Spectral properties of the temporal evolution of brain network structure

Disordered beta thinned ensemble with applications

It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. The purpose of the present study is to deepen this kind of approach by performing a more comprehensive spectral analysis that measures both the local- and long-range statistics. We have found that, as a common feature, spectra of this kind can exhibit a situation in which local statistics are relatively quenched while the long-range ones show large fluctuations. By combining three extensions of the standard random matrix theory (RMT) and considering long spectra, we demonstrate that this phenomenon occurs when disorder and level incompleteness are introduced in an RMT spectrum. Consequently, the long-range statistics follow Taylor's law, suggesting the presence of a fluctuation scaling (FS) mechanism in this kind of spectra. Applications of the combined ensemble are then presented for spectra originate from several very diverse areas, including complex networks, COVID-19 time series, and quantitative linguistics, which demonstrate that short- and long-range statistics reflect the rigid and elastic characteristics of a given spectrum, respectively. These observations may shed some light on spectral data classification.

Flexible brain transitions between hierarchical network segregation and integration associated with cognitive performance during a multisource interference task

Cognition involves locally segregated and globally integrated processing. This process is hierarchically organized and linked to evidence from hierarchical modules in brain networks. However, researchers have not clearly determined how flexible transitions between these hierarchical processes are associated with cognitive behavior. Here, we designed a multisource interference task (MSIT) and introduced the nested-spectral partition (NSP) method to detect hierarchical modules in brain functional networks. By defining hierarchical segregation and integration across multiple levels, we showed that the MSIT requires higher network segregation in the whole brain and most functional systems but generates higher integration in the control system. Meanwhile, brain networks have more flexible transitions between segregated and integrated configurations in the task state. Crucially, higher functional flexibility in the resting state, less flexibility in the task state and more efficient switching of the brain from resting to task states were associated with better task performance. Our hierarchical modular analysis was more effective at detecting alterations in functional organization and the phenotype of cognitive performance than graph-based network measures at a single level.

Transcranial photobiomodulation changes topology, synchronizability, and complexity of resting state brain networks

Objective. Transcranial photobiomodulation (tPBM) is a recently proposed non-invasive brain stimulation approach with various effects on the nervous system from the cells to the whole brain networks. Specially in the neural network level, tPBM can alter the topology and synchronizability of functional brain networks. However, the functional properties of the neural networks after tPBM are still poorly clarified.Approach. Here, we employed electroencephalography and different methods (conventional and spectral) in the graph theory analysis to track the significant effects of tPBM on the resting state brain networks. The non-parametric statistical analysis showed that just one short-term tPBM session over right medial frontal pole can significantly change both topological (i.e. clustering coefficient, global efficiency, local efficiency, eigenvector centrality) and dynamical (i.e. energy, largest eigenvalue, and entropy) features of resting state brain networks.Main results. The topological results revealed that tPBM can reduce local processing, centrality, and laterality. Furthermore, the increased centrality of central electrode was observed.Significance. These results suggested that tPBM can alter topology of resting state brain network to facilitate the neural information processing. On the other hand, the dynamical results showed that tPBM reduced stability of synchronizability and increased complexity in the resting state brain networks. These effects can be considered in association with the increased complexity of connectivity patterns among brain regions and the enhanced information propagation in the resting state brain networks. Overall, both topological and dynamical features of brain networks suggest that although tPBM decreases local processing (especially in the right hemisphere) and disrupts synchronizability of network, but it can increase the level of information transferring and processing in the brain network.

Synchrony and Complexity in State-Related EEG Networks: An Application of Spectral Graph Theory

The brain may be considered as a synchronized dynamic network with several coherent dynamical units. However, concerns remain whether synchronizability is a stable state in the brain networks. If so, which index can best reveal the synchronizability in brain networks? To answer these questions, we tested the application of the spectral graph theory and the Shannon entropy as alternative approaches in neuroimaging. We specifically tested the alpha rhythm in the resting-state eye closed (rsEC) and the resting-state eye open (rsEO) conditions, a well-studied classical example of synchrony in neuroimaging EEG. Since the synchronizability of alpha rhythm is more stable during the rsEC than the rsEO, we hypothesized that our suggested spectral graph theory indices (as reliable measures to interpret the synchronizability of brain signals) should exhibit higher values in the rsEC than the rsEO condition. We performed two separate analyses of two different datasets (as elementary and confirmatory studies). Based on the results of both studies and in agreement with our hypothesis, the spectral graph indices revealed higher stability of synchronizability in the rsEC condition. The k-mean analysis indicated that the spectral graph indices can distinguish the rsEC and rsEO conditions by considering the synchronizability of brain networks. We also computed correlations among the spectral indices, the Shannon entropy, and the topological indices of brain networks, as well as random networks. Correlation analysis indicated that although the spectral and the topological properties of random networks are completely independent, these features are significantly correlated with each other in brain networks. Furthermore, we found that complexity in the investigated brain networks is inversely related to the stability of synchronizability. In conclusion, we revealed that the spectral graph theory approach can be reliably applied to study the stability of synchronizability of state-related brain networks.

