Improved state change estimation in dynamic functional connectivity using hidden semi-Markov models

NaDyNet: A toolbox for dynamic network analysis of naturalistic stimuli

Experiments with naturalistic stimuli (e.g., listening to stories or watching movies) are emerging paradigms in brain function research. The content of naturalistic stimuli is rich and continuous. The fMRI signals of naturalistic stimuli are complex and include different components. A major challenge is isolate the stimuli-induced signals while simultaneously tracking the brain's responses to these stimuli in real-time. To this end, we have developed a user-friendly graphical interface toolbox called NaDyNet (Naturalistic Dynamic Network Toolbox), which integrates existing dynamic brain network analysis methods and their improved versions. The main features of NaDyNet are: 1) extracting signals of interest from naturalistic fMRI signals; 2) incorporating six commonly used dynamic analysis methods and three static analysis methods; 3) improved versions of these dynamic methods by adopting inter-subject analysis to eliminate the effects of non-interest signals; 4) performing K-means clustering analysis to identify temporally reoccurring states along with their temporal and spatial attributes; 5) Visualization of spatiotemporal results. We then introduced the rationale for incorporating inter-subject analysis to improve existing dynamic brain network analysis methods and presented examples by analyzing naturalistic fMRI data. We hope that this toolbox will promote the development of naturalistic neuroscience. The toolbox is available at https://github.com/yuanbinke/Naturalistic-Dynamic-Network-Toolbox.

Time Persistence of the FMRI Resting-State Functional Brain Networks

Time persistence is a fundamental property of many complex physical and biological systems; thus understanding the phenomenon in the brain is of high importance. Time persistence has been explored at the level of stand-alone neural time-series, but since the brain functions as an interconnected network, it is essential to examine time persistence at the network level. Changes in resting-state networks have been previously investigated using both dynamic (i.e., examining connectivity states) and static functional connectivity (i.e., test-retest reliability), but no systematic investigation of the time persistence as a network was conducted, particularly across different timescales (i.e., seconds, minutes, dozens of seconds, days) and different brain subnetworks. Additionally, individual differences in network time persistence have not been explored. Here, we devised a new framework to estimate network time persistence at both the link (i.e., connection) and node levels. In a comprehensive series analysis of three functional MRI resting-state datasets including both sexes, we established that (1) the resting-state functional brain network becomes gradually less similar to itself for the gaps up to 23 min within the run and even less similar for the gap between the days; (2) network time persistence varies across functional networks, while the sensory networks are more persistent than nonsensory networks; (3) participants show stable individual characteristic persistence, which has a genetic component; and (4) individual characteristic persistence could be linked to behavioral performance. Overall, our detailed characterization of network time persistence sheds light on the potential role of time persistence in brain functioning and cognition.

Contrasting topologies of synchronous and asynchronous functional brain networks

We generated asynchronous functional networks (aFNs) using a novel method called optimal causation entropy and compared aFN topology with the correlation-based synchronous functional networks (sFNs), which are commonly used in network neuroscience studies. Functional magnetic resonance imaging (fMRI) time series from 212 participants of the National Consortium on Alcohol and Neurodevelopment in Adolescence study were used to generate aFNs and sFNs. As a demonstration of how aFNs and sFNs can be used in tandem, we used multivariate mixed effects models to determine whether age interacted with node efficiency to influence connection probabilities in the two networks. After adjusting for differences in network density, aFNs had higher global efficiency but lower local efficiency than the sFNs. In the aFNs, nodes with the highest outgoing global efficiency tended to be in the brainstem and orbitofrontal cortex. aFN nodes with the highest incoming global efficiency tended to be members of the default mode network in sFNs. Age interacted with node global efficiency in aFNs and node local efficiency in sFNs to influence connection probability. We conclude that the sFN and aFN both offer information about functional brain connectivity that the other type of network does not.

A novel method for sparse dynamic functional connectivity analysis from resting-state fMRI

BACKGROUND

There is growing interest in understanding the dynamic functional connectivity (DFC) between distributed brain regions. However, it remains challenging to reliably estimate the temporal dynamics from resting-state functional magnetic resonance imaging (rs-fMRI) due to the limitations of current methods.

NEW METHODS

We propose a new model called HDP-HSMM-BPCA for sparse DFC analysis of high-dimensional rs-fMRI data, which is a temporal extension of probabilistic principal component analysis using Bayesian nonparametric hidden semi-Markov model (HSMM). Specifically, we utilize a hierarchical Dirichlet process (HDP) prior to remove the parametric assumption of the HMM framework, overcoming the limitations of the standard HMM. An attractive superiority is its ability to automatically infer the state-specific latent space dimensionality within the Bayesian formulation.

RESULTS

The experiment results of synthetic data show that our model outperforms the competitive models with relatively higher estimation accuracy. In addition, the proposed framework is applied to real rs-fMRI data to explore sparse DFC patterns. The findings indicate that there is a time-varying underlying structure and sparse DFC patterns in high-dimensional rs-fMRI data.

