Metastable chimera states in community-structured oscillator networks

Analyzing asymmetry in brain hierarchies with a linear state-space model of resting-state fMRI data

This study challenges the traditional focus on zero-lag statistics in resting-state functional magnetic resonance imaging (rsfMRI) research. Instead, it advocates for considering time-lag interactions to unveil the directionality and asymmetries of the brain hierarchy. Effective connectivity (EC), the state matrix in dynamical causal modeling (DCM), is a commonly used metric for studying dynamical properties and causal interactions within a linear state-space system description. Here, we focused on how time-lag statistics are incorporated within the framework of DCM resulting in an asymmetric EC matrix. Our approach involves decomposing the EC matrix, revealing a steady-state differential cross-covariance matrix that is responsible for modeling information flow and introducing time-irreversibility. Specifically, the system's dynamics, influenced by the off-diagonal part of the differential covariance, exhibit a curl steady-state flow component that breaks detailed balance and diverges the dynamics from equilibrium. Our empirical findings indicate that the EC matrix's outgoing strengths correlate with the flow described by the differential cross covariance, while incoming strengths are primarily driven by zero-lag covariance, emphasizing conditional independence over directionality.

Does Cognitive Load Affect Measures of Consciousness?

BACKGROUND

Developing and testing methods for reliably measuring the state of consciousness of individuals is important for both basic research and clinical purposes. In recent years, several promising measures of consciousness, grounded in theoretical developments, have been proposed. However, the degrees to which these measures are affected by changes in brain activity that are not related to changes in the degree of consciousness has not been well tested. In this study, we examined whether several of these measures are modulated by the loading of cognitive resources.

METHODS

We recorded electroencephalography (EEG) from 12 participants in two conditions: (1) while passively attending to sensory stimuli related to the measures and (2) during increased cognitive load consisting of a demanding working memory task. We investigated whether a set of proposed objective EEG-based measures of consciousness differed between the passive and the cognitively demanding conditions.

RESULTS

The P300b event-related potential (sensitive to conscious awareness of deviance from an expected pattern in auditory stimuli) was significantly affected by concurrent performance on a working memory task, whereas various measures based on signal diversity of spontaneous and perturbed EEG were not.

CONCLUSION

Because signal diversity-based measures of spontaneous or perturbed EEG are not sensitive to the degree of cognitive load, we suggest that these measures may be used in clinical situations where attention, sensory processing, or command following might be impaired.

Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity

Oscillatory complex networks in the metastable regime have been used to study the emergence of integrated and segregated activity in the brain, which are hypothesised to be fundamental for cognition. Yet, the parameters and the underlying mechanisms necessary to achieve the metastable regime are hard to identify, often relying on maximising the correlation with empirical functional connectivity dynamics. Here, we propose and show that the brain's hierarchically modular mesoscale structure alone can give rise to robust metastable dynamics and (metastable) chimera states in the presence of phase frustration. We construct unweighted 3-layer hierarchical networks of identical Kuramoto-Sakaguchi oscillators, parameterized by the average degree of the network and a structural parameter determining the ratio of connections between and within blocks in the upper two layers. Together, these parameters affect the characteristic timescales of the system. Away from the critical synchronization point, we detect the emergence of metastable states in the lowest hierarchical layer coexisting with chimera and metastable states in the upper layers. Using the Laplacian renormalization group flow approach, we uncover two distinct pathways towards achieving the metastable regimes detected in these distinct layers. In the upper layers, we show how the symmetry-breaking states depend on the slow eigenmodes of the system. In the lowest layer instead, metastable dynamics can be achieved as the separation of timescales between layers reaches a critical threshold. Our results show an explicit relationship between metastability, chimera states, and the eigenmodes of the system, bridging the gap between harmonic based studies of empirical data and oscillatory models.

The virtual multiple sclerosis patient

Multiple sclerosis (MS) diagnosis typically involves assessing clinical symptoms, MRI findings, and ruling out alternative explanations. While myelin damage broadly affects conduction speeds, traditional tests focus on specific white-matter tracts, which may not reflect overall impairment accurately. In this study, we integrate diffusion tensor immaging (DTI) and magnetoencephalography (MEG) data into individualized virtual brain models to estimate conduction velocities for MS patients and controls. Using Bayesian inference, we demonstrated a causal link between empirical spectral changes and inferred slower conduction velocities in patients. Remarkably, these velocities proved superior predictors of clinical disability compared to structural damage. Our findings underscore a nuanced relationship between conduction delays and large-scale brain dynamics, suggesting that individualized velocity alterations at the whole-brain level contribute causatively to clinical outcomes in MS.

The evolution of whole-brain turbulent dynamics during recovery from traumatic brain injury

It has been previously shown that traumatic brain injury (TBI) is associated with reductions in metastability in large-scale networks in resting-state fMRI (rsfMRI). However, little is known about how TBI affects the local level of synchronization and how this evolves during the recovery trajectory. Here, we applied a novel turbulent dynamics framework to investigate whole-brain dynamics using an rsfMRI dataset from a cohort of moderate to severe TBI patients and healthy controls (HCs). We first examined how several measures related to turbulent dynamics differ between HCs and TBI patients at 3, 6, and 12 months post-injury. We found a significant reduction in these empirical measures after TBI, with the largest change at 6 months post-injury. Next, we built a Hopf whole-brain model with coupled oscillators and conducted in silico perturbations to investigate the mechanistic principles underlying the reduced turbulent dynamics found in the empirical data. A simulated attack was used to account for the effect of focal lesions. This revealed a shift to lower coupling parameters in the TBI dataset and, critically, decreased susceptibility and information-encoding capability. These findings confirm the potential of the turbulent framework to characterize longitudinal changes in whole-brain dynamics and in the reactivity to external perturbations after TBI.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Effects of multisession cathodal transcranial direct current stimulation with cognitive training on sociocognitive functioning and brain dynamics in autism: A double-blind, sham-controlled, randomized EEG study

BACKGROUND

Few treatment options are available for targeting core symptoms of autism spectrum disorder (ASD). The development of treatments that target common neural circuit dysfunctions caused by known genetic defects, namely, disruption of the excitation/inhibition (E/I) balance, is promising. Transcranial direct current stimulation (tDCS) is capable of modulating the E/I balance in healthy individuals, yet its clinical and neurobiological effects in ASD remain elusive.