Random matrix theory for analysing the brain functional network in lower limb motor imagery

We use random matrix theory (RMT) to investigate the statistical properties of brain functional networks in lower limb motor imagery. Functional connectivity was calculated by Pearson correlation coefficient (PCC), mutual information (MTI) and phase locking value (PLV) extracted from EEG signals. We found that when the measured subjects imagined the movements of their lower limbs the spectral density as well as the level spacings displayed deviations from the random matrix prediction. In particular, a significant difference between the left and right foot imaginary movements was observed in the maximum eigenvalue from the PCC, which can provide a theoretical basis for further study on the classification of unilateral movement of lower limbs.

Topics and trends in artificial intelligence assisted human brain research

Artificial intelligence (AI) assisted human brain research is a dynamic interdisciplinary field with great interest, rich literature, and huge diversity. The diversity in research topics and technologies keeps increasing along with the tremendous growth in application scope of AI-assisted human brain research. A comprehensive understanding of this field is necessary to assess research efficacy, (re)allocate research resources, and conduct collaborations. This paper combines the structural topic modeling (STM) with the bibliometric analysis to automatically identify prominent research topics from the large-scale, unstructured text of AI-assisted human brain research publications in the past decade. Analyses on topical trends, correlations, and clusters reveal distinct developmental trends of these topics, promising research orientations, and diverse topical distributions in influential countries/regions and research institutes. These findings help better understand scientific and technological AI-assisted human brain research, provide insightful guidance for resource (re)allocation, and promote effective international collaborations.

Sample Entropy Combined with the K-Means Clustering Algorithm Reveals Six Functional Networks of the Brain

Identifying brain regions contained in brain functional networks and functions of brain functional networks is of great significance in understanding the complexity of the human brain. The 160 regions of interest (ROIs) in the human brain determined by the Dosenbach’s template have been divided into six functional networks with different functions. In the present paper, the complexity of the human brain is characterized by the sample entropy (SampEn) of dynamic functional connectivity (FC) which is obtained by analyzing the resting-state functional magnetic resonance imaging (fMRI) data acquired from healthy participants. The 160 ROIs are clustered into six clusters by applying the K-means clustering algorithm to the SampEn of dynamic FC as well as the static FC which is also obtained by analyzing the resting-state fMRI data. The six clusters obtained from the SampEn of dynamic FC and the static FC show very high overlap and consistency ratios with the six functional networks. Furthermore, for four of six clusters, the overlap ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC, and for five of six clusters, the consistency ratios corresponding to the SampEn of dynamic FC are larger than that corresponding to the static FC. The results show that the combination of machine learning methods and the FC obtained using the blood oxygenation level-dependent (BOLD) signals can identify the functional networks of the human brain, and nonlinear dynamic characteristics of the FC are more effective than the static characteristics of the FC in identifying brain functional networks and the complexity of the human brain.

Random Matrix Analysis of Ca2+ Signals in β-Cell Collectives

Even within small organs like pancreatic islets, different endocrine cell types and subtypes form a heterogeneous collective to sense the chemical composition of the extracellular solution and compute an adequate hormonal output. Erroneous cellular processing and hormonal output due to challenged heterogeneity result in various disorders with diabetes mellitus as a flagship metabolic disease. Here we attempt to address the aforementioned functional heterogeneity with comparing pairwise cell-cell cross-correlations obtained from simultaneous measurements of cytosolic calcium responses in hundreds of islet cells in an optical plane to statistical properties of correlations predicted by the random matrix theory (RMT). We find that the bulk of the empirical eigenvalue spectrum is almost completely described by RMT prediction, however, the deviating eigenvalues that exist below and above RMT spectral edges suggest that there are local and extended modes driving the correlations. We also show that empirical nearest neighbor spacing of eigenvalues follows universal RMT properties regardless of glucose stimulation, but that number variance displays clear separation from RMT prediction and can differentiate between empirical spectra obtained under non-stimulated and stimulated conditions. We suggest that RMT approach provides a sensitive tool to assess the functional cell heterogeneity and its effects on the spatio-temporal dynamics of a collective of beta cells in pancreatic islets in physiological resting and stimulatory conditions, beyond the current limitations of molecular and cellular biology.

