Resting state MEG oscillations show long-range temporal correlations of phase synchrony that break down during finger movement

Entropy and fractal analysis of brain-related neurophysiological signals in Alzheimer's and Parkinson's disease

Brain-related neuronal recordings, such as local field potential, electroencephalogram and magnetoencephalogram, offer the opportunity to study the complexity of the human brain at different spatial and temporal scales. The complex properties of neuronal signals are intrinsically related to the concept of 'scale-free' behavior and irregular dynamic, which cannot be fully described through standard linear methods, but can be measured by nonlinear indexes. A remarkable application of these analysis methods on electrophysiological recordings is the deep comprehension of the pathophysiology of neurodegenerative diseases, that has been shown to be associated to changes in brain activity complexity. In particular, a decrease of global complexity has been associated to Alzheimer's disease, while a local increase of brain signals complexity characterizes Parkinson's disease. Despite the recent proliferation of studies using fractal and entropy-based analysis, the application of these techniques is still far from clinical practice, due to the lack of an agreement about their correct estimation and a conclusive and shared interpretation. Along with the aim of helping towards the realization of a multidisciplinary audience to approach nonlinear methods based on the concepts of fractality and irregularity, this survey describes the implementation and proper employment of the mostly known and applied indexes in the context of Alzheimer's and Parkinson's diseases.

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.

Mixtures of large-scale dynamic functional brain network modes

Accurate temporal modelling of functional brain networks is essential in the quest for understanding how such networks facilitate cognition. Researchers are beginning to adopt time-varying analyses for electrophysiological data that capture highly dynamic processes on the order of milliseconds. Typically, these approaches, such as clustering of functional connectivity profiles and Hidden Markov Modelling (HMM), assume mutual exclusivity of networks over time. Whilst a powerful constraint, this assumption may be compromising the ability of these approaches to describe the data effectively. Here, we propose a new generative model for functional connectivity as a time-varying linear mixture of spatially distributed statistical "modes". The temporal evolution of this mixture is governed by a recurrent neural network, which enables the model to generate data with a rich temporal structure. We use a Bayesian framework known as amortised variational inference to learn model parameters from observed data. We call the approach DyNeMo (for Dynamic Network Modes), and show using simulations it outperforms the HMM when the assumption of mutual exclusivity is violated. In resting-state MEG, DyNeMo reveals a mixture of modes that activate on fast time scales of 100-150 ms, which is similar to state lifetimes found using an HMM. In task MEG data, DyNeMo finds modes with plausible, task-dependent evoked responses without any knowledge of the task timings. Overall, DyNeMo provides decompositions that are an approximate remapping of the HMM's while showing improvements in overall explanatory power. However, the magnitude of the improvements suggests that the HMM's assumption of mutual exclusivity can be reasonable in practice. Nonetheless, DyNeMo provides a flexible framework for implementing and assessing future modelling developments.

The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus

This is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars. In prequel II, the network effect was introduced to explain how the collective dynamics of a complex network can transform a many-body non-linear dynamical system modeled using the integer calculus (IC) into a single-body fractional stochastic rate equation. Note that these essays are about biomedical phenomena that have historically been improperly modeled using the IC and how fractional calculus (FC) models better explain experimental results. This essay presents the biomedical entailment of the FC, but it is not a mathematical discussion in the sense that we are not concerned with the formal infrastucture, which is cited, but we are concerned with what that infrastructure entails. For example, the health of a physiologic network is characterized by the width of the multifractal spectrum associated with its time series, and which becomes narrower with the onset of certain pathologies. Physiologic time series that have explicitly related pathology to a narrowing of multifractal time series include but are not limited to heart rate variability (HRV), stride rate variability (SRV) and breath rate variability (BRV). The efficiency of the transfer of information due to the interaction between two such complex networks is determined by their relative spectral width, with information being transferred from the network with the broader to that with the narrower width. A fractional-order differential equation, whose order is random, is shown to generate a multifractal time series, thereby providing a FC model of the information exchange between complex networks. This equivalence between random fractional derivatives and multifractality has not received the recognition in the bioapplications literature we believe it warrants.

