Brain Network Features Research Articles

Investigation of phase synchronization in functional brain networks of children with ADHD using nonlinear recurrence measure

Investigation of phase synchronization in functional brain networks of children with ADHD using nonlinear recurrence measure

An Explainable Statistical Method for Seizure Prediction Using Brain Functional Connectivity from EEG.

Epilepsy is a group of chronic neurological disorders characterized by recurrent and abrupt seizures. The accurate prediction of seizures can reduce the burdens of this disorder. Now, existing studies use brain network features to classify patients' preictal or interictal states, enabling seizure prediction. However, most predicting methods are based on deep learning techniques, which have weak interpretability and high computational complexity. To address these issues, in this study, we proposed a novel two-stage statistical method that is interpretable and easy to compute. We used two datasets to evaluate the performance of the proposed method, including the well-known public dataset CHB-MIT. In the first stage, we estimated the dynamic brain functional connectivity network for each epoch. Then, in the second stage, we used the derived network predictor for seizure prediction. We illustrated the results of our method in seizure prediction in two datasets separately. For the FH-PKU dataset, our approach achieved an AUC value of 0.963, a prediction sensitivity of 93.1%, and a false discovery rate of 7.7%. For the CHB-MIT dataset, our approach achieved an AUC value of 0.940, a prediction sensitivity of 93.0%, and a false discovery rate of 11.1%, outperforming existing state-of-the-art methods. Significance. This study proposed an explainable statistical method, which can estimate the brain network using the scalp EEG method and use the net-work predictor to predict epileptic seizures. Availability and Implementation. R Source code is available at https://github.com/HaoChen1994/Seizure-Prediction.

MV2Net: Multi-Variate Multi-View Brain Network Comparison over Uncertain Data.

Visually identifying effective bio-markers from human brain networks poses non-trivial challenges to the field of data visualization and analysis. Existing methods in the literature and neuroscience practice are generally limited to the study of individual connectivity features in the brain (e.g., the strength of neural connection among brain regions). Pairwise comparisons between contrasting subject groups (e.g., the diseased and the healthy controls) are normally performed. The underlying neuroimaging and brain network construction process is assumed to have 100% fidelity. Yet, real-world user requirements on brain network visual comparison lean against these assumptions. In this work, we present MV^2Net, a visual analytics system that tightly integrates multi-variate multi-view visualization for brain network comparison with an interactive wrangling mechanism to deal with data uncertainty. On the analysis side, the system integrates multiple extraction methods on diffusion and geometric connectivity features of brain networks, an anomaly detection algorithm for data quality assessment, single- and multi-connection feature selection methods for bio-marker detection. On the visualization side, novel designs are introduced which optimize network comparisons among contrasting subject groups and related connectivity features. Our design provides level-of-detail comparisons, from juxtaposed and explicit-coding views for subject group comparisons, to high-order composite view for correlation of network comparisons, and to fiber tract detail view for voxel-level comparisons. The proposed techniques are inspired and evaluated in expert studies, as well as through case analyses on diffusion and geometric bio-markers of certain neurology diseases. Results in these experiments demonstrate the effectiveness and superiority of MV^2Net over state-of-the-art approaches.

Connectivity between default mode and frontoparietal networks mediates the association between global amyloid-β and episodic memory.

Βeta-amyloid (Aβ) is a neurotoxic protein that deposits early in the pathogenesis of preclinical Alzheimer's disease. We aimed to identify network connectivity that may alter the negative effect of Aβ on cognition. Following assessment of memory performance, resting-state fMRI, and mean cortical PET-Aβ, a total of 364 older adults (286 with clinical dementia rating [CDR-0], 59 with CDR-0.5 and 19 with CDR-1, mean age: 74.0 ± 6.4 years) from the OASIS-3 sample were included in the analysis. Across all participants, a partial least squares regression showed that lower connectivity between posterior medial default mode and frontoparietal networks, higher within-default mode, and higher visual-motor connectivity predict better episodic memory. These connectivities partially mediate the effect of Aβ on episodic memory. These results suggest that connectivity strength between the precuneus cortex and the superior frontal gyri may alter the negative effect of Aβ on episodic memory. In contrast, education was associated with different functional connectivity patterns. In conclusion, functional characteristics of specific brain networks may help identify amyloid-positive individuals with a higher likelihood of memory decline, with implications for AD clinical trials.

