Interpreting null models of resting-state functional MRI dynamics: not throwing the model out with the hypothesis

Mapping Dynamic Metabolic Energy Distribution in Brain Networks using fMRI: A Novel Dynamic Time Warping Framework

Understanding how metabolic energy is distributed across brain networks is essential for elucidating healthy brain function and neurological disorders. Research has established the link between blood flow changes and glucose metabolic processes that fuel neural activity. Here, we introduce a novel framework based on the normalized dynamic time warping algorithm robust to neural temporal variability, enabling reliable insights into metabolic energy demands using functional magnetic resonance imaging data. Our findings indicate that healthy brains maintain balanced energy distribution, whereas imbalances are more pronounced in schizophrenia with links to both positive and negative symptoms, particularly during rapid neural processes. Additionally, we identified a dynamic state that supports the brain criticality theory and is associated with higher-order cognitive abilities, demonstrating our framework's functional and clinical relevance. By linking metabolic energy distribution to neural dynamics, this framework provides a novel way to estimate and quantify the brain's maintenance of functional balance in a broadly applicable manner for studying brain health and disorders.

Deciphering Multiway Multiscale Brain Network Connectivity: Insights from Birth to 6 Months

Converging evidence suggests that understanding the human brain requires more than just examining pairwise functional brain interactions. The human brain is a complex, nonlinear system, and focusing solely on linear pairwise functional connectivity often overlooks important nonlinear and higher-order relationships. Infancy is a critical period marked by significant brain development that could contribute to future learning, health, and life success. Exploring higher-order functional relationships in the brain can provide insight into brain function and development. To the best of our knowledge, there is no existing research on multiway, multiscale brain network interactions in infants. In this study, we comprehensively investigate the interactions among brain intrinsic connectivity networks (ICNs), including both pairwise (pair-FNC) and triple relationships (tri-FNC). We focused on an infant dataset collected between birth and six months, a critical period for brain maturation. Our results revealed significant hierarchical, multiway, multiscale brain functional network interactions in the infant brain. These findings suggest that tri-FNC provide additional insights beyond what pairwise interactions reveal during early brain development. The tri-FNC predominantly involve the default mode, sensorimotor, visual, limbic, language, salience, and central executive domains. Notably, these triplet networks align with the classical triple network model of the human brain, which includes the default mode network, the salience network, and the central executive network. This suggests that the brain network system might already be initially established during the first six months of infancy. Interestingly, tri-FNC in the default mode and salience domains showed significantly stronger nonlinear interactions with age compared to pair-FNC. We also found that pair-FNC were less effective at detecting these networks. The present study suggests that exploring tri-FNC can offer additional insights beyond pair-FNC by capturing higher-order nonlinear interactions, potentially yielding more reliable biomarkers to characterize developmental trajectories.

Spatiotemporal Complexity in the Psychotic Brain

Psychotic disorders, such as schizophrenia and bipolar disorder, pose significant diagnostic challenges with major implications on mental health. The measures of resting-state fMRI spatiotemporal complexity offer a powerful tool for identifying irregularities in brain activity. To capture global brain connectivity, we employed information-theoretic metrics, overcoming the limitations of pairwise correlation analysis approaches. This enables a more comprehensive exploration of higher-order interactions and multiscale intrinsic connectivity networks (ICNs) in the psychotic brain. In this study, we provide converging evidence suggesting that the psychotic brain exhibits states of randomness across both spatial and temporal dimensions. To further investigate these disruptions, we estimated brain network connectivity using redundancy and synergy measures, aiming to assess the integration and segregation of topological information in the psychotic brain. Our findings reveal a disruption in the balance between redundant and synergistic information, a phenomenon we term brainquake in this study, which highlights the instability and disorganization of brain networks in psychosis. Moreover, our exploration of higher-order topological functional connectivity reveals profound disruptions in brain information integration. Aberrant information interactions were observed across both cortical and subcortical ICNs. We specifically identified the most easily affected irregularities in the sensorimotor, visual, temporal, default mode, and fronto-parietal networks, as well as in the hippocampal and amygdalar regions, all of which showed disruptions. These findings underscore the severe impact of psychotic states on multiscale critical brain networks, suggesting a profound alteration in the brain's complexity and organizational states.

