Interplay between functional connectivity and scale-free dynamics in intrinsic fMRI networks

Frequency modulation increases the specificity of time-resolved connectivity: A resting-state fMRI study

Representing data using time-resolved networks is valuable for analyzing functional data of the human brain. One commonly used method for constructing time-resolved networks from data is sliding window Pearson correlation (SWPC). One major limitation of SWPC is that it applies a high-pass filter to the activity time series. Therefore, if we select a short window (desirable to estimate rapid changes in connectivity), we will remove important low-frequency information. Here, we propose an approach based on single sideband modulation (SSB) in communication theory. This allows us to select shorter windows to capture rapid changes in the time-resolved functional network connectivity (trFNC). We use simulation and real resting-state functional magnetic resonance imaging (fMRI) data to demonstrate the superior performance of SSB+SWPC compared to SWPC. We also compare the recurring trFNC patterns between individuals with the first episode of psychosis (FEP) and typical controls (TC) and show that FEPs stay more in states that show weaker connectivity across the whole brain. A result exclusive to SSB+SWPC is that TCs stay more in a state with negative connectivity between subcortical and cortical regions. Based on all the results, we argue that SSB+SWPC is more sensitive for capturing temporal variation in trFNC.

Decreased long-range temporal correlations in the resting-state functional magnetic resonance imaging blood-oxygen-level-dependent signal reflect motor sequence learning up to 2 weeks following training

Decreased long-range temporal correlations (LRTC) in brain signals can be used to measure cognitive effort during task execution. Here, we examined how learning a motor sequence affects long-range temporal memory within resting-state functional magnetic resonance imaging signal. Using the Hurst exponent (HE), we estimated voxel-wise LRTC and assessed changes over 5 consecutive days of training, followed by a retention scan 12 days later. The experimental group learned a complex visuomotor sequence while a complementary control group performed tightly matched movements. An interaction analysis revealed that HE decreases were specific to the complex sequence and occurred in well-known motor sequence learning associated regions including left supplementary motor area, left premotor cortex, left M1, left pars opercularis, bilateral thalamus, and right striatum. Five regions exhibited moderate to strong negative correlations with overall behavioral performance improvements. Following learning, HE values returned to pretraining levels in some regions, whereas in others, they remained decreased even 2 weeks after training. Our study presents new evidence of HE's possible relevance for functional plasticity during the resting-state and suggests that a cortical subset of sequence-specific regions may continue to represent a functional signature of learning reflected in decreased long-range temporal dependence after a period of inactivity.

Resting-state fractal brain connectivity is associated with impaired cognitive performance in healthy aging

Aging affects cognitive functions even in the absence of ongoing pathologies. The neurophysiological basis of age-related cognitive decline (CD), however, is not completely understood. Alterations in both functional brain connectivity and in the fractal scaling of neuronal dynamics have been linked to aging and cognitive performance. Recently, fractal connectivity (FrC) has been proposed - combining the two concepts - for capturing long-term interactions among brain regions. FrC was shown to be influenced by increased mental workload; however, no prior studies investigated how resting-state FrC relates to cognitive performance and plausible CD in healthy aging. We recruited 19 healthy elderly (HE) and 24 young control (YC) participants, who underwent resting-state electroencephalography (EEG) measurements and comprehensive cognitive evaluation using 7 tests of the Cambridge Neurophysiological Test Automated Battery. FrC networks were reconstructed from EEG data using the recently introduced multiple-resampling cross-spectral analysis (MRCSA). Elderly individuals could be characterized with increased response latency and reduced performance in 4-4 tasks, respectively, with both reaction time and accuracy being affected in two tasks. Auto- and cross-spectral exponents - characterizing regional fractal dynamics and FrC, respectively, - were found reduced in HE when compared to YC over most of the cortex. Additionally, fractal scaling of frontoparietal connections expressed an inverse relationship with task performance in visual memory and sustained attention domains in elderly, but not in young individuals. Our results confirm that the fractal nature of brain connectivity - as captured by MRCSA - is affected in healthy aging. Furthermore, FrC appears as a sensitive neurophysiological marker of age-related CD.

Hierarchical network structure as the source of hierarchical dynamics (power-law frequency spectra) in living and non-living systems: How state-trait continua (body plans, personalities) emerge from first principles in biophysics

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.

Behavioral and biologic characteristics of cancer-related cognitive impairment biotypes

Psychiatric diagnosis is moving away from symptom-based classification and towards multi-dimensional, biologically-based characterization, or biotyping. We previously identified three biotypes of chemotherapy-related cognitive impairment based on functional brain connectivity. In this follow-up study of 80 chemotherapy-treated breast cancer survivors and 80 non-cancer controls, we evaluated additional factors to help explain biotype expression: neurofunctional stability, brain age, apolipoprotein (APOE) genotype, and psychoneurologic symptoms. We also compared the discriminative ability of a traditional, symptom-based cognitive impairment definition with that of biotypes. We found significant differences in cortical brain age (F = 10.50, p < 0.001), neurofunctional stability (F = 2.83, p = 0.041), APOE e4 genotype (X2 = 7.68, p = 0.050), and psychoneurological symptoms (Pillai = 0.378, p < 0.001) across the three biotypes. The more resilient Biotype 2 demonstrated significantly higher neurofunctional stability compared to the other biotypes. Symptom-based classification of cognitive impairment did not differentiate biologic or other behavioral variables, suggesting that traditional categorization of cancer-related cognitive effects may miss important characteristics which could inform targeted treatment strategies. Additionally, biotyping, but not symptom-typing, was able to distinguish survivors with cognitive versus psychological effects. Our results suggest that Biotype 1 survivors might benefit from first addressing symptoms of anxiety and fatigue, Biotype 3 might benefit from a treatment plan which includes sleep hygiene, and Biotype 2 might benefit most from cognitive skills training or rehabilitation. Future research should include additional demographic and clinical information to further investigate biotype expression related to risk and resilience and examine integration of more clinically feasible imaging approaches.