Changes of brain network characteristics in patients with depression before and after precise repetitive transcranial magnetic stimulation

Objective: To investigate the changes of brain network characteristics in patients with depression before and after precise repetitive transcranial magnetic stimulation (rTMS) treatment. Methods: Patients with depression in the Second Affiliated Hospital of Xinxiang Medical University and healthy volunteers in the community of Xinxiang city from February 2018 to March 2019 were simultaneously recruited. The left dorsolateral prefrontal cortex was precisely selected as the stimulation target through the latest Human Brainnetome Atlas, and the near infrared navigation was used to achieve accurate brain stimulation treatment in combination with the structural magnetic resonance data. Moreover, functional connectivity was analyzed before and after rTMS treatment in significantly altered brain areas of patients with depression. Results: Nineteen patients (11 males and 8 females) with depression were included, aged (34±11) years. Meanwhile, 22 healthy controls (9 males and 13 females), aged (30±9) years, were also enrolled. Functional connectivity of insular cortex was decreased in depression patients when the insula was analyzed as the target area (P<0.05). The functional connection from insula to middle frontal lobe and superior parietal lobe in patients with depression decreased before rTMS treatment (P<0.05), but increased after rTMS treatment (P<0.05). The functional connection between dIg_L of the insula and the right middle prefrontal lobe was correlated with Beck Anxiety Index (BAI) before rTMS treatment and Beck Depression Index (BDI) after rTMS treatment (r=0.737, P=0.003; r=0.696, P=0.005). Conclusions: Abnormal functional connectivity of insula may be the brain imaging mechanism of rTMS treatment. Precise brain region selection based on Human Brainnetome Atlas provides a new technical method for clinical rTMS precision treatment.

Features of the resting-state functional brain network of children with autism spectrum disorder: EEG source-level analysis

Features of the resting-state functional brain network of children with autism spectrum disorder: EEG source-level analysis

Functional network characteristics based on EEG of patients in acute ischemic stroke: A pilot study.

Functional network characteristics based on EEG of patients in acute ischemic stroke: A pilot study.

Deep Forest With Multi-Channel Message Passing and Neighborhood Aggregation Mechanisms for Brain Network Classification.

As a novel deep learning method, deep forest has achieved excellent classification performance on many small-scale datasets, thus providing a new opportunity to accurately classify brain networks (BNs) on limited fMRI data. Though there are a few explorations about classifying BNs using deep forest, they only adopt sliding windows to extract adjacent features of BNs and fail to use prior knowledge to strengthen the features more relevant to brain diseases. In this paper, we propose a deep forest framework with multi-channel message passing and neighborhood aggregation mechanisms (DF-MCMPNA) to extract and aggregate long-range multi-channel topological features. Firstly, we use the three intrinsic connectivity networks (ICNs) and the whole-brain to form four feature extraction channels. Secondly, we present a multi-channel message passing mechanism and a channel-shared neighborhood aggregation mechanism to recursively extract long-range multi-channel topological features, where the first mechanism can learn local topological features in each channel and the second mechanism can fuse multi-channel topological features. Finally, the extracted features are fed into the casForst to perform further feature learning and classification. Experimental results on ABIDE I, ABIDE II, and ADHD-200 datasets show that the DF-MCMPNA outperforms several state-of-the-art methods on classification performance and accurately identifies abnormal brain regions.

Inhibition explains the relationship between the efficiency of brain networks and adaptive outcomes in pediatric brain tumor survivors.