COMPARISON WITH EXISTING METHODS

Compared with the existing DFC approaches based on HMM, our method overcomes the limitations of standard HMM. The observation model of HDP-HSMM-BPCA can discover the underlying temporal structure of rs-fMRI data. Furthermore, the relevant sparse DFC construction algorithm provides a scheme for estimating sparse DFC.

CONCLUSION

We describe a new computational framework for sparse DFC analysis to discover the underlying temporal structure of rs-fMRI data, which will facilitate the study of brain functional connectivity.

NHSMM-MAR-sdNC: A novel data-driven computational framework for state-dependent effective connectivity analysis

The brain exhibits intrinsic dynamics characterized by spontaneous spatiotemporal reorganization of neural activity or metastability, which is associated closely with functional integration and segregation. Compared to dynamic functional connectivity, state-dependent effective connectivity (i.e., dynamic effective connectivity) is more suitable for exploring the metastability as its ability to infer causalities between brain regions. However, methods for state-dependent effective connectivity are scarce and urgently needed. In this study, a novel data-driven computational framework, named NHSMM-MAR-sdNC integrating nonparametric hidden semi-Markov model combined with multivariate autoregressive model and state-dependent new causality, is proposed to investigate the state-dependent effective connectivity. The framework is not constrained by any biological assumptions. Furthermore, state number can be inferred from the observed data directly and the state duration distributions will be estimated explicitly rather than restricted by geometric form, which overcomes limitations of hidden Markov model. Experimental results of synthetic data show that the framework can identify the state number adaptively and the state-dependent causality networks accurately. The dynamics of state-related causality networks are also revealed by the new method on real-world resting-state fMRI data. Our method provides a new data-driven computational framework for identifying state-dependent effective connectivity, which will facilitate the identification and assessment of metastability and itinerant dynamics of the brain.

A survey of brain functional network extraction methods using fMRI data

Functional network (FN) analyses play a pivotal role in uncovering insights into brain function and understanding the pathophysiology of various brain disorders. This paper focuses on classical and advanced methods for deriving brain FNs from functional magnetic resonance imaging (fMRI) data. We systematically review their foundational principles, advantages, shortcomings, and interrelations, encompassing both static and dynamic FN extraction approaches. In the context of static FN extraction, we present hypothesis-driven methods such as region of interest (ROI)-based approaches as well as data-driven methods including matrix decomposition, clustering, and deep learning. For dynamic FN extraction, both window-based and windowless methods are surveyed with respect to the estimation of time-varying FN and the subsequent computation of FN states. We also discuss the scope of application of the various methods and avenues for future improvements.

Contrasting topologies of synchronous and asynchronous functional brain networks

We generated asynchronous functional networks (aFNs) using a novel method called optimal causation entropy (oCSE) and compared aFN topology to the correlation-based synchronous functional networks (sFNs) which are commonly used in network neuroscience studies. Functional magnetic resonance imaging (fMRI) time series from 212 participants of the National Consortium on Alcohol and NeuroDevelopment in Adolescence (NCANDA) study were used to generate aFNs and sFNs. As a demonstration of how aFNs and sFNs can be used in tandem, we used multivariate mixed effects models to determine whether age interacted with node efficiency to influence connection probabilities in the two networks. After adjusting for differences in network density, aFNs had higher global efficiency but lower local efficiency than the sFNs. In the aFNs, nodes with the highest outgoing global efficiency tended to be in the brainstem and orbitofrontal cortex. aFN nodes with the highest incoming global efficiency tended to be members of the Default Mode Network (DMN) in sFNs. Age interacted with node global efficiency in aFNs and node local efficiency in sFNs to influence connection probability. We conclude that the sFN and aFN both offer information about functional brain connectivity which the other type of network does not.

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

Data-driven MEG analysis to extract fMRI resting-state networks

The electrophysiological basis of resting-state networks (RSN) is still under debate. In particular, no principled mechanism has been determined that is capable of explaining all RSN equally well. While magnetoencephalography (MEG) and electroencephalography are the methods of choice to determine the electrophysiological basis of RSN, no standard analysis pipeline of RSN yet exists. In this article, we compare the two main existing data-driven analysis strategies for extracting RSNs from MEG data and introduce a third approach. The first approach uses phase-amplitude coupling to determine the RSN. The second approach extracts RSN through an independent component analysis of the Hilbert envelope in different frequency bands, while the third new approach uses a singular value decomposition instead. To evaluate these approaches, we compare the MEG-RSN to the functional magnetic resonance imaging (fMRI)-RSN from the same subjects. Overall, it was possible to extract RSN with MEG using all three techniques, which matched the group-specific fMRI-RSN. Interestingly the new approach based on SVD yielded significantly higher correspondence to five out of seven fMRI-RSN than the two existing approaches. Importantly, with this approach, all networks-except for the visual network-had the highest correspondence to the fMRI networks within one frequency band. Thereby we provide further insights into the electrophysiological underpinnings of the fMRI-RSNs. This knowledge will be important for the analysis of the electrophysiological connectome.