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.

Dynamics of Long-Range Temporal Correlations in Broadband EEG During Different Motor Execution and Imagery Tasks

Brain activity is composed of oscillatory and broadband arrhythmic components; however, there is more focus on oscillatory sensorimotor rhythms to study movement, but temporal dynamics of broadband arrhythmic electroencephalography (EEG) remain unexplored. We have previously demonstrated that broadband arrhythmic EEG contains both short- and long-range temporal correlations that change significantly during movement. In this study, we build upon our previous work to gain a deeper understanding of these changes in the long-range temporal correlation (LRTC) in broadband EEG and contrast them with the well-known LRTC in alpha oscillation amplitude typically found in the literature. We investigate and validate changes in LRTCs during five different types of movements and motor imagery tasks using two independent EEG datasets recorded with two different paradigms-our finger tapping dataset with single self-initiated asynchronous finger taps and publicly available EEG dataset containing cued continuous movement and motor imagery of fists and feet. We quantified instantaneous changes in broadband LRTCs by detrended fluctuation analysis on single trial 2 s EEG sliding windows. The broadband LRTC increased significantly (p < 0.05) during all motor tasks as compared to the resting state. In contrast, the alpha oscillation LRTC, which had to be computed on longer stitched EEG segments, decreased significantly (p < 0.05) consistently with the literature. This suggests the complementarity of underlying fast and slow neuronal scale-free dynamics during movement and motor imagery. The single trial broadband LRTC gave high average binary classification accuracy in the range of 70.54±10.03% to 76.07±6.40% for all motor execution and imagery tasks and hence can be used in brain-computer interface (BCI). Thus, we demonstrate generalizability, robustness, and reproducibility of novel motor neural correlate, the single trial broadband LRTC, during different motor execution and imagery tasks in single asynchronous and cued continuous motor-BCI paradigms and its contrasting behavior with LRTC in alpha oscillation amplitude.

Altered Temporal Structure of Neural Phase Synchrony in Patients With Autism Spectrum Disorder

Functional connectivity, quantified by phase synchrony, between brain regions is known to be aberrant in patients with autism spectrum disorder (ASD). Here, we evaluated the long-range temporal correlations of time-varying phase synchrony (TV-PS) of electrocortical oscillations in patients with ASD as well as typically developing people using detrended fluctuation analysis (DFA) after validating the scale-invariance of the TV-PS time series. By comparing the DFA exponents between the two groups, we found that those of the TV-PS time series of high-gamma oscillations were significantly attenuated in patients with ASD. Furthermore, the regions involved in aberrant TV-PS time series were mainly within the social ability and cognition-related cortical networks. These results support the notion that abnormal social functions observed in patients with ASD may be caused by the highly volatile phase synchrony states of electrocortical oscillations.

Why Brain Criticality Is Clinically Relevant: A Scoping Review

The past 25 years have seen a strong increase in the number of publications related to criticality in different areas of neuroscience. The potential of criticality to explain various brain properties, including optimal information processing, has made it an increasingly exciting area of investigation for neuroscientists. Recent reviews on this topic, sometimes termed brain criticality, make brief mention of clinical applications of these findings to several neurological disorders such as epilepsy, neurodegenerative disease, and neonatal hypoxia. Other clinicallyrelevant domains - including anesthesia, sleep medicine, developmental-behavioral pediatrics, and psychiatry - are seldom discussed in review papers of brain criticality. Thorough assessments of these application areas and their relevance for clinicians have also yet to be published. In this scoping review, studies of brain criticality involving human data of all ages are evaluated for their current and future clinical relevance. To make the results of these studies understandable to a more clinical audience, a review of the key concepts behind criticality (e.g., phase transitions, long-range temporal correlation, self-organized criticality, power laws, branching processes) precedes the discussion of human clinical studies. Open questions and forthcoming areas of investigation are also considered.