OBJECTIVE

This double-blind, randomized, sham-controlled trial investigated the effects of multisession cathodal prefrontal tDCS coupled with online cognitive remediation on social functioning, information processing efficiency and the E/I balance in ASD patients aged 14-21 years.

METHODS

Sixty individuals were randomly assigned to receive either active or sham tDCS (10 sessions in total, 20 min/session, stimulation intensity: 1.5 mA, cathode: F3, anode: Fp2, size of electrodes: 25 cm2) combined with 20 min of online cognitive remediation. Social functioning, information processing efficiency during cognitive tasks, and theta- and gamma-band E/I balance were measured one day before and after the treatment.

RESULTS

Compared to sham tDCS, active cathodal tDCS was effective in enhancing overall social functioning [F(1, 58) = 6.79, p = .012, ηp2 = 0.105, 90% CI: (0.013, 0.234)] and information processing efficiency during cognitive tasks [F(1, 58) = 10.07, p = .002, ηp2 = 0.148, 90% CI: (0.034, 0.284)] in these individuals. Electroencephalography data showed that this cathodal tDCS protocol was effective in reducing the theta-band E/I ratio of the cortical midline structures [F(1, 58) = 4.65, p = .035, ηp2 = 0.074, 90% CI: (0.010, 0.150)] and that this reduction significantly predicted information processing efficiency enhancement (b = -2.546, 95% BCa CI: [-4.979, -0.113], p = .041).

CONCLUSION

Our results support the use of multisession cathodal tDCS over the left dorsolateral prefrontal cortex combined with online cognitive remediation for reducing the elevated theta-band E/I ratio in sociocognitive information processing circuits in ASD patients, resulting in more adaptive regulation of global brain dynamics that is associated with enhanced information processing efficiency after the intervention.

Effects of prefrontal transcranial direct current stimulation on social functioning in autism spectrum disorder: A randomized clinical trial

LAY ABSTRACT

Currently available pharmacological and behavioral interventions for adolescents and young adults with autism spectrum disorder (ASD) yield only modest effect in alleviating their core behavioral and cognitive symptoms, and some of these treatment options are associated with undesirable side effects. Hence, developing effective treatment protocols is urgently needed. Given emerging evidence shows that the abnormal connections of the frontal brain regions contribute to the manifestations of ASD behavioral and cognitive impairments, noninvasive treatment modalities that are capable in modulating brain connections, such as transcranial direct current stimulation (tDCS), have been postulated to be potentially promising for alleviating core symptoms in ASD. However, whether tDCS can reduce behavioral symptoms and enhance cognitive performance in ASD remains unclear. This randomized controlled trial involving 105 adolescents and young adults with ASD showed that multiple sessions of a tDCS protocol, which was paired up with computerized cognitive training, was effective in improving social functioning in adolescents and young adults with ASD. No prolonged and serious side effects were observed. With more future studies conducted in different clinical settings that recruit participants from a wider age range, this tDCS protocol may be potentially beneficial to a broad spectrum of individuals with autism.

Task-relevant brain dynamics among cognitive subsystems induced by regional stimulation in a whole-brain computational model

Cognition involves the global integration of distributed brain regions that are known to work cohesively as cognitive subsystems during brain functioning. Empirical evidence has suggested that spatiotemporal phase relationships between brain regions, measured as synchronization and metastability, may encode important task-relevant information. However, it remains largely unknown how phase relationships aggregate at the level of cognitive subsystems under different cognitive processing. Here, we probe this question by simulating task-relevant brain dynamics through regional stimulation of a whole-brain dynamical network model operating in the resting-state dynamical regime. The model is constructed with structurally embedded Stuart-Laudon oscillators and then fitted with human resting-state functional magnetic resonance imaging data. Based on this framework, we first demonstrate the plausibility of introducing the cognitive system partition into the modeling analysis framework by showing that the clustering of regions across functional networks is better circumscribed by the predefined partition. At the cognitive subsystem level, we focus on how task-relevant phase dynamics are organized in terms of synchronization and metastability. We found that patterns of cognitive synchronization are more task specific, whereas patterns of cognitive metastability are more consistent across different states, suggesting it may encode a more task-general property during cognitive processing, an inherent property conferred by brain organization. This consistent network architecture in cognitive metastability may be related to the distinct functional responses of realistic cognitive systems. We also provide empirical evidence to partially support our computational results. Our paper may provide insights for the mechanisms underlying task-relevant brain dynamics, and establish a model-based link between brain structure, dynamics, and cognition, a fundamental step for computationally aided brain interventions.

The influence of childhood emotional neglect experience on brain dynamic functional connectivity in young adults

Background: Childhood emotional neglect (CEN) confers a great risk for developing multiple psychiatric disorders; however, the neural basis for this association remains unknown. Using a dynamic functional connectivity approach, this study aimed to examine the effects of CEN experience on functional brain networks in young adults.Method: In total, 21 healthy young adults with CEN experience and 26 without childhood trauma experience were recruited. The childhood trauma experience was assessed using the childhood trauma questionnaire (CTQ), and eligible participants underwent resting-state functional MRI. Sliding windows and k-means clustering were used to identify temporal features of large-scale functional connectivity states (frequency, mean dwell time, and transition numbers).Result: Dynamic analysis revealed two separate connection states: state 1 was more frequent and characterized by extensive weak connections between the brain regions. State 2 was relatively infrequent and characterized by extensive strong connections between the brain regions. Compared to the control group, the CEN group had a longer mean dwell time in state 1 and significantly decreased transition numbers between states 1 and 2.Conclusion: The CEN experience affects the temporal properties of young adults' functional brain connectivity. Young adults with CEN experience tend to be stable in state 1 (extensive weak connections between the brain regions), reducing transitions between states, and reflecting impaired metastability or functional network flexibility.

