Graph-theoretical analysis for energy landscape reveals the organization of state transitions in the resting-state human cerebral cortex

Development of brain metastable dynamics during the equivalent of the third gestational trimester

Metastability, a concept from dynamical systems theory, provides a framework for understanding how the brain shifts between various functional states and underpins essential cognitive, behavioural, and social function. While studied in adults, metastability in early brain development has only received recent attention. As the brain undergoes dramatic functional and structural changes over the third gestational trimester, here we review how these are reflected in changes in brain metastable dynamics in preterm, preterm at term-equivalent and full-term neonates. We synthesize findings from EEG, fMRI, fUS, and computational models, focusing on the spatial distribution and temporal dynamics of metastable states, which include functional integration and segregation, signal predictability and complexity. Despite fragmented evidence, studies suggest that neonatal metastability develops over the equivalent of the third gestational trimester, with increasing ability for integration-segregation, broader range of metastable states, faster metastable state transitions and greater signal complexity. Preterms at term-equivalent age exhibit immature metastability features compared to full-terms. We explain and interpret these changes in terms of maturation of the brain in a free energy landscape and establishment of cognitive functions.

Low-frequency repetitive transcranial magnetic stimulation alters the individual functional dynamical landscape

Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive approach to modulate brain activity and behavior in humans. Still, how individual resting-state brain dynamics after rTMS evolves across different functional configurations is rarely studied. Here, using resting state fMRI data from healthy subjects, we aimed to examine the effects of rTMS to individual large-scale brain dynamics. Using Topological Data Analysis based Mapper approach, we construct the precise dynamic mapping (PDM) for each participant. To reveal the relationship between PDM and canonical functional representation of the resting brain, we annotated the graph using relative activation proportion of a set of large-scale resting-state networks (RSNs) and assigned the single brain volume to corresponding RSN-dominant or a hub state (not any RSN was dominant). Our results show that (i) low-frequency rTMS could induce changed temporal evolution of brain states; (ii) rTMS didn't alter the hub-periphery configurations underlined resting-state brain dynamics; and (iii) the rTMS effects on brain dynamics differ across the left frontal and occipital lobe. In conclusion, low-frequency rTMS significantly alters the individual temporo-spatial dynamics, and our finding further suggested a potential target-dependent alteration of brain dynamics. This work provides a new perspective to comprehend the heterogeneous effect of rTMS.

Triple-network analysis of Alzheimer's disease based on the energy landscape

Introduction

Research on the brain activity during resting state has found that brain activation is centered around three networks, including the default mode network (DMN), the salient network (SN), and the central executive network (CEN), and switches between multiple modes. As a common disease in the elderly, Alzheimer's disease (AD) affects the state transitions of functional networks in the resting state.

Methods

Energy landscape, as a new method, can intuitively and quickly grasp the statistical distribution of system states and information related to state transition mechanisms. Therefore, this study mainly uses the energy landscape method to study the changes of the triple-network brain dynamics in AD patients in the resting state.

Results

AD brain activity patterns are in an abnormal state, and the dynamics of patients with AD tend to be unstable, with an unusually high flexibility in switching between states. Also , the subjects' dynamic features are correlated with clinical index.

Discussion

The atypical balance of large-scale brain systems in patients with AD is associated with abnormally active brain dynamics. Our study are helpful for further understanding the intrinsic dynamic characteristics and pathological mechanism of the resting-state brain in AD patients.

Age Related Functional Connectivity Signature Extraction Using Energy-Based Machine Learning Techniques

The study of brain connectivity plays an important role in understanding the functional organizations of the brain. It also helps to identify connectivity signatures that can be used for evaluating neural disorders and monitoring treatment efficacy. In this work, age-related changes in brain connectivity are studied to obtain aging signatures based on various modeling techniques. These include an energy-based machine learning technique to identify brain network interaction differences between two age groups with a large (30 years) age gap between them. Disconnectivity graphs and activation maps of the seven prominent resting-state networks (RSN) were obtained from functional MRI data of old and young adult subjects. Two-sample t-tests were performed on the local minimums with Bonferroni correction to control the family-wise error rate. These local minimums are connectivity states showing not only which brain regions but also how strong they are working together. They work as aging signatures that can be used to differentiate young and old groups. We found that the attention network's connectivity signature is a state with all the regions working together and young subjects have a stronger average connectivity among these regions. We have also found a common pattern between young and old subjects where the left and right brain regions of the frontal network are sometimes working separately instead of together. In summary, in this work, we combined machine learning and statistical approaches to extract connectivity signatures, which can be utilized to distinguish aging brains and monitor possible treatment efficacy.