Research has found altered brain network connectivity in pediatric brain tumor survivors. Efficient brain networks are critical for performing complex behaviors involved in adaptive functioning (AF). The present study explored relationships between structural brain network characteristics and AF in survivors. We examined whether this relationship is mediated by inhibition and cognitive flexibility, important cognitive abilities for AF. Thirty-seven young adult survivors and 37 matched healthy controls (HC; overall Mage = 23.1, SD = 4.9) underwent neuropsychological assessment. Informants completed the Scales of Independent Behavior-Revised (SIB-R) interview. Color-Word Interference Inhibition and Inhibition-Switching from the Delis-Kaplan Executive Functioning System measured inhibition and cognitive flexibility performance. Deterministic tractography was performed on diffusion-weighted imaging, the Automated Anatomical Labeling (AAL) atlas defined nodes, and edges were the average fractional anisotropy between nodes. Global efficiency (GE), average clustering coefficient (CC), and density were computed. Partial correlations and analysis of indirect effects were conducted. There were significant relationships between GE and all SIB-R scales, but findings with CC were limited to two subscales. Inhibition was moderately related to GE, but this was no longer significant after Holm's correction. Cognitive flexibility was not found to be related to graph metrics. Finally, significant indirect effects were found such that inhibition explained the relationship between GE and SIB-R Motor and Social/Communication. Based on these findings, higher levels of brain network integration, as measured by GE, is related to inhibition in survivors, which facilitates proficient adaptive motor and social/communication skills. Future work should investigate tumor location and treatment factors as potential moderators of the relationships found in this study to better understand specific risk factors in this group. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Brain network characteristics and cognitive performance in motor subtypes of Parkinson's disease: A resting state fMRI study

IntroductionParkinson's disease (PD) is a heterogeneous disorder with great variability in motor and non-motor manifestations. It is hypothesized that different motor subtypes are characterized by different neuropsychiatric and cognitive symptoms, but the underlying correlates in cerebral connectivity remain unknown. Our aim is to compare brain network connectivity between the postural instability and gait disorder (PIGD) and tremor-dominant (TD) subtypes, using both a within- and between-network analysis. MethodsThis cross-sectional resting-state fMRI study includes 81 PD patients, 54 belonging to the PIGD and 27 to the TD subgroup. Group-level spatial maps were created using independent component analysis. Differences in functional connectivity were investigated using dual regression analysis and inter-network connectivity analysis. An additional voxel-based morphometry analysis was performed to examine if results were influenced by grey matter atrophy. ResultsThe PIGD subgroup scored worse than the TD subgroup on all cognitive domains. Resting-state fMRI network analyses suggested that the connection between the visual and sensorimotor network is a potential differentiator between PIGD and TD subgroups. However, after correcting for dopaminergic medication use these results were not significant anymore. There was no between-group difference in grey matter volume. ConclusionDespite clear motor and cognitive differences between the PIGD and TD subtypes, no significant differences were found in network connectivity. Methodological challenges, substantial symptom heterogeneity and many involved variables make analyses and hypothesis building around PD subtypes highly complex. More sensitive visualisation methods combined with machine learning approaches may be required in the search for characteristic underpinnings of PD subtypes.

Alteration in topological organization characteristics of gray matter covariance networks in patients with prediabetes.

Prediabetes is associated with an increased risk of cognitive impairment and neurodegenerative diseases. However, the exact mechanism of prediabetes-related brain diseases has not been fully elucidated. The brain structure of patients with prediabetes has been damaged to varying degrees, and these changes may affect the topological characteristics of large-scale brain networks. The structural covariance of connected gray matter has been demonstrated valuable in inferring large-scale structural brain networks. The alterations of gray matter structural covariance networks in prediabetes remain unclear. This study aims to examine the topological features and robustness of gray matter structural covariance networks in prediabetes. A total of 48 subjects were enrolled in this study, including 23 patients with prediabetes (the PD group) and 25 age-and sex-matched healthy controls (the Ctr group). All subjects' high-resolution 3D T1 images of the brain were collected by a 3.0 Tesla MR machine. Mini-mental state examination was used to evaluate the cognitive status of each subject. We calculated the gray matter volume of 116 brain regions with automated anatomical labeling (AAL) template, and constructed gray matter structural covariance networks by thresholding interregional structural correlation matrices as well as graph theoretical analysis. The area under the curve (AUC) in conjunction with permutation testing was employed for testing the differences in network measures, which included small world parameter (Sigma), normalized clustering coefficient (Gamma), normalized path length (Lambda), global efficiency, characteristic path length, local efficiency, mean clustering coefficient, and network robustness parameters. The network in both groups followed small-world characteristics, showing that Sigma was greater than 1, the Lambda was much higher than 1, and Gamma was close to 1. Compared with the Ctr group, the network of the PD group showed increased Sigma, Lambda, and Gamma across a range of network sparsity. The Gamma of the PD group was significantly higher than that in the Ctr group in the network sparsity range of 0.12-0.16, but there was no difference between the 2 groups (all P>0.05). The grey matter network showed an increased characteristic path length and a decreased global efficiency in the PD group, but AUC analysis showed that there was no significant difference between groups (all P>0.05). For the network separation measures, the local efficiency and mean clustering coefficient of the gray matter network in the PD group were significantly increased and AUC analysis also confirmed it (P=0.001 and P=0.004, respectively). In addition, network robustness analysis showed that the grey matter network of the PD group was more vulnerable to random damage (P=0.001). The prediabetic gray matter network shows an increased average clustering coefficient and local efficiency, and is more vulnerable to random damage than the healthy control, suggesting that the topological characteristics of the prediabetes grey matter covariant network have changed (network separation enhanced and network robustness reduced), which may provide new insights into the brain damage relevant to the disease.

