Bursty properties revealed in large-scale brain networks with a point-based method for dynamic functional connectivity

Temporal networks in biology and medicine: a survey on models, algorithms, and tools

The use of static graphs for modelling and analysis of biological and biomedical data plays a key role in biomedical research. However, many real-world scenarios present dynamic behaviours resulting in both node and edges modification as well as feature evolution. Consequently, ad-hoc models for capturing these evolutions along the time have been introduced, also referred to as dynamic, temporal, time-varying graphs. Here, we focus on temporal graphs, i.e., graphs whose evolution is represented by a sequence of time-ordered snapshots. Each snapshot represents a graph active in a particular timestamp. We survey temporal graph models and related algorithms, presenting fundamentals aspects and the recent advances. We formally define temporal graphs, focusing on the problem setting and we present their main applications in biology and medicine. We also present temporal graph embedding and the application to recent problems such as epidemic modelling. Finally, we further state some promising research directions in the area. Main results of this study include a systematic review of fundamental temporal network problems and their algorithmic solutions considered in the literature, in particular those having application in computational biology and medicine. We also include the main software developed in this context.

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.

Dynamic Functional Connectivity as a complex random walk: Definitions and the dFCwalk toolbox

•We have developed a framework to describe the dynamics of Functional Connectivity (dFC) estimated from brain activity time-series as a complex random walk in the space of possible functional networks. This conceptual and methodological framework considers dFC as a smooth reconfiguration process, combining "liquid" and "coordinated" aspects. Unlike other previous approaches, our method does not require the explicit extraction of discrete connectivity states.•In our previous work, we introduced several metrics for the quantitative characterization of the dFC random walk. First, dFC speed analyses extract the distribution of the time-resolved rate of reconfiguration of FC along time. These distributions have a clear peak (typical dFC speed, that can already serve as a biomarker) and fat tails (denoting deviations from Gaussianity that can be detected by suitable scaling analyses of FC network streams). Second, meta-connectivity (MC) analyses identify groups of functional links whose fluctuations co-vary in time and that define veritable dFC modules organized along specific dFC meta-hub controllers (differing from conventional FC modules and hubs). The decomposition of whole-brain dFC by MC allows performing dFC speed analyses separately for each of the detected dFC modules.•We present here blocks and pipelines for dFC random walk analyses that are made easily available through a dedicated MATLABⓇ toolbox (dFCwalk), openly downloadable. Although we applied such analyses mostly to fMRI resting state data, in principle our methods can be extended to any type of neural activity (from Local Field Potentials to EEG, MEG, fNIRS, etc.) or even non-neural time-series.

High-amplitude cofluctuations in cortical activity drive functional connectivity

Resting-state functional connectivity is used throughout neuroscience to study brain organization and to generate biomarkers of development, disease, and cognition. The processes that give rise to correlated activity are, however, poorly understood. Here we decompose resting-state functional connectivity using a temporal unwrapping procedure to assess the contributions of moment-to-moment activity cofluctuations to the overall connectivity pattern. This approach temporally resolves functional connectivity at a timescale of single frames, which enables us to make direct comparisons of cofluctuations of network organization with fluctuations in the blood oxygen level-dependent (BOLD) time series. We show that surprisingly, only a small fraction of frames exhibiting the strongest cofluctuation amplitude are required to explain a significant fraction of variance in the overall pattern of connection weights as well as the network's modular structure. These frames coincide with frames of high BOLD activity amplitude, corresponding to activity patterns that are remarkably consistent across individuals and identify fluctuations in default mode and control network activity as the primary driver of resting-state functional connectivity. Finally, we demonstrate that cofluctuation amplitude synchronizes across subjects during movie watching and that high-amplitude frames carry detailed information about individual subjects (whereas low-amplitude frames carry little). Our approach reveals fine-scale temporal structure of resting-state functional connectivity and discloses that frame-wise contributions vary across time. These observations illuminate the relation of brain activity to functional connectivity and open a number of directions for future research.