Scale-Free Dynamics in Instantaneous Alpha Frequency Fluctuations: Validation, Test-Retest Reliability and Its Relationship with Task Manipulations

Previous studies showed that scale-free structures and long-range temporal correlations are ubiquitous in physiological signals (e.g., electroencephalography). This is supposed to be associated with optimized information processing in human brain. The instantaneous alpha frequency (IAF) (i.e., the instantaneous frequency of alpha band of human EEG signals) may dictate the resolution at which information is sampled and/or processed by cortical neurons. To the best of our knowledge, no research has examined the scale-free dynamics and potential functional significance of IAF. Here, through three studies (Study 1: 25 participants; Study 2: 82 participants; Study 3: 26 participants), we investigated the possibility that time series of IAF exhibit scale-free property through maximum likelihood based detrended fluctuation analysis (ML-DFA). This technique could provide the scaling exponent (i.e., DFA exponent) on the basis of presence of scale-freeness being validated. Then the test-retest reliability (Study 1) and potential influencing factors (Study 2 and Study 3) of DFA exponent of IAF fluctuations were investigated. Firstly, the scale-free property was found to be inherent in IAF fluctuations with fairly high test-retest reliability over the parietal-occipital region. Moreover, the task manipulations could potentially modulate the DFA exponent of IAF fluctuations. Specifically, in Study 2, we found that the DFA exponent of IAF fluctuations in eye-closed resting-state condition was significantly larger than that in eye-open resting-state condition. In Study 3, we found that the DFA exponent of IAF fluctuations in eye-open resting-state condition was significantly larger than that in visual n-back tasks. The DFA exponent of IAF fluctuations in the 0-back task was significantly larger than in the 2-back and 3-back tasks. The results in studies 2 and 3 indicated that: (1) a smaller DFA exponent of IAF fluctuations should signify more efficient online visual information processing; (2) the scaling property of IAF fluctuations could reflect the physiological arousal level of participants.

Scale-free dynamics of core-periphery topography

The human brain's cerebral cortex exhibits a topographic division into higher-order transmodal core and lower-order unimodal periphery regions. While timescales between the core and periphery region diverge, features of their power spectra, especially scale-free dynamics during resting-state and their mdulation in task states, remain unclear. To answer this question, we investigated the ~1/f-like pink noise manifestation of scale-free dynamics in the core-periphery topography during rest and task states applying infra-slow inter-trial intervals up to 1 min falling inside the BOLD's infra-slow frequency band. The results demonstrate (1) higher resting-state power-law exponent (PLE) in the core compared to the periphery region; (2) significant PLE increases in task across the core and periphery regions; and (3) task-related PLE increases likely followed the task's atypically low event rates, namely the task's periodicity (inter-trial interval = 52-60 s; 0.016-0.019 Hz). A computational model and a replication dataset that used similar infra-slow inter-trial intervals provide further support for our main findings. Altogether, the results show that scale-free dynamics differentiate core and periphery regions in the resting-state and mediate task-related effects.

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.

Drowsiness detection from polysomnographic data using multivariate selfsimilarity and eigen-wavelet analysis

Because drowsiness is a major cause in vehicle accidents, its automated detection is critical. Scale-free temporal dynamics is known to be typical of physiological and body rhythms. The present work quantifies the benefits of applying a recent and original multivariate selfsimilarity analysis to several modalities of polysomnographic measurements (heart rate, blood pressure, electroencephalogram and respiration), from the MIT-BIH Polysomnographic Database, to better classify drowsiness-related sleep stages. Clinical relevance- This study shows that probing jointly temporal dynamics amongst polysomnographic measurements, with a proposed original multivariate multiscale approach, yields a gain of above 5% in the Area-under-Curve quanti-fying drowsiness-related sleep stage classification performance compared to univariate analysis.

Monofractal analysis of functional magnetic resonance imaging: An introductory review

The following review will aid readers in providing an overview of scale-free dynamics and monofractal analysis, as well as its applications and potential in functional magnetic resonance imaging (fMRI) neuroscience and clinical research. Like natural phenomena such as the growth of a tree or crashing ocean waves, the brain expresses scale-invariant, or fractal, patterns in neural signals that can be measured. While neural phenomena may represent both monofractal and multifractal processes and can be quantified with many different interrelated parameters, this review will focus on monofractal analysis using the Hurst exponent (H). Monofractal analysis of fMRI data is an advanced analysis technique that measures the complexity of brain signaling by quantifying its degree of scale-invariance. As such, the H value of the blood oxygenation level-dependent (BOLD) signal specifies how the degree of correlation in the signal may mediate brain functions. This review presents a brief overview of the theory of fMRI monofractal analysis followed by notable findings in the field. Through highlighting the advantages and challenges of the technique, the article provides insight into how to best conduct fMRI fractal analysis and properly interpret the findings with physiological relevance. Furthermore, we identify the future directions necessary for its progression towards impactful functional neuroscience discoveries and widespread clinical use. Ultimately, this presenting review aims to build a foundation of knowledge among readers to facilitate greater understanding, discussion, and use of this unique yet powerful imaging analysis technique.

Multiple-Resampling Cross-Spectral Analysis: An Unbiased Tool for Estimating Fractal Connectivity With an Application to Neurophysiological Signals

Investigating scale-free (i.e., fractal) functional connectivity in the brain has recently attracted increasing attention. Although numerous methods have been developed to assess the fractal nature of functional coupling, these typically ignore that neurophysiological signals are assemblies of broadband, arrhythmic activities as well as oscillatory activities at characteristic frequencies such as the alpha waves. While contribution of such rhythmic components may bias estimates of fractal connectivity, they are also likely to represent neural activity and coupling emerging from distinct mechanisms. Irregular-resampling auto-spectral analysis (IRASA) was recently introduced as a tool to separate fractal and oscillatory components in the power spectrum of neurophysiological signals by statistically summarizing the power spectra obtained when resampling the original signal by several non-integer factors. Here we introduce multiple-resampling cross-spectral analysis (MRCSA) as an extension of IRASA from the univariate to the bivariate case, namely, to separate the fractal component of the cross-spectrum between two simultaneously recorded neural signals by applying the same principle. MRCSA does not only provide a theoretically unbiased estimate of the fractal cross-spectrum (and thus its spectral exponent) but also allows for computing the proportion of scale-free coupling between brain regions. As a demonstration, we apply MRCSA to human electroencephalographic recordings obtained in a word generation paradigm. We show that the cross-spectral exponent as well as the proportion of fractal coupling increases almost uniformly over the cortex during the rest-task transition, likely reflecting neural desynchronization. Our results indicate that MRCSA can be a valuable tool for scale-free connectivity studies in characterizing various cognitive states, while it also can be generalized to other applications outside the field of neuroscience.