Structure and dynamics analysis of brain functional hypernetworks based on the null models

Brain functional hypernetworks that can characterize the complex and multivariate interactions among multiple brain regions have been widely used in the diagnosis and prediction of brain diseases. However, there are few studies on the structure and dynamics of brain functional hypernetworks. Such studies can help to explore how the important functional features of brain functional hypernetworks characterize the working and pathological mechanisms of the human brain. Therefore, this article introduces the hypernetwork null model to analyze the dependencies between the features of interest. Specifically, first, based on the original brain functional hypernetwork, this article proposed the optimized hyper dK-series algorithm with hyperedges to construct null models that preserved the different node attributes and hyperedge attributes of the original brain functional hypernetwork, respectively. Next, based on the original hypernetwork model and the null model, multiple node attributes and hyperedge attributes were respectively introduced. Then, the level of similarity and correlation between the topological attributes of the original brain functional hypernetwork and the topological attributes of the brain functional hypernetwork null model were calculated to analyze the dependencies between the features of interest. The results showed that there were differences in the level of dependence between the features of interest. Node degree is the main dependency attribute for multiple metrics. Hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient are partial dependency attributes for some metrics. The dependency attributes and level of dependency are the same for the hypernetwork clustering coefficients-HCC2 and HCC3. This indicates that the node degree is redundant with respect to other attributes, while the hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient perhaps contain other topology information. In addition, there is redundancy between HCC2 and HCC3. Therefore, the effects of these redundant attributes need to be considered when performing network analysis.

On null models for temporal small-worldness in brain dynamics

Brain dynamics can be modeled as a temporal brain network starting from the activity of different brain regions in functional magnetic resonance imaging (fMRI) signals. When validating hypotheses about temporal networks, it is important to use an appropriate statistical null model that shares some features with the treated empirical data. The purpose of this work is to contribute to the theory of temporal null models for brain networks by introducing the random temporal hyperbolic (RTH) graph model, an extension of the random hyperbolic (RH) graph, known in the study of complex networks for its ability to reproduce crucial properties of real-world networks. We focus on temporal small-worldness which, in the static case, has been extensively studied in real-world complex networks and has been linked to the ability of brain networks to efficiently exchange information. We compare the RTH graph model with standard null models for temporal networks and show it is the null model that best reproduces the small-worldness of resting brain activity. This ability to reproduce fundamental features of real brain networks, while adding only a single parameter compared with classical models, suggests that the RTH graph model is a promising tool for validating hypotheses about temporal brain networks.

Whole-brain multivariate hemodynamic deconvolution for functional MRI with stability selection

Conventionally, analysis of functional MRI (fMRI) data relies on available information about the experimental paradigm to establish hypothesized models of brain activity. However, this information can be inaccurate, incomplete or unavailable in multiple scenarios such as resting-state, naturalistic paradigms or clinical conditions. In these cases, blind estimates of neuronal-related activity can be obtained with paradigm-free analysis methods such as hemodynamic deconvolution. Yet, current formulations of the hemodynamic deconvolution problem have three important limitations: (1) their efficacy strongly depends on the appropriate selection of regularization parameters, (2) being univariate, they do not take advantage of the information present across the brain, and (3) they do not provide any measure of statistical certainty associated with each detected event. Here we propose a novel approach that addresses all these limitations. Specifically, we introduce multivariate sparse paradigm free mapping (Mv-SPFM), a novel hemodynamic deconvolution algorithm that operates at the whole brain level and adds spatial information via a mixed-norm regularization term over all voxels. Additionally, Mv-SPFM employs a stability selection procedure that removes the need to select regularization parameters and also lets us obtain an estimate of the true probability of having a neuronal-related BOLD event at each voxel and time-point based on the area under the curve (AUC) of the stability paths. Besides, we present a formulation tailored for multi-echo fMRI acquisitions (MvME-SPFM), which allows us to better isolate fluctuations of BOLD origin on the basis of their linear dependence with the echo time (TE) and to assign physiologically interpretable units (i.e., changes in the apparent transverse relaxation ΔR2∗) to the resulting deconvolved events. Remarkably, we demonstrate that Mv-SPFM achieves comparable performance even when using a single-echo formulation. We demonstrate that this algorithm outperforms existing state-of-the-art deconvolution approaches, and shows higher spatial and temporal agreement with the activation maps and BOLD signals obtained with a standard model-based linear regression approach, even at the level of individual neuronal events. Furthermore, we show that by employing stability selection, the performance of the algorithm depends less on the selection of temporal and spatial regularization parameters λ and ρ. Consequently, the proposed algorithm provides more reliable estimates of neuronal-related activity, here in terms of ΔR2∗, for the study of the dynamics of brain activity when no information about the timings of the BOLD events is available. This algorithm will be made publicly available as part of the splora Python package.

