Perturbation of whole-brain dynamics in silico reveals mechanistic differences between brain states

The alterations of repetitive transcranial magnetic stimulation on the energy landscape of resting-state networks differ across the human cortex

Repetitive transcranial magnetic stimulation (rTMS) is a promising intervention tool for the noninvasive modulation of brain activity and behavior in neuroscience research and clinical settings. However, the resting-state dynamic evolution of large-scale functional brain networks following rTMS has rarely been investigated. Here, using resting-state fMRI images collected from 23 healthy individuals before (baseline) and after 1 Hz rTMS of the left frontal (FRO) and occipital (OCC) lobes, we examined the different effects of rTMS on brain dynamics across the human cortex. By fitting a pairwise maximum entropy model (pMEM), we constructed an energy landscape for the baseline and poststimulus conditions by fitting a pMEM. We defined dominant brain states (local minima) in the energy landscape with synergistic activation and deactivation patterns of large-scale functional networks. We calculated state dynamics including appearance probability, transitions and duration. The results showed that 1 Hz rTMS induced increased and decreased state probability, transitions and duration when delivered to the FRO and OCC targets, respectively. Most importantly, the shortest path and minimum cost between dominant brain states were altered after stimulation. The absolute sum of the costs from the source states to the destinations was lower after OCC stimulation than after FRO stimulation. In conclusion, our study characterized the dynamic trajectory of state transitions in the energy landscape and suggested that local rTMS can induce significant dynamic perturbation involving stimulated and distant functional networks, which aligns with the modern view of the dynamic and complex brain. Our results suggest low-dimensional mapping of rTMS-induced brain adaption, which will contribute to a broader and more effective application of rTMS in clinical settings.

Psychedelics and disorders of consciousness: the current landscape and the path forward

Modern medicine has been shaken by the surge of psychedelic science that proposes a new approach to mitigate mental disorders, such as depression and post-traumatic stress disorder. Clinical trials to investigate whether psychedelic substances can treat psychiatric conditions are now underway, yet less discussion gravitates around their use in neurological disorders due to brain injury. One suggested implementation of brain-complexity enhancing psychedelics is to treat people with post-comatose disorders of consciousness (DoC). In this article, we discuss the rationale of this endeavour, examining possible outcomes of such experiments by postulating the existence of an optimal level of complexity. We consider the possible counterintuitive effects of both psychedelics and DoC on the functional connectivity of the default mode network and its possible impact on selfhood. We also elaborate on the role of computational modelling in providing complementary information to experimental studies, both contributing to our understanding of the treatment mechanisms and providing a path towards personalized medicine. Finally, we update the discourse surrounding the ethical considerations, encompassing clinical and scientific values.

Re-awakening the brain: Forcing transitions in disorders of consciousness by external in silico perturbation

A fundamental challenge in neuroscience is accurately defining brain states and predicting how and where to perturb the brain to force a transition. Here, we investigated resting-state fMRI data of patients suffering from disorders of consciousness (DoC) after coma (minimally conscious and unresponsive wakefulness states) and healthy controls. We applied model-free and model-based approaches to help elucidate the underlying brain mechanisms of patients with DoC. The model-free approach allowed us to characterize brain states in DoC and healthy controls as a probabilistic metastable substate (PMS) space. The PMS of each group was defined by a repertoire of unique patterns (i.e., metastable substates) with different probabilities of occurrence. In the model-based approach, we adjusted the PMS of each DoC group to a causal whole-brain model. This allowed us to explore optimal strategies for promoting transitions by applying off-line in silico probing. Furthermore, this approach enabled us to evaluate the impact of local perturbations in terms of their global effects and sensitivity to stimulation, which is a model-based biomarker providing a deeper understanding of the mechanisms underlying DoC. Our results show that transitions were obtained in a synchronous protocol, in which the somatomotor network, thalamus, precuneus and insula were the most sensitive areas to perturbation. This motivates further work to continue understanding brain function and treatments of disorders of consciousness.

A synergetic turn in cognitive neuroscience of brain diseases

Despite significant improvements in our understanding of brain diseases, many barriers remain. Cognitive neuroscience faces four major challenges: complex structure-function associations; disease phenotype heterogeneity; the lack of transdiagnostic models; and oversimplified cognitive approaches restricted to the laboratory. Here, we propose a synergetics framework that can help to perform the necessary dimensionality reduction of complex interactions between the brain, body, and environment. The key solutions include low-dimensional spatiotemporal hierarchies for brain-structure associations, whole-brain modeling to handle phenotype diversity, model integration of shared transdiagnostic pathophysiological pathways, and naturalistic frameworks balancing experimental control and ecological validity. Creating whole-brain models with reduced manifolds combined with ecological measures can improve our understanding of brain disease and help identify novel interventions. Synergetics provides an integrated framework for future progress in clinical and cognitive neuroscience, pushing the boundaries of brain health and disease toward more mature, naturalistic approaches.