Fractal-Based Analysis of fMRI BOLD Signal During Naturalistic Viewing Conditions

Background: Temporal fractals are characterized by prominent scale-invariance and self-similarity across time scales. Monofractal analysis quantifies this scaling behavior in a single parameter, the Hurst exponent (H). Higher H reflects greater correlation in the signal structure, which is taken as being more fractal. Previous fMRI studies have observed lower H during conventional tasks relative to resting state conditions, and shown that H is negatively correlated with task difficulty and novelty. To date, no study has investigated the fractal dynamics of BOLD signal during naturalistic conditions. Methods: We performed fractal analysis on Human Connectome Project 7T fMRI data (n = 72, 41 females, mean age 29.46 ± 3.76 years) to compare H across movie-watching and rest. Results: In contrast to previous work using conventional tasks, we found higher H values for movie relative to rest (mean difference = 0.014; p = 5.279 × 10^-7; 95% CI [0.009, 0.019]). H was significantly higher in movie than rest in the visual, somatomotor and dorsal attention networks, but was significantly lower during movie in the frontoparietal and default networks. We found no cross-condition differences in test-retest reliability of H. Finally, we found that H of movie-derived stimulus properties (e.g., luminance changes) were fractal whereas H of head motion estimates were non-fractal. Conclusions: Overall, our findings suggest that movie-watching induces fractal signal dynamics. In line with recent work characterizing connectivity-based brain state dynamics during movie-watching, we speculate that these fractal dynamics reflect the configuring and reconfiguring of brain states that occurs during naturalistic processing, and are markedly different than dynamics observed during conventional tasks.

Functional brain-heart interplay extends to the multifractal domain

The study of functional brain-heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain-heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain-heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain-heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

A Quantitative Data-Driven Analysis Framework for Resting-State Functional Magnetic Resonance Imaging: A Study of the Impact of Adult Age

The objective of this study is to introduce a new quantitative data-driven analysis (QDA) framework for the analysis of resting-state fMRI (R-fMRI) and use it to investigate the effect of adult age on resting-state functional connectivity (RFC). Whole-brain R-fMRI measurements were conducted on a 3T clinical MRI scanner in 227 healthy adult volunteers (N = 227, aged 18-76 years old, male/female = 99/128). With the proposed QDA framework we derived two types of voxel-wise RFC metrics: the connectivity strength index and connectivity density index utilizing the convolutions of the cross-correlation histogram with different kernels. Furthermore, we assessed the negative and positive portions of these metrics separately. With the QDA framework we found age-related declines of RFC metrics in the superior and middle frontal gyri, posterior cingulate cortex (PCC), right insula and inferior parietal lobule of the default mode network (DMN), which resembles previously reported results using other types of RFC data processing methods. Importantly, our new findings complement previously undocumented results in the following aspects: (1) the PCC and right insula are anti-correlated and tend to manifest simultaneously declines of both the negative and positive connectivity strength with subjects' age; (2) separate assessment of the negative and positive RFC metrics provides enhanced sensitivity to the aging effect; and (3) the sensorimotor network depicts enhanced negative connectivity strength with the adult age. The proposed QDA framework can produce threshold-free and voxel-wise RFC metrics from R-fMRI data. The detected adult age effect is largely consistent with previously reported studies using different R-fMRI analysis approaches. Moreover, the separate assessment of the negative and positive contributions to the RFC metrics can enhance the RFC sensitivity and clarify some of the mixed results in the literature regarding to the DMN and sensorimotor network involvement in adult aging.

Multifractal Functional Connectivity Analysis of Electroencephalogram Reveals Reorganization of Brain Networks in a Visual Pattern Recognition Paradigm

The human brain consists of anatomically distant neuronal assemblies that are interconnected via a myriad of synapses. This anatomical network provides the neurophysiological wiring framework for functional connectivity (FC), which is essential for higher-order brain functions. While several studies have explored the scale-specific FC, the scale-free (i.e., multifractal) aspect of brain connectivity remains largely neglected. Here we examined the brain reorganization during a visual pattern recognition paradigm, using bivariate focus-based multifractal (BFMF) analysis. For this study, 58 young, healthy volunteers were recruited. Before the task, 3-3 min of resting EEG was recorded in eyes-closed (EC) and eyes-open (EO) states, respectively. The subsequent part of the measurement protocol consisted of 30 visual pattern recognition trials of 3 difficulty levels graded as Easy, Medium, and Hard. Multifractal FC was estimated with BFMF analysis of preprocessed EEG signals yielding two generalized Hurst exponent-based multifractal connectivity endpoint parameters, H(2) and ΔH ₁₅; with the former indicating the long-term cross-correlation between two brain regions, while the latter captures the degree of multifractality of their functional coupling. Accordingly, H(2) and ΔH ₁₅ networks were constructed for every participant and state, and they were characterized by their weighted local and global node degrees. Then, we investigated the between- and within-state variability of multifractal FC, as well as the relationship between global node degree and task performance captured in average success rate and reaction time. Multifractal FC increased when visual pattern recognition was administered with no differences regarding difficulty level. The observed regional heterogeneity was greater for ΔH ₁₅ networks compared to H(2) networks. These results show that reorganization of scale-free coupled dynamics takes place during visual pattern recognition independent of difficulty level. Additionally, the observed regional variability illustrates that multifractal FC is region-specific both during rest and task. Our findings indicate that investigating multifractal FC under various conditions - such as mental workload in healthy and potentially in diseased populations - is a promising direction for future research.

Separating scale-free and oscillatory components of neural activity in schizophrenia

INTRODUCTION

Alterations in narrow-band spectral power of electroencephalography (EEG) recordings are commonly reported in patients with schizophrenia (SZ). It is well established however that electrophysiological signals comprise a broadband scale-free (or fractal) component generated by mechanisms different from those producing oscillatory neural activity. Despite this known feature, it has not yet been investigated if spectral abnormalities found in SZ could be attributed to scale-free or oscillatory brain function.