Intrinsic neural timescales relate to the dynamics of infraslow neural waves

The human brain is a highly dynamic organ that operates across a variety of timescales, the intrinsic neural timescales (INT). In addition to the INT, the neural waves featured by its phase-related processes including their cycles with peak/trough and rise/fall play a key role in shaping the brain's neural activity. However, the relationship between the brain's ongoing wave dynamics and INT remains yet unclear. In this study, we utilized functional magnetic resonance imaging (fMRI) rest and task data from the Human Connectome Project (HCP) to investigate the relationship of infraslow wave dynamics [as measured in terms of speed by changes in its peak frequency (PF)] with INT. Our findings reveal that: (i) the speed of phase dynamics (PF) is associated with distinct parts of the ongoing phase cycles, namely higher PF in peak/trough and lower PF in rise/fall; (ii) there exists a negative correlation between phase dynamics (PF) and INT such that slower PF relates to longer INT; (iii) exposure to a movie alters both PF and INT across the different phase cycles, yet their negative correlation remains intact. Collectively, our results demonstrate that INT relates to infraslow phase dynamics during both rest and task states.

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.

Subcortical influences on the topology of cortical networks align with functional processing hierarchies

fMRI of the human brain reveals spatiotemporal patterns of functional connectivity (FC), forming distinct cortical networks. Lately, subcortical contributions to these configurations are receiving renewed interest, but investigations rarely focus explicitly on their effects on cortico-cortical FC. Here, we employ a straightforward multivariable approach and graph-theoretic tools to assess subcortical impact on topological features of cortical networks. Given recent evidence showing that structures like the thalamus and basal ganglia integrate input from multiple networks, we expect increased segregation between cortical networks after removal of subcortical effects on their FC patterns. We analyze resting state data of young and healthy participants (male and female; N = 100) from the human connectome project. We find that overall, the cortical network architecture becomes less segregated, and more integrated, when subcortical influences are accounted for. Underlying these global effects are the following trends: 'Transmodal' systems become more integrated with the rest of the network, while 'unimodal' networks show the opposite effect. For single nodes this hierarchical organization is reflected by a close correspondence with the spatial layout of the principal gradient of FC (Margulies et al., 2016). Lastly, we show that the limbic system is significantly less coherent with subcortical influences removed. The findings are validated in a (split-sample) replication dataset. Our results provide new insight regarding the interplay between subcortex and cortical networks, by putting the integrative impact of subcortex in the context of macroscale patterns of cortical organization.

Group Surrogate Data Generating Models and similarity quantification of multivariate time-series: A resting-state fMRI study

Advancements in non-invasive brain analysis through novel approaches such as big data analytics and in silico simulation are essential for explaining brain function and associated pathologies. In this study, we extend the vector auto-regressive surrogate technique from a single multivariate time-series to group data using a novel Group Surrogate Data Generating Model (GSDGM). This methodology allowed us to generate biologically plausible human brain dynamics representative of a large human resting-state (rs-fMRI) dataset obtained from the Human Connectome Project. Simultaneously, we defined a novel similarity measure, termed the Multivariate Time-series Ensemble Similarity Score (MTESS). MTESS showed high accuracy and f-measure in subject identification, and it can directly compare the similarity between two multivariate time-series. We used MTESS to analyze both human and marmoset rs-fMRI data. Our results showed similarity differences between cortical and subcortical regions. We also conducted MTESS and state transition analysis between single and group surrogate techniques, and confirmed that a group surrogate approach can generate plausible group centroid multivariate time-series. Finally, we used GSDGM and MTESS for the fingerprint analysis of human rs-fMRI data, successfully distinguishing normal and outlier sessions. These new techniques will be useful for clinical applications and in silico simulation.

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.