Functional brain connectivity predicts sleep duration in youth and adults

Sleep is critical to a variety of cognitive functions and insufficient sleep can have negative consequences for mood and behavior across the lifespan. An important open question is how sleep duration is related to functional brain organization which may in turn impact cognition. To characterize the functional brain networks related to sleep across youth and young adulthood, we analyzed data from the publicly available Human Connectome Project (HCP) dataset, which includes n-back task-based and resting-state fMRI data from adults aged 22-35 years (task n = 896; rest n = 898). We applied connectome-based predictive modeling (CPM) to predict participants' mean sleep duration from their functional connectivity patterns. Models trained and tested using 10-fold cross-validation predicted self-reported average sleep duration for the past month from n-back task and resting-state connectivity patterns. We replicated this finding in data from the 2-year follow-up study session of the Adolescent Brain Cognitive Development (ABCD) Study, which also includes n-back task and resting-state fMRI for adolescents aged 11-12 years (task n = 786; rest n = 1274) as well as Fitbit data reflecting average sleep duration per night over an average duration of 23.97 days. CPMs trained and tested with 10-fold cross-validation again predicted sleep duration from n-back task and resting-state functional connectivity patterns. Furthermore, demonstrating that predictive models are robust across independent datasets, CPMs trained on rest data from the HCP sample successfully generalized to predict sleep duration in the ABCD Study sample and vice versa. Thus, common resting-state functional brain connectivity patterns reflect sleep duration in youth and young adults.

Statistical Brain Network Analysis

The recent fusion of network science and neuroscience has catalyzed a paradigm shift in how we study the brain and led to the field of brain network analysis. Brain network analyses hold great potential in helping us understand normal and abnormal brain function by providing profound clinical insight into links between system-level properties and health and behavioral outcomes. Nonetheless, methods for statistically analyzing networks at the group and individual levels have lagged behind. We have attempted to address this need by developing three complementary statistical frameworks-a mixed modeling framework, a distance regression framework, and a hidden semi-Markov modeling framework. These tools serve as synergistic fusions of statistical approaches with network science methods, providing needed analytic foundations for whole-brain network data. Here we delineate these approaches, briefly survey related tools, and discuss potential future avenues of research. We hope this review catalyzes further statistical interest and methodological development in the field.

Locus coeruleus integrity predicts ease of attaining and maintaining neural states of high attentiveness

The locus coeruleus (LC), a small subcortical structure in the brainstem, is the brain's principal source of norepinephrine. It plays a primary role in regulating stress, the sleep-wake cycle, and attention, and its degradation is associated with aging and neurodegenerative diseases associated with cognitive deficits (e.g., Parkinson's, Alzheimer's). Yet precisely how norepinephrine drives brain networks to support healthy cognitive function remains poorly understood - partly because LC's small size makes it difficult to study noninvasively in humans. Here, we characterized LC's influence on brain dynamics using a hidden Markov model fitted to functional neuroimaging data from healthy young adults across four attention-related brain networks and LC. We modulated LC activity using a behavioral paradigm and measured individual differences in LC magnetization transfer contrast. The model revealed five hidden states, including a stable state dominated by salience-network activity that occurred when subjects actively engaged with the task. LC magnetization transfer contrast correlated with this state's stability across experimental manipulations and with subjects' propensity to enter into and remain in this state. These results provide new insight into LC's role in driving spatiotemporal neural patterns associated with attention, and demonstrate that variation in LC integrity can explain individual differences in these patterns even in healthy young adults.

Brain effective connectome based on fMRI and DTI data: Bayesian causal learning and assessment

Neuroscientific studies aim to find an accurate and reliable brain Effective Connectome (EC). Although current EC discovery methods have contributed to our understanding of brain organization, their performances are severely constrained by the short sample size and poor temporal resolution of fMRI data, and high dimensionality of the brain connectome. By leveraging the DTI data as prior knowledge, we introduce two Bayesian causal discovery frameworks -the Bayesian GOLEM (BGOLEM) and Bayesian FGES (BFGES) methods- that offer significantly more accurate and reliable ECs and address the shortcomings of the existing causal discovery methods in discovering ECs based on only fMRI data. Moreover, to numerically assess the improvement in the accuracy of ECs with our method on empirical data, we introduce the Pseudo False Discovery Rate (PFDR) as a new computational accuracy metric for causal discovery in the brain. Through a series of simulation studies on synthetic and hybrid data (combining DTI from the Human Connectome Project (HCP) subjects and synthetic fMRI), we demonstrate the effectiveness of our proposed methods and the reliability of the introduced metric in discovering ECs. By employing the PFDR metric, we show that our Bayesian methods lead to significantly more accurate results compared to the traditional methods when applied to the Human Connectome Project (HCP) data. Additionally, we measure the reproducibility of discovered ECs using the Rogers-Tanimoto index for test-retest data and show that our Bayesian methods provide significantly more reliable ECs than traditional methods. Overall, our study's numerical and visual results highlight the potential for these frameworks to significantly advance our understanding of brain functionality.