METHODS

In this study, we analyzed resting-state EEG recordings of 14 SZ patients and 14 healthy controls. Scale-free and oscillatory components of the power spectral density (PSD) were separated, and band-limited power (BLP) of the original (mixed) PSD, as well as its fractal and oscillatory components, was estimated in five frequency bands. The scaling property of the fractal component was characterized by its spectral exponent in two distinct frequency ranges (1-13 and 13-30 Hz).

RESULTS

Analysis of the mixed PSD revealed a decrease of BLP in the delta band in SZ over the central regions; however, this difference could be attributed almost exclusively to a shift of power toward higher frequencies in the fractal component. Broadband neural activity expressed a true bimodal nature in all except frontal regions. Furthermore, both low- and high-range spectral exponents exhibited a characteristic topology over the cortex in both groups.

CONCLUSION

Our results imply strong functional significance of scale-free neural activity in SZ and suggest that abnormalities in PSD may emerge from alterations of the fractal and not only the oscillatory components of neural activity.

Scale-Free Coupled Dynamics in Brain Networks Captured by Bivariate Focus-Based Multifractal Analysis

While most connectivity studies investigate functional connectivity (FC) in a scale-dependent manner, coupled neural processes may also exhibit broadband dynamics, manifesting as power-law scaling of their measures of interdependence. Here we introduce the bivariate focus-based multifractal (BFMF) analysis as a robust tool for capturing such scale-free relations and use resting-state electroencephalography (EEG) recordings of 12 subjects to demonstrate its performance in reconstructing physiological networks. BFMF was employed to characterize broadband FC between 62 cortical regions in a pairwise manner, with all investigated connections being tested for true bivariate multifractality. EEG channels were also grouped to represent the activity of six resting-state networks (RSNs) in the brain, thus allowing for the analysis of within- and between- RSNs connectivity, separately. Most connections featured true bivariate multifractality, which could be attributed to the genuine scale-free coupling of neural dynamics. Bivariate multifractality showed a characteristic topology over the cortex that was highly concordant among subjects. Long-term autocorrelation was higher in within-RSNs, while the degree of multifractality was generally found stronger in between-RSNs connections. These results offer statistical evidence of the bivariate multifractal nature of functional coupling in the brain and validate BFMF as a robust method to capture such scale-independent coupled dynamics.

Revisiting Functional Connectivity for Infraslow Scale-Free Brain Dynamics Using Complex Wavelets

The analysis of human brain functional networks is achieved by computing functional connectivity indices reflecting phase coupling and interactions between remote brain regions. In magneto- and electroencephalography, the most frequently used functional connectivity indices are constructed based on Fourier-based cross-spectral estimation applied to specific fast and band-limited oscillatory regimes. Recently, infraslow arrhythmic fluctuations (below the 1 Hz) were recognized as playing a leading role in spontaneous brain activity. The present work aims to propose to assess functional connectivity from fractal dynamics, thus extending the assessment of functional connectivity to the infraslow arrhythmic or scale-free temporal dynamics of M/EEG-quantified brain activity. Instead of being based on Fourier analysis, new Imaginary Coherence and weighted Phase Lag indices are constructed from complex-wavelet representations. Their performances are first assessed on synthetic data by means of Monte-Carlo simulations, and they are then compared favorably against the classical Fourier-based indices. These new assessments of functional connectivity indices are also applied to MEG data collected on 36 individuals both at rest and during the learning of a visual motion discrimination task. They demonstrate a higher statistical sensitivity, compared to their Fourier counterparts, in capturing significant and relevant functional interactions in the infraslow regime and modulations from rest to task. Notably, the consistent overall increase in functional connectivity assessed from fractal dynamics from rest to task correlated with a change in temporal dynamics as well as with improved performance in task completion, which suggests that the complex-wavelet weighted Phase Lag index is the sole index is able to capture brain plasticity in the infraslow scale-free regime.

Altered Weibull Degree Distribution in Resting-State Functional Brain Networks Is Associated With Cognitive Decline in Mild Cognitive Impairment

The topological organization of human brain networks can be mathematically characterized by the connectivity degree distribution of network nodes. However, there is no clear consensus on whether the topological structure of brain networks follows a power law or other probability distributions, and whether it is altered in Alzheimer's disease (AD). Here we employed resting-state functional MRI and graph theory approaches to investigate the fitting of degree distributions of the whole-brain functional networks and seven subnetworks in healthy subjects and individuals with amnestic mild cognitive impairment (aMCI), i.e., the prodromal stage of AD, and whether they are altered and correlated with cognitive performance in patients. Forty-one elderly cognitively healthy controls and 30 aMCI subjects were included. We constructed functional connectivity matrices among brain voxels and examined nodal degree distributions that were fitted by maximum likelihood estimation. In the whole-brain networks and all functional subnetworks, the connectivity degree distributions were fitted better by the Weibull distribution [f(x)~x^(β−1)e^(−λxβ)] than power law or power law with exponential cutoff. Compared with the healthy control group, the aMCI group showed lower Weibull β parameters (shape factor) in both the whole-brain networks and all seven subnetworks (false-discovery rate-corrected, p < 0.05). These decreases of the Weibull β parameters in the whole-brain networks and all subnetworks except for ventral attention were associated with reduced cognitive performance in individuals with aMCI. Thus, we provided a short-tailed model to capture intrinsic connectivity structure of the human brain functional networks in health and disease.

Relationship Between Basic Properties of BOLD Fluctuations and Calculated Metrics of Complexity in the Human Connectome Project

Resting state functional MRI (rs-fMRI) creates a rich four-dimensional data set that can be analyzed in a variety of ways. As more researchers come to view the brain as a complex dynamical system, tools are increasingly being drawn from other fields to characterize the complexity of the brain's activity. However, given that the signal measured with rs-fMRI arises from the hemodynamic response to neural activity, the extent to which complexity metrics reflect neural complexity as compared to signal properties related to image quality remains unknown. To provide some insight into this question, correlation dimension, approximate entropy and Lyapunov exponent were calculated for different rs-fMRI scans from the same subject to examine their reliability. The metrics of complexity were then compared to several properties of the rs-fMRI signal from each brain area to determine if basic signal features could explain differences in the complexity metrics. Differences in complexity across brain areas were highly reliable and were closely linked to differences in the frequency profiles of the rs-fMRI signal. The spatial distributions of the complexity and frequency metrics suggest that they are both influenced by location-dependent signal properties that can obscure changes related to neural activity.