The Structured Mind at Rest: Low-Frequency Oscillations Reflect Interactive Dynamics Between Spontaneous Brain Activity and a Common Architecture for Task Control

The Common Model of Cognition (CMC) has been proposed as a high level framework through which functional neuroimaging data can be predicted and interpreted. Previous work has found the CMC is capable of predicting brain activity across a variety of tasks, but it has not been tested on resting state data. This paper adapts a previously used method for comparing theoretical models of brain structure, Dynamic Causal Modeling, for the task-free environment of resting state, and compares the CMC against six alternate architectural frameworks while also separately modeling spontaneous low-frequency oscillations. For a large sample of subjects from the Human Connectome Project, the CMC provides the best account of resting state brain activity, suggesting the presence of a general purpose structure of connections in the brain that drives activity when at rest and when performing directed task behavior. At the same time, spontaneous brain activity was found to be present and significant across all frequencies and in all regions. Together, these results suggest that, at rest, spontaneous low-frequency oscillations interact with the general cognitive architecture for task-based activity. The possible functional implications of these findings are discussed.

Alterations in white matter network dynamics in patients with schizophrenia and bipolar disorder

Emerging evidence suggests white matter network abnormalities in patients with schizophrenia (SZ) and bipolar disorder (BD), but the alterations in dynamics of the white matter network in patients with SZ and BD are largely unknown. The white matter network of patients with SZ (n = 45) and BD (n = 47) and that of healthy controls (HC, n = 105) were constructed. We used dynamics network control theory to quantify the dynamics metrics of the network, including controllability and synchronizability, to measure the ability to transfer between different states. Experiments show that the patients with SZ and BD showed decreasing modal controllability and synchronizability and increasing average controllability. The correlations between the average controllability and synchronizability of patients were broken, especially for those with SZ. The patients also showed alterations in brain regions with supercontroller roles and their distribution in the cognitive system. Finally, we were able to accurately discriminate and predict patients with SZ and BD. Our findings provide novel dynamic metrics evidence that patients with SZ and BD are characterized by a selective disruption of brain network controllability, potentially leading to reduced brain state transfer capacity, and offer new guidance for the clinical diagnosis of mental illness.

Situational Understanding in the Human and the Machine

The Air Force research programs envision developing AI technologies that will ensure battlespace dominance, by radical increases in the speed of battlespace understanding and decision-making. In the last half century, advances in AI have been concentrated in the area of machine learning. Recent experimental findings and insights in systems neuroscience, the biophysics of cognition, and other disciplines provide converging results that set the stage for technologies of machine understanding and machine-augmented Situational Understanding. This paper will review some of the key ideas and results in the literature, and outline new suggestions. We define situational understanding and the distinctions between understanding and awareness, consider examples of how understanding-or lack of it-manifest in performance, and review hypotheses concerning the underlying neuronal mechanisms. Suggestions for further R&D are motivated by these hypotheses and are centered on the notions of Active Inference and Virtual Associative Networks.

Empirical Bayes estimation of pairwise maximum entropy model for nonlinear brain state dynamics