Dissecting unsupervised learning through hidden Markov modeling in electrophysiological data

Unsupervised, data-driven methods are commonly used in neuroscience to automatically decompose data into interpretable patterns. These patterns differ from one another depending on the assumptions of the models. How these assumptions affect specific data decompositions in practice, however, is often unclear, which hinders model applicability and interpretability. For instance, the hidden Markov model (HMM) automatically detects characteristic, recurring activity patterns (so-called states) from time series data. States are defined by a certain probability distribution, whose state-specific parameters are estimated from the data. But what specific features, from all of those that the data contain, do the states capture? That depends on the choice of probability distribution and on other model hyperparameters. Using both synthetic and real data, we aim to better characterize the behavior of two HMM types that can be applied to electrophysiological data. Specifically, we study which differences in data features (such as frequency, amplitude, or signal-to-noise ratio) are more salient to the models and therefore more likely to drive the state decomposition. Overall, we aim at providing guidance for the appropriate use of this type of analysis on one- or two-channel neural electrophysiological data and an informed interpretation of its results given the characteristics of the data and the purpose of the analysis.NEW & NOTEWORTHY Compared with classical supervised methods, unsupervised methods of analysis have the advantage to be freer of subjective biases. However, it is not always clear what aspects of the data these methods are most sensitive to, which complicates interpretation. Focusing on the hidden Markov model, commonly used to describe electrophysiological data, we explore in detail the nature of its estimates through simulations and real data examples, providing important insights about what to expect from these models.

Smooth online parameter estimation for time varying VAR models with application to rat local field potential activity data

Multivariate time series data appear often as realizations of non-stationary processes where the covariance matrix or spectral matrix smoothly evolve over time. Most of the current approaches estimate the time-varying spectral properties only retrospectively - that is, after the entire data has been observed. Retrospective estimation is a major limitation in many adaptive control applications where it is important to estimate these properties and detect changes in the system as they happen in real-time. To overcome this limitation, we develop an online estimation procedure that gives a real-time update of the time-varying parameters as new observations arrive. One approach to modeling non-stationary time series is to fit time-varying vector autoregressive models (tv-VAR). However, one major obstacle in online estimation of such models is the computational cost due to the high-dimensionality of the parameters. Existing methods such as the Kalman filter or local least squares are feasible. However, they are not always suitable because they provide noisy estimates and can become prohibitively costly as the dimension of the time series increases. In our brain signal application, it is critical to develop a robust method that can estimate, in real-time, the properties of the underlying stochastic process, in particular, the spectral brain connectivity measures. For these reasons we propose a new smooth online parameter estimation approach (SOPE) that has the ability to control for the smoothness of the estimates with a reasonable computational complexity. Consequently, the models are fit in real-time even for high dimensional time series. We demonstrate that our proposed SOPE approach is as good as the Kalman filter in terms of mean-squared error for small dimensions. However, unlike the Kalman filter, the SOPE has lower computational cost and hence scalable for higher dimensions. Finally, we apply the SOPE method to local field potential activity data from the hippocampus of a rat performing an odor sequence memory task. As demonstrated in the video, the proposed SOPE method is able to capture the dynamics of the connectivity as the rat samples the different odor stimuli.

TOPOLOGICAL LEARNING FOR BRAIN NETWORKS

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.

Revealing human sensitivity to a latent temporal structure of changes

Precisely timed behavior and accurate time perception plays a critical role in our everyday lives, as our wellbeing and even survival can depend on well-timed decisions. Although the temporal structure of the world around us is essential for human decision making, we know surprisingly little about how representation of temporal structure of our everyday environment impacts decision making. How does the representation of temporal structure affect our ability to generate well-timed decisions? Here we address this question by using a well-established dynamic probabilistic learning task. Using computational modeling, we found that human subjects' beliefs about temporal structure are reflected in their choices to either exploit their current knowledge or to explore novel options. The model-based analysis illustrates a large within-group and within-subject heterogeneity. To explain these results, we propose a normative model for how temporal structure is used in decision making, based on the semi-Markov formalism in the active inference framework. We discuss potential key applications of the presented approach to the fields of cognitive phenotyping and computational psychiatry.