Scale-free amplitude modulation of low-frequency fluctuations in episodic migraine

Arrhythmic fluctuations in neural activity occur at many levels of the nervous system. Such activity does not have a characteristic temporal periodicity but can exhibit statistical similarities, most commonly power-law scaling behavior, which is indicative of scale-free dynamics. The recurrence of scaling laws across many different systems and its manifestation in behavior has prompted a search for unifying principles in human brain function. With this in mind, a focused search for abnormities in scale-free dynamics is of considerable clinical relevance to migraine and other clinical pain disorders. Here, we examined the scale-free properties of the resting-state functional magnetic resonance imaging (fMRI) signal in the broadband frequency range known to be related to spontaneous neural activity (0.01-0.1 Hz). In a large cohort of episodic migraine patients (N = 40), we observed that the strength of long-range temporal correlations in the fMRI signal (captured by the scaling exponent α) was significantly higher in the sensorimotor network compared with healthy controls. Increases in the scaling exponent were positively correlated with fMRI signal variance and negatively correlated with the patient's self-reported headache intensity. These changes in the fMRI signal suggest that the temporal structure of amplitude fluctuations carries valuable information about the dynamic state of the underlying neuronal networks and ensuing sensory impairments in migraine. The demonstrated scaling laws pose a novel quantitative approach for examining clinically relevant interindividual variability in migraine and other pain disorders.

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

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

Quantifying Functional Links between Brain and Heartbeat Dynamics in the Multifractal Domain: a Preliminary Analysis

Quantification of brain-heart interplay (BHI) has mainly been performed in the time and frequency domains. However, such functional interactions are likely to involve nonlinear dynamics associated with the two systems. To this extent, in this preliminary study we investigate the functional coupling between multifractal properties of Electroencephalography (EEG) and Heart Rate Variability (HRV) series using a channel- and time scale-wise maximal information coefficient analysis. Experimental results were gathered from 24 healthy volunteers undergoing a resting state and a cold-pressure test, and suggest that significant changes between the two experimental conditions might be associated with nonlinear quantifiers of the multifractal spectrum. Particularly, major brain-heart functional coupling was associated with the secondorder cumulant of the multifractal spectrum. We conclude that a functional nonlinear relationship between brain- and heartbeat-related multifractal sprectra exist, with higher values associated with the resting state.

Model-based whole-brain effective connectivity to study distributed cognition in health and disease

Neuroimaging techniques are now widely used to study human cognition. The functional associations between brain areas have become a standard proxy to describe how cognitive processes are distributed across the brain network. Among the many analysis tools available, dynamic models of brain activity have been developed to overcome the limitations of original connectivity measures such as functional connectivity. This goes in line with the many efforts devoted to the assessment of directional interactions between brain areas from the observed neuroimaging activity. This opinion article provides an overview of our model-based whole-brain effective connectivity to analyze fMRI data, while discussing the pros and cons of our approach with respect to other established approaches. Our framework relies on the multivariate Ornstein-Uhlenbeck (MOU) process and is thus referred to as MOU-EC. Once tuned, the model provides a directed connectivity estimate that reflects the dynamical state of BOLD activity, which can be used to explore cognition. We illustrate this approach using two applications on task-evoked fMRI data. First, as a connectivity measure, MOU-EC can be used to extract biomarkers for task-specific brain coordination, understood as the patterns of areas exchanging information. The multivariate nature of connectivity measures raises several challenges for whole-brain analysis, for which machine-learning tools present some advantages over statistical testing. Second, we show how to interpret changes in MOU-EC connections in a collective and model-based manner, bridging with network analysis. Our framework provides a comprehensive set of tools that open exciting perspectives to study distributed cognition, as well as neuropathologies.

Functional Integration and Segregation in Multiplex Brain Networks for Alzheimer's Disease

Growing evidence links impairment of brain functions in Alzheimer's disease (AD) with disruptions of brain functional connectivity. However, whether the AD brain shows similar changes from a dynamic or cross-frequency view remains poorly explored. This paper provides an effective framework to investigate the properties of multiplex brain networks in AD considering inter-frequency and temporal dynamics. Using resting-state EEG signals, two types of multiplex networks were reconstructed separately considering the network interactions between different frequency bands or time points. We further applied multiplex network features to characterize functional integration and segregation of the cross-frequency or time-varying networks. Finally, machine learning methods were employed to evaluate the performance of multiplex-network-based indexes for detection of AD. Results revealed that the brain networks of AD patients are disrupted with reduced segregation particularly in the left occipital area for both cross-frequency and time-varying networks. However, the alteration of integration differs among brain regions and may show an increasing trend in the frontal area of AD brain. By combining the features of integration and segregation in time-varying networks, the best classification performance was achieved with an accuracy of 92.5%. These findings suggest that our multiplex framework can be applied to explore functional integration and segregation of brain networks and characterize the abnormalities of brain function. This may shed new light on the brain network analysis and extend our understanding of brain function in patients with neurological diseases.