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.

On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is often much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and the exact value of each parameter is frequently less interesting than the distribution of the parameters. In this paper, we aim to estimate the distribution of the parameters in the mesoscopic neuronal network model from the macroscopic experimental data, for example, the BOLD (blood oxygen level dependent) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently and identically distributed from certain distributions with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the Leaky Integral-Fire (LIF) neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with high preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.

Brain dynamics predictive of response to psilocybin for treatment-resistant depression

Psilocybin therapy for depression has started to show promise, yet the underlying causal mechanisms are not currently known. Here, we leveraged the differential outcome in responders and non-responders to psilocybin (10 and 25 mg, 7 days apart) therapy for depression-to gain new insights into regions and networks implicated in the restoration of healthy brain dynamics. We used large-scale brain modelling to fit the spatiotemporal brain dynamics at rest in both responders and non-responders before treatment. Dynamic sensitivity analysis of systematic perturbation of these models enabled us to identify specific brain regions implicated in a transition from a depressive brain state to a healthy one. Binarizing the sample into treatment responders (>50% reduction in depressive symptoms) versus non-responders enabled us to identify a subset of regions implicated in this change. Interestingly, these regions correlate with in vivo density maps of serotonin receptors 5-hydroxytryptamine 2a and 5-hydroxytryptamine 1a, which psilocin, the active metabolite of psilocybin, has an appreciable affinity for, and where it acts as a full-to-partial agonist. Serotonergic transmission has long been associated with depression, and our findings provide causal mechanistic evidence for the role of brain regions in the recovery from depression via psilocybin.

Bibliometric and visualized analysis of dynamic balance and brain function using web of science and CiteSpace from 1995 to 2022

Purpose

This study aims to explore the dynamic balance of human beings and investigate the relationship between functional structure as well as functional connectivity. Through a comprehensive bibliometric and visual analysis of the research literature from 1995 to 2022, we quantitatively display the development of the dynamic balance and brain structure as well as functional connection. Our objective is to present new trends and frontiers in the study of dynamic balance and brain function through bibliometrics software, providing valuable insights for future research in this domain.

Methods

The literature on dynamic balance, brain structure and functional connectivity between 1995 and 2022 was retrieved from the Web of Science database. We employed CiteSpace software to analyze various aspects, including the year of publication, journal, authors, keywords, institutions, countries, and references. Based on the analysis results, a co-reference map was generated to visually observe research hotspots and knowledge structures.

Results

A total of 1533 records were retrieved during the survey period (1995-2022), with a gradually increase in the number of annual publications. Notably, the data suggests a notable increase in publications between 2020 and 2021. The number of publications increased by 20 % from 2020 to 2021. The journal "Proceedings of the National Academy of Sciences (PNAS)" emerged as the most prolific journal. Among the cited authors, Deco and Gustavo ranked at the top. Key research terms in this field include "neural network", "functional connectivity", "dynamic", "model" and "brain". Particularly, the keyword "neural network" exhibited the strongest growth. The analysis of keywords cluster revealed the top 10 clusters of research themes. Oxford University stood out as the most productive institution, while the United States held the greatest influence with the highest number of publications and centrality. The reference cluster analysis further demonstrated the top 10 clusters in the literature.

Conclusion

Through the use of CiteSpace software, this study performed a comprehensive bibliometric and visual analysis of the Web of Science research literature on human dynamic balance and brain structural as well as functional connectivity over the past few decades. This may help researchers identify new perspectives on potential collaborators as well as collaborating institutions, hot topics, and research frontiers in the research field. The results provided an intuitive displayed overview of research trends, hotspots and frontiers in this field, facilitating a general understanding of its progression. Through unremitting efforts, it provides valuable guidance and reference for future research work.