Transcranial stimulation of alpha oscillations modulates brain state dynamics in sustained attention

The brain operates an advanced complex system to support mental activities. Cognition is thought to emerge from dynamic states of the complex brain system, which are organized spatially through large-scale neural networks and temporally via neural synchrony. However, specific mechanisms underlying these processes remain obscure. Applying high-definition alpha-frequency transcranial alternating-current stimulation (HD α-tACS) in a continuous performance task (CPT) during functional resonance imaging (fMRI), we causally elucidate these major organizational architectures in a key cognitive operation-sustained attention. We demonstrated that α-tACS enhanced both electroencephalogram (EEG) alpha power and sustained attention, in a correlated fashion. Akin to temporal fluctuations inherent in sustained attention, our hidden Markov modeling (HMM) of fMRI timeseries uncovered several recurrent, dynamic brain states, which were organized through a few major neural networks and regulated by the alpha oscillation. Specifically, during sustain attention, α-tACS regulated the temporal dynamics of the brain states by suppressing a Task-Negative state (characterized by activation of the default mode network/DMN) and Distraction state (with activation of the ventral attention and visual networks). These findings thus linked dynamic states of major neural networks and alpha oscillations, providing important insights into systems-level mechanisms of attention. They also highlight the efficacy of non-invasive oscillatory neuromodulation in probing the functioning of the complex brain system and encourage future clinical applications to improve neural systems health and cognitive performance.

Co-evolving dynamics and topology in a coupled oscillator model of resting brain function

Dynamic models of ongoing BOLD fMRI brain dynamics and models of communication strategies have been two important approaches to understanding how brain network structure constrains function. However, dynamic models have yet to widely incorporate one of the most important insights from communication models: the brain may not use all of its connections in the same way or at the same time. Here we present a variation of a phase delayed Kuramoto coupled oscillator model that dynamically limits communication between nodes on each time step. An active subgraph of the empirically derived anatomical brain network is chosen in accordance with the local dynamic state on every time step, thus coupling dynamics and network structure in a novel way. We analyze this model with respect to its fit to empirical time-averaged functional connectivity, finding that, with the addition of only one parameter, it significantly outperforms standard Kuramoto models with phase delays. We also perform analyses on the novel time series of active edges it produces, demonstrating a slowly evolving topology moving through intermittent episodes of integration and segregation. We hope to demonstrate that the exploration of novel modeling mechanisms and the investigation of dynamics of networks in addition to dynamics on networks may advance our understanding of the relationship between brain structure and function.

Multiscale effects of excitatory-inhibitory homeostasis in lesioned cortical networks: A computational study

Stroke-related disruptions in functional connectivity (FC) often spread beyond lesioned areas and, given the localized nature of lesions, it is unclear how the recovery of FC is orchestrated on a global scale. Since recovery is accompanied by long-term changes in excitability, we propose excitatory-inhibitory (E-I) homeostasis as a driving mechanism. We present a large-scale model of the neocortex, with synaptic scaling of local inhibition, showing how E-I homeostasis can drive the post-lesion restoration of FC and linking it to changes in excitability. We show that functional networks could reorganize to recover disrupted modularity and small-worldness, but not network dynamics, suggesting the need to consider forms of plasticity beyond synaptic scaling of inhibition. On average, we observed widespread increases in excitability, with the emergence of complex lesion-dependent patterns related to biomarkers of relevant side effects of stroke, such as epilepsy, depression and chronic pain. In summary, our results show that the effects of E-I homeostasis extend beyond local E-I balance, driving the restoration of global properties of FC, and relating to post-stroke symptomatology. Therefore, we suggest the framework of E-I homeostasis as a relevant theoretical foundation for the study of stroke recovery and for understanding the emergence of meaningful features of FC from local dynamics.

The synchronizing role of multiplexing noise: Exploring Kuramoto oscillators and breathing chimeras

The synchronization of spatiotemporal patterns in a two-layer multiplex network of identical Kuramoto phase oscillators is studied, where each layer is a non-locally coupled ring. Particular focus is on the role played by a noisy inter-layer communication. It is shown that modulating the inter-layer coupling strength by uncommon noise has a significant impact on the dynamics of the network, in particular, that modulating the interlayer coupling by noise can counter-intuitively induce synchronization in networks. It is further shown that increasing the noise intensity has many other analogous effects to that of increasing the interlayer coupling strength. For example, the noise intensity can also induce state transitions in a similar way, in some cases causing the layers to completely synchronize within themselves. It is discussed how such disturbances may in many cases be beneficial to multilayer systems. These effects are demonstrated both for white noise and for other kinds of colored noise. A "floating" breathing chimera state is also discovered in this system.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

Metastability as a candidate neuromechanistic biomarker of schizophrenia pathology

The disconnection hypothesis of schizophrenia proposes that symptoms of the disorder arise as a result of aberrant functional integration between segregated areas of the brain. The concept of metastability characterizes the coexistence of competing tendencies for functional integration and functional segregation in the brain, and is therefore well suited for the study of schizophrenia. In this study, we investigate metastability as a candidate neuromechanistic biomarker of schizophrenia pathology, including a demonstration of reliability and face validity. Group-level discrimination, individual-level classification, pathophysiological relevance, and explanatory power were assessed using two independent case-control studies of schizophrenia, the Human Connectome Project Early Psychosis (HCPEP) study (controls n = 53, non-affective psychosis n = 82) and the Cobre study (controls n = 71, cases n = 59). In this work we extend Leading Eigenvector Dynamic Analysis (LEiDA) to capture specific features of dynamic functional connectivity and then implement a novel approach to estimate metastability. We used non-parametric testing to evaluate group-level differences and a naïve Bayes classifier to discriminate cases from controls. Our results show that our new approach is capable of discriminating cases from controls with elevated effect sizes relative to published literature, reflected in an up to 76% area under the curve (AUC) in out-of-sample classification analyses. Additionally, our new metric showed explanatory power of between 81-92% for measures of integration and segregation. Furthermore, our analyses demonstrated that patients with early psychosis exhibit intermittent disconnectivity of subcortical regions with frontal cortex and cerebellar regions, introducing new insights about the mechanistic bases of these conditions. Overall, these findings demonstrate reliability and face validity of metastability as a candidate neuromechanistic biomarker of schizophrenia pathology.

Driving brain state transitions in major depressive disorder through external stimulation

Major depressive disorder (MDD) as a dysfunction of neural circuits and brain networks has been established in modern neuroimaging sciences. However, the brain state transitions between MDD and health through external stimulation remain unclear, which limits translation to clinical contexts and demonstrable clinical utility. We propose a framework of the large-scale whole-brain network model for MDD linking the underlying anatomical connectivity with functional dynamics obtained from diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI). Then, we further explored the optimal brain regions to promote the transition of brain states between MDD and health through external stimulation of the model. Based on the whole-brain model successfully fitting the brain state space in MDD and the health, we demonstrated that the transition from MDD to health is achieved by the excitatory activation of the limbic system and from health to MDD by the inhibitory stimulation of the reward circuit. Our finding provides novel biophysical evidence for the neural mechanism of MDD and its recovery and allows the discovery of new stimulation targets for MDD recovery.

