Dynamic Functional Network Research Articles

NDCN-Brain: An Extensible Dynamic Functional Brain Network Model.

As an extension of the static network, the dynamic functional brain network can show continuous changes in the brain’s connections. Then, limited by the length of the fMRI signal, it is difficult to show every instantaneous moment in the construction of a dynamic network and there is a lack of effective prediction of the dynamic changes of the network after the signal ends. In this paper, an extensible dynamic brain function network model is proposed. The model utilizes the ability of extracting and predicting the instantaneous state of the dynamic network of neural dynamics on complex networks (NDCN) and constructs a dynamic network model structure that can provide more than the original signal range. Experimental results show that every snapshot in the network obtained by the proposed method has a usable network structure and that it also has a good classification result in the diagnosis of cognitive impairment diseases.

Dynamic functional connectivity patterns associated with dementia risk

BackgroundThis study assesses the relationships between dynamic functional network connectivity (DFNC) and dementia risk.MethodsDFNC of the default mode (DMN), salience (SN), and executive control networks was assessed in 127 cognitively unimpaired older adults. Stepwise regressions were performed with dementia risk and protective factors and biomarkers as predictors of DFNC.ResultsAssociations were found between times spent in (i) a “weakly connected” state and lower self-reported engagement in early- and mid-life cognitive activity and higher LDL cholesterol; (ii) a “SN-negatively connected” state and higher blood pressure, higher depression score, and lower body mass index (BMI); (iii) a “strongly connected” state and higher self-reported engagement in early-life cognitive activity, Preclinical Alzheimer’s cognitive composite-5 score, and BMI; and (iv) a “DMN-negatively connected” state and higher self-reported engagement in early- and mid-life stimulating activities and lower LDL cholesterol and blood pressure. The lower number of state transitions was associated with lower brain perfusion.ConclusionDFNC states are differentially associated with dementia risk and could underlie reserve.

Dynamics of intrinsic whole-brain functional connectivity in abstinent males with methamphetamine use disorder

BackgroundThe global prevalence of methamphetamine use disorder (MUD) and the associated economic burden are increasing, but effective pharmacological treatment is lacking. Therefore, understanding the neurological mechanisms underlying MUD is essential to develop clinical strategies and improve patient care. Individuals with MUD can show static brain network abnormalities during the resting state, but their alterations in dynamic functional network connectivity (dFNC) are unclear. MethodsIn this study, we obtained resting-state functional magnetic resonance imaging from 42 males with MUD and 41 healthy controls. Sliding-window and spatial independent component analyses with a k-means clustering algorithm were used to assess the recurring functional connectivity states. The temporal properties of the dFNC, including fraction and dwelling time of each state and the number of transitions between different states, were compared between the two groups. In addition, the relationships between the temporal properties of the dFNC and clinical characteristics of the MUDs, including their anxiety and depressive symptoms, were further explored. ResultsWhile the two groups shared many similarities in their dFNC, the occurrence of a highly integrated functional network state and a state featuring balanced integration and segregation in the MUDs significantly correlated with the total drug usage (Spearman's rho = 0.47, P = 0.002) and duration of abstinence (Spearman's rho = 0.38, P = 0.013), respectively. ConclusionsThe observed results in our study demonstrate that methamphetamines can affect dFNC, which may reflect the drug's influence on cognitive abilities. Our study justifies further studies into the effects of MUD on dynamic neural mechanisms.

Aberrant static and dynamic functional network connectivity in heart failure with preserved ejection fraction.

AimsHeart failure may lead to brain functional alterations related to cognitive impairment. This study aimed to detect alterations of static functional network connectivity (FNC) and dynamic FNC in heart failure with preserved ejection fraction (HFpEF) and to estimate the association between the altered FNC and clinical features related to HFpEF.Methods and resultsThe clinical and resting‐state functional magnetic resonance imaging (fMRI) data of HFpEF patients (n = 35) and healthy controls (HCs) (n = 35) were acquired at baseline. Resting‐state networks (RSNs) were established based on independent component analysis (ICA) and FNC analyses were performed. The associations between the FNC abnormalities and clinical features related to HFpEF were analysed. Compared with HCs, HFpEF patients showed decreased functional connectivity within the default mode network, left frontoparietal network, and right frontoparietal network and increased functional connectivity within the right frontoparietal network and visual network. Negative correlations were observed between decreased dynamic FNC and the left ventricular end‐diastolic diameter (LVDd) (r = −0.435, P = 0.015) as well as the left ventricular end‐systolic diameter (LVDs) (r = −0.443, P = 0.013).ConclusionsThe FNC disruption and altered temporal properties of functional dynamics in HFpEF patients may reflect the neural mechanisms of brain injury after HFpEF, which may deepen our understanding of the disease.

