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

Cross-module switching diversity of brain network nodes in resting and cognitive states

Large-scale brain network dynamics reflect state change in brain activities and have potential effects on cognition. Such dynamics can be described by node temporal switching between modules; however, there are only a few studies on the influence of brain network node switching on brain cognition. Based on the functional magnetic resonance imaging (fMRI) data of resting and task states, we constructed dynamic functional networks using overlap sliding-time windows and applied multilayer network analysis to study the behaviours of nodes across brain modules. We found that (i) nodes with a high level switching rate in the resting-state mainly come from the default network, while nodes with a low level of switching rate mainly come from the visual network, (ii) nodes with a high switching rate have lower clustering coefficients and shorter characteristic path lengths, which are mainly affected by the somatomotor network and dorsal attention network; and (iii) in task states, there is still a negative correlation between switching rate, clustering coefficient and characteristic path length. However, the main subsystems that affect brain functions are regulated by the tasks. Our findings not only reveal the relevant characteristics of network node switching behaviours but also provide new insights for further understanding the complex functions of the brain.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09894-z.

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.

Cohesive communities in dynamic brain functional networks

In large-scale brain network dynamics, brain nodes switching between modules has been found to correlate with cognition. However, how the brain nodes engage in this kind of reorganization of modules is unclear. Based on a functional magnetic resonance imaging dataset, we construct dynamic brain functional networks and investigate nodal module temporal dynamic behavior by applying the multilayer network analysis approach. We reveal three cohesive communities that are groups of brain nodes linked in the same community during brain module dynamic reorganization. We show that the cohesive communities have higher clustering coefficients and lower characteristic path lengths than the controlled community, indicating cohesive communities are the parts of brain networks with high information processing efficiency. The smaller sample entropy of functional connectivity in cohesive communities also proves their property of being more "static" compared with the controlled community in brain dynamics. Specifically, compared with the controlled community, the functional connectivity of cohesive communities is restricted strictly by structure connectivity and shows more similarity to structure connectivity. More importantly, we find that the cohesive communities are stable not only in the resting state but also when processing cognitive tasks. Our results not only show that cohesive communities may be the fundamental community organization to support brain network dynamics but also provide insights into the intrinsic structural relationship between the resting state and task states of the brain.

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.

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.

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.

Dynamic Default Mode Network across Different Brain States

The default mode network (DMN) is a complex dynamic network that is critical for understanding cognitive function. However, whether dynamic topological reconfiguration of the DMN occurs across different brain states, and whether this potential reorganization is associated with prior learning or experience is unclear. To better understand the temporally changing topology of the DMN, we investigated both nodal and global dynamic DMN-topology metrics across different brain states. We found that DMN topology changes over time and those different patterns are associated with different brain states. Further, the nodal and global topological organization can be rebuilt by different brain states. These results indicate that the post-task, resting-state topology of the brain network is dynamically altered as a function of immediately prior cognitive experience, and that these modulated networks are assembled in the subsequent state. Together, these findings suggest that the changing topology of the DMN may play an important role in characterizing brain states.