Modular slowing of resting-state dynamic functional connectivity as a marker of cognitive dysfunction induced by sleep deprivation

Dynamic Functional Connectivity (dFC) in the resting state (rs) is considered as a correlate of cognitive processing. Describing dFC as a flow across morphing connectivity configurations, our notion of dFC speed quantifies the rate at which FC networks evolve in time. Here we probe the hypothesis that variations of rs dFC speed and cognitive performance are selectively interrelated within specific functional subnetworks. In particular, we focus on Sleep Deprivation (SD) as a reversible model of cognitive dysfunction. We found that whole-brain level (global) dFC speed significantly slows down after 24h of SD. However, the reduction in global dFC speed does not correlate with variations of cognitive performance in individual tasks, which are subtle and highly heterogeneous. On the contrary, we found strong correlations between performance variations in individual tasks -including Rapid Visual Processing (RVP, assessing sustained visual attention)- and dFC speed quantified at the level of functional sub-networks of interest. Providing a compromise between classic static FC (no time) and global dFC (no space), modular dFC speed analyses allow quantifying a different speed of dFC reconfiguration independently for sub-networks overseeing different tasks. Importantly, we found that RVP performance robustly correlates with the modular dFC speed of a characteristic frontoparietal module.

Dynamic Functional Connectivity between order and randomness and its evolution across the human adult lifespan

Functional Connectivity (FC) during resting-state or task conditions is not static but inherently dynamic. Yet, there is no consensus on whether fluctuations in FC may resemble isolated transitions between discrete FC states rather than continuous changes. This quarrel hampers advancing the study of dynamic FC. This is unfortunate as the structure of fluctuations in FC can certainly provide more information about developmental changes, aging, and progression of pathologies. We merge the two perspectives and consider dynamic FC as an ongoing network reconfiguration, including a stochastic exploration of the space of possible steady FC states. The statistical properties of this random walk deviate both from a purely "order-driven" dynamics, in which the mean FC is preserved, and from a purely "randomness-driven" scenario, in which fluctuations of FC remain uncorrelated over time. Instead, dynamic FC has a complex structure endowed with long-range sequential correlations that give rise to transient slowing and acceleration epochs in the continuous flow of reconfiguration. Our analysis for fMRI data in healthy elderly revealed that dynamic FC tends to slow down and becomes less complex as well as more random with increasing age. These effects appear to be strongly associated with age-related changes in behavioural and cognitive performance.

Investigating time-varying functional connectivity derived from the Jackknife Correlation method for distinguishing between emotions in fMRI data

Investigating human brain activity during expressing emotional states provides deep insight into complex cognitive functions and neurological correlations inside the brain. To be able to resemble the brain function in the best manner, a complex and natural stimulus should be applied as well, the method used for data analysis should have fewer assumptions, simplifications, and parameter adjustment. In this study, we examined a functional magnetic resonance imaging dataset obtained during an emotional audio-movie stimulus associated with human life. We used Jackknife Correlation (JC) method to derive a representation of time-varying functional connectivity. We applied different binary measures and thoroughly investigated two weighted measures to study different properties of binary and weighted temporal networks. Using this approach, we indicated different aspects of human brain function during expressing different emotions. The findings of global and nodal measures could demonstrate a significant difference between emotions and significant regions in each emotion, respectively. Also, the temporal centrality properties of nodes were different in emotional states. Ultimately, we showed that the resulting measures of temporal snapshots created by JC method can distinguish between different emotions.

Statistical model for dynamically-changing correlation matrices with application to brain connectivity

BACKGROUND

Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI.

NEW METHOD

To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm.

RESULTS

The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified.

COMPARISON WITH EXISTING METHODS

We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states.