Modeling the Ongoing Dynamics of Short and Long-Range Temporal Correlations in Broadband EEG During Movement

Electroencephalogram (EEG) undergoes complex temporal and spectral changes during voluntary movement intention. Characterization of such changes has focused mostly on narrowband spectral processes such as Event-Related Desynchronization (ERD) in the sensorimotor rhythms because EEG is mostly considered as emerging from oscillations of the neuronal populations. However, the changes in the temporal dynamics, especially in the broadband arrhythmic EEG have not been investigated for movement intention detection. The Long-Range Temporal Correlations (LRTC) are ubiquitously present in several neuronal processes, typically requiring longer timescales to detect. In this paper, we study the ongoing changes in the dynamics of long- as well as short-range temporal dependencies in the single trial broadband EEG during movement intention. We obtained LRTC in 2 s windows of broadband EEG and modeled it using the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model which allowed simultaneous modeling of short- and long-range temporal correlations. There were significant (p < 0.05) changes in both broadband long- and short-range temporal correlations during movement intention and execution. We discovered that the broadband LRTC and narrowband ERD are complementary processes providing distinct information about movement because eliminating LRTC from the signal did not affect the ERD and conversely, eliminating ERD from the signal did not affect LRTC. Exploring the possibility of applications in Brain Computer Interfaces (BCI), we used hybrid features with combinations of LRTC, ARFIMA, and ERD to detect movement intention. A significantly higher (p < 0.05) classification accuracy of 88.3 ± 4.2% was obtained using the combination of ARFIMA and ERD features together, which also predicted the earliest movement at 1 s before its onset. The ongoing changes in the long- and short-range temporal correlations in broadband EEG contribute to effectively capturing the motor command generation and can be used to detect movement successfully. These temporal dependencies provide different and additional information about the movement.

25 years of criticality in neuroscience - established results, open controversies, novel concepts

Twenty-five years ago, Dunkelmann and Radons (1994) showed that neural networks can self-organize to a critical state. In models, the critical state offers a number of computational advantages. Thus this hypothesis, and in particular the experimental work by Beggs and Plenz (2003), has triggered an avalanche of research, with thousands of studies referring to it. Nonetheless, experimental results are still contradictory. How is it possible, that a hypothesis has attracted active research for decades, but nonetheless remains controversial? We discuss the experimental and conceptual controversy, and then present a parsimonious solution that (i) unifies the contradictory experimental results, (ii) avoids disadvantages of a critical state, and (iii) enables rapid, adaptive tuning of network properties to task requirements.

Attenuated long-range temporal correlations of electrocortical oscillations in patients with autism spectrum disorder

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The LRTCs of beta and low-gamma oscillations were significantly attenuated in ASD patients compared to TD participants.

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The regions with attenuated LRTCs were mainly located in certain social functions related cortical networks.

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ASD is associated with highly volatile neuronal states of electrocortical oscillations.

The aim of this study was to investigate the long-range temporal correlations (LRTCs) of instantaneous amplitude of electrocortical oscillations in patients with autism spectrum disorder (ASD). Using the resting-state electroencephalography (EEG) of 15 patients with ASD (aged between 5˜18 years, mean age = 11.6 years, SD = 4.4 years) and 18 typical developing (TD) people (aged between 5˜18 years, mean age = 8.9 years, SD = 2.4 years), we estimated the LRTCs of neuronal oscillations amplitude of 84 predefined cortical regions of interest using detrended fluctuation analysis (DFA) after confirming the presence of scale invariance. We found that the DFA exponents of instantaneous amplitude of beta and low-gamma oscillations were significantly attenuated in patients with ASD compared to TD participants. Moreover, the regions with attenuated DFA exponent were mainly located in social functions related cortical networks, including the default mode network (DMN), the mirror neuron system (MNS) and the salience network (SN). These findings suggest that ASD is associated with highly volatile neuronal states of electrocortical oscillations, which may be related to social and cognitive dysfunction in patients with ASD.

A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener–Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.

Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two?

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both.

Characterization of Noise Signatures of Involuntary Head Motion in the Autism Brain Imaging Data Exchange Repository

The variability inherently present in biophysical data is partly contributed by disparate sampling resolutions across instrumentations. This poses a potential problem for statistical inference using pooled data in open access repositories. Such repositories combine data collected from multiple research sites using variable sampling resolutions. One example is the Autism Brain Imaging Data Exchange repository containing thousands of imaging and demographic records from participants in the spectrum of autism and age-matched neurotypical controls. Further, statistical analyses of groups from different diagnoses and demographics may be challenging, owing to the disparate number of participants across different clinical subgroups. In this paper, we examine the noise signatures of head motion data extracted from resting state fMRI data harnessed under different sampling resolutions. We characterize the quality of the noise in the variability of the raw linear and angular speeds for different clinical phenotypes in relation to age-matched controls. Further, we use bootstrapping methods to ensure compatible group sizes for statistical comparison and report the ranges of physical involuntary head excursions of these groups. We conclude that different sampling rates do affect the quality of noise in the variability of head motion data and, consequently, the type of random process appropriate to characterize the time series data. Further, given a qualitative range of noise, from pink to brown noise, it is possible to characterize different clinical subtypes and distinguish them in relation to ranges of neurotypical controls. These results may be of relevance to the pre-processing stages of the pipeline of analyses of resting state fMRI data, whereby head motion enters the criteria to clean imaging data from motion artifacts.

Attenuation of temporal correlations of neuronal oscillations in patients with mild spastic diplegia

The aim of this study was to investigate the temporal correlations of neuronal oscillations in patients with mild spastic diplegia (MSD). Resting-state electroencephalography (EEG) was recorded from 15 male adolescent and young adult patients with MSD and 15 healthy controls. We characterized the temporal correlations of neuronal oscillations, both on long temporal scale (i.e., >1 second) and short-to-intermediate temporal scale (i.e., <≈1 second) using detrended fluctuation analysis (DFA) and an analysis of the life- and waiting-time statistics of oscillation bursts respectively. The DFA exponents at alpha and beta bands, the life-time biomarker of alpha oscillation, and the life- and waiting-time biomarkers of beta oscillation were significantly attenuated in the patients compared with controls. Moreover, altered scalp distributions of some temporal correlation measures were found at alpha and beta bands in these patients. All these findings suggest that MSD is associated with highly volatile neuronal states of alpha and beta oscillations on short-to-intermediate and much longer time scales, which may be related to cognitive dysfunction in patients with MSD.

The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity

In this paper we investigated the dopaminergic modulation of neuronal interactions occurring in the subthalamic nucleus (STN) during Parkinson's disease (PD). We utilized linear measures of local and long range synchrony such as power and coherence, as well as Detrended Fluctuation Analysis for Phase Synchrony (DFA-PS)- a recently developed non-linear method that computes the extent of long tailed autocorrelations present in the phase interactions between two coupled signals. Through analysis of local field potentials (LFPs) taken from the STN we seek to determine changes in the neurodynamics that may underpin the pathophysiology of PD in a group of 12 patients who had undergone surgery for deep brain stimulation. We demonstrate up modulation of alpha-theta (5-12 Hz) band power in response to L-DOPA treatment, whilst low beta band power (15-20 Hz) band-power is suppressed. We also find evidence for significant local connectivity within the region surrounding STN although there was evidence for its modulation via administration of L-DOPA. Further to this we present evidence for a positive correlation between the phase ordering of bilateral STN interactions and the severity of bradykinetic and rigidity symptoms in PD. Although, the ability of non-linear measures to predict clinical state did not exceed standard measures such as beta power, these measures may help identify the connections which play a role in pathological dynamics.