Hierarchical integrated and segregated processing in the functional brain default mode network within attention-deficit/hyperactivity disorder

The hierarchical modular organization of functional networks in the brain is crucial for supporting diverse cognitive functions. Functional disorders in the brain are associated with an abnormal hierarchical modular organization. The default mode network (DMN) is a complex dynamic network that is linked to specialized cognitive functions and clinically relevant information. In this study, we hypothesize that hierarchical functional segregation and integration of the DMN within attention-deficit/hyperactivity disorder (ADHD) is abnormal. We investigated topological metrics of both segregation and integration in different hierarchical subnetworks of the DMN between patients with ADHD and healthy controls. We found that the hierarchical functional integration and segregation of the DMN decreased and increased, respectively, in ADHD. Our results also indicated that the abnormalities in the DMN are intrinsically caused by changes in functional segregation and integration in its higher-level subnetworks. To better understand the temporally dynamic changes in the hierarchical functional integration and segregation of the DMN within ADHD, we further analyzed the dynamic transitions between functional segregation and integration. We found that the adaptive reorganizational ability of brain network states decreased in ADHD patients, which indicated less adaptive regulation between the DMN subnetworks in ADHD for supporting correspondingly normal cognitive function. From the perspective of hierarchical functional segregation and integration, our results further provide evidence to support dysfunctional brain cognitive functions within ADHD linked to brain network segregation and integration.

Functional Connectivity Pattern Analysis Underlying Neural Oscillation Synchronization during Deception

To characterize system cognitive processes during deception, event-related coherence was computed to investigate the functional connectivity among brain regions underlying neural oscillation synchronization. In this study, 15 participants were randomly assigned to honesty or deception groups and were instructed to tell the truth or lie when facing certain stimuli. Meanwhile, event-related potential signals were recorded using a 64-channel electroencephalography cap. Event-related coherence was computed separately in four frequency bands (delta (1-3.5 Hz), theta (4-7 Hz), alpha (8-13 Hz), and beta (14-30 HZ)) for the long-range intrahemispheric electrode pairs (F3P3, F4P4, F3T7, F4T8, F3O1, and F4O2). The results indicated that deceptive responses elicited greater connectivities in the frontoparietal and frontotemporal networks than in the frontooccipital network. Furthermore, the deception group displayed lower values of coherence in the frontoparietal electrode pairs in the alpha and beta bands than the honesty group. In particular, increased coherence in the delta and theta bands on specific left frontoparietal electrode pairs was observed. Additionally, the deception group exhibited higher values of coherence in the delta band and lower values of coherence in the beta band on the frontotemporal electrode pairs than did the honesty group. These data indicated that the active cognitive processes during deception include changes in ensemble activities between the frontal and parietal/temporal regions.

Spectral properties of complex networks

This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part of the spectrum, and (c) degenerate eigenvalues, based on the intrinsic properties of eigenvalues and the phenomena they capture. We have reviewed the works done for spectra of various popular model networks, such as the Erdős-Rényi random networks, scale-free networks, 1-d lattice, small-world networks, and various different real-world networks. Additionally, potential applications of spectral properties for natural processes have been reviewed.

Crossover in nonstandard random-matrix spectral fluctuations without unfolding

Recently, singular value decomposition (SVD) was applied to standard Gaussian ensembles of random-matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the β-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a crossover between soft and rigid behavior. In this way, possible artifacts introduced applying unfolding techniques are avoided. By using the trend modes, we perform data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.

Connectivity in fMRI: Blind Spots and Breakthroughs

In recent years, driven by scientific and clinical concerns, there has been an increased interest in the analysis of functional brain networks. The goal of these analyses is to better understand how brain regions interact, how this depends upon experimental conditions and behavioral measures and how anomalies (disease) can be recognized. In this paper, we provide, first, a brief review of some of the main existing methods of functional brain network analysis. But rather than compare them, as a traditional review would do, instead, we draw attention to their significant limitations and blind spots. Then, second, relevant experts, sketch a number of emerging methods, which can break through these limitations. In particular we discuss five such methods. The first two, stochastic block models and exponential random graph models, provide an inferential basis for network analysis lacking in the exploratory graph analysis methods. The other three addresses: network comparison via persistent homology, time-varying connectivity that distinguishes sample fluctuations from neural fluctuations, and network system identification that draws inferential strength from temporal autocorrelation.

Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6-7% of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.

Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation

The gliotransmitter glutamate released from astrocytes can modulate neuronal firing by activating neuronal N-methyl-D-aspartic acid (NMDA) receptors. This enables astrocytic glutamate(AG) to be involved in neuronal physiological and pathological functions. Based on empirical results and classical neuron-glial "tripartite synapse" model, we propose a practical model to describe extracellular AG oscillation, in which the fluctuation of AG depends on the threshold of calcium concentration, and the effect of AG degradation is considered as well. We predict the seizure-like discharges under the dysfunction of AG degradation duration. Consistent with our prediction, the suppression of AG uptake by astrocytic transporters, which operates by modulating the AG degradation process, can account for the emergence of epilepsy.