The pairwise maximum entropy model (pMEM) has recently gained widespread attention to exploring the nonlinear characteristics of brain state dynamics observed in resting-state functional magnetic resonance imaging (rsfMRI). Despite its unique advantageous features, the practical application of pMEM for individuals is limited as it requires a much larger sample than conventional rsfMRI scans. Thus, this study proposes an empirical Bayes estimation of individual pMEM using the variational expectation-maximization algorithm (VEM-MEM). The performance of the VEM-MEM is evaluated for several simulation setups with various sample sizes and network sizes. Unlike conventional maximum likelihood estimation procedures, the VEM-MEM can reliably estimate the individual model parameters, even with small samples, by effectively incorporating the group information as the prior. As a test case, the individual rsfMRI of children with attention deficit hyperactivity disorder (ADHD) is analyzed compared to that of typically developed children using the default mode network, executive control network, and salient network, obtained from the Healthy Brain Network database. We found that the nonlinear dynamic properties uniquely established on the pMEM differ for each group. Furthermore, pMEM parameters are more sensitive to group differences and are better associated with the behavior scores of ADHD compared to the Pearson correlation-based functional connectivity. The simulation and experimental results suggest that the proposed method can reliably estimate the individual pMEM and characterize the dynamic properties of individuals by utilizing empirical information of the group brain state dynamics.

State-Dependent Effective Connectivity in Resting-State fMRI

The human brain at rest exhibits intrinsic dynamics transitioning among the multiple metastable states of the inter-regional functional connectivity. Accordingly, the demand for exploring the state-specific functional connectivity increases for a deeper understanding of mental diseases. Functional connectivity, however, lacks information about the directed causal influences among the brain regions, called effective connectivity. This study presents the dynamic causal modeling (DCM) framework to explore the state-dependent effective connectivity using spectral DCM for the resting-state functional MRI (rsfMRI). We established the sequence of brain states using the hidden Markov model with the multivariate autoregressive coefficients of rsfMRI, summarizing the functional connectivity. We decomposed the state-dependent effective connectivity using a parametric empirical Bayes scheme that models the effective connectivity of consecutive windows with the time course of the discrete states as regressors. We showed the plausibility of the state-dependent effective connectivity analysis in a simulation setting. To test the clinical applicability, we applied the proposed method to characterize the state- and subtype-dependent effective connectivity of the default mode network in children with combined-type attention deficit hyperactivity disorder (ADHD-C) compared with age-matched, typically developed children (TDC). All 88 children were subtyped according to the occupation times (i.e., dwell times) of the three dominant functional connectivity states, independently of clinical diagnosis. The state-dependent effective connectivity differences between ADHD-C and TDC according to the subtypes and those between the subtypes of ADHD-C were expressed mainly in self-inhibition, magnifying the importance of excitation inhibition balance in the subtyping. These findings provide a clear motivation for decomposing the state-dependent dynamic effective connectivity and state-dependent analysis of the directed coupling in exploring mental diseases.

Interindividual Signatures of fMRI Temporal Fluctuations

The complexity and variability of human brain activity, such as quantified from Functional Magnetic Resonance Imaging (fMRI) time series, have been widely studied as potential markers of healthy and pathological states. However, the extent to which fMRI temporal features exhibit stable markers of inter-individual differences in brain function across healthy young adults is currently an open question. In this study, we draw upon two widely used time-series measures-a nonlinear complexity measure (sample entropy; SampEn) and a spectral measure of low-frequency content (fALFF)-to capture dynamic properties of resting-state fMRI in a large sample of young adults from the Human Connectome Project. We observe that these two measures are closely related, and that both generate reproducible patterns across brain regions over four different fMRI runs, with intra-class correlations of up to 0.8. Moreover, we find that both metrics can uniquely differentiate subjects with high identification rates (ca. 89%). Canonical correlation analysis revealed a significant relationship between multivariate brain temporal features and behavioral measures. Overall, these findings suggest that regional profiles of fMRI temporal characteristics may provide stable markers of individual differences, and motivate future studies to further probe relationships between fMRI time series metrics and behavior.

A reachable probability approach for the analysis of spatio-temporal dynamics in the human functional network

The dynamic architecture of the human brain has been consistently observed. However, there is still limited modeling work to elucidate how neuronal circuits are hierarchically and flexibly organized in functional systems. Here we proposed a reachable probability approach based on non-homogeneous Markov chains, to characterize all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level. We proved at the theoretical level the convergence of the functional brain network system, and demonstrated that this approach is able to detect network steady states across connectivity structure, particularly in areas of the default mode network. We further explored the dynamically hierarchical functional organization centered at the primary sensory cortices. We observed smaller optimal reachable steps to their local functional regions, and differentiated patterns in larger optimal reachable steps for primary perceptual modalities. The reachable paths with the largest and second largest transition probabilities between primary sensory seeds via multisensory integration regions were also tracked to explore the flexibility and plasticity of the multisensory integration. The present work provides a novel approach to depict both the stable and flexible hierarchical connectivity organization of the human brain.

