Spontaneous brain network activity: Analysis of its temporal complexity

Studying time-resolved functional connectivity via communication theory: on the complementary nature of phase synchronization and sliding window Pearson correlation

Time-resolved functional connectivity (trFC) assesses the time-resolved coupling between brain regions using functional magnetic resonance imaging (fMRI) data. This study aims to compare two techniques used to estimate trFC, to investigate their similarities and differences when applied to fMRI data. These techniques are the sliding window Pearson correlation (SWPC), an amplitude-based approach, and phase synchronization (PS), a phase-based technique. To accomplish our objective, we used resting-state fMRI data from the Human Connectome Project (HCP) with 827 subjects (repetition time: 0.7s) and the Function Biomedical Informatics Research Network (fBIRN) with 311 subjects (repetition time: 2s), which included 151 schizophrenia patients and 160 controls. Our simulations reveal distinct strengths in two connectivity methods: SWPC captures high-magnitude, low-frequency connectivity, while PS detects low-magnitude, high-frequency connectivity. Stronger correlations between SWPC and PS align with pronounced fMRI oscillations. For fMRI data, higher correlations between SWPC and PS occur with matched frequencies and smaller SWPC window sizes (∼30s), but larger windows (∼88s) sacrifice clinically relevant information. Both methods identify a schizophrenia-associated brain network state but show different patterns: SWPC highlights low anti-correlations between visual, subcortical, auditory, and sensory-motor networks, while PS shows reduced positive synchronization among these networks. In sum, our findings underscore the complementary nature of SWPC and PS, elucidating their respective strengths and limitations without implying the superiority of one over the other.

The brain's "dark energy" puzzle: How strongly is glucose metabolism linked to resting-state brain activity?

Brain glucose metabolism, which can be investigated at the macroscale level with [18F]FDG PET, displays significant regional variability for reasons that remain unclear. Some of the functional drivers behind this heterogeneity may be captured by resting-state functional magnetic resonance imaging (rs-fMRI). However, the full extent to which an fMRI-based description of the brain's spontaneous activity can describe local metabolism is unknown. Here, using two multimodal datasets of healthy participants, we built a multivariable multilevel model of functional-metabolic associations, assessing multiple functional features, describing the 1) rs-fMRI signal, 2) hemodynamic response, 3) static and 4) time-varying functional connectivity, as predictors of the human brain's metabolic architecture. The full model was trained on one dataset and tested on the other to assess its reproducibility. We found that functional-metabolic spatial coupling is nonlinear and heterogeneous across the brain, and that local measures of rs-fMRI activity and synchrony are more tightly coupled to local metabolism. In the testing dataset, the degree of functional-metabolic spatial coupling was also related to peripheral metabolism. Overall, although a significant proportion of regional metabolic variability can be described by measures of spontaneous activity, additional efforts are needed to explain the remaining variance in the brain's 'dark energy'.

Neurobiologically realistic neural network enables cross-scale modeling of neural dynamics

Fundamental principles underlying computation in multi-scale brain networks illustrate how multiple brain areas and their coordinated activity give rise to complex cognitive functions. Whereas brain activity has been studied at the micro- to meso-scale to reveal the connections between the dynamical patterns and the behaviors, investigations of neural population dynamics are mainly limited to single-scale analysis. Our goal is to develop a cross-scale dynamical model for the collective activity of neuronal populations. Here we introduce a bio-inspired deep learning approach, termed NeuroBondGraph Network (NBGNet), to capture cross-scale dynamics that can infer and map the neural data from multiple scales. Our model not only exhibits more than an 11-fold improvement in reconstruction accuracy, but also predicts synchronous neural activity and preserves correlated low-dimensional latent dynamics. We also show that the NBGNet robustly predicts held-out data across a long time scale (2 weeks) without retraining. We further validate the effective connectivity defined from our model by demonstrating that neural connectivity during motor behaviour agrees with the established neuroanatomical hierarchy of motor control in the literature. The NBGNet approach opens the door to revealing a comprehensive understanding of brain computation, where network mechanisms of multi-scale activity are critical.