Learning Brain Dynamics of Evolving Manifold Functional MRI Data Using Geometric-Attention Neural Network

Functional connectivities (FC) of brain network manifest remarkable geometric patterns, which is the gateway to understanding brain dynamics. In this work, we present a novel geometric-attention neural network to characterize the time-evolving brain state change from the functional neuroimages by tracking the trajectory of functional dynamics on high-dimension Riemannian manifold of symmetric positive definite (SPD) matrices. Specifically, we put the spotlight on learning the common state-specific manifold signatures that represent the underlying cognition. In this context, the driving force of our neural network is tied up with the learning of the evolution functionals on the Riemannian manifold of SPD matrix that underlies the known evolving brain states. To do so, we train a convolution neural network (CNN) on the Riemannian manifold of SPD matrices to seek for the putative low-dimension feature representations, followed by an end-to-end recurrent neural network (RNN) to yield the time-varying mapping function of SPD matrices which fits the evolutionary trajectories of the underlying states. Furthermore, we devise a geometric attention mechanism in CNN, allowing us to discover the latent geometric patterns in SPD matrices that are associated with the underlying states. Notably, our work has the potential to understand how brain function emerges behavior by investigating the geometrical patterns from functional brain networks, which is essentially a correlation matrix of neuronal activity signals. Our proposed manifold-based neural network achieves promising results in predicting brain state changes on both simulated data and task functional neuroimaging data from Human Connectome Project, which implies great applicability in neuroscience studies.

Complexity changes in functional state dynamics suggest focal connectivity reductions

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013; Adhikari et al., 2017; Li et al., 2018). However, many of these studies have not accounted for the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivity via a Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations.

Inferring Brain State Dynamics Underlying Naturalistic Stimuli Evoked Emotion Changes With dHA-HMM

The brain functional mechanisms underlying emotional changes have been primarily studied based on the traditional task design with discrete and simple stimuli. However, the brain state transitions when exposed to continuous and naturalistic stimuli with rich affection variations remain poorly understood. This study proposes a dynamic hyperalignment algorithm (dHA) to functionally align the inter-subject neural activity. The hidden Markov model (HMM) was used to study how the brain dynamics responds to emotion during long-time movie-viewing activity. The results showed that dHA significantly improved inter-subject consistency and allowed more consistent temporal HMM states across participants. Afterward, grouping the emotions in a clustering dendrogram revealed a hierarchical grouping of the HMM states. Further emotional sensitivity and specificity analyses of ordered states revealed the most significant differences in happiness and sadness. We then compared the activation map in HMM states during happiness and sadness and found significant differences in the whole brain, but strong activation was observed during both in the superior temporal gyrus, which is related to the early process of emotional prosody processing. A comparison of the inter-network functional connections indicates unique functional connections of the memory retrieval and cognitive network with the cerebellum network during happiness. Moreover, the persistent bilateral connections among salience, cognitive, and sensorimotor networks during sadness may reflect the interaction between high-level cognitive networks and low-level sensory networks. The main results were verified by the second session of the dataset. All these findings enrich our understanding of the brain states related to emotional variation during naturalistic stimuli.

Uncovering hidden resting state dynamics: A new perspective on auditory verbal hallucinations

In the absence of sensory stimulation, the brain transits between distinct functional networks. Network dynamics such as transition patterns and the time the brain stays in each network link to cognition and behavior and are subject to much investigation. Auditory verbal hallucinations (AVH), the temporally fluctuating unprovoked experience of hearing voices, are associated with aberrant resting state network activity. However, we lack a clear understanding of how different networks contribute to aberrant activity over time. An accurate characterization of latent network dynamics and their relation to neurocognitive changes necessitates methods that capture the sub-second temporal fluctuations of the networks' functional connectivity signatures. Here, we critically evaluate the assumptions and sensitivity of several approaches commonly used to assess temporal dynamics of brain connectivity states in M/EEG and fMRI research, highlighting methodological constraints and their clinical relevance to AVH. Identifying altered brain connectivity states linked to AVH can facilitate the detection of predictive disease markers and ultimately be valuable for generating individual risk profiles, differential diagnosis, targeted intervention, and treatment strategies.

Data and model considerations for estimating time-varying functional connectivity in fMRI

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Time-varying FC models sometimes fail to detect temporal changes in fMRI data.

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Between-subject and within-session FC variability affect model stasis.

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The choice of parcellation affects model stasis in real fMRI data.

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The number of observations and free parameters per state critically affect model stasis.

Functional connectivity (FC) in the brain has been shown to exhibit subtle but reliable modulations within a session. One way of estimating time-varying FC is by using state-based models that describe fMRI time series as temporal sequences of states, each with an associated, characteristic pattern of FC. However, the estimation of these models from data sometimes fails to capture changes in a meaningful way, such that the model estimation assigns entire sessions (or the largest part of them) to a single state, therefore failing to capture within-session state modulations effectively; we refer to this phenomenon as the model becoming static, or model stasis. Here, we aim to quantify how the nature of the data and the choice of model parameters affect the model's ability to detect temporal changes in FC using both simulated fMRI time courses and resting state fMRI data. We show that large between-subject FC differences can overwhelm subtler within-session modulations, causing the model to become static. Further, the choice of parcellation can also affect the model's ability to detect temporal changes. We finally show that the model often becomes static when the number of free parameters per state that need to be estimated is high and the number of observations available for this estimation is low in comparison. Based on these findings, we derive a set of practical recommendations for time-varying FC studies, in terms of preprocessing, parcellation and complexity of the model.