A phenomenological model of whole brain dynamics using a network of neural oscillators with power-coupling

We present a general, trainable oscillatory neural network as a large-scale model of brain dynamics. The model has a cascade of two stages - an oscillatory stage and a complex-valued feedforward stage - for modelling the relationship between structural connectivity and functional connectivity from neuroimaging data under resting brain conditions. Earlier works of large-scale brain dynamics that used Hopf oscillators used linear coupling of oscillators. A distinctive feature of the proposed model employs a novel form of coupling known as power coupling. Oscillatory networks based on power coupling can accurately model arbitrary multi-dimensional signals. Training the lateral connections in the oscillator layer is done by a modified form of Hebbian learning, whereas a variation of the complex backpropagation algorithm does training in the second stage. The proposed model can not only model the empirical functional connectivity with remarkable accuracy (correlation coefficient between simulated and empirical functional connectivity- 0.99) but also identify default mode network regions. In addition, we also inspected how structural loss in the brain can cause significant aberration in simulated functional connectivity and functional connectivity dynamics; and how it can be restored with optimized model parameters by an in silico perturbational study.

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.

Computational modelling in disorders of consciousness: Closing the gap towards personalised models for restoring consciousness

Disorders of consciousness are complex conditions characterised by persistent loss of responsiveness due to brain injury. They present diagnostic challenges and limited options for treatment, and highlight the urgent need for a more thorough understanding of how human consciousness arises from coordinated neural activity. The increasing availability of multimodal neuroimaging data has given rise to a wide range of clinically- and scientifically-motivated modelling efforts, seeking to improve data-driven stratification of patients, to identify causal mechanisms for patient pathophysiology and loss of consciousness more broadly, and to develop simulations as a means of testing in silico potential treatment avenues to restore consciousness. As a dedicated Working Group of clinicians and neuroscientists of the international Curing Coma Campaign, here we provide our framework and vision to understand the diverse statistical and generative computational modelling approaches that are being employed in this fast-growing field. We identify the gaps that exist between the current state-of-the-art in statistical and biophysical computational modelling in human neuroscience, and the aspirational goal of a mature field of modelling disorders of consciousness; which might drive improved treatments and outcomes in the clinic. Finally, we make several recommendations for how the field as a whole can work together to address these challenges.

TMS-evoked responses are driven by recurrent large-scale network dynamics

A compelling way to disentangle the complexity of the brain is to measure the effects of spatially and temporally synchronized systematic perturbations. In humans, this can be non-invasively achieved by combining transcranial magnetic stimulation (TMS) and electroencephalography (EEG). Spatiotemporally complex and long-lasting TMS-EEG evoked potential (TEP) waveforms are believed to result from recurrent, re-entrant activity that propagates broadly across multiple cortical and subcortical regions, dispersing from and later re-converging on, the primary stimulation site. However, if we loosely understand the TEP of a TMS-stimulated region as the impulse response function of a noisy underdamped harmonic oscillator, then multiple later activity components (waveform peaks) should be expected even for an isolated network node in the complete absence of recurrent inputs. Thus emerges a critically important question for basic and clinical research on human brain dynamics: what parts of the TEP are due to purely local dynamics, what parts are due to reverberant, re-entrant network activity, and how can we distinguish between the two? To disentangle this, we used source-localized TMS-EEG analyses and whole-brain connectome-based computational modelling. Results indicated that recurrent network feedback begins to drive TEP responses from 100 ms post-stimulation, with earlier TEP components being attributable to local reverberatory activity within the stimulated region. Subject-specific estimation of neurophysiological parameters additionally indicated an important role for inhibitory GABAergic neural populations in scaling cortical excitability levels, as reflected in TEP waveform characteristics. The novel discoveries and new software technologies introduced here should be of broad utility in basic and clinical neuroscience research.

LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create "archetype" Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r = 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than in the placebo one, especially in homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than in the placebo condition (p = 9 × 10-5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p = 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13, p = 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity-especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state.

The effect of external stimulation on functional networks in the aging healthy human brain

Understanding the brain changes occurring during aging can provide new insights for developing treatments that alleviate or reverse cognitive decline. Neurostimulation techniques have emerged as potential treatments for brain disorders and to improve cognitive functions. Nevertheless, given the ethical restrictions of neurostimulation approaches, in silico perturbation protocols based on causal whole-brain models are fundamental to gaining a mechanistic understanding of brain dynamics. Furthermore, this strategy could serve to identify neurophysiological biomarkers differentiating between age groups through an exhaustive exploration of the global effect of all possible local perturbations. Here, we used a resting-state fMRI dataset divided into middle-aged (N =310, <65 years) and older adults (N =310, $\geq $65) to characterize brain states in each group as a probabilistic metastable substate (PMS) space. We showed that the older group exhibited a reduced capability to access a metastable substate that overlaps with the rich club. Then, we fitted the PMS to a whole-brain model and applied in silico stimulations in each node to force transitions from the brain states of the older- to the middle-aged group. We found that the precuneus was the best stimulation target. Overall, these findings could have important implications for designing neurostimulation interventions for reversing the effects of aging on whole-brain dynamics.