Heterogeneity of dynamic synergetic configurations of salience network in children with autism spectrum disorder

Atypical functional connectivity (FC) patterns have been identified in autism spectrum disorders (ASD), especially within salience network (SN) and between SN and default mode network (DMN) and central executive network (CEN). But whether the dynamic configuration of intra-SN and inter-SN (SN with DMN and CEN) FC in ASD is also heterogeneous remains unknown. Based on the resting-state functional magnetic resonance imaging data from 105 ASD and 102 typically-developing controls (TC), we calculated the time-varying FC of intra-SN and inter-SN (SN with DMN and CEN). Then, the joint recurrence features for the time-varying FC were calculated to assess how the SN dynamically recruits different configurations of network segregation and integration in ASD, that is, synergies, from the dynamical systems perspective. We analyzed the differences in synergetic patterns between ASD subtypes obtained by k-means clustering algorithm based on the synergy of SN and TC, and investigated the relationships between synergy of SN and severity of clinical symptoms of ASD for ASD subtypes. Two ASD subtypes were revealed, where the synergy of SN in ASD subtype 1 has lower stability and periodicity compared to the TC, and ASD subtype 2 exhibits the opposite alteration. Synergy of SN for ASD subtype 1 and 2 was found to predict the severity of communication impairments and restricted and repetitive behaviors in ASD, respectively. These results suggest the existence of subtypes with distinct patterns of the synergy of SN in ASD, and provide insight into the complex pathophysiological mechanism of clinical manifestations of ASD.

Dynamical interactions reconfigure the gradient of cortical timescales

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

The complexity of the stream of consciousness

Typical consciousness can be defined as an individual-specific stream of experiences. Modern consciousness research on dynamic functional connectivity uses clustering techniques to create common bases on which to compare different individuals. We propose an alternative approach by combining modern theories of consciousness and insights arising from phenomenology and dynamical systems theory. This approach enables a representation of an individual's connectivity dynamics in an intrinsically-defined, individual-specific landscape. Given the wealth of evidence relating functional connectivity to experiential states, we assume this landscape is a proxy measure of an individual's stream of consciousness. By investigating the properties of this landscape in individuals in different states of consciousness, we show that consciousness is associated with short term transitions that are less predictable, quicker, but, on average, more constant. We also show that temporally-specific connectivity states are less easily describable by network patterns that are distant in time, suggesting a richer space of possible states. We show that the cortex, cerebellum and subcortex all display consciousness-relevant dynamics and discuss the implication of our results in forming a point of contact between dynamical systems interpretations and phenomenology.

Mode decomposition-based time-varying phase synchronization for fMRI

Recently, there has been significant interest in measuring time-varying functional connectivity (TVC) 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. However, this requires the a priori choice of type and cut-off frequencies for the bandpass filter needed to perform the analysis. Here we explore alternative approaches based on the use of various mode decomposition (MD) techniques that provide a more data driven solution to this issue. These techniques allow for the data driven decomposition of signals jointly into narrow-band components at different frequencies, thus fulfilling the requirements needed to measure PS. We explore several variants of MD, including empirical mode decomposition (EMD), bivariate EMD (BEMD), noise-assisted multivariate EMD (na-MEMD), and introduce the use of multivariate variational mode decomposition (MVMD) in the context of estimating time-varying PS. We contrast the approaches using a series of simulations and application to rs-fMRI data. Our results show that MVMD outperforms other evaluated MD approaches, and further suggests that this approach can be used as a tool to reliably investigate time-varying PS in rs-fMRI data.

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.

Edge-based network analysis reveals frequency-specific network dynamics in aberrant anxiogenic processing in rats