A mixed-modeling framework for whole-brain dynamic network analysis

The emerging area of dynamic brain network analysis has gained considerable attention in recent years. However, development of multivariate statistical frameworks that allow for examining the associations between phenotypic traits and dynamic patterns of system-level properties of the brain, and drawing statistical inference about such associations, has largely lagged behind. To address this need we developed a mixed-modeling framework that allows for assessing the relationship between any desired phenotype and dynamic patterns of whole-brain connectivity and topology. This novel framework also allows for simulating dynamic brain networks with respect to desired covariates. Unlike current tools, which largely use data-driven methods, our model-based method enables aligning neuroscientific hypotheses with the analytic approach. We demonstrate the utility of this model in identifying the relationship between fluid intelligence and dynamic brain networks by using resting-state fMRI (rfMRI) data from 200 participants in the Human Connectome Project (HCP) study. We also demonstrate the utility of this model to simulate dynamic brain networks at both group and individual levels. To our knowledge, this approach provides the first model-based statistical method for examining dynamic patterns of system-level properties of the brain and their relationships to phenotypic traits as well as simulating dynamic brain networks.

In recent years, a growing body of studies have aimed at analyzing the brain as a complex dynamic system by using various neuroimaging data. This has opened new avenues to answer compelling questions about the brain function in health and disease. However, methods that allow for providing statistical inference about how the complex interactions of the brain are associated with desired phenotypes are to be developed for a more profound insight. This study introduces a promising regression-based model to relate dynamic brain networks to desired phenotypes and provide statistical inference. Moreover, it can be used for simulating dynamic brain networks with respect to desired phenotypes at the group and individual levels.

High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns

Our thoughts arise from coordinated patterns of interactions between brain structures that change with our ongoing experiences. High-order dynamic correlations in neural activity patterns reflect different subgraphs of the brain's functional connectome that display homologous lower-level dynamic correlations. Here we test the hypothesis that high-level cognition is reflected in high-order dynamic correlations in brain activity patterns. We develop an approach to estimating high-order dynamic correlations in timeseries data, and we apply the approach to neuroimaging data collected as human participants either listen to a ten-minute story or listen to a temporally scrambled version of the story. We train across-participant pattern classifiers to decode (in held-out data) when in the session each neural activity snapshot was collected. We find that classifiers trained to decode from high-order dynamic correlations yield the best performance on data collected as participants listened to the (unscrambled) story. By contrast, classifiers trained to decode data from scrambled versions of the story yielded the best performance when they were trained using first-order dynamic correlations or non-correlational activity patterns. We suggest that as our thoughts become more complex, they are reflected in higher-order patterns of dynamic network interactions throughout the brain.

Beyond fingerprinting: Choosing predictive connectomes over reliable connectomes

Recent years have seen a surge of research on variability in functional brain connectivity within and between individuals, with encouraging progress toward understanding the consequences of this variability for cognition and behavior. At the same time, well-founded concerns over rigor and reproducibility in psychology and neuroscience have led many to question whether functional connectivity is sufficiently reliable, and call for methods to improve its reliability. The thesis of this opinion piece is that when studying variability in functional connectivity-both across individuals and within individuals over time-we should use behavior prediction as our benchmark rather than optimize reliability for its own sake. We discuss theoretical and empirical evidence to compel this perspective, both when the goal is to study stable, trait-level differences between people, as well as when the goal is to study state-related changes within individuals. We hope that this piece will be useful to the neuroimaging community as we continue efforts to characterize inter- and intra-subject variability in brain function and build predictive models with an eye toward eventual real-world applications.

Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning

This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.

When the time is right: Temporal dynamics of brain activity in healthy aging and dementia

Brain activity and communications are complex phenomena that dynamically unfold over time. However, in contrast with the large number of studies reporting neuroanatomical differences in activation relative to young adults, changes of temporal dynamics of neural activity during normal and pathological aging have been grossly understudied and are still poorly known. Here, we synthesize the current state of knowledge from MEG and EEG studies that aimed at specifying the effects of healthy and pathological aging on local and network dynamics, and discuss the clinical and theoretical implications of these findings. We argue that considering the temporal dynamics of brain activations and networks could provide a better understanding of changes associated with healthy aging, and the progression of neurodegenerative disease. Recent research has also begun to shed light on the association of these dynamics with other imaging modalities and with individual differences in cognitive performance. These insights hold great potential for driving new theoretical frameworks and development of biomarkers to aid in identifying and treating age-related cognitive changes.