Resting-State Functional Connectivity Impairment in Patients with Major Depressive Episode.

This study aims to develop new approaches to characterize brain networks to potentially contribute to a better understanding of mechanisms involved in depression. We recruited 90 subjects: 49 healthy controls (HC) and 41 patients with a major depressive episode (MDE). All subjects underwent clinical evaluation and functional resting-state MRI. The data were processed investigating functional connectivity network measures across the two groups using Brain Connectivity Toolbox. The statistical inferences were developed at a functional network level, using a false discovery rate method. Linear discriminant analysis was used to differentiate between the two groups. Significant differences in functional connectivity (FC) between depressed patients vs. healthy controls was demonstrated, with brain regions including the lingual gyrus, cerebellum, midcingulate cortex and thalamus more prominent in healthy subjects as compared to depression where the orbitofrontal cortex emerged as a key node. Linear discriminant analysis demonstrated that full-connectivity matrices were the most precise in differentiating between depression vs. health subjects. The study provides supportive evidence for impaired functional connectivity networks in MDE patients.

Graph Theoretical Analysis of EEG Functional Connectivity Patterns and Fusion with Physiological Signals for Emotion Recognition

Emotion recognition is a key attribute for realizing advances in human–computer interaction, especially when using non-intrusive physiological sensors, such as electroencephalograph (EEG) and electrocardiograph. Although functional connectivity of EEG has been utilized for emotion recognition, the graph theory analysis of EEG connectivity patterns has not been adequately explored. The exploitation of brain network characteristics could provide valuable information regarding emotions, while the combination of EEG and peripheral physiological signals can reveal correlation patterns of human internal state. In this work, a graph theoretical analysis of EEG functional connectivity patterns along with fusion between EEG and peripheral physiological signals for emotion recognition has been proposed. After extracting functional connectivity from EEG signals, both global and local graph theory features are extracted. Those features are concatenated with statistical features from peripheral physiological signals and fed to different classifiers and a Convolutional Neural Network (CNN) for emotion recognition. The average accuracy on the DEAP dataset using CNN was 55.62% and 57.38% for subject-independent valence and arousal classification, respectively, and 83.94% and 83.87% for subject-dependent classification. Those scores went up to 75.44% and 78.77% for subject-independent classification and 88.27% and 90.84% for subject-dependent classification using a feature selection algorithm, exceeding the current state-of-the-art results.

A robust core architecture of functional brain networks supports topological resilience and cognitive performance in middle- and old-aged adults

Aging is associated with gradual changes in cognition, yet some individuals exhibit protection against age-related cognitive decline. The topological characteristics of brain networks that promote protection against cognitive decline in aging are unknown. Here, we investigated whether the robustness and resilience of brain networks, queried via the delineation of the brain's core network structure, relate to age and cognitive performance in a cross-sectional dataset of healthy middle- and old-aged adults (n = 478, ages 40 to 90 y). First, we decomposed each subject's functional brain network using k-shell decomposition and found that age was negatively associated with robust core network structures. Next, we perturbed these networks, via attack simulations, and found that resilience of core brain network nodes also declined in relationship to age. We then partitioned our dataset into middle- (ages 40 to 65 y, n = 300) and old- (ages 65 to 90 y, n = 178) aged subjects and observed that older individuals had less robust core connectivity and resilience. Following these analyses, we found that episodic memory was positively related to robust connectivity and core resilience, particularly within the default node, limbic, and frontoparietal control networks. Importantly, we found that age-related differences in episodic memory were positively related to core resilience, which indicates a potential role for core resilience in protection against cognitive decline. Together, these findings suggest that robust core connectivity and resilience of brain networks could facilitate high cognitive performance in aging.