Uncovering interactions between edges of brain networks can reveal the organizational principle of the networks and also their dysregulations underlying aberrant behaviours such as in neuropsychiatric diseases. In this study, we looked into the applicability of edge-based network analysis in uncovering possible network mechanisms of aberrant anxiogenic processing. Utilizing a rat model of prodromal Parkinson's disease we examined how a dorsomedial striatum-tied associative network (DSAN) may mediate context-based anxiogenic behaviour. Following dopamine depletion in the dorsomedial striatum, an exaggerated bottom-up signalling (posterior parietal-hippocampal-retrosplenial to anterior prefrontal-cingulate-amygdala regions) and gradient specific to the theta frequency in this network was observed. This change was accompanied by increased anxiety behaviour of the animals. By employing an edge-based approach in correlating informational flow (phase transfer entropy) with functional connectivity of all edges of this network, we further explore how the abnormal bottom-up signalling might be explained by alterations to the informational flow-connectivity motifs in the network. Our results demonstrate usage of edge-based network analysis in revealing concurrent informational processing and functional organization dynamics across multiple pathways in a brain network. This approach in unveiling network abnormalities and its impact on behavioural outcomes would be useful in probing the network basis of neuropsychiatric conditions.

Network dynamics scale with levels of awareness

Small world topologies are thought to provide a valuable insight into human brain organisation and consciousness. However, functional magnetic resonance imaging studies in consciousness have not yielded consistent results. Given the importance of dynamics for both consciousness and cognition, here we investigate how the diversity of small world dynamics (quantified by sample entropy; dSW-E¹) scales with decreasing levels of awareness (i.e., sedation and disorders of consciousness). Paying particular attention to result reproducibility, we show that dSW-E is a consistent predictor of levels of awareness even when controlling for the underlying functional connectivity dynamics. We find that dSW-E of subcortical and cortical areas are predictive, with the former showing higher and more robust effect sizes across analyses. We find that the network dynamics of intermodular communication in the cerebellum also have unique predictive power for levels of awareness. Consequently, we propose that the dynamic reorganisation of the functional information architecture, in particular of the subcortex, is a characteristic that emerges with awareness and has explanatory power beyond that of the complexity of dynamic functional connectivity.

Dynamic expression of brain functional systems disclosed by fine-scale analysis of edge time series

Functional connectivity (FC) describes the statistical dependence between neuronal populations or brain regions in resting-state fMRI studies and is commonly estimated as the Pearson correlation of time courses. Clustering or community detection reveals densely coupled sets of regions constituting resting-state networks or functional systems. These systems manifest most clearly when FC is sampled over longer epochs but appear to fluctuate on shorter timescales. Here, we propose a new approach to reveal temporal fluctuations in neuronal time series. Unwrapping FC signal correlations yields pairwise co-fluctuation time series, one for each node pair or edge, and allows tracking of fine-scale dynamics across the network. Co-fluctuations partition the network, at each time step, into exactly two communities. Sampled over time, the overlay of these bipartitions, a binary decomposition of the original time series, very closely approximates functional connectivity. Bipartitions exhibit characteristic spatiotemporal patterns that are reproducible across participants and imaging runs, capture individual differences, and disclose fine-scale temporal expression of functional systems. Our findings document that functional systems appear transiently and intermittently, and that FC results from the overlay of many variable instances of system expression. Potential applications of this decomposition of functional connectivity into a set of binary patterns are discussed.

Cortical maturation from childhood to adolescence is reflected in resting state EEG signal complexity

Endogenous cortical fluctuations captured by electroencephalograms (EEGs) reflect activity in large-scale brain networks that exhibit dynamic patterns over multiple time scales. Developmental changes in the coordination and integration of brain function leads to greater complexity in population level neural dynamics. In this study we examined multiscale entropy, a measure of signal complexity, in resting-state EEGs in a large (N = 405) cross-sectional sample of children and adolescents (9–16 years). Our findings showed consistent age-dependent increases in EEG complexity that are distributed across multiple temporal scales and spatial regions. Developmental changes were most robust as the age gap between groups increased, particularly between late childhood and adolescence, and were most prominent over fronto-central scalp regions. These results suggest that the transition from late childhood to adolescence is characterized by age-dependent changes in the underlying complexity of endogenous brain networks.

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.