Network analysis of whole-brain fMRI dynamics: A new framework based on dynamic communicability

Neuroimaging techniques such as MRI have been widely used to explore the associations between brain areas. Structural connectivity (SC) captures the anatomical pathways across the brain and functional connectivity (FC) measures the correlation between the activity of brain regions. These connectivity measures have been much studied using network theory in order to uncover the distributed organization of brain structures, in particular FC for task-specific brain communication. However, the application of network theory to study FC matrices is often "static" despite the dynamic nature of time series obtained from fMRI. The present study aims to overcome this limitation by introducing a network-oriented analysis applied to whole-brain effective connectivity (EC) useful to interpret the brain dynamics. Technically, we tune a multivariate Ornstein-Uhlenbeck (MOU) process to reproduce the statistics of the whole-brain resting-state fMRI signals, which provides estimates for MOU-EC as well as input properties (similar to local excitabilities). The network analysis is then based on the Green function (or network impulse response) that describes the interactions between nodes across time for the estimated dynamics. This model-based approach provides time-dependent graph-like descriptor, named communicability, that characterize the roles that either nodes or connections play in the propagation of activity within the network. They can be used at both global and local levels, and also enables the comparison of estimates from real data with surrogates (e.g. random network or ring lattice). In contrast to classical graph approaches to study SC or FC, our framework stresses the importance of taking the temporal aspect of fMRI signals into account. Our results show a merging of functional communities over time, moving from segregated to global integration of the network activity. Our formalism sets a solid ground for the analysis and interpretation of fMRI data, including task-evoked activity.

Differences in MEG and EEG power-law scaling explained by a coupling between spatial coherence and frequency: a simulation study

Electrophysiological signals (electroencephalography, EEG, and magnetoencephalography, MEG), as many natural processes, exhibit scale-invariance properties resulting in a power-law (1/f) spectrum. Interestingly, EEG and MEG differ in their slopes, which could be explained by several mechanisms, including non-resistive properties of tissues. Our goal in the present study is to estimate the impact of space/frequency structure of source signals as a putative mechanism to explain spectral scaling properties of neuroimaging signals. We performed simulations based on the summed contribution of cortical patches with different sizes (ranging from 0.4 to 104.2 cm²). Small patches were attributed signals of high frequencies, whereas large patches were associated with signals of low frequencies, on a logarithmic scale. The tested parameters included i) the space/frequency structure (range of patch sizes and frequencies) and ii) the amplitude factor c parametrizing the spatial scale ratios. We found that the space/frequency structure may cause differences between EEG and MEG scale-free spectra that are compatible with real data findings reported in previous studies. We also found that below a certain spatial scale, there were no more differences between EEG and MEG, suggesting a limit for the resolution of both methods.Our work provides an explanation of experimental findings. This does not rule out other mechanisms for differences between EEG and MEG, but suggests an important role of spatio-temporal structure of neural dynamics. This can help the analysis and interpretation of power-law measures in EEG and MEG, and we believe our results can also impact computational modeling of brain dynamics, where different local connectivity structures could be used at different frequencies.

The Impact of Frequency Scale on the Response Sensitivity and Reliability of Cortical Neurons to 1/fβ Input Signals

What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f0 power spectrum, pink noise 1/f, and brown noises 1/f2) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f0 with short-term correlations for a broad frequency range, and also higher than 1/f2 for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f0 white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.

Spontaneous Brain Activity Predicts Task-Evoked Activity During Animate Versus Inanimate Touch

The spontaneous activity of the brain is characterized by an elaborate temporal structure with scale-free properties as indexed by the power law exponent (PLE). We test the hypothesis that spontaneous brain activity modulates task-evoked activity during interactions with animate versus inanimate stimuli. For this purpose, we developed a paradigm requiring participants to actively touch either animate (real hand) or inanimate (mannequin hand) stimuli. Behaviorally, participants perceived the animate target as closer in space, temporally more synchronous with their own self, and more personally relevant, compared with the inanimate. Neuronally, we observed a modulation of task-evoked activity by animate versus inanimate interactions in posterior insula, in medial prefrontal cortex, comprising anterior cingulate cortex, and in medial superior frontal gyrus. Among these regions, an increased functional connectivity was shown between posterior insula and perigenual anterior cingulate cortex (PACC) during animate compared with inanimate interactions and during resting state. Importantly, PLE during spontaneous brain activity in PACC correlated positively with PACC task-evoked activity during animate versus inanimate stimuli. In conclusion, we demonstrate that brain spontaneous activity in PACC can be related to the distinction between animate and inanimate stimuli and thus might be specifically tuned to align our brain with its animate environment.

Increased scale-free dynamics in salience network in adult high-functioning autism

Autism spectrum disorder (ASD) is clinically characterized by extremely slow and inflexible behavior. The neuronal mechanisms of these symptoms remain unclear though. Using fMRI, we investigate the resting state's temporal structure in the frequency domain (scale-free activity as measured with Power-Law Exponent, PLE, and Spectral Entropy, SE) and temporal variance (neural variability) in high-functioning, adult ASD comparing them with schizophrenic and neurotypical subjects. We show that ASD is characterized by high PLE in salience network, especially in dorsal anterior cingulate. This increase in PLE was 1) specific for salience network; 2) independent of other measures such as neuronal variability/SD and functional connectivity, which did not show any significant difference; 3) detected in two independent samples of ASD but not in the schizophrenia sample. Among salience network subregions, dorsal anterior cingulate cortex exhibited PLE differences between ASD and neurotypicals in both samples, showing high robustness in ROC curves values. Salience network abnormal temporal structure was confirmed by SE, which was strongly anticorrelated with PLE and thus decreased in ASD. Taken together, our findings show abnormal temporal structure (but normal temporal variance) in resting state salience network in adult high-functioning ASD. The abnormally high PLE indicates a relative predominance of slower over faster frequencies, which may underlie the slow adaptation to unexpected changes and the inflexible behavior observed in autistic individuals. The specificity of abnormal PLE in salience network suggests its potential utility as biomarker in ASD.

Fractal Analysis of BOLD Time Series in a Network Associated With Waiting Impulsivity

Fractal phenomena can be found in numerous scientific areas including neuroscience. Fractals are structures, in which the whole has the same shape as its parts. A specific structure known as pink noise (also called fractal or 1/f noise) is one key fractal manifestation, exhibits both stability and adaptability, and can be addressed via the Hurst exponent (H). FMRI studies using H on regional fMRI time courses used fractality as an important characteristic to unravel neural networks from artificial noise. In this fMRI-study, we examined 103 healthy male students at rest and while performing the 5-choice serial reaction time task. We addressed fractality in a network associated with waiting impulsivity using the adaptive fractal analysis (AFA) approach to determine H. We revealed the fractal nature of the impulsivity network. Furthermore, fractality was influenced by individual impulsivity in terms of decreasing fractality with higher impulsivity in regions of top-down control (left middle frontal gyrus) as well as reward processing (nucleus accumbens and anterior cingulate cortex). We conclude that fractality as determined via H is a promising marker to quantify deviations in network functions at an early stage and, thus, to be able to inform preventive interventions before the manifestation of a disorder.

