns.

Leveraging edge-centric networks complements existing network-level inference for functional connectomes

The human connectome is modular with distinct brain regions clustering together to form large-scale communities, or networks. This concept has recently been leveraged in novel inferencing procedures by averaging the edge-level statistics within networks to induce more powerful inferencing at the network level. However, these networks are constructed based on the similarity between pairs of nodes. Emerging work has described novel edge-centric networks, which instead use the similarity between pairs of edges to construct networks. In this work, we use these edge-centric networks in a network-level inferencing procedure and compare this novel method to traditional inferential procedures and the network-level procedure using node-centric networks. We use data from the Human Connectome Project, the Healthy Brain Network, and the Philadelphia Neurodevelopmental Cohort and use a resampling technique with various sample sizes (n=40, 80, 120) to probe the power and specificity of each method. Across datasets and sample sizes, using the edge-centric networks outperforms using node-centric networks for inference as well as edge-level FDR correction and NBS. Additionally, the edge-centric networks were found to be more consistent in clustering effect sizes of similar values as compared to node-centric networks, although node-centric networks often had a lower average within-network effect size variability. Together, these findings suggest that using edge-centric networks for network-level inference can procure relatively powerful results while remaining similarly accurate to the underlying edge-level effects across networks, complementing previous inferential methods.

BOLD cofluctuation 'events' are predicted from static functional connectivity

Recent work identified single time points ("events") of high regional cofluctuation in functional Magnetic Resonance Imaging (fMRI) which contain more large-scale brain network information than other, low cofluctuation time points. This suggested that events might be a discrete, temporally sparse signal which drives functional connectivity (FC) over the timeseries. However, a different, not yet explored possibility is that network information differences between time points are driven by sampling variability on a constant, static, noisy signal. Using a combination of real and simulated data, we examined the relationship between cofluctuation and network structure and asked if this relationship was unique, or if it could arise from sampling variability alone. First, we show that events are not discrete - there is a gradually increasing relationship between network structure and cofluctuation; ∼50% of samples show very strong network structure. Second, using simulations we show that this relationship is predicted from sampling variability on static FC. Finally, we show that randomly selected points can capture network structure about as well as events, largely because of their temporal spacing. Together, these results suggest that, while events exhibit particularly strong representations of static FC, there is little evidence that events are unique timepoints that drive FC structure. Instead, a parsimonious explanation for the data is that events arise from a single static, but noisy, FC structure.

Edge-centric analysis of time-varying functional brain networks with applications in autism spectrum disorder

The interaction between brain regions changes over time, which can be characterized using time-varying functional connectivity (tvFC). The common approach to estimate tvFC uses sliding windows and offers limited temporal resolution. An alternative method is to use the recently proposed edge-centric approach, which enables the tracking of moment-to-moment changes in co-fluctuation patterns between pairs of brain regions. Here, we first examined the dynamic features of edge time series and compared them to those in the sliding window tvFC (sw-tvFC). Then, we used edge time series to compare subjects with autism spectrum disorder (ASD) and healthy controls (CN). Our results indicate that relative to sw-tvFC, edge time series captured rapid and bursty network-level fluctuations that synchronize across subjects during movie-watching. The results from the second part of the study suggested that the magnitude of peak amplitude in the collective co-fluctuations of brain regions (estimated as root sum square (RSS) of edge time series) is similar in CN and ASD. However, the trough-to-trough duration in RSS signal is greater in ASD, compared to CN. Furthermore, an edge-wise comparison of high-amplitude co-fluctuations showed that the within-network edges exhibited greater magnitude fluctuations in CN. Our findings suggest that high-amplitude co-fluctuations captured by edge time series provide details about the disruption of functional brain dynamics that could potentially be used in developing new biomarkers of mental disorders.

Static and Dynamic Functional Connectivity Alterations in Alzheimer's Disease and Neuropsychiatric Diseases

To date, numerous studies have documented various alterations in resting brain activity in Alzheimer's disease (AD) and other neuropsychiatric diseases. In particular, disease-related alterations of functional connectivity (FC) in the resting state networks (RSN) have been documented. Altered FC in RSN is useful not only for interpreting the phenotype of diseases but also for diagnosing the diseases. More recently, several studies proposed the dynamics of resting-brain activity as a useful marker for detecting altered RSNs related to AD and other diseases. In contrast to previous studies, which focused on FC calculated using an entire fMRI scan (static FC), these newer studies focused the on temporal dynamics of FC within the scan (dynamic FC) to provide more sensitive measures to characterize RSNs. However, despite the increasing popularity of dFC, several studies cautioned that the results obtained in commonly used analyses for dFC require careful interpretation. In this mini-review, we review recent studies exploring alterations of static and dynamic functional connectivity in AD and other neuropsychiatric diseases. We then discuss how to utilize and interpret dFC for studying resting brain activity in diseases.

Time-resolved structure-function coupling in brain networks

The relationship between structural and functional connectivity in the brain is a key question in systems neuroscience. Modern accounts assume a single global structure-function relationship that persists over time. Here we study structure-function coupling from a dynamic perspective, and show that it is regionally heterogeneous. We use a temporal unwrapping procedure to identify moment-to-moment co-fluctuations in neural activity, and reconstruct time-resolved structure-function coupling patterns. We find that patterns of dynamic structure-function coupling are region-specific. We observe stable coupling in unimodal and transmodal cortex, and dynamic coupling in intermediate regions, particularly in insular cortex (salience network) and frontal eye fields (dorsal attention network). Finally, we show that the variability of a region’s structure-function coupling is related to the distribution of its connection lengths. Collectively, our findings provide a way to study structure-function relationships from a dynamic perspective.

Temporal unwrapping analysis of diffusion weighted MRI connectivity and functional MRI scans reveals that the coupling between structure and function in the human brain is regionally heterogeneous and provides a framework to evaluate these relationships from a dynamic perspective.

Edge-centric analysis of stroke patients: An alternative approach for biomarkers of lesion recovery

Most neuroimaging studies of post-stroke recovery rely on analyses derived from standard node-centric functional connectivity to map the distributed effects in stroke patients. Here, given the importance of nonlocal and diffuse damage, we use an edge-centric approach to functional connectivity in order to provide an alternative description of the effects of this disorder. These techniques allow for the rendering of metrics such as normalized entropy, which describes the diversity of edge communities at each node. Moreover, the approach enables the identification of high amplitude co-fluctuations in fMRI time series. We found that normalized entropy is associated with stroke lesion severity and continually increases across the time of patients' recovery. Furthermore, high amplitude co-fluctuations not only relate to the lesion severity but are also associated with patients' level of recovery. The current study is the first edge-centric application for a clinical population in a longitudinal dataset and demonstrates how a different perspective for functional data analysis can further characterize topographic modulations of brain dynamics.

Edges in brain networks: Contributions to models of structure and function

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