Temporal complexity of fMRI is reproducible and correlates with higher order cognition

It has been hypothesized that resting state networks (RSNs), extracted from resting state functional magnetic resonance imaging (rsfMRI), likely display unique temporal complexity fingerprints, quantified by their multiscale entropy patterns (McDonough and Nashiro, 2014). This is a hypothesis with a potential capacity for developing digital biomarkers of normal brain function, as well as pathological brain dysfunction. Nevertheless, a limitation of McDonough and Nashiro (2014) was that rsfMRI data from only 20 healthy individuals was used for the analysis. To validate this hypothesis in a larger cohort, we used rsfMRI datasets of 987 healthy young adults from the Human Connectome Project (HCP), aged 22-35, each with four 14.4-min rsfMRI recordings and parcellated into 379 brain regions. We quantified multiscale entropy of rsfMRI time series averaged at different cortical and sub-cortical regions. We performed effect-size analysis on the data in 8 RSNs. Given that the morphology of multiscale entropy is affected by the choice of its tolerance parameter (r) and embedding dimension (m), we repeated the analyses at multiple values of r and m including the values used in McDonough and Nashiro (2014). Our results reinforced high temporal complexity in the default mode and frontoparietal networks. Lowest temporal complexity was observed in the subcortical areas and limbic system. We investigated the effect of temporal resolution (determined by the repetition time T_R) after downsampling of rsfMRI time series at two rates. At a low temporal resolution, we observed increased entropy and variance across datasets. Test-retest analysis showed that findings were likely reproducible across individuals over four rsfMRI runs, especially when the tolerance parameter r is equal to 0.5. The results confirmed that the relationship between functional brain connectivity strengths and rsfMRI temporal complexity changes over time scales. Finally, a non-random correlation was observed between temporal complexity of RSNs and fluid intelligence suggesting that complex dynamics of the human brain is an important attribute of high-level brain function.

Disrupted dynamic local brain functional connectivity patterns in generalized anxiety disorder

Previous studies have reported abnormalities in static brain activity and connectivity in patients with generalized anxiety disorder (GAD). However, the dynamic patterns of brain connectivity in patients with GAD have not been fully explored. In this study, we aimed to investigate the dynamic local brain functional connectivity in patients with GAD using dynamic regional phase synchrony (DRePS), a newly developed method for assessing intrinsic dynamic local functional connectivity. Seventy-four patients with GAD and 74 healthy controls (HCs) were enrolled and underwent resting-state functional magnetic resonance imaging. Compared to the HCs, patients with GAD exhibited decreased DRePS values in the bilateral caudate, left hippocampus, left anterior insula, left inferior frontal gyrus, and right fusiform gyrus extending to inferior temporal gyrus. The DRePS value of the left hippocampus was negatively correlated with the Hamilton Anxiety Rating Scale scores. Moreover, these abnormal DRePS patterns could be used to distinguish patients with GAD from HCs in an independent sample (18 patients with GAD and 21 HCs). Our findings provide further evidence on brain dysfunction in GAD from the perspective of the dynamic behaviour of local connections, suggesting that patients with GAD may have an insufficient brain adaptation. This study provides new insights into the neurocognitive mechanism of GAD and could potentially inform the diagnosis and treatment of this disease. Future studies on GAD could benefit from combining the DRePS method with task-related functional magnetic resonance imaging and non-invasive brain stimulation.

Time-varying nodal measures with temporal community structure: A cautionary note to avoid misinterpretation

In network neuroscience, temporal network models have gained popularity. In these models, network properties have been related to cognition and behavior. Here, we demonstrate that calculating nodal properties that are dependent on temporal community structure (such as the participation coefficient [PC]) in time‐varying contexts can potentially lead to misleading results. Specifically, with regards to the participation coefficient, increases in integration can be inferred when the opposite is occurring. Further, we present a temporal extension to the PC measure (temporal PC) that circumnavigates this problem by jointly considering all community partitions assigned to a node through time. The proposed method allows us to track a node's integration through time while adjusting for the possible changes in the community structure of the overall network.