Behavioural relevance of spontaneous, transient brain network interactions in fMRI

How spontaneously fluctuating functional magnetic resonance imaging (fMRI) signals in different brain regions relate to behaviour has been an open question for decades. Correlations in these signals, known as functional connectivity, can be averaged over several minutes of data to provide a stable representation of the functional network architecture for an individual. However, associations between these stable features and behavioural traits have been shown to be dominated by individual differences in anatomy. Here, using kernel learning tools, we propose methods to assess and compare the relation between time-varying functional connectivity, time-averaged functional connectivity, structural brain data, and non-imaging subject behavioural traits. We applied these methods to Human Connectome Project resting-state fMRI data to show that time-varying fMRI functional connectivity, detected at time-scales of a few seconds, has associations with some behavioural traits that are not dominated by anatomy. Despite time-averaged functional connectivity accounting for the largest proportion of variability in the fMRI signal between individuals, we found that some aspects of intelligence could only be explained by time-varying functional connectivity. The finding that time-varying fMRI functional connectivity has a unique relationship to population behavioural variability suggests that it might reflect transient neuronal communication fluctuating around a stable neural architecture.

Children with attention-deficit/hyperactivity disorder spend more time in hyperconnected network states and less time in segregated network states as revealed by dynamic connectivity analysis

Previous studies in children with attention-deficit/hyperactivity disorder (ADHD) have observed functional brain network disruption on a whole-brain level, as well as on a sub-network level, particularly as related to the default mode network, attention-related networks, and cognitive control-related networks. Given behavioral findings that children with ADHD have more difficulty sustaining attention and more extreme moment-to-moment fluctuations in behavior than typically developing (TD) children, recently developed methods to assess changes in connectivity over shorter time periods (i.e., "dynamic functional connectivity"), may provide unique insight into dysfunctional network organization in ADHD. Thus, we performed a dynamic functional connectivity (FC) analysis on resting state fMRI data from 38 children with ADHD and 79 TD children. We used Hidden semi-Markov models (HSMMs) to estimate six network states, as well as the most probable sequence of states for each participant. We quantified the dwell time, sojourn time, and transition probabilities across states. We found that children with ADHD spent less total time in, and switched more quickly out of, anticorrelated states involving the default mode network and task-relevant networks as compared to TD children. Moreover, children with ADHD spent more time in a hyperconnected state as compared to TD children. These results provide novel evidence that underlying dynamics may drive the differences in static FC patterns that have been observed in ADHD and imply that disrupted FC dynamics may be a mechanism underlying the behavioral symptoms and cognitive deficits commonly observed in children with ADHD.

Evaluating phase synchronization methods in fMRI: A comparison study and new approaches

In recent years there has been growing interest in measuring time-varying functional connectivity between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. There are several ways to perform such analyses, and we compare methods that utilize a PS metric together with a sliding window, referred to here as windowed phase synchronization (WPS), with those that directly measure the instantaneous phase synchronization (IPS). In particular, IPS has recently gained popularity as it offers single time-point resolution of time-resolved fMRI connectivity. In this paper, we discuss the underlying assumptions required for performing PS analyses and emphasize the importance of band-pass filtering the data to obtain valid results. Further, we contrast this approach with the use of Empirical Mode Decomposition (EMD) to achieve similar goals. We review various methods for evaluating PS and introduce a new approach within the IPS framework denoted the cosine of the relative phase (CRP). We contrast methods through a series of simulations and application to rs-fMRI data. Our results indicate that CRP outperforms other tested methods and overcomes issues related to undetected temporal transitions from positive to negative associations common in IPS analysis. Further, in contrast to phase coherence, CRP unfolds the distribution of PS measures, which benefits subsequent clustering of PS matrices into recurring brain states.

A unified approach for characterizing static/dynamic connectivity frequency profiles using filter banks

Static and dynamic functional network connectivity (FNC) are typically studied separately, which makes us unable to see the full spectrum of connectivity in each analysis. Here, we propose an approach called filter-banked connectivity (FBC) to estimate connectivity while preserving its full frequency range and subsequently examine both static and dynamic connectivity in one unified approach. First, we demonstrate that FBC can estimate connectivity across multiple frequencies missed by a sliding-window approach. Next, we use FBC to estimate FNC in a resting-state fMRI dataset including schizophrenia patients (SZ) and typical controls (TC). The FBC results are clustered into different network states. Some states showed weak low-frequency strength and as such were not captured in the window-based approach. Additionally, we found that SZs tend to spend more time in states exhibiting higher frequencies compared with TCs who spent more time in lower frequency states. Finally, we show that FBC enables us to analyze static and dynamic connectivity in a unified way. In summary, FBC offers a novel way to unify static and dynamic connectivity analyses and can provide additional information about the frequency profile of connectivity patterns.

Modified models and simulations for estimating dynamic functional connectivity in resting state functional magnetic resonance imaging