Characterising Alzheimer's Disease with EEG-based Energy Landscape Analysis

Alzheimer's disease (AD) is one of the most common neurodegenerative diseases, with around 50 million patients worldwide. Accessible and non-invasive methods of diagnosing and characterising AD are therefore urgently required. Electroencephalography (EEG) fulfils these criteria and is often used when studying AD. Several features derived from EEG were shown to predict AD with high accuracy, e.g. signal complexity and synchronisation. However, the dynamics of how the brain transitions between stable states have not been properly studied in the case of AD and EEG. Energy landscape analysis is a method that can be used to quantify these dynamics. This work presents the first application of this method to both AD and EEG. Energy landscape assigns energy value to each possible state, i.e. pattern of activations across brain regions. The energy is inversely proportional to the probability of occurrence. By studying the features of energy landscapes of 20 AD patients and 20 age-matched healthy counterparts (HC), significant differences are found. The dynamics of AD patients' EEG are shown to be more constrained - with more local minima, less variation in basin size, and smaller basins. We show that energy landscapes can predict AD with high accuracy, performing significantly better than baseline models. Moreover, these findings are replicated in a separate dataset including 9 AD and 10 HC above 70 years old.

Bayesian estimation of maximum entropy model for individualized energy landscape analysis of brain state dynamics

The pairwise maximum entropy model (MEM) for resting state functional MRI (rsfMRI) has been used to generate energy landscape of brain states and to explore nonlinear brain state dynamics. Researches using MEM, however, has mostly been restricted to fixed‐effect group‐level analyses, using concatenated time series across individuals, due to the need for large samples in the parameter estimation of MEM. To mitigate the small sample problem in analyzing energy landscapes for individuals, we propose a Bayesian estimation of individual MEM using variational Bayes approximation (BMEM). We evaluated the performances of BMEM with respect to sample sizes and prior information using simulation. BMEM showed advantages over conventional maximum likelihood estimation in reliably estimating model parameters for individuals with small sample data, particularly utilizing the empirical priors derived from group data. We then analyzed individual rsfMRI of the Human Connectome Project to show the usefulness of MEM in differentiating individuals and in exploring neural correlates for human behavior. MEM and its energy landscape properties showed high subject specificity comparable to that of functional connectivity. Canonical correlation analysis identified canonical variables for MEM highly associated with cognitive scores. Inter‐individual variations of cognitive scores were also reflected in energy landscape properties such as energies, occupation times, and basin sizes at local minima. We conclude that BMEM provides an efficient method to characterize dynamic properties of individuals using energy landscape analysis of individual brain states.

A Computational Framework for Controlling the Self-Restorative Brain Based on the Free Energy and Degeneracy Principles

The brain is a non-linear dynamical system with a self-restoration process, which protects itself from external damage but is often a bottleneck for clinical treatment. To treat the brain to induce the desired functionality, formulation of a self-restoration process is necessary for optimal brain control. This study proposes a computational model for the brain's self-restoration process following the free-energy and degeneracy principles. Based on this model, a computational framework for brain control is established. We posited that the pre-treatment brain circuit has long been configured in response to the environmental (the other neural populations') demands on the circuit. Since the demands persist even after treatment, the treated circuit's response to the demand may gradually approximate the pre-treatment functionality. In this framework, an energy landscape of regional activities, estimated from resting-state endogenous activities by a pairwise maximum entropy model, is used to represent the pre-treatment functionality. The approximation of the pre-treatment functionality occurs via reconfiguration of interactions among neural populations within the treated circuit. To establish the current framework's construct validity, we conducted various simulations. The simulations suggested that brain control should include the self-restoration process, without which the treatment was not optimal. We also presented simulations for optimizing repetitive treatments and optimal timing of the treatment. These results suggest a plausibility of the current framework in controlling the non-linear dynamical brain with a self-restoration process.

Abnormal dynamics of functional connectivity in first-episode and treatment-naive patients with obsessive-compulsive disorder

AIM

The aim of this study was to assess the whole-brain dynamic functional connectivity of first-episode and treatment-naive patients with obsessive-compulsive disorder (OCD) and to investigate the clinical correlations of abnormal changes in dynamic functional connectivity.

METHODS

Twenty-nine patients in our hospital diagnosed with first-episode OCD and 29 healthy controls matched for age, sex, and education were included in our study. Resting-state functional magnetic resonance imaging scans were performed on a 3.0-Tesla magnetic resonance scanner in our hospital. Three temporal metrics of connectivity state expression were calculated: (i) fraction of time; (ii) mean dwell time; and (iii) number of transitions. The Yale-Brown Obsessive-Compulsive Scale was used to assess the severity of OCD symptoms.

RESULTS

In the comparison of dynamic functional connectivity indicators, we found that there were significant differences in the number of transitions among the four functional connectivity states but no significant differences in the fraction of time or the mean dwell time. The total Yale-Brown Obsessive-Compulsive Scale score was positively correlated with the number of transitions. In the validation analysis, when the size of the sliding window changed, there was still a significant difference in the number of transitions between OCD patients and healthy controls.

CONCLUSION

The functional networks of OCD patients have lost the correct dynamic rhythm, which may be considered as a potential marker for OCD and for new directions for its intervention.

Sparse coupled logistic regression to estimate co-activation and modulatory influences of brain regions

Accurate mapping of the functional interactions between remote brain areas with resting-state functional magnetic resonance imaging requires the quantification of their underlying dynamics. In conventional methodological pipelines, a spatial scale of interest is first selected, and dynamic analysis then proceeds at this hypothesised level of complexity. If large-scale functional networks or states are studied, more local regional rearrangements are then not described, potentially missing important neurobiological information. Here, we propose a novel mathematical framework that jointly estimates resting-state functional networks, and spatially more localised cross-regional modulations. To do so, the changes in activity of each brain region are modelled by a logistic regression including co-activation coefficients (reflective of network assignment, as they highlight simultaneous activations across areas) and causal interplays (denoting finer regional cross-talks, when one region active at timetmodulates thettot+1 transition likelihood of another area). A two-parameter L1 regularisation scheme is used to make these two sets of coefficients sparse: one controls overall sparsity, while the other governs the trade-off between co-activations and causal interplays, enabling to properly fit the data despite the yet unknown balance between both types of couplings. Across a range of simulation settings, we show that the framework successfully retrieves the two types of cross-regional interactions at once. Performance across noise and sample size settings was globally on par with that of other existing methods, with the potential to reveal more precise information missed by alternative approaches. Preliminary application to experimental data revealed that in the resting brain, co-activations and causal modulations co-exist with a varying balance across regions. Our methodological pipeline offers a conceptually elegant alternative for the assessment of functional brain dynamics, and can be downloaded at https://c4science.ch/source/Sparse_logistic_regression.git.

Energy landscape of resting magnetoencephalography reveals fronto-parietal network impairments in epilepsy

Juvenile myoclonic epilepsy (JME) is a form of idiopathic generalized epilepsy. It is yet unclear to what extent JME leads to abnormal network activation patterns. Here, we characterized statistical regularities in magnetoencephalograph (MEG) resting-state networks and their differences between JME patients and controls by combining a pairwise maximum entropy model (pMEM) and novel energy landscape analyses for MEG. First, we fitted the pMEM to the MEG oscillatory power in the front-oparietal network (FPN) and other resting-state networks, which provided a good estimation of the occurrence probability of network states. Then, we used energy values derived from the pMEM to depict an energy landscape, with a higher energy state corresponding to a lower occurrence probability. JME patients showed fewer local energy minima than controls and had elevated energy values for the FPN within the theta, beta, and gamma bands. Furthermore, simulations of the fitted pMEM showed that the proportion of time the FPN was occupied within the basins of energy minima was shortened in JME patients. These network alterations were highlighted by significant classification of individual participants employing energy values as multivariate features. Our findings suggested that JME patients had altered multistability in selective functional networks and frequency bands in the fronto-parietal cortices.