Dynamic synergetic configurations of resting-state networks in ADHD

Attention deficit hyperactivity disorder (ADHD) is characterized by high distractibility and impaired executive functions. Notably, there is mounting evidence suggesting that ADHD could be regarded as a default mode network (DMN) disorder. In particular, failure in regulating the dynamics of activity and interactions of the DMN and cognitive control networks have been hypothesized as the main source of task interference causing attentional problems. On the other hand, previous studies indicated pronounced fluctuations in the strength of functional connections over time, particularly for the inter-network connections between the DMN and fronto-parietal control networks. Hence, characterization of connectivity disturbances in ADHD requires a thorough assessment of time-varying functional connectivity (FC). In this study, we proposed a dynamical systems perspective to assess how the DMN over time recruits different configurations of network segregation and integration. Specifically, we were interested in configurations for which both intra- and inter-network connections are retained, as opposed to commonly used methods which assess network segregation as a single measure. From resting-state fMRI data, we extracted three different stable configurations of FC patterns for the DMN, namely synergies. We provided evidence supporting our hypothesis that ADHD differs compared to controls, both in terms of recruitment rate and topology of specific synergies between resting-state networks. In addition, we found a relationship between synergetic cooperation patterns of the DMN with cognitive control networks and a behavioral measure which is sensitive to ADHD-related symptoms, namely the Stroop color-word task.

Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates

Whole-brain computational modeling based on structural connectivity has shown great promise in successfully simulating fMRI BOLD signals with temporal coactivation patterns that are highly similar to empirical functional connectivity patterns during resting state. Importantly, previous studies have shown that spontaneous fluctuations in coactivation patterns of distributed brain regions have an inherent dynamic nature with regard to the frequency spectrum of intrinsic brain oscillations. In this modeling study, we introduced frequency dynamics into a system of coupled oscillators, where each oscillator represents the local mean-field model of a brain region. We first showed that the collective behavior of interacting oscillators reproduces previously shown features of brain dynamics. Second, we examined the effect of simulated lesions in gray matter by applying an in silico perturbation protocol to the brain model. We present a new approach to map the effects of vulnerability in brain networks and introduce a measure of regional hazardousness based on mapping of the degree of divergence in a feature space.

Increased brain entropy of resting-state fMRI mediates the relationship between depression severity and mental health-related quality of life in late-life depressed elderly

BACKGROUND

Entropy analysis is a computational method used to quantify the complexity in a system, and loss of brain complexity is hypothesized to be related to mental disorders. Here, we applied entropy analysis to the resting-state functional magnetic resonance imaging (rs-fMRI) signal in subjects with late-life depression (LLD), an illness combined with emotion dysregulation and aging effect.

METHODS

A total of 35 unremitted depressed elderly and 22 control subjects were recruited. Multiscale entropy (MSE) analysis was performed in the entire brain, 90 automated anatomical labeling-parcellated ROIs, and five resting networks in each study participant.

LIMITATIONS

Due to ethical concerns, all the participants were under medication during the study.

RESULTS

Regionally, subjects with LLD showed decreased entropy only in the right posterior cingulate gyrus but had universally increased entropy in affective processing (putamen and thalamus), sensory, motor, and temporal nodes across different time scales. We also found higher entropy in the left frontoparietal network (FPN), which partially mediated the negative correlation between depression severity and mental components of the quality of life, reflecting the possible neural compensation during depression treatment.

CONCLUSION

MSE provides a novel and complementary approach in rs-fMRI analysis. The temporal-spatial complexity in the resting brain may provide the adaptive variability beneficial for the elderly with depression.

Range Entropy: A Bridge between Signal Complexity and Self-Similarity

Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, ApEn and SampEn are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.

Changes in EEG multiscale entropy and power-law frequency scaling during the human sleep cycle

We explored changes in multiscale brain signal complexity and power-law scaling exponents of electroencephalogram (EEG) frequency spectra across several distinct global states of consciousness induced in the natural physiological context of the human sleep cycle. We specifically aimed to link EEG complexity to a statistically unified representation of the neural power spectrum. Further, by utilizing surrogate-based tests of nonlinearity we also examined whether any of the sleep stage-dependent changes in entropy were separable from the linear stochastic effects contained in the power spectrum. Our results indicate that changes of brain signal entropy throughout the sleep cycle are strongly time-scale dependent. Slow wave sleep was characterized by reduced entropy at short time scales and increased entropy at long time scales. Temporal signal complexity (at short time scales) and the slope of EEG power spectra appear, to a large extent, to capture a common phenomenon of neuronal noise, putatively reflecting cortical balance between excitation and inhibition. Nonlinear dynamical properties of brain signals accounted for a smaller portion of entropy changes, especially in stage 2 sleep.