As understanding the nature of brain networks through dynamic functional connectivity (dFC) estimation is of paramount significant, the introduction and revision of blood-oxygen-level dependent (BOLD) signal simulation methods in brain regions and dFC estimation methods have gained significant ground in recent years. Based on the observation of BOLD signals with multivariate nonnormal distribution in functional magnetic resonance imaging (fMRI) images, we first propose a copula-based method for the production of these signals, in which nonnormal data are generated with a selected time-varying covariance matrix. Therefore, we can compare the performance of models in the cases where brain signals have a multivariate nonnormal distribution. Then, two kendallized exponentially weighted moving average (KEWMA) and kendallized dynamic conditional correlation (KDCC) multivariate volatility models are introduced which are based on two well-known and commonly used exponentially weighted moving average (EMWA) and dynamic conditional correlation (DCC) models. The results show that KDCC model can estimate conditional correlation significantly far better than the former ones (ie, DCC, standardized dynamic conditional correlation, EWMA, and standardized exponentially weighted moving average) on both types of data (ie, multivariate normal and nonnormal). In the next step, the bivariate normal distribution in Iranian resting state fMRI data is confirmed by using statistical tests, and it is shown that the dynamic nature of FC is not optimally detected using prevalent methods. Two alternative Portmanteau and rank-based tests are proposed for the examination of conditional heteroscedasticity in data. Finally, dFC in these data is estimated by employing the KDCC model.

Spatiotemporal analysis of event-related fMRI to reveal cognitive states

Cognitive science has a rich history of developing theories of processing that characterize the mental steps involved in performance of many tasks. Recent work in neuroimaging and machine learning has greatly improved our ability to link cognitive processes with what is happening in the brain. This article analyzes a hidden semi-Markov model-multivoxel pattern-analysis (HSMM-MVPA) methodology that we have developed for inferring the sequence of brain states one traverses in the performance of a cognitive task. The method is applied to a functional magnetic resonance imaging (fMRI) experiment where task boundaries are known that should separate states. The method is able to accurately identify those boundaries. Then, applying the method to synthetic data, we explore more fully those factors that influence performance of the method: signal-to-noise ratio, numbers of states, state sojourn times, and numbers of underlying experimental conditions. The results indicate the types of experimental tasks where applications of the HSMM-MVPA method are likely to yield accurate and insightful results.

Functional connectivity predicts changes in attention observed across minutes, days, and months

The ability to sustain attention differs across people and changes within a single person over time. Although recent work has demonstrated that patterns of functional brain connectivity predict individual differences in sustained attention, whether these same patterns capture fluctuations in attention within individuals remains unclear. Here, across five independent studies, we demonstrate that the sustained attention connectome-based predictive model (CPM), a validated model of sustained attention function, generalizes to predict attentional state from data collected across minutes, days, weeks, and months. Furthermore, the sustained attention CPM is sensitive to within-subject state changes induced by propofol as well as sevoflurane, such that individuals show functional connectivity signatures of stronger attentional states when awake than when under deep sedation and light anesthesia. Together, these results demonstrate that fluctuations in attentional state reflect variability in the same functional connectivity patterns that predict individual differences in sustained attention.

Questions and controversies in the study of time-varying functional connectivity in resting fMRI

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

Investigating the impact of autocorrelation on time-varying connectivity

In recent years, a number of studies have reported on the existence of time-varying functional connectivity (TVC) in resting-state functional magnetic resonance imaging (rs-fMRI) data. The sliding-window technique is currently one of the most commonly used methods to estimate TVC. Although previous studies have shown that autocorrelation can negatively impact estimates of static functional connectivity, its impact on TVC estimates is not well known at this time. In this paper, we show both theoretically and empirically that the existence of autocorrelation within a time series can inflate the sampling variability of TVC estimated using the sliding-window technique. This can in turn increase the risk of misinterpreting noise as true TVC and negatively impact subsequent estimation of whole-brain time-varying FC profiles, or "brain states". The latter holds as more variable input measures lead to more variable output measures in the state estimation procedure. Finally, we demonstrate that prewhitening the data prior to analysis can lower the variance of the estimated TVC and improve brain state estimation. These results suggest that careful consideration is required when making inferences on TVC.

Altered transient brain dynamics in multiple sclerosis: Treatment or pathology?

Multiple sclerosis (MS) is a demyelinating, neuroinflammatory, and -degenerative disease that affects the brain's neurophysiological functioning through brain atrophy, a reduced conduction velocity and decreased connectivity. Currently, little is known on how MS affects the fast temporal dynamics of activation and deactivation of the different large-scale, ongoing brain networks. In this study, we investigated whether these temporal dynamics are affected in MS patients and whether these changes are induced by the pathology or by the use of benzodiazepines (BZDs), an important symptomatic treatment that aims at reducing insomnia, spasticity and anxiety and reinforces the inhibitory effect of GABA. To this aim, we employed a novel method capable of detecting these fast dynamics in 90 MS patients and 46 healthy controls. We demonstrated a less dynamic frontal default mode network in male MS patients and a reduced activation of the same network in female MS patients, regardless of BZD usage. Additionally, BZDs strongly altered the brain's dynamics by increasing the time spent in the deactivating sensorimotor network and the activating occipital network. Furthermore, BZDs induced a decreased power in the theta band and an increased power in the beta band. The latter was strongly expressed in those states without activation of the sensorimotor network. In summary, we demonstrate gender-dependent changes to the brain dynamics in the frontal DMN and strong effects from BZDs. This study is the first to characterise the effect of multiple sclerosis and BZDs in vivo in a spatially, temporally and spectrally defined way.