Geometric learning of functional brain network on the correlation manifold

The correlation matrix is a typical representation of node interactions in functional brain network analysis. The analysis of the correlation matrix to characterize brain networks observed in several neuroimaging modalities has been conducted predominantly in the Euclidean space by assuming that pairwise interactions are mutually independent. One way to take account of all interactions in the network as a whole is to analyze the correlation matrix under some geometric structure. Recent studies have focused on the space of correlation matrices as a strict subset of symmetric positive definite (SPD) matrices, which form a unique mathematical structure known as the Riemannian manifold. However, mathematical operations of the correlation matrix under the SPD geometry may not necessarily be coherent (i.e., the structure of the correlation matrix may not be preserved), necessitating a post-hoc normalization. The contribution of the current paper is twofold: (1) to devise a set of inferential methods on the correlation manifold and (2) to demonstrate its applicability in functional network analysis. We present several algorithms on the correlation manifold, including measures of central tendency, cluster analysis, hypothesis testing, and low-dimensional embedding. Simulation and real data analysis support the application of the proposed framework for brain network analysis.

Temporal Evolution of Multiday, Epileptic Functional Networks Prior to Seizure Occurrence

Epilepsy is one of the most common neurological disorders, characterized by the occurrence of repeated seizures. Given that epilepsy is considered a network disorder, tools derived from network neuroscience may confer the valuable ability to quantify the properties of epileptic brain networks. In this study, we use well-established brain network metrics (i.e., mean strength, variance of strength, eigenvector centrality, betweenness centrality) to characterize the temporal evolution of epileptic functional networks over several days prior to seizure occurrence. We infer the networks using long-term electroencephalographic recordings from 12 people with epilepsy. We found that brain network metrics are variable across days and show a circadian periodicity. In addition, we found that in 9 out of 12 patients the distribution of the variance of strength in the day (or even two last days) prior to seizure occurrence is significantly different compared to the corresponding distributions on all previous days. Our results suggest that brain network metrics computed fromelectroencephalographic recordings could potentially be used to characterize brain network changes that occur prior to seizures, and ultimately contribute to seizure warning systems.

Transcriptomic and connectomic correlates of differential spatial patterning among gliomas.

Unravelling the complex events driving grade-specific spatial distribution of brain tumour occurrence requires rich datasets from both healthy individuals and patients. Here, we combined open-access data from The Cancer Genome Atlas, the UK Biobank and the Allen Brain Human Atlas to disentangle how the different spatial occurrences of glioblastoma multiforme and low-grade gliomas are linked to brain network features and the normative transcriptional profiles of brain regions. From MRI of brain tumour patients, we first constructed a grade-related frequency map of the regional occurrence of low-grade gliomas and the more aggressive glioblastoma multiforme. Using associated mRNA transcription data, we derived a set of differential gene expressions from glioblastoma multiforme and low-grade gliomas tissues of the same patients. By combining the resulting values with normative gene expressions from post-mortem brain tissue, we constructed a grade-related expression map indicating which brain regions express genes dysregulated in aggressive gliomas. Additionally, we derived an expression map of genes previously associated with tumour subtypes in a genome-wide association study (tumour-related genes). There were significant associations between grade-related frequency, grade-related expression and tumour-related expression maps, as well as functional brain network features (specifically, nodal strength and participation coefficient) that are implicated in neurological and psychiatric disorders. These findings identify brain network dynamics and transcriptomic signatures as key factors in regional vulnerability for glioblastoma multiforme and low-grade glioma occurrence, placing primary brain tumours within a well established framework of neurological and psychiatric cortical alterations.

Effects of different exercise intensities of race-walking on brain functional connectivity as assessed by functional near-infrared spectroscopy.