Abnormal Dynamic Functional Network Connectivity in Adults with Autism Spectrum Disorder.

This study sought to explore changes of brain dynamic functional network connectivity (dFNC) in adults with autism spectrum disorder (ASD) and investigate their relationship with clinical manifestations. Resting-state functional magnetic resonance imaging (rs-fMRI) data were acquired from 78adult ASD patients from autism brain imaging data exchange datasets, and 65age-matched healthy controls subjects from the local community. Independent component analysis was conducted to evaluate dFNC patterns on the basis of 13independent components (ICs) within 11resting-state networks (RSN), namely, auditory network (AUDN), basal ganglia network (BGN), language network (LN), sensorimotor network (SMN), precuneus network (PUCN), salience network (SN), visuospatial network (VSN), dorsal default mode network (dDMN), high visual network (hVIS), primary visual network (pVIS), ventral default mode network (vDMN). Fraction time, mean dwell time, number of transitions, and RSN connectivity were calculated for group comparisons. Correlation analyses were performed between abnormal metrics and autism diagnostic observation schedule (ADOS) scores. Compared with controls, ASD patients had higher fraction time and mean dwell time in state2 (P = 0.017, P = 0.014). Reduced dFNC was found in the SMN with PUCN, SMN with hVIS, and increased dFNC was observed in the dDMN with SN in state2 in the ASD group. Fraction time and mean dwell time was positively correlated with stereotyped behavior scores of ADOS. The findings demonstrated the importance of evaluating transient alterations in specific neural networks of adult ASD patients. The abnormal metrics and connectivity may be related to symptoms such as stereotyped behavior.

Enhancing Emotion Recognition Using Region-Specific Electroencephalogram Data and Dynamic Functional Connectivity.

Recognizing the emotional states of humans through EEG signals are of great significance to the progress of human-computer interaction. The present study aimed to perform automatic recognition of music-evoked emotions through region-specific information and dynamic functional connectivity of EEG signals and a deep learning neural network. EEG signals of 15 healthy volunteers were collected when different emotions (high-valence-arousal vs. low-valence-arousal) were induced by a musical experimental paradigm. Then a sequential backward selection algorithm combining with deep neural network called Xception was proposed to evaluate the effect of different channel combinations on emotion recognition. In addition, we also assessed whether dynamic functional network of frontal cortex, constructed through different trial number, may affect the performance of emotion cognition. Results showed that the binary classification accuracy based on all 30 channels was 70.19%, the accuracy based on all channels located in the frontal region was 71.05%, and the accuracy based on the best channel combination in the frontal region was 76.84%. In addition, we found that the classification performance increased as longer temporal functional network of frontal cortex was constructed as input features. In sum, emotions induced by different musical stimuli can be recognized by our proposed approach though region-specific EEG signals and time-varying functional network of frontal cortex. Our findings could provide a new perspective for the development of EEG-based emotional recognition systems and advance our understanding of the neural mechanism underlying emotion processing.

Abnormal Dynamic Functional Networks in Subjective Cognitive Decline and Alzheimer's Disease.

Subjective cognitive decline (SCD) is considered to be the preclinical stage of Alzheimer's disease (AD) and has the potential for the early diagnosis and intervention of AD. It was implicated that CSF-tau, which increases very early in the disease process in AD, has a high sensitivity and specificity to differentiate AD from normal aging, and the highly connected brain regions behaved more tau burden in patients with AD. Thus, a highly connected state measured by dynamic functional connectivity may serve as the early changes of AD. In this study, forty-five normal controls (NC), thirty-six individuals with SCD, and thirty-five patients with AD were enrolled to obtain the resting-state functional magnetic resonance imaging scanning. Sliding windows, Pearson correlation, and clustering analysis were combined to investigate the different levels of information transformation states. Three states, namely, the low state, the middle state, and the high state, were characterized based on the strength of functional connectivity between each pair of brain regions. For the global dynamic functional connectivity analysis, statistically significant differences were found among groups in the three states, and the functional connectivity in the middle state was positively correlated with cognitive scales. Furthermore, the whole brain was parcellated into four networks, namely, default mode network (DMN), cognitive control network (CCN), sensorimotor network (SMN), and occipital-cerebellum network (OCN). For the local network analysis, statistically significant differences in CCN for low state and SMN for middle state and high state were found in normal controls and patients with AD. Meanwhile, the differences were also found in normal controls and individuals with SCD. In addition, the functional connectivity in SMN for high state was positively correlated with cognitive scales. Converging results showed the changes in dynamic functional states in individuals with SCD and patients with AD. In addition, the changes were mainly in the high strength of the functional connectivity state.