CONCLUSIONS

We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

Resting-state functional MRI studies on infant brains: A decade of gap-filling efforts

Resting-state functional MRI (rs-fMRI) is one of the most prevalent brain functional imaging modalities. Previous rs-fMRI studies have mainly focused on adults and elderly subjects. Recently, infant rs-fMRI studies have become an area of active research. After a decade of gap filling studies, many facets of the brain functional development from early infancy to toddler has been uncovered. However, infant rs-fMRI is still in its infancy. The image analysis tools for neonates and young infants can be quite different from those for adults. From data analysis to result interpretation, more questions and issues have been raised, and new hypotheses have been formed. With the anticipated availability of unprecedented high-resolution rs-fMRI and dedicated analysis pipelines from the Baby Connectome Project (BCP), it is important now to revisit previous findings and hypotheses, discuss and comment existing issues and problems, and make a "to-do-list" for the future studies. This review article aims to comprehensively review a decade of the findings, unveiling hidden jewels of the fields of developmental neuroscience and neuroimage computing. Emphases will be given to early infancy, particularly the first few years of life. In this review, an end-to-end summary, from infant rs-fMRI experimental design to data processing, and from the development of individual functional systems to large-scale brain functional networks, is provided. A comprehensive summary of the rs-fMRI findings in developmental patterns is highlighted. Furthermore, an extensive summary of the neurodevelopmental disorders and the effects of other hazardous factors is provided. Finally, future research trends focusing on emerging dynamic functional connectivity and state-of-the-art functional connectome analysis are summarized. In next decade, early infant rs-fMRI and developmental connectome study could be one of the shining research topics.

Brain network segregation and integration during an epoch-related working memory fMRI experiment

The characterization of brain subnetwork segregation and integration has previously focused on changes that are detectable at the level of entire sessions or epochs of imaging data. In this study, we applied time-varying functional connectivity analysis together with temporal network theory to calculate point-by-point estimates in subnetwork segregation and integration during an epoch-based (2-back, 0-back, baseline) working memory fMRI experiment as well as during resting-state. This approach allowed us to follow task-related changes in subnetwork segregation and integration at a high temporal resolution. At a global level, the cognitively more taxing 2-back epochs elicited an overall stronger response of integration between subnetworks compared to the 0-back epochs. Moreover, the visual, sensorimotor and fronto-parietal subnetworks displayed characteristic and distinct temporal profiles of segregation and integration during the 0- and 2-back epochs. During the interspersed epochs of baseline, several subnetworks, including the visual, fronto-parietal, cingulo-opercular and dorsal attention subnetworks showed pronounced increases in segregation. Using a drift diffusion model we show that the response time for the 2-back trials are correlated with integration for the fronto-parietal subnetwork and correlated with segregation for the visual subnetwork. Our results elucidate the fast-evolving events with regard to subnetwork integration and segregation that occur in an epoch-related task fMRI experiment. Our findings suggest that minute changes in subnetwork integration are of importance for task performance.

Simulations to benchmark time-varying connectivity methods for fMRI

There is a current interest in quantifying time-varying connectivity (TVC) based on neuroimaging data such as fMRI. Many methods have been proposed, and are being applied, revealing new insight into the brain's dynamics. However, given that the ground truth for TVC in the brain is unknown, many concerns remain regarding the accuracy of proposed estimates. Since there exist many TVC methods it is difficult to assess differences in time-varying connectivity between studies. In this paper, we present tvc_benchmarker, which is a Python package containing four simulations to test TVC methods. Here, we evaluate five different methods that together represent a wide spectrum of current approaches to estimating TVC (sliding window, tapered sliding window, multiplication of temporal derivatives, spatial distance and jackknife correlation). These simulations were designed to test each method's ability to track changes in covariance over time, which is a key property in TVC analysis. We found that all tested methods correlated positively with each other, but there were large differences in the strength of the correlations between methods. To facilitate comparisons with future TVC methods, we propose that the described simulations can act as benchmark tests for evaluation of methods. Using tvc_benchmarker researchers can easily add, compare and submit their own TVC methods to evaluate its performance.