IntroductionRace-walking is a sport that mimics normal walking and running. Previous studies on sports science mainly focused on the cardiovascular and musculoskeletal systems. However, there is still a lack of research on the central nervous system, especially the real-time changes in brain network characteristics during race-walking exercise. This study aimed to use a network perspective to investigate the effects of different exercise intensities on brain functional connectivity.Materials and methodsA total of 16 right-handed healthy young athletes were recruited as participants in this study. The cerebral cortex concentration of oxyhemoglobin was measured by functional near-infrared spectroscopy in the bilateral prefrontal cortex (PFC), the motor cortex (MC) and occipital cortex (OC) during resting and race-walking states. Three specific periods as time windows corresponding to different exercise intensities were divided from the race-walking time of participants, including initial, intermediate and sprint stages. The brain activation and functional connectivity (FC) were calculated to describe the 0.01-0.1 Hz frequency-specific cortical activities.ResultsCompared to the resting state, FC changes mainly exist between MC and OC in the initial stage, while PFC was involved in FC changes in the intermediate stage, and FC changes in the sprint stage were widely present in PFC, MC and OC. In addition, from the initial-development to the sprint stage, the significant changes in FC were displayed in PFC and MC.ConclusionThis brain functional connectivity-based study confirmed that hemodynamic changes at different exercise intensities reflected different brain network-specific characteristics. During race-walking exercise, more extensive brain activation might increase information processing speed. Increased exercise intensity could facilitate the integration of neural signals such as proprioception, motor control and motor planning, which may be an important factor for athletes to maintain sustained motor coordination and activity control at high intensity. This study was beneficial to understanding the neural mechanisms of brain networks under different exercise intensities.

Brain Network Research of Skilled Shooters in the Shooting Preparation Stage under the Condition of Limited Sensory Function

Shooting is a sport dominated by psychological factors. Hence, disturbing the shooter’s sensory function during aiming will seriously affect his psychological state and shooting performance. Electroencephalograph (EEG) measurements of 30 skilled marksmen in the shooting preparation stage under noisy disturbance, weak light, and normal conditions were recorded. Therefore, the differences in neural mechanisms in the shooter’s brain during shooting aiming in different disturbance conditions were explored using an analytical approach that employs functional connectivity and brain network analysis based on graph theory. The relationship between these brain network characteristics and shooting performance was also compared. The results showed that (1) the average connection strength in the beta frequency band and connection intensity in the left and right temporal lobes of the shooters under noise disturbance were significantly higher than those under the other two conditions, and their brain networks also showed a higher global and local efficiency. In addition, (2) the functional connection intensity in the occipital region of the beta band was higher than that in the normal condition in the weak-light condition. The information interaction in the left parietal region also increased continually during the shooting process. (3) Furthermore, the shooters’ eigenvector centrality in the temporal and occipital regions with limited sensory function in the two conditions was lower than those in the normal condition. These findings suggest that noise disturbance activates the arousal level of the shooter’s brain and enhances the information processing efficiency of the brain network; however, it increases the mental workload. In weak-light conditions, shooters focus more on visual information processing during aiming and strengthen the inhibition of functions in the brain regions unrelated to shooting behavior. Audiovisual disturbance renders the cortical regions equivalent to the audiovisual perception function in the shooter’s brain less important in the entire brain network than in the normal condition. Therefore, these findings reveal the effect of audiovisual disturbance on the functional network of the cortex in the shooting preparation stage and provide a theoretical basis for further understanding the neural mechanism of the shooting process under sensory disturbances.

Method for persistent topological features extraction of schizophrenia patients’ electroencephalography signal based on persistent homology

With the development of network science and graph theory, brain network research has unique advantages in explaining those mental diseases, the neural mechanism of which is unclear. Additionally, it can provide a new perspective in revealing the pathophysiological mechanism of brain diseases from the system level. The selection of threshold plays an important role in brain networks construction. There are no generally accepted criteria for determining the proper threshold. Therefore, based on the topological data analysis of persistent homology theory, this study developed a multi-scale brain network modeling analysis method, which enables us to quantify various persistent topological features at different scales in a coherent manner. In this method, the Vietoris–Rips filtering algorithm is used to extract dynamic persistent topological features by gradually increasing the threshold in the range of full-scale distances. Subsequently, the persistent topological features are visualized using barcodes and persistence diagrams. Finally, the stability of persistent topological features is analyzed by calculating the Bottleneck distances and Wasserstein distances between the persistence diagrams. Experimental results show that compared with the existing methods, this method can extract the topological features of brain networks more accurately and improves the accuracy of diagnostic and classification. This work not only lays a foundation for exploring the higher-order topology of brain functional networks in schizophrenia patients, but also enhances the modeling ability of complex brain systems to better understand, analyze, and predict their dynamic behaviors.