Abnormal intrinsic brain functional network dynamics in patients with cervical spondylotic myelopathy

The specific topological changes in dynamic functional networks and their role in cervical spondylotic myelopathy (CSM) brain function reorganization remain unclear. This study aimed to investigate the dynamic functional connection (dFC) of patients with CSM, focusing on the temporal characteristics of the functional connection state patterns and the variability of network topological organization. Eighty-eight patients with CSM and 77 healthy controls (HCs) were recruited for resting-state functional magnetic resonance imaging. We applied the sliding time window analysis method and K-means clustering analysis to capture the dFC variability patterns of the two groups. The graph-theoretical approach was used to investigate the variance in the topological organization of whole-brain functional networks. All participants showed four types of dynamic functional connection states. The mean dwell time in state 2 was significantly different between the two groups. Particularly, the mean dwell time in state 2 was significantly longer in the CSM group than in the healthy control group. Among the four states, switching of relative brain networks mainly included the executive control network (ECN), salience network (SN), default mode network (DMN), language network (LN), visual network (VN), auditory network (AN), precuneus network (PN), and sensorimotor network (SMN). Additionally, the topological properties of the dynamic network were variable in patients with CSM. Dynamic functional connection states may offer new insights into intrinsic functional activities in CSM brain networks. The variance of topological organization may suggest instability of the brain networks in patients with CSM.

P77. Whole Brain Dynamic Functional Network Connectivity Features are Linked to Spatial Orientation in Healthy Young Adults

The ability to perceive where one's body is in relation to the external physical world is known as spatial orientation. While several studies have examined how brain networks affect spatial orientation, none have examined how resting-state brain dynamic functional network connectivity (dFNC) affects spatial orientation. This study explores the link between spatial orientation and brain dFNC in healthy young adults.

P541. Dynamic Functional Network Connectivity Features Overlap Across Psychotic Disorders

Dynamic functional network connectivity (dFNC) is a powerful approach that has shown the ability to differentiate patients and healthy control (HC). There is a need to better understand the relationship between schizophrenia (SZ), bipolar (BP), and schizoaffective disorder (SAD). Here we focus on evaluating dFNC features overlap across multiple psychotic disorders.

The measurements of the similarity of dynamic brain functional network

Brain functional network changes over time along with the process of brain development, disease, and aging. However, most of the available measurements for evaluation of the difference (or similarity) between the individual brain functional networks are for charactering static networks, which do not work with the dynamic characteristics of the brain networks that typically involve a long-span and large-scale evolution over the time. The current study proposes an index for measuring the similarity of dynamic brain networks, named as dynamic network similarity (DNS). It measures the similarity by combining the "evolutional" and "structural" properties of the dynamic network. Four sets of simulated dynamic networks with different evolutional and structural properties (varying amplitude of changes, trend of changes, distribution of connectivity strength, range of connectivity strength) were generated to validate the performance of DNS. In addition, real world imaging datasets, acquired from 13 stroke patients who were treated by transcranial direct current stimulation (tDCS), were used to further validate the proposed method and compared with the traditional similarity measurements that were developed for static network similarity. The results showed that DNS was significantly correlated with the varying amplitude of changes, trend of changes, distribution of connectivity strength and range of connectivity strength of the dynamic networks. DNS was able to appropriately measure the significant similarity of the dynamics of network changes over the time for the patients before and after the tDCS treatments. However, the traditional methods failed, which showed significantly differences between the data before and after the tDCS treatments. The experiment results demonstrate that DNS may robustly measure the similarity of evolutional and structural properties of dynamic networks. The new method appears to be superior to the traditional methods in that the new one is capable of assessing the temporal similarity of dynamic functional imaging data.

A review of MEG dynamic brain network research.

The dynamic description of neural networks has attracted the attention of researchers for dynamic networks may carry more information compared with resting-state networks. As a non-invasive electrophysiological data with high temporal and spatial resolution, magnetoencephalogram (MEG) can provide rich information for the analysis of dynamic functional brain networks. In this review, the development of MEG brain network was summarized. Several analysis methods such as sliding window, Hidden Markov model, and time-frequency based methods used in MEG dynamic brain network studies were discussed. Finally, the current research about multi-modal brain network analysis and their applications with MEG neurophysiology, which are prospected to be one of the research directions in the future, were concluded.

Altered Temporal Variations of Functional Connectivity Associated With Surgical Outcomes in Drug-Resistant Temporal Lobe Epilepsy.

BackgroundCurrently, more than one-third of patients with drug-resistant temporal lobe epilepsy (TLE) continue to develop seizures after resection surgery. Dynamic functional network connectivity (DFNC) analyses, capturing temporal properties of functional connectivity during MRI acquisition, may help us identify unfavorable surgical outcomes. The purpose of this work was to explore the association of DFNC variations of preoperative resting-state MRI and surgical outcomes in patients with drug-resistant TLE.MethodsWe evaluated 61 patients with TLE matched for age and gender with 51 healthy controls (HC). Patients with TLE were classified as seizure-free (n = 39) and not seizure-free (n = 16) based on the Engel surgical outcome scale. Six patients were unable to confirm the postoperative status and were not included in the subgroup analysis. The DFNC was calculated using group spatial independent component analysis and the sliding window approach.ResultsDynamic functional network connectivity analyses suggested two distinct connectivity “States.” The dynamic connectivity state of patients with TLE was different from HC. TLE subgroup analyses showed not seizure-free (NSF) patients spent significantly more time in State II compared to seizure-free (SF) patients and HC. Further, the number of transitions from State II to State I was significantly lower in NSF patients. SF patients had compensatory enhancement of DFNC strengths between default and dorsal attention network, as well as within the default network. While reduced DFNC strengths of within-network and inter-network were both observed in NSF patients, patients with abnormally temporal properties and more extension DFNC strength alterations were less likely to receive seizure freedom.ConclusionsOur study indicates that DFNC could offer a better understanding of dynamic neural impairment mechanisms of drug-resistant TLE functional network, epileptic brain network reorganization, and provide an additional preoperative evaluation support for surgical treatment of drug-resistant TLE.

Multiframe Evolving Dynamic Functional Connectivity (EVOdFNC): A Method for Constructing and Investigating Functional Brain Motifs.

The study of brain network connectivity as a time-varying property began relatively recently and, to date, has remained primarily concerned with capturing a handful of discrete static states that characterize connectivity as measured on a timescale shorter than that of the full scan. Capturing group-level representations of temporally evolving patterns of connectivity is a challenging and important next step in fully leveraging the information available in large resting state functional magnetic resonance imaging (rs-fMRI) studies. We introduce a flexible, extensible data-driven framework for the stable identification of group-level multiframe (movie-style) dynamic functional network connectivity (dFNC) states. Our approach employs uniform manifold approximation and embedding (UMAP) to produce a continuity-preserving planar embedding of high-dimensional time-varying measurements of whole-brain functional network connectivity. Planar linear exemplars summarizing dominant dynamic trends across the population are computed from local linear approximations to the two-dimensional 2D embedded trajectories. A high-dimensional representation of each 2D exemplar segment is obtained by averaging the dFNC observations corresponding to the n planar nearest neighbors of τ evenly spaced points along the 2D line segment representation (where n is the UMAP number-of-neighbors parameter and τ is the temporal duration of trajectory segments being approximated). Each of the 2D exemplars thus “lifts” to a multiframe high-dimensional dFNC trajectory of length τ. The collection of high-dimensional temporally evolving dFNC representations (EVOdFNCs) derived in this manner are employed as dynamic basis objects with which to characterize observed high-dimensional dFNC trajectories, which are then expressed as weighted combination of these basis objects. Our approach yields new insights into anomalous patterns of fluidly varying whole-brain connectivity that are significantly associated with schizophrenia as a broad diagnosis as well as with certain symptoms of this serious disorder. Importantly, we show that relative to conventional hidden Markov modeling with single-frame unvarying dFNC summary states, EVOdFNCs are more sensitive to positive symptoms of schizophrenia including hallucinations and delusions, suggesting that a more dynamic characterization is needed to help illuminate such a complex brain disorder.

Aberrant dynamic structure-function relationship of rich-club organization in treatment-naïve newly diagnosed juvenile myoclonic epilepsy.

Neuroimaging studies have shown that juvenile myoclonic epilepsy (JME) is characterized by impaired brain networks. However, few studies have investigated the potential disruptions in rich‐club organization—a core feature of the brain networks. Moreover, it is unclear how structure–function relationships dynamically change over time in JME. Here, we quantify the anatomical rich‐club organization and dynamic structural and functional connectivity (SC–FC) coupling in 47 treatment‐naïve newly diagnosed patients with JME and 40 matched healthy controls. Dynamic functional network efficiency and its association with SC–FC coupling were also calculated to examine the supporting of structure–function relationship to brain information transfer. The results showed that the anatomical rich‐club organization was disrupted in the patient group, along with decreased connectivity strength among rich‐club hub nodes. Furthermore, reduced SC–FC coupling in rich‐club organization of the patients was found in two functionally independent dynamic states, that is the functional segregation state (State 1) and the strong somatomotor‐cognitive control interaction state (State 5); and the latter was significantly associated with disease severity. In addition, the relationships between SC–FC coupling of hub nodes connections and functional network efficiency in State 1 were found to be absent in patients. The aberrant dynamic SC–FC coupling of rich‐club organization suggests a selective influence of densely interconnected network core in patients with JME at the early phase of the disease, offering new insights and potential biomarkers into the underlying neurodevelopmental basis of behavioral and cognitive impairments observed in JME.

Dynamic Resting-State Network Biomarkers of Antidepressant Treatment Response

BackgroundDelivery of effective antidepressant treatment has been hampered by a lack of objective tools for predicting or monitoring treatment response. This study aimed to address this gap by testing novel dynamic resting-state functional network markers of antidepressant response. MethodsThe Establishing Moderators and Biosignatures of Antidepressant Response in Clinical Care (EMBARC) study randomized adults with major depressive disorder to 8 weeks of either sertraline or placebo, and depression severity was evaluated longitudinally. Participants completed resting-state neuroimaging pretreatment and again after 1 week of treatment (n = 259 eligible for analyses). Coactivation pattern analyses identified recurrent whole-brain states of spatial coactivation, and computed time spent in each state for each participant was the main dynamic measure. Multilevel modeling estimated the associations between pretreatment network dynamics and sertraline response and between early (pretreatment to 1 week) changes in network dynamics and sertraline response. ResultsDynamic network markers of early sertraline response included increased time in network states consistent with canonical default and salience networks, together with decreased time in network states characterized by coactivation of cingulate and ventral limbic or temporal regions. The effect of sertraline on depression recovery was mediated by these dynamic network changes. In contrast, early changes in dynamic functioning of corticolimbic and frontoinsular-default networks were related to patterns of symptom recovery common across treatment groups. ConclusionsDynamic resting-state markers of early antidepressant response or general recovery may assist development of clinical tools for monitoring and predicting effective intervention.

A Triple-Network Dynamic Connection Study in Alzheimer's Disease.

Alzheimer's disease (AD) was associated with abnormal organization and function of large-scale brain networks. We applied group independent component analysis (Group ICA) to construct the triple-network consisting of the saliency network (SN), the central executive network (CEN), and the default mode network (DMN) in 25 AD, 60 mild cognitive impairment (MCI) and 60 cognitively normal (CN) subjects. To explore the dynamic functional network connectivity (dFNC), we investigated dynamic time-varying triple-network interactions in subjects using Group ICA analysis based on k-means clustering (GDA-k-means). The mean of brain state-specific network interaction indices (meanNII) in the three groups (AD, MCI, CN) showed significant differences by ANOVA analysis. To verify the robustness of the findings, a support vector machine (SVM) was taken meanNII, gender and age as features to classify. This method obtained accuracy values of 95, 94, and 77% when classifying AD vs. CN, AD vs. MCI, and MCI vs. CN, respectively. In our work, the findings demonstrated that the dynamic characteristics of functional interactions of the triple-networks contributed to studying the underlying pathophysiology of AD. It provided strong evidence for dysregulation of brain dynamics of AD.

Dynamic brain functional network based on EEG microstate during sensory gating in schizophrenia

Objective. Cognitive impairment is one of the core symptoms of schizophrenia, with an emphasis on dysfunctional information processing. Sensory gating deficits have consistently been reported in schizophrenia, but the underlying physiological mechanism is not well-understood. We report the discovery and characterization of P50 dynamic brain connections based on microstate analysis. Approach. We identify five main microstates associated with the P50 response and the difference between the first and second click presentation (S1-S2-P50) in first-episode schizophrenia (FESZ) patients, ultra-high-risk individuals (UHR) and healthy controls (HCs). We used the signal segments composed of consecutive time points with the same microstate label to construct brain functional networks. Main results. The microstate with a prefrontal extreme location during the response to the S1 of P50 are statistically different in duration, occurrence and coverage among the FESZ, UHR and HC groups. In addition, a microstate with anterior–posterior orientation was found to be associated with S1-S2-P50 and its coverage was found to differ among the FESZ, UHR and HC groups. Source location of microstates showed that activated brain regions were mainly concentrated in the right temporal lobe. Furthermore, the connectivities between brain regions involved in P50 processing of HC were widely different from those of FESZ and UHR. Significance. Our results indicate that P50 suppression deficits in schizophrenia may be due to both aberrant baseline sensory perception and adaptation to repeated stimulus. Our findings provide new insight into the mechanisms of P50 suppression in the early stage of schizophrenia.

Statelets: Capturing recurrent transient variations in dynamic functional network connectivity

Dynamic functional network connectivity (dFNC) analysis is a widely used approach for capturing brain activation patterns, connectivity states, and network organization. However, a typical sliding window plus clustering (SWC) approach for analyzing dFNC models the system through a fixed sequence of connectivity states. SWC assumes connectivity patterns span throughout the brain, but they are relatively spatially constrained and temporally short‐lived in practice. Thus, SWC is neither designed to capture transient dynamic changes nor heterogeneity across subjects/time. We propose a state‐space time series summarization framework called “statelets” to address these shortcomings. It models functional connectivity dynamics at fine‐grained timescales, adapting time series motifs to changes in connectivity strength, and constructs a concise yet informative representation of the original data that conveys easily comprehensible information about the phenotypes. We leverage the earth mover distance in a nonstandard way to handle scale differences and utilize kernel density estimation to build a probability density profile for local motifs. We apply the framework to study dFNC of patients with schizophrenia (SZ) and healthy control (HC). Results demonstrate SZ subjects exhibit reduced modularity in their brain network organization relative to HC. Statelets in the HC group show an increased recurrence across the dFNC time‐course compared to the SZ. Analyzing the consistency of the connections across time reveals significant differences within visual, sensorimotor, and default mode regions where HC subjects show higher consistency than SZ. The introduced approach also enables handling dynamic information in cross‐modal and multimodal applications to study healthy and disordered brains.

EEG microstate correlates of emotion dynamics and stimulation content during video watching.

EEG microstates have been widely adopted to understand the complex and dynamic-changing process in dynamic brain systems, but how microstates are temporally modulated by emotion dynamics is still unclear. An investigation of EEG microstates under video-evoking emotion dynamics modulation would provide a novel insight into the understanding of temporal dynamics of functional brain networks. In the present study, we postulate that emotional states dynamically modulate the microstate patterns, and perform an in-depth investigation between EEG microstates and emotion dynamics under a video-watching task. By mapping from subjective-experienced emotion states and objective-presented stimulation content to EEG microstates, we gauge the comprehensive associations among microstates, emotions, and multimedia stimulation. The results show that emotion dynamics could be well revealed by four EEG microstates (MS1, MS2, MS3, and MS4), where MS3 and MS4 are found to be highly correlated to different emotion states (emotion task effect and level effect) and the affective information involved in the multimedia content (visual and audio). In this work, we reveal the microstate patterns related to emotion dynamics from sensory and stimulation dimensions, which deepens the understanding of the neural representation under emotion dynamics modulation and will be beneficial for the future study of brain dynamic systems.