A common framework for the problem of deriving estimates of dynamic functional brain connectivity

The research field of dynamic functional connectivity explores the temporal properties of brain connectivity. To date, many methods have been proposed, which are based on quite different assumptions. In order to understand in which way the results from different techniques can be compared to each other, it is useful to be able to formulate them within a common theoretical framework. In this study, we describe such a framework that is suitable for many of the dynamic functional connectivity methods that have been proposed. Our overall intention was to derive a theoretical framework that was constructed such that a wide variety of dynamic functional connectivity techniques could be expressed and evaluated within the same framework. At the same time, care was given to the fact that key features of each technique could be easily illustrated within the framework and thus highlighting critical assumptions that are made. We aimed to create a common framework which should serve to assist comparisons between different analytical methods for dynamic functional brain connectivity and promote an understanding of their methodological advantages as well as potential drawbacks.

Hybrid High-order Functional Connectivity Networks Using Resting-state Functional MRI for Mild Cognitive Impairment Diagnosis

Conventional functional connectivity (FC), referred to as low-order FC, estimates temporal correlation of the resting-state functional magnetic resonance imaging (rs-fMRI) time series between any pair of brain regions, simply ignoring the potentially high-level relationship among these brain regions. A high-order FC based on “correlation’s correlation” has emerged as a new approach for abnormality detection of brain disease. However, separate construction of the low- and high-order FC networks overlooks information exchange between the two FC levels. Such a higher-level relationship could be more important for brain diseases study. In this paper, we propose a novel framework, namely “hybrid high-order FC networks” by exploiting the higher-level dynamic interaction among brain regions for early mild cognitive impairment (eMCI) diagnosis. For each sliding window-based rs-fMRI sub-series, we construct a whole-brain associated high-order network, by estimating the correlations between the topographical information of the high-order FC sub-network from one brain region and that of the low-order FC sub-network from another brain region. With multi-kernel learning, complementary features from multiple time-varying FC networks constructed at different levels are fused for eMCI classification. Compared with other state-of-the-art methods, the proposed framework achieves superior diagnosis accuracy, and hence could be promising for understanding pathological changes of brain connectome.

From static to temporal network theory: Applications to functional brain connectivity

Network neuroscience has become an established paradigm to tackle questions related to the functional and structural connectome of the brain. Recently, interest has been growing in examining the temporal dynamics of the brain's network activity. Although different approaches to capturing fluctuations in brain connectivity have been proposed, there have been few attempts to quantify these fluctuations using temporal network theory. This theory is an extension of network theory that has been successfully applied to the modeling of dynamic processes in economics, social sciences, and engineering article but it has not been adopted to a great extent within network neuroscience. The objective of this article is twofold: (i) to present a detailed description of the central tenets of temporal network theory and describe its measures, and; (ii) to apply these measures to a resting-state fMRI dataset to illustrate their utility. Furthermore, we discuss the interpretation of temporal network theory in the context of the dynamic functional brain connectome. All the temporal network measures and plotting functions described in this article are freely available as the Python package Teneto.

On Stabilizing the Variance of Dynamic Functional Brain Connectivity Time Series

Assessment of dynamic functional brain connectivity based on functional magnetic resonance imaging (fMRI) data is an increasingly popular strategy to investigate temporal dynamics of the brain's large-scale network architecture. Current practice when deriving connectivity estimates over time is to use the Fisher transformation, which aims to stabilize the variance of correlation values that fluctuate around varying true correlation values. It is, however, unclear how well the stabilization of signal variance performed by the Fisher transformation works for each connectivity time series, when the true correlation is assumed to be fluctuating. This is of importance because many subsequent analyses either assume or perform better when the time series have stable variance or adheres to an approximate Gaussian distribution. In this article, using simulations and analysis of resting-state fMRI data, we analyze the effect of applying different variance stabilization strategies on connectivity time series. We focus our investigation on the Fisher transformation, the Box-Cox (BC) transformation and an approach that combines both transformations. Our results show that, if the intention of stabilizing the variance is to use metrics on the time series, where stable variance or a Gaussian distribution is desired (e.g., clustering), the Fisher transformation is not optimal and may even skew connectivity time series away from being Gaussian. Furthermore, we show that the suboptimal performance of the Fisher transformation can be substantially improved by including an additional BC transformation after the dynamic functional connectivity time series has been Fisher transformed.