Metastability, fractal scaling, and synergistic information processing: What phase relationships reveal about intrinsic brain activity

Dynamic functional connectivity (dFC) in resting-state fMRI holds promise to deliver candidate biomarkers for clinical applications. However, the reliability and interpretability of dFC metrics remain contested. Despite a myriad of methodologies and resulting measures, few studies have combined metrics derived from different conceptualizations of brain functioning within the same analysis - perhaps missing an opportunity for improved interpretability. Using a complexity-science approach, we assessed the reliability and interrelationships of a battery of phase-based dFC metrics including tools originating from dynamical systems, stochastic processes, and information dynamics approaches. Our analysis revealed novel relationships between these metrics, which allowed us to build a predictive model for integrated information using metrics from dynamical systems and information theory. Furthermore, global metastability - a metric reflecting simultaneous tendencies for coupling and decoupling - was found to be the most representative and stable metric in brain parcellations that included cerebellar regions. Additionally, spatiotemporal patterns of phase-locking were found to change in a slow, non-random, continuous manner over time. Taken together, our findings show that the majority of characteristics of resting-state fMRI dynamics reflect an interrelated dynamical and informational complexity profile, which is unique to each acquisition. This finding challenges the interpretation of results from cross-sectional designs for brain neuromarker discovery, suggesting that individual life-trajectories may be more informative than sample means.

Impaired Brain Information Transmission Efficiency and Flexibility in Parkinson’s Disease and Rapid Eye Movement Sleep Behavior Disorder: Evidence from Functional Connectivity and Functional Dynamics

Parkinson’s disease (PD) is a common neurodegenerative disorder. Rapid eye movement sleep behavior disorder (RBD) is one of the prodromal symptoms of PD. Studies have shown that brain information transmission is affected in PD patients. Consequently, we hypothesized that brain information transmission is impaired in RBD and PD. To prove our hypothesis, we performed functional connectivity (FC) and functional dynamics analysis of three aspects—based on the whole brain, within the resting-state network (RSN), and the interaction between RSNs—using normal control (NC) (n = 21), RBD (n = 24), and PD (n = 45) resting-state functional magnetic resonance imaging (rs-fMRI) data sets. Furthermore, we tested the explanatory power of FC and functional dynamics for the clinical features. Our results found that the global functional dynamics and FC of RBD and PD were impaired. Within RSN, the impairment concentrated in the visual network (VIS) and sensorimotor network (SMN), and the impaired degree of SMN in RBD was higher than that in PD. On the interaction between RSNs, RBD showed a widespread decrease, and PD showed a focal decrease which concentrated in SMN and VIS. Finally, we proved FC and functional dynamics were related to clinical features. These differences confirmed that brain information transmission efficiency and flexibility are impaired in RBD and PD, and these impairments are associated with the clinical features of patients.

Basins of attraction of chimera states on networks

Networks of identical coupled oscillators display a remarkable spatiotemporal pattern, the chimera state, where coherent oscillations coexist with incoherent ones. In this paper we show quantitatively in terms of basin stability that stable and breathing chimera states in the original two coupled networks typically have very small basins of attraction. In fact, the original system is dominated by periodic and quasi-periodic chimera states, in strong contrast to the model after reduction, which can not be uncovered by the Ott-Antonsen ansatz. Moreover, we demonstrate that the curve of the basin stability behaves bimodally after the system being subjected to even large perturbations. Finally, we investigate the emergence of chimera states in brain network, through inducing perturbations by stimulating brain regions. The emerged chimera states are quantified by Kuramoto order parameter and chimera index, and results show a weak and negative correlation between these two metrics.

Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome

A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations and their link with neural activity remain under debate. Here, we revisit the mechanistic hypothesis that transient brain rhythms are a signature of metastable synchronization, occurring at reduced collective frequencies due to delays between brain areas. We consider a system of damped oscillators in the presence of background noise - approximating the short-lived gamma-frequency oscillations generated within neuronal circuits - coupled according to the diffusion weighted tractography between brain areas. Varying the global coupling strength and conduction speed, we identify a critical regime where spatially and spectrally resolved metastable oscillatory modes (MOMs) emerge at sub-gamma frequencies, approximating the MEG power spectra from 89 healthy individuals at rest. Further, we demonstrate that the frequency, duration, and scale of MOMs - as well as the frequency-specific envelope functional connectivity - can be controlled by global parameters, while the connectome structure remains unchanged. Grounded in the physics of delay-coupled oscillators, these numerical analyses demonstrate how interactions between locally generated fast oscillations in the connectome spacetime structure can lead to the emergence of collective brain rhythms organized in space and time.

Unifying turbulent dynamics framework distinguishes different brain states

Significant advances have been made by identifying the levels of synchrony of the underlying dynamics of a given brain state. This research has demonstrated that non-conscious dynamics tend to be more synchronous than in conscious states, which are more asynchronous. Here we go beyond this dichotomy to demonstrate that different brain states are underpinned by dissociable spatiotemporal dynamics. We investigated human neuroimaging data from different brain states (resting state, meditation, deep sleep and disorders of consciousness after coma). The model-free approach was based on Kuramoto's turbulence framework using coupled oscillators. This was extended by a measure of the information cascade across spatial scales. Complementarily, the model-based approach used exhaustive in silico perturbations of whole-brain models fitted to these measures. This allowed studying of the information encoding capabilities in given brain states. Overall, this framework demonstrates that elements from turbulence theory provide excellent tools for describing and differentiating between brain states.

May the 4C's be with you: an overview of complexity-inspired frameworks for analysing resting-state neuroimaging data

Competing and complementary models of resting-state brain dynamics contribute to our phenomenological and mechanistic understanding of whole-brain coordination and communication, and provide potential evidence for differential brain functioning associated with normal and pathological behaviour. These neuroscientific theories stem from the perspectives of physics, engineering, mathematics and psychology and create a complicated landscape of domain-specific terminology and meaning, which, when used outside of that domain, may lead to incorrect assumptions and conclusions within the neuroscience community. Here, we review and clarify the key concepts of connectivity, computation, criticality and coherence-the 4C's-and outline a potential role for metastability as a common denominator across these propositions. We analyse and synthesize whole-brain neuroimaging research, examined through functional magnetic imaging, to demonstrate that complexity science offers a principled and integrated approach to describe, and potentially understand, macroscale spontaneous brain functioning.