Impact of Healthy Aging on Multifractal Hemodynamic Fluctuations in the Human Prefrontal Cortex

Fluctuations in resting-state cerebral hemodynamics show scale-free behavior over two distinct scaling ranges. Changes in such bimodal (multi) fractal pattern give insight to altered cerebrovascular or neural function. Our main goal was to assess the distribution of local scale-free properties characterizing cerebral hemodynamics and to disentangle the influence of aging on these multifractal parameters. To this end, we obtained extended resting-state records (N = 2¹⁴) of oxyhemoglobin (HbO), deoxyhemoglobin (HbR) and total hemoglobin (HbT) concentration time series with continuous-wave near-infrared spectroscopy technology from the brain cortex. 52 healthy volunteers were enrolled in this study: 24 young (30.6 ± 8.2 years), and 28 elderly (60.5 ± 12.0 years) subjects. Using screening tests on power-law, multifractal noise, and shuffled data sets we evaluated the presence of true multifractal hemodynamics reflecting long-range correlation (LRC). Subsequently, scaling-range adaptive bimodal signal summation conversion (SSC) was performed based on standard deviation (σ) of signal windows across a range of temporal scales (s). Building on moments of different order (q) of the measure, σ(s), multifractal SSC yielded generalized Hurst exponent function, H(q), and singularity spectrum, D(h) separately for a fast and slow component (the latter dominating the highest temporal scales). Parameters were calculated reflecting the estimated measure at s = N (focus), degree of LRC [Hurst exponent, H(2) and maximal Hölder exponent, h_max] and measuring strength of multifractality [full-width-half-maximum of D(h) and ΔH₁₅ = H(−15)−H(15)]. Correlation-based signal improvement (CBSI) enhanced our signal in terms of interpreting changes due to neural activity or local/systemic hemodynamic influences. We characterized the HbO-HbR relationship with the aid of fractal scale-wise correlation coefficient, r_σ(s) and SSC-based multifractal covariance analysis. In the majority of subjects, cerebral hemodynamic fluctuations proved bimodal multifractal. In case of slow component of raw HbT, h_max, and Ĥ(2) were lower in the young group explained by a significantly increased r_σ(s) among elderly at high temporal scales. Regarding the fast component of CBSI-pretreated HbT and that of HbO-HbR covariance, h_max, and focus were decreased in the elderly group. These observations suggest an attenuation of neurovascular coupling reflected by a decreased autocorrelation of the neuronal component concomitant with an accompanying increased autocorrelation of the non-neuronal component in the elderly group.

Novel analysis of fNIRS acquired dynamic hemoglobin concentrations: application in young children with autism spectrum disorder

A novel analysis of the spatial complexity of functional connectivity (SCFC) was proposed to investigate the spatial complexity of multiple dynamic functional connectivity series in an fNIRS study, using an approach combining principal component analysis and normalized entropy. The analysis was designed to describe the complex spatial features of phase synchrony based dynamic functional connectivity (dFC), which are unexplained in traditional approaches. The feasibility and validity of this method were verified in a sample of young patients with autism spectrum disorders (ASD). Our results showed that there were information exchange deficits in the right prefrontal cortex (PFC) of children with ASD, with markedly higher interregion SCFCs between the right PFC and other brain regions than those of normal controls. Furthermore, the global SCFC was significantly higher in young patients with ASD, along with considerably higher intraregion SCFCs in the prefrontal and temporal lobes which represents more diverse information exchange in these areas. The study suggests a novel method to analyze the fNIRS required dynamic hemoglobin concentrations by using concepts of SCFC. Moreover, the clinical results extend our understanding of ASD pathology, suggesting the crucial role of the right PFC during the information exchange process.

Analysis of fMRI data using noise-diffusion network models: a new covariance-coding perspective

Since the middle of the 1990s, studies of resting-state fMRI/BOLD data have explored the correlation patterns of activity across the whole brain, which is referred to as functional connectivity (FC). Among the many methods that have been developed to interpret FC, a recently proposed model-based approach describes the propagation of fluctuating BOLD activity within the recurrently connected brain network by inferring the effective connectivity (EC). In this model, EC quantifies the strengths of directional interactions between brain regions, viewed from the proxy of BOLD activity. In addition, the tuning procedure for the model provides estimates for the local variability (input variances) to explain how the observed FC is generated. Generalizing, the network dynamics can be studied in the context of an input-output mapping-determined by EC-for the second-order statistics of fluctuating nodal activities. The present paper focuses on the following detection paradigm: observing output covariances, how discriminative is the (estimated) network model with respect to various input covariance patterns? An application with the model fitted to experimental fMRI data-movie viewing versus resting state-illustrates that changes in local variability and changes in brain coordination go hand in hand.

Time scale properties of task and resting-state functional connectivity: Detrended partial cross-correlation analysis

Functional connectivity analysis is an essential tool for understanding brain function. Previous studies showed that brain regions are functionally connected through low-frequency signals both within the default mode network (DMN) and task networks. However, no studies have directly compared the time scale (frequency) properties of network connectivity during task versus rest, or examined how they relate to task performance. Here, using fMRI data collected from sixty-eight subjects at rest and during a stop signal task, we addressed this issue with a novel functional connectivity measure based on detrended partial cross-correlation analysis (DPCCA). DPCCA has the advantage of quantifying correlations between two variables in different time scales while controlling for the influence of other variables. The results showed that the time scales of within-network connectivity of the DMN and task networks are modulated in opposite directions across rest and task, with the time scale increased during rest vs. task in the DMN and vice versa in task networks. In regions of interest analysis, the within-network connectivity time scale of the pre-supplementary motor area - a medial prefrontal cortical structure of the task network and critical to proactive inhibitory control - correlated inversely with Barratt impulsivity and stop signal reaction time. Together, these findings demonstrate that time scale properties of brain networks may vary across mental states and provide evidence in support of a role of low frequency fluctuations of BOLD signals in behavioral control.