Unbiased and efficient sampling of timeseries reveals redundancy of brain network and gradient structure

Many studies in human neuroscience seek to understand the structure of brain networks and gradients. Few studies, however, have tested the redundancy between these outwardly distinct features. Here, we developed methods to directly enable such tests. We built on insights from linear algebra to develop methods for unbiased and efficient sampling of timeseries with network or gradient constraints. We used these methods to show considerable redundancy between popular definitions of network and gradient structure in functional MRI data. On the one hand, we found that network constraints largely accounted for the structure of three major gradients. On the other hand, we found that gradient constraints largely accounted for the structure of seven major networks. Our results imply that some networks and gradients may denote discrete and continuous representations of the same aspects of functional MRI data. We suggest that integrated explanations can reduce redundancy by avoiding the attribution of independent existence or function to these features.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Time-resolved correlation of distributed brain activity tracks E-I balance and accounts for diverse scale-free phenomena

Much of systems neuroscience posits the functional importance of brain activity patterns that lack natural scales of sizes, durations, or frequencies. The field has developed prominent, and sometimes competing, explanations for the nature of this scale-free activity. Here, we reconcile these explanations across species and modalities. First, we link estimates of excitation-inhibition (E-I) balance with time-resolved correlation of distributed brain activity. Second, we develop an unbiased method for sampling time series constrained by this time-resolved correlation. Third, we use this method to show that estimates of E-I balance account for diverse scale-free phenomena without need to attribute additional function or importance to these phenomena. Collectively, our results simplify existing explanations of scale-free brain activity and provide stringent tests on future theories that seek to transcend these explanations.

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.

A spatiotemporal complexity architecture of human brain activity

The human brain operates in large-scale functional networks. These networks are an expression of temporally correlated activity across brain regions, but how global network properties relate to the neural dynamics of individual regions remains incompletely understood. Here, we show that the brain's network architecture is tightly linked to critical episodes of neural regularity, visible as spontaneous "complexity drops" in functional magnetic resonance imaging signals. These episodes closely explain functional connectivity strength between regions, subserve the propagation of neural activity patterns, and reflect interindividual differences in age and behavior. Furthermore, complexity drops define neural activity states that dynamically shape the connectivity strength, topological configuration, and hierarchy of brain networks and comprehensively explain known structure-function relationships within the brain. These findings delineate a principled complexity architecture of neural activity-a human "complexome" that underpins the brain's functional network organization.

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.

External drivers of BOLD signal's non-stationarity

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

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.

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.

Null models in network neuroscience

Recent advances in imaging and tracing technology provide increasingly detailed reconstructions of brain connectomes. Concomitant analytic advances enable rigorous identification and quantification of functionally important features of brain network architecture. Null models are a flexible tool to statistically benchmark the presence or magnitude of features of interest, by selectively preserving specific architectural properties of brain networks while systematically randomizing others. Here we describe the logic, implementation and interpretation of null models of connectomes. We introduce randomization and generative approaches to constructing null networks, and outline a taxonomy of network methods for statistical inference. We highlight the spectrum of null models - from liberal models that control few network properties, to conservative models that recapitulate multiple properties of empirical networks - that allow us to operationalize and test detailed hypotheses about the structure and function of brain networks. We review emerging scenarios for the application of null models in network neuroscience, including for spatially embedded networks, annotated networks and correlation-derived networks. Finally, we consider the limits of null models, as well as outstanding questions for the field.

A mathematical perspective on edge-centric brain functional connectivity

Edge time series are increasingly used in brain imaging to study the node functional connectivity (nFC) dynamics at the finest temporal resolution while avoiding sliding windows. Here, we lay the mathematical foundations for the edge-centric analysis of neuroimaging time series, explaining why a few high-amplitude cofluctuations drive the nFC across datasets. Our exposition also constitutes a critique of the existing edge-centric studies, showing that their main findings can be derived from the nFC under a static null hypothesis that disregards temporal correlations. Testing the analytic predictions on functional MRI data from the Human Connectome Project confirms that the nFC can explain most variation in the edge FC matrix, the edge communities, the large cofluctuations, and the corresponding spatial patterns. We encourage the use of dynamic measures in future research, which exploit the temporal structure of the edge time series and cannot be replicated by static null models.

On co-activation pattern analysis and non-stationarity of resting brain activity

The non-stationarity of resting-state brain activity has received increasing attention in recent years. Functional connectivity (FC) analysis with short sliding windows and coactivation pattern (CAP) analysis are two widely used methods for assessing the dynamic characteristics of brain activity observed with functional magnetic resonance imaging (fMRI). However, the statistical nature of the dynamics captured by these techniques needs to be verified. In this study, we found that the results of CAP analysis were similar for real fMRI data and simulated stationary data with matching covariance structures and spectral contents. We also found that, for both the real and simulated data, CAPs were clustered into spatially heterogeneous modules. Moreover, for each of the modules in the real data, a spatially similar module was found in the simulated data. The present results suggest that care needs to be taken when interpreting observations drawn from CAP analysis as it does not necessarily reflect non-stationarity or a mixture of states in resting brain activity.