Emerging chimera states under nonidentical counter-rotating oscillators

Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting corotating and counter-rotating systems. To illustrate the impact of counter-rotating frequencies, we consider a network of nonidentical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state in the oscillatory regime. Following this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity (P) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through a chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P symmetry, whereas the chimera state preserves the P symmetry only partially. To demonstrate the occurrence of such partial symmetry-breaking (chimera) state, we use basin stability analysis and discover that partial symmetry breaking exists as a result of the coexistence of symmetry-preserving and symmetry-breaking behavior in the initial state space. Further, a measure of the strength of P symmetry is established to quantify the P symmetry in the observed dynamical states. Subsequently, the dynamical transitions are investigated in the parametric spaces. Finally, by increasing the network size, the robustness of the chimera state is also inspected, and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related reduced phase. model as well as in other coupled models such as the globally coupled van der Pol and Rössler oscillators.

Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.

Transcranial stimulation of alpha oscillations up-regulates the default mode network

The default mode network (DMN) is the most-prominent intrinsic connectivity network, serving as a key architecture of the brain's functional organization. Conversely, dysregulated DMN is characteristic of major neuropsychiatric disorders. However, the field still lacks mechanistic insights into the regulation of the DMN and effective interventions for DMN dysregulation. The current study approached this problem by manipulating neural synchrony, particularly alpha (8 to 12 Hz) oscillations, a dominant intrinsic oscillatory activity that has been increasingly associated with the DMN in both function and physiology. Using high-definition alpha-frequency transcranial alternating current stimulation (α-tACS) to stimulate the cortical source of alpha oscillations, in combination with simultaneous electroencephalography and functional MRI (EEG-fMRI), we demonstrated that α-tACS (versus Sham control) not only augmented EEG alpha oscillations but also strengthened fMRI and (source-level) alpha connectivity within the core of the DMN. Importantly, increase in alpha oscillations mediated the DMN connectivity enhancement. These findings thus identify a mechanistic link between alpha oscillations and DMN functioning. That transcranial alpha modulation can up-regulate the DMN further highlights an effective noninvasive intervention to normalize DMN functioning in various disorders.

Symmetry-breaking mechanism for the formation of cluster chimera patterns

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which cluster synchronization and chimera patterns originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. At variance with the standard approach where synchronization arises as a collective behavior of coupled oscillators, in our model, the system initially sets on a homogeneous fixed-point regime, and, only due to a global instability principle, collective oscillations emerge. Following a combination of the network modularity and the model's parameters, one or more clusters of oscillators become incoherent within yielding a particular class of patterns that we here name cluster chimera states.

Integrated information as a common signature of dynamical and information-processing complexity

The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific progress. Nonetheless, given the shared theoretical goals between both approaches, it is reasonable to conjecture the existence of underlying common signatures that capture interesting behavior in both dynamical and information-processing systems. Here, we argue that a pragmatic use of integrated information theory (IIT), originally conceived in theoretical neuroscience, can provide a potential unifying framework to study complexity in general multivariate systems. By leveraging metrics put forward by the integrated information decomposition framework, our results reveal that integrated information can effectively capture surprisingly heterogeneous signatures of complexity-including metastability and criticality in networks of coupled oscillators as well as distributed computation and emergent stable particles in cellular automata-without relying on idiosyncratic, ad hoc criteria. These results show how an agnostic use of IIT can provide important steps toward bridging the gap between informational and dynamical approaches to complex systems.

Test–Retest Reliability of Synchrony and Metastability in Resting State fMRI

In recent years, interest has been growing in dynamic characteristic of brain signals from resting-state functional magnetic resonance imaging (rs-fMRI). Synchrony and metastability, as neurodynamic indexes, are considered as one of methods for analyzing dynamic characteristics. Although much research has studied the analysis of neurodynamic indices, few have investigated its reliability. In this paper, the datasets from the Human Connectome Project have been used to explore the test–retest reliabilities of synchrony and metastability from multiple angles through intra-class correlation (ICC). The results showed that both of these indexes had fair test–retest reliability, but they are strongly affected by the field strength, the spatial resolution, and scanning interval, less affected by the temporal resolution. Denoising processing can help improve their ICC values. In addition, the reliability of neurodynamic indexes was affected by the node definition strategy, but these effects were not apparent. In particular, by comparing the test–retest reliability of different resting-state networks, we found that synchrony of different networks was basically stable, but the metastability varied considerably. Among these, DMN and LIM had a relatively higher test–retest reliability of metastability than other networks. This paper provides a methodological reference for exploring the brain dynamic neural activity by using synchrony and metastability in fMRI signals.

Capturing the non-stationarity of whole-brain dynamics underlying human brain states

Brain dynamics depicts an extremely complex energy landscape that changes over time, and its characterisation is a central unsolved problem in neuroscience. We approximate the non-stationary landscape sustained by the human brain through a novel mathematical formalism that allows us characterise the attractor structure, i.e. the stationary points and their connections. Due to its time-varying nature, the structure of the global attractor and the corresponding number of energy levels changes over time. We apply this formalism to distinguish quantitatively between the different human brain states of wakefulness and different stages of sleep, as a step towards future clinical applications.

Integrative Models of Brain Structure and Dynamics: Concepts, Challenges, and Methods

The anatomical architecture of the brain constrains the dynamics of interactions between various regions. On a microscopic scale, neural plasticity regulates the connections between individual neurons. This microstructural adaptation facilitates coordinated dynamics of populations of neurons (mesoscopic scale) and brain regions (macroscopic scale). However, the mechanisms acting on multiple timescales that govern the reciprocal relationship between neural network structure and its intrinsic dynamics are not well understood. Studies empirically investigating such relationships on the whole-brain level rely on macroscopic measurements of structural and functional connectivity estimated from various neuroimaging modalities such as Diffusion-weighted Magnetic Resonance Imaging (dMRI), Electroencephalography (EEG), Magnetoencephalography (MEG), and functional Magnetic Resonance Imaging (fMRI). dMRI measures the anisotropy of water diffusion along axonal fibers, from which structural connections are estimated. EEG and MEG signals measure electrical activity and magnetic fields induced by the electrical activity, respectively, from various brain regions with a high temporal resolution (but limited spatial coverage), whereas fMRI measures regional activations indirectly via blood oxygen level-dependent (BOLD) signals with a high spatial resolution (but limited temporal resolution). There are several studies in the neuroimaging literature reporting statistical associations between macroscopic structural and functional connectivity. On the other hand, models of large-scale oscillatory dynamics conditioned on network structure (such as the one estimated from dMRI connectivity) provide a platform to probe into the structure-dynamics relationship at the mesoscopic level. Such investigations promise to uncover the theoretical underpinnings of the interplay between network structure and dynamics and could be complementary to the macroscopic level inquiries. In this article, we review theoretical and empirical studies that attempt to elucidate the coupling between brain structure and dynamics. Special attention is given to various clinically relevant dimensions of brain connectivity such as the topological features and neural synchronization, and their applicability for a given modality, spatial or temporal scale of analysis is discussed. Our review provides a summary of the progress made along this line of research and identifies challenges and promising future directions for multi-modal neuroimaging analyses.