Spatio-temporal modeling of connectome-scale brain network interactions via time-evolving graphs

Many recent literature studies have revealed interesting dynamics patterns of functional brain networks derived from fMRI data. However, it has been rarely explored how functional networks spatially overlap (or interact) and how such connectome-scale network interactions temporally evolve. To explore these unanswered questions, this paper presents a novel framework for spatio-temporal modeling of connectome-scale functional brain network interactions via two main effective computational methodologies. First, to integrate, pool and compare brain networks across individuals and their cognitive states under task performances, we designed a novel group-wise dictionary learning scheme to derive connectome-scale consistent brain network templates that can be used to define the common reference space of brain network interactions. Second, the temporal dynamics of spatial network interactions is modeled by a weighted time-evolving graph, and then a data-driven unsupervised learning algorithm based on the dynamic behavioral mixed-membership model (DBMM) is adopted to identify behavioral patterns of brain networks during the temporal evolution process of spatial overlaps/interactions. Experimental results on the Human Connectome Project (HCP) task fMRI data showed that our methods can reveal meaningful, diverse behavior patterns of connectome-scale network interactions. In particular, those networks' behavior patterns are distinct across HCP tasks such as motor, working memory, language and social tasks, and their dynamics well correspond to the temporal changes of specific task designs. In general, our framework offers a new approach to characterizing human brain function by quantitative description for the temporal evolution of spatial overlaps/interactions of connectome-scale brain networks in a standard reference space.

Spatially regularized multifractal analysis for fMRI data

Scale-free dynamics is nowadays a massively used paradigm to model infraslow macroscopic brain activity. Multifractal analysis is becoming the standard tool to characterize scale-free dynamics. It is commonly used on various modalities of neuroimaging data to evaluate whether arrhythmic fluctuations in ongoing or evoked brain activity are related to pathologies (Alzheimer, epilepsy) or task performance. The success of multifractal analysis in neurosciences remains however so far contrasted: While it lead to relevant findings on M/EEG data, less clear impact was shown when applied to fMRI data. This is mostly due to their poor time resolution and very short duration as well as to the fact that analysis remains performed voxelwise. To take advantage of the large amount of voxels recorded jointly in fMRI, the present contribution proposes the use of a recently introduced Bayesian formalism for multifractal analysis, that regularizes the estimation of the multifractality parameter of a given voxel using information from neighbor voxels. The benefits of this regularized multifractal analysis are illustrated by comparison against classical multifractal analysis on fMRI data collected on one subject, at rest and during a working memory task: Though not yet statistically significant, increased multifractality is observed in task-negative and task-positive networks, respectively.

Effective connectivity inferred from fMRI transition dynamics during movie viewing points to a balanced reconfiguration of cortical interactions

Our behavior entails a flexible and context-sensitive interplay between brain areas to integrate information according to goal-directed requirements. However, the neural mechanisms governing the entrainment of functionally specialized brain areas remain poorly understood. In particular, the question arises whether observed changes in the regional activity for different cognitive conditions are explained by modifications of the inputs to the brain or its connectivity? We observe that transitions of fMRI activity between areas convey information about the tasks performed by 19 subjects, watching a movie versus a black screen (rest). We use a model-based framework that explains this spatiotemporal functional connectivity pattern by the local variability for 66 cortical regions and the network effective connectivity between them. We find that, among the estimated model parameters, movie viewing affects to a larger extent the local activity, which we interpret as extrinsic changes related to the increased stimulus load. However, detailed changes in the effective connectivity preserve a balance in the propagating activity and select specific pathways such that high-level brain regions integrate visual and auditory information, in particular boosting the communication between the two brain hemispheres. These findings speak to a dynamic coordination underlying the functional integration in the brain.

Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach.

Task-based dynamic functional connectivity: Recent findings and open questions

The temporal evolution of functional connectivity (FC) within the confines of individual scans is nowadays often explored with functional neuroimaging. This is particularly true for resting-state; yet, FC-dynamics have also been investigated as subjects engage on numerous tasks. It is these research efforts that constitute the core of this survey. First, empirical observations on how FC differs between task and rest-independent of temporal scale-are reviewed, as they underscore how, despite overall preservation of network topography, the brain's FC does reconfigure in systematic ways to accommodate task demands. Next, reports on the relationships between instantaneous FC and perception/performance in subsequent trials are discussed. Similarly, research where different aspects of task-concurrent FC-dynamics are explored or utilized to predict ongoing mental states are also examined. The manuscript finishes with an incomplete list of challenges that hopefully fuels future work in this vibrant area of neuroscientific research. Overall, this review concludes that task-concurrent FC-dynamics, when properly characterized, are relevant to behavior, and that their translational value holds considerable promise.

Inverse stochastic resonance in networks of spiking neurons

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron's intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

Critical dynamics of endogenous fluctuations predict cognitive flexibility in the Go/NoGo task

Fluctuations with power-law scaling and long-range temporal correlations (LRTCs) are characteristic to human psychophysical performance. Systems operating in a critical state exhibit such LRTCs, but phenomenologically similar fluctuations and LRTCs may also be caused by slow decay of the system’s memory without the system being critical. Theoretically, criticality endows the system with the greatest representational capacity and flexibility in state transitions. Without criticality, however, slowly decaying system memory would predict inflexibility. We addressed these contrasting predictions of the ‘criticality’ and ‘long-memory’ candidate mechanisms of human behavioral LRTCs by using a Go/NoGo task wherein the commission errors constitute a measure of cognitive flexibility. Response time (RT) fluctuations in this task exhibited power-law frequency scaling, autocorrelations, and LRTCs. We show here that the LRTC scaling exponents, quantifying the strength of long-range correlations, were negatively correlated with the commission error rates. Strong LRTCs hence parallel optimal cognitive flexibility and, in line with the criticality hypothesis, indicate a functionally advantageous state. This conclusion was corroborated by a positive correlation between the LRTC scaling exponents and executive functions measured with the Rey-Osterrieth Complex Figure test. Our results hence support the notion that LRTCs arise from critical dynamics that is functionally significant for human cognitive performance.