A practical comparison of algorithms for the measurement of multiscale entropy in neural time series data

There is a broad family of statistical methods for capturing time series regularity, with increasingly widespread adoption by the neuroscientific community. A common feature of these methods is that they permit investigators to quantify the entropy of brain signals - an index of unpredictability/complexity. Despite the proliferation of algorithms for computing entropy from neural time series data there is scant evidence concerning their relative stability and efficiency. Here we evaluated several different algorithmic implementations (sample, fuzzy, dispersion and permutation) of multiscale entropy in terms of their stability across sessions, internal consistency and computational speed, accuracy and precision using a combination of electroencephalogram (EEG) and synthetic 1/ƒ noise signals. Overall, we report fair to excellent internal consistency and longitudinal stability over a one-week period for the majority of entropy estimates, with several caveats. Computational timing estimates suggest distinct advantages for dispersion and permutation entropy over other entropy estimates. Considered alongside the psychometric evidence, we suggest several ways in which researchers can maximize computational resources (without sacrificing reliability), especially when working with high-density M/EEG data or multivoxel BOLD time series signals.

Spontaneous brain network activity: Analysis of its temporal complexity

The brain operates in a complex way. The temporal complexity underlying macroscopic and spontaneous brain network activity is still to be understood. In this study, we explored the brain's complexity by combining functional connectivity, graph theory, and entropy analyses in 25 healthy people using task-free functional magnetic resonance imaging. We calculated the pairwise instantaneous phase synchrony between 8,192 brain nodes for a total of 200 time points. This resulted in graphs for which time series of clustering coefficients (the "cliquiness" of a node) and participation coefficients (the between-module connectivity of a node) were estimated. For these two network metrics, sample entropy was calculated. The procedure produced a number of results: (1) Entropy is higher for the participation coefficient than for the clustering coefficient. (2) The average clustering coefficient is negatively related to its associated entropy, whereas the average participation coefficient is positively related to its associated entropy. (3) The level of entropy is network-specific to the participation coefficient, but not to the clustering coefficient. High entropy for the participation coefficient was observed in the default-mode, visual, and motor networks. These results were further validated using an independent replication dataset. Our work confirms that brain networks are temporally complex. Entropy is a good candidate metric to explore temporal network alterations in diseases with paroxysmal brain disruptions, including schizophrenia and epilepsy.

The dynamics of functional connectivity in neocortical focal epilepsy

Focal epilepsy is characterised by paroxysmal events, reflecting changes in underlying local brain networks. To capture brain network activity at the maximal temporal resolution of the acquired functional magnetic resonance imaging (fMRI) data, we have previously developed a novel analysis framework called Dynamic Regional Phase Synchrony (DRePS). DRePS measures instantaneous mean phase coherence within neighbourhoods of brain voxels. We use it here to examine how the dynamics of the functional connections of regional brain networks are altered in neocortical focal epilepsy. Using task-free fMRI data from 21 subjects with focal epilepsy and 21 healthy controls, we calculated the power spectral density of DRePS, which is a measure of signal variability in local connectivity estimates. Whole-brain averaged power spectral density of DRePS, or signal variability of local connectivity, was significantly higher in epilepsy subjects compared to healthy controls. Maximal increase in DRePS spectral power was seen in bilateral inferior frontal cortices, ipsilateral mid-cingulate gyrus, superior temporal gyrus, caudate head, and contralateral cerebellum. Our results provide further evidence of common brain abnormalities across people with focal epilepsy. We postulate that dynamic changes in specific cortical brain areas may help maintain brain function in the presence of pathological epileptiform network activity in neocortical focal epilepsy.

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Focal epilepsy is a disease defined by its inherent paroxysmal brain changes.

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However, most fMRI connectivity methods do not capture dynamic brain network activity.

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We use our recently developed method, DRePS, to identify abnormal dynamic brain networks in focal epilepsy.

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Fluctuations of dynamic brain network activity were increased in the frontal-temporal cortex, cingulum and cerebellum, in focal epilepsy.

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These regions may be involved in (re-)gaining cortical homeostasis in an otherwise abnormal brain.