Modular origins of high-amplitude cofluctuations in fine-scale functional connectivity dynamics

The topology of structural brain networks shapes brain dynamics, including the correlation structure of brain activity (functional connectivity) as estimated from functional neuroimaging data. Empirical studies have shown that functional connectivity fluctuates over time, exhibiting patterns that vary in the spatial arrangement of correlations among segregated functional systems. Recently, an exact decomposition of functional connectivity into frame-wise contributions has revealed fine-scale dynamics that are punctuated by brief and intermittent episodes (events) of high-amplitude cofluctuations involving large sets of brain regions. Their origin is currently unclear. Here, we demonstrate that similar episodes readily appear in silico using computational simulations of whole-brain dynamics. As in empirical data, simulated events contribute disproportionately to long-time functional connectivity, involve recurrence of patterned cofluctuations, and can be clustered into distinct families. Importantly, comparison of event-related patterns of cofluctuations to underlying patterns of structural connectivity reveals that modular organization present in the coupling matrix shapes patterns of event-related cofluctuations. Our work suggests that brief, intermittent events in functional dynamics are partly shaped by modular organization of structural connectivity.

Structured patterns of activity in pulse-coupled oscillator networks with varied connectivity

Identifying coordinated activity within complex systems is essential to linking their structure and function. We study collective activity in networks of pulse-coupled oscillators that have variable network connectivity and integrate-and-fire dynamics. Starting from random initial conditions, we see the emergence of three broad classes of behaviors that differ in their collective spiking statistics. In the first class (“temporally-irregular”), all nodes have variable inter-spike intervals, and the resulting firing patterns are irregular. In the second (“temporally-regular”), the network generates a coherent, repeating pattern of activity in which all nodes fire with the same constant inter-spike interval. In the third (“chimeric”), subgroups of coherently-firing nodes coexist with temporally-irregular nodes. Chimera states have previously been observed in networks of oscillators; here, we find that the notions of temporally-regular and chimeric states encompass a much richer set of dynamical patterns than has yet been described. We also find that degree heterogeneity and connection density have a strong effect on the resulting state: in binomial random networks, high degree variance and intermediate connection density tend to produce temporally-irregular dynamics, while low degree variance and high connection density tend to produce temporally-regular dynamics. Chimera states arise with more frequency in networks with intermediate degree variance and either high or low connection densities. Finally, we demonstrate that a normalized compression distance, computed via the Lempel-Ziv complexity of nodal spike trains, can be used to distinguish these three classes of behavior even when the phase relationship between nodes is arbitrary.

On a Quantitative Approach to Clinical Neuroscience in Psychiatry: Lessons from the Kuramoto Model

The human brain is a complex system comprising subregions that dynamically exchange information between its various parts through synchronization. These dynamic, complex interactions ultimately play a role in perception, emotion, cognition, and behavior, as well as in various maladaptive neurologic and psychiatric processes. It is therefore important to understand how brain dynamics might be implicated in these processes. Over the past few years, network neuroscience and computational neuroscience have highlighted the importance of measures such as metastability (a property whereby members of an oscillating system tend to linger at the edge of synchronicity without permanently becoming synchronized) in quantifying brain dynamics. Altered metastability has been implicated in various psychiatric illnesses, such as traumatic brain injury and Alzheimer's disease. Computational models, which range in complexity, have been used to assess how various parameters affect metastability, synchronization, and functional connectivity. These models, though limited, can act as heuristics in understanding brain dynamics. This article (aimed at the clinical psychiatrist who might not possess an extensive mathematical background) is intended to provide a brief and qualitative summary of studies that have used a specific, highly simplified computational model of coupled oscillators (Kuramoto model) for understanding brain dynamics-which might bear some relevance to clinical psychiatry.

Brain States and Transitions: Insights from Computational Neuroscience

Within the field of computational neuroscience there are great expectations of finding new ways to rebalance the complex dynamic system of the human brain through controlled pharmacological or electromagnetic perturbation. Yet many obstacles remain between the ability to accurately predict how and where best to perturb to force a transition from one brain state to another. The foremost challenge is a commonly agreed definition of a given brain state. Recent progress in computational neuroscience has made it possible to robustly define brain states and force transitions between them. Here, we review the state of the art and propose a framework for determining the functional hierarchical organization describing any given brain state. We describe the latest advances in creating sophisticated whole-brain computational models with interacting neuronal and neurotransmitter systems that can be studied fully in silico to predict and design novel pharmacological and electromagnetic interventions to rebalance them in disease.

Neural and subjective effects of inhaled N,N-dimethyltryptamine in natural settings

BACKGROUND

N,N-dimethyltryptamine is a short-acting psychedelic tryptamine found naturally in many plants and animals. Few studies to date have addressed the neural and psychological effects of N,N-dimethyltryptamine alone, either administered intravenously or inhaled in freebase form, and none have been conducted in natural settings.

AIMS

Our primary aim was to study the acute effects of inhaled N,N-dimethyltryptamine in natural settings, focusing on questions tuned to the advantages of conducting field research, including the effects of contextual factors (i.e. "set" and "setting"), the possibility of studying a comparatively large number of subjects, and the relaxed mental state of participants consuming N,N-dimethyltryptamine in familiar and comfortable settings.

METHODS

We combined state-of-the-art wireless electroencephalography with psychometric questionnaires to study the neural and subjective effects of naturalistic N,N-dimethyltryptamine use in 35 healthy and experienced participants.