Strength-dependent perturbation of whole-brain model working in different regimes reveals the role of fluctuations in brain dynamics

Despite decades of research, there is still a lack of understanding of the role and generating mechanisms of the ubiquitous fluctuations and oscillations found in recordings of brain dynamics. Here, we used whole-brain computational models capable of presenting different dynamical regimes to reproduce empirical data's turbulence level. We showed that the model's fluctuations regime fitted to turbulence more faithfully reproduces the empirical functional connectivity compared to oscillatory and noise regimes. By applying global and local strength-dependent perturbations and subsequently measuring the responsiveness of the model, we revealed each regime's computational capacity demonstrating that brain dynamics is shifted towards fluctuations to provide much-needed flexibility. Importantly, fluctuation regime stimulation in a brain region within a given resting state network modulates that network, aligned with previous empirical and computational studies. Furthermore, this framework generates specific, testable empirical predictions for human stimulation studies using strength-dependent rather than constant perturbation. Overall, the whole-brain models fitted to the level of empirical turbulence together with functional connectivity unveil that the fluctuation regime best captures empirical data, and the strength-dependent perturbative framework demonstrates how this regime provides maximal flexibility to the human brain.

A perturbative approach to study information communication in brain networks

How communication among neuronal ensembles shapes functional brain dynamics is a question of fundamental importance to neuroscience. Communication in the brain can be viewed as a product of the interaction of node activities with the structural network over which these activities flow. The study of these interactions is, however, restricted by the difficulties in describing the complex dynamics of the brain. There is thus a need to develop methods to study these network-dynamical interactions and how they impact information flow, without having to ascertain dynamics a priori or resort to restrictive analytical approaches. Here, we adapt a recently established network analysis method based on perturbations, it to a neuroscientific setting to study how information flow in the brain can raise from properties of underlying structure. For proof-of-concept, we apply the approach on in silico whole-brain models. We expound on the functional implications of the distributions of metrics that capture network-dynamical interactions, termed net influence and flow. We also study the network-dynamical interactions at the level of resting-state networks. An attractive feature of this method is its simplicity, which allows a direct translation to an experimental or clinical setting, such as for identifying targets for stimulation studies or therapeutic interventions.

Effects of classic psychedelic drugs on turbulent signatures in brain dynamics

Psychedelic drugs show promise as safe and effective treatments for neuropsychiatric disorders, yet their mechanisms of action are not fully understood. A fundamental hypothesis is that psychedelics work by dose-dependently changing the functional hierarchy of brain dynamics, but it is unclear whether different psychedelics act similarly. Here, we investigated the changes in the brain's functional hierarchy associated with two different psychedelics (LSD and psilocybin). Using a novel turbulence framework, we were able to determine the vorticity, that is, the local level of synchronization, that allowed us to extend the standard global time-based measure of metastability to become a local-based measure of both space and time. This framework produced detailed signatures of turbulence-based hierarchical change for each psychedelic drug, revealing consistent and discriminate effects on a higher level network, that is, the default mode network. Overall, our findings directly support a prior hypothesis that psychedelics modulate (i.e., "compress") the functional hierarchy and provide a quantification of these changes for two different psychedelics. Implications for therapeutic applications of psychedelics are discussed.

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.

From Brain-Body Function to Conscious Interactions

In this review, we discuss empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience. First, we motivate the discussion through evidence regarding the dynamic brain. Second, we review different brain-body couplings associated with conscious experience and its potential role in driving brain dynamics. Third, we introduce the machinery of multilayer networks to account for several types of interactions in brain-body systems. Then, a multilayer structure consists of two main generalizations: a formal semantic to study biological systems, and an integrative account for several signatures and models of consciousness. Finally, under this framework, we define composition of layers to account for entangled features of brain-body systems related to conscious experience. As such, a multilayer mathematical framework is highly integrative and thus may be more complete than other models. In this short review, we discuss a variety of empirical results inspiring the introduction of a formal mathematical multilayer model for the biological neuroscience of conscious experience.