RESULTS

We observed that N,N-dimethyltryptamine significantly decreased the power of alpha (8-12 Hz) oscillations throughout all scalp locations, while simultaneously increasing power of delta (1-4 Hz) and gamma (30-40 Hz) oscillations. Gamma power increases correlated with subjective reports indicative of some features of mystical-type experiences. N,N-dimethyltryptamine also increased global synchrony and metastability in the gamma band while decreasing those measures in the alpha band.

CONCLUSIONS

Our results are consistent with previous studies of psychedelic action in the human brain, while at the same time the results suggest potential electroencephalography markers of mystical-type experiences in natural settings, thus highlighting the importance of investigating these compounds in the contexts where they are naturally consumed.

Experimental investigation on the susceptibility of minimal networks to a change in topology and number of oscillators

Understanding the global dynamical behavior of a network of coupled oscillators has been a topic of immense research in many fields of science and engineering. Various factors govern the resulting dynamical behavior of such networks, including the number of oscillators and their coupling schemes. Although these factors are seldom significant in large populations, a small change in them can drastically affect the global behavior in small populations. In this paper, we perform an experimental investigation on the effect of these factors on the coupled behavior of a minimal network of candle-flame oscillators. We observe that strongly coupled oscillators exhibit the global behavior of in-phase synchrony and amplitude death, irrespective of the number and the topology of oscillators. However, when they are weakly coupled, their global behavior exhibits the intermittent occurrence of multiple stable states in time. We report the experimental discovery of partial amplitude death in a network of candle-flame oscillators, in addition to the observation of other dynamical states including clustering, chimera, and weak chimera. We also show that closed-loop networks tend to hold global synchronization for longer duration as compared to open-loop networks.

Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons

We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.

Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death

Neurodegenerative diseases, such as Alzheimer's or Parkinson's disease, show characteristic degradation of structural brain networks. This degradation eventually leads to changes in the network dynamics and degradation of cognitive functions. Here, we model the progression in terms of coupled physical processes: The accumulation of toxic proteins, given by a nonlinear reaction-diffusion transport process, yields an evolving brain connectome characterized by weighted edges on which a neuronal-mass model evolves. The progression of the brain functions can be tested by simulating the resting-state activity on the evolving brain network. We show that while the evolution of edge weights plays a minor role in the overall progression of the disease, dynamic biomarkers predict a transition over a period of 10 years associated with strong cognitive decline.

Whole-Brain Models to Explore Altered States of Consciousness from the Bottom Up

The scope of human consciousness includes states departing from what most of us experience as ordinary wakefulness. These altered states of consciousness constitute a prime opportunity to study how global changes in brain activity relate to different varieties of subjective experience. We consider the problem of explaining how global signatures of altered consciousness arise from the interplay between large-scale connectivity and local dynamical rules that can be traced to known properties of neural tissue. For this purpose, we advocate a research program aimed at bridging the gap between bottom-up generative models of whole-brain activity and the top-down signatures proposed by theories of consciousness. Throughout this paper, we define altered states of consciousness, discuss relevant signatures of consciousness observed in brain activity, and introduce whole-brain models to explore the biophysics of altered consciousness from the bottom-up. We discuss the potential of our proposal in view of the current state of the art, give specific examples of how this research agenda might play out, and emphasize how a systematic investigation of altered states of consciousness via bottom-up modeling may help us better understand the biophysical, informational, and dynamical underpinnings of consciousness.

Metastable neural dynamics underlies cognitive performance across multiple behavioural paradigms

Despite resting state networks being associated with a variety of cognitive abilities, it remains unclear how these local areas act in concert to express particular cognitive operations. Theoretical and empirical accounts indicate that large-scale resting state networks reconcile dual tendencies towards integration and segregation by operating in a metastable regime of their coordination dynamics. Metastability may confer important behavioural qualities by binding distributed local areas into large-scale neurocognitive networks. We tested this hypothesis by analysing fMRI data in a large cohort of healthy individuals (N = 566) and comparing the metastability of the brain's large-scale resting network architecture at rest and during the performance of several tasks. Metastability was estimated using a well-defined collective variable capturing the level of 'phase-locking' between large-scale networks over time. Task-based reasoning was principally characterised by high metastability in cognitive control networks and low metastability in sensory processing areas. Although metastability between resting state networks increased during task performance, cognitive ability was more closely linked to spontaneous activity. High metastability in the intrinsic connectivity of cognitive control networks was linked to novel problem solving or fluid intelligence, but was less important in tasks relying on previous experience or crystallised intelligence. Crucially, subjects with resting architectures similar or 'pre-configured' to a task-general arrangement demonstrated superior cognitive performance. Taken together, our findings support a key linkage between the spontaneous metastability of large-scale networks in the cerebral cortex and cognition.

A Brief Review of Chimera State in Empirical Brain Networks

Understanding the human brain and its functions has always been an interesting and challenging problem. Recently, a significant progress on this problem has been achieved on the aspect of chimera state where a coexistence of synchronized and unsynchronized states can be sustained in identical oscillators. This counterintuitive phenomenon is closely related to the unihemispheric sleep in some marine mammals and birds and has recently gotten a hot attention in neural systems, except the previous studies in non-neural systems such as phase oscillators. This review will briefly summarize the main results of chimera state in neuronal systems and pay special attention to the network of cerebral cortex, aiming to accelerate the study of chimera state in brain networks. Some outlooks are also discussed.

Dynamical Mechanisms of Interictal Resting-State Functional Connectivity in Epilepsy

Drug-resistant focal epilepsy is a large-scale brain networks disorder characterized by altered spatiotemporal patterns of functional connectivity (FC), even during interictal resting state (RS). Although RS-FC-based metrics can detect these changes, results from RS functional magnetic resonance imaging (RS-fMRI) studies are unclear and difficult to interpret, and the underlying dynamical mechanisms are still largely unknown. To better capture the RS dynamics, we phenomenologically extended the neural mass model of partial seizures, the Epileptor, by including two neuron subpopulations of epileptogenic and nonepileptogenic type, making it capable of producing physiological oscillations in addition to the epileptiform activity. Using the neuroinformatics platform The Virtual Brain, we reconstructed 14 epileptic and 5 healthy human (of either sex) brain network models (BNMs), based on individual anatomical connectivity and clinically defined epileptogenic heatmaps. Through systematic parameter exploration and fitting to neuroimaging data, we demonstrated that epileptic brains during interictal RS are associated with lower global excitability induced by a shift in the working point of the model, indicating that epileptic brains operate closer to a stable equilibrium point than healthy brains. Moreover, we showed that functional networks are unaffected by interictal spikes, corroborating previous experimental findings; additionally, we observed higher excitability in epileptogenic regions, in agreement with the data. We shed light on new dynamical mechanisms responsible for altered RS-FC in epilepsy, involving the following two key factors: (1) a shift of excitability of the whole brain leading to increased stability; and (2) a locally increased excitability in the epileptogenic regions supporting the mixture of hyperconnectivity and hypoconnectivity in these areas.

SIGNIFICANCE STATEMENT Advances in functional neuroimaging provide compelling evidence for epilepsy-related brain network alterations, even during the interictal resting state (RS). However, the dynamical mechanisms underlying these changes are still elusive. To identify local and network processes behind the RS-functional connectivity (FC) spatiotemporal patterns, we systematically manipulated the local excitability and the global coupling in the virtual human epileptic patient brain network models (BNMs), complemented by the analysis of the impact of interictal spikes and fitting to the neuroimaging data. Our results suggest that a global shift of the dynamic working point of the brain model, coupled with locally hyperexcitable node dynamics of the epileptogenic networks, provides a mechanistic explanation of the epileptic processes during the interictal RS period. These, in turn, are associated with the changes in FC.

Itinerant complexity in networks of intrinsically bursting neurons

Active neurons can be broadly classified by their intrinsic oscillation patterns into two classes characterized by spiking or bursting. Here, we show that networks of identical bursting neurons with inhibitory pulsatory coupling exhibit itinerant dynamics. Using the relative phases of bursts between neurons, we numerically demonstrate that the network exhibits endogenous transitions between multiple modes of transient synchrony. This is true even for bursts consisting of two spikes. In contrast, our simulations reveal that networks of identical singlet-spiking neurons do not exhibit such complexity. These results suggest a role for bursting dynamics in realizing itinerant complexity in neural circuits.

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.

Meditation Increases the Entropy of Brain Oscillatory Activity

We address the hypothesis that the entropy of neural dynamics indexes the intensity and quality of conscious content. Previous work established that serotonergic psychedelics can have a dysregulating effect on brain activity, leading to subjective effects that present a considerable overlap with the phenomenology of certain meditative states. Here we propose that the prolonged practice of meditation results in endogenous increased entropy of brain oscillatory activity. We estimated the entropy of band-specific oscillations during the meditative state of traditions classified as 'focused attention' (Himalayan Yoga), 'open monitoring' (Vipassana), and 'open awareness' (Isha Shoonya Yoga). Among all traditions, Vipassana resulted in the highest entropy increases, predominantly in the alpha and low/high gamma bands. In agreement with previous studies, all meditation traditions increased the global coherence in the gamma band, but also stabilized gamma-range dynamics by lowering the metastability. Finally, machine learning classifiers could successfully generalize between certain pairs of meditation traditions based on the scalp distribution of gamma band entropies. Our results extend previous findings on the spectral changes observed during meditation, showing how long-term practice can lead to the capacity for achieving brain states of high entropy. This constitutes an example of an endogenous, self-induced high entropy state.

Alpha oscillation, criticality, and responsiveness in complex brain networks

Brains in unconsciousness are characterized by significantly limited responsiveness to stimuli. Even during conscious wakefulness, responsiveness is highly dependent on ongoing brain activity, specifically, of alpha oscillations (∼10 Hz). We hypothesized that the variety of brain responses to external stimuli result from the interaction between state-specific and transient alpha oscillations and stimuli. To justify this hypothesis, we simulated various alpha oscillations in the human brain network, modulating criticality (a balanced state between order and disorder), and investigated specific alpha oscillation properties (instantaneous amplitude, phase, and global synchronization) that induce a large or small response. As a result, we found that the alpha oscillations near a critical state show a more complex and long-lasting response, which is more prominent when stimuli are given to globally desynchronized and low-amplitude oscillations. We also found specific phases of alpha oscillation that barely respond to stimuli, which implies the presence of temporal windows in the alpha cycle for a large or small response. The results explain why brain responses are so variable across conscious and unconscious states and across time windows even during conscious wakefulness, and emphasize the importance of considering ongoing alpha oscillations for effective brain stimulation.

Responsiveness of the brain varies depending on the brain states (wakefulness, sleep, anesthesia, and traumatic injuries) and even during wakefulness, resulting in various responses to the same stimulus. What makes those different responses across brain states and even across time windows in conscious state? What is an effective way to obtain the largest response to external stimulus? To answer those questions, we simulated various alpha oscillations (∼10 Hz) in a large-scale brain network and found state-specific alpha oscillation properties that show large or small responsiveness. Notably, the results suggest the presence of temporal windows in alpha cycle that inhibit external information integration and emphasize considering the large/small responsiveness conditions for effective brain stimulation.

Abnormal dynamic functional network connectivity in unmedicated bipolar and major depressive disorders based on the triple-network model

BACKGROUND

Previous studies have analyzed brain functional connectivity to reveal the neural physiopathology of bipolar disorder (BD) and major depressive disorder (MDD) based on the triple-network model [involving the salience network, default mode network (DMN), and central executive network (CEN)]. However, most studies assumed that the brain intrinsic fluctuations throughout the entire scan are static. Thus, we aimed to reveal the dynamic functional network connectivity (dFNC) in the triple networks of BD and MDD.

METHODS

We collected resting state fMRI data from 51 unmedicated depressed BD II patients, 51 unmedicated depressed MDD patients, and 52 healthy controls. We analyzed the dFNC by using an independent component analysis, sliding window correlation and k-means clustering, and used the parameters of dFNC state properties and dFNC variability for group comparisons.

RESULTS

The dFNC within the triple networks could be clustered into four configuration states, three of them showing dense connections (States 1, 2, and 4) and the other one showing sparse connections (State 3). Both BD and MDD patients spent more time in State 3 and showed decreased dFNC variability between posterior DMN and right CEN (rCEN) compared with controls. The MDD patients showed specific decreased dFNC variability between anterior DMN and rCEN compared with controls.

CONCLUSIONS

This study revealed more common but less specific dFNC alterations within the triple networks in unmedicated depressed BD II and MDD patients, which indicated their decreased information processing and communication ability and may help us to understand their abnormal affective and cognitive functions clinically.

Synchronization route to weak chimera in four candle-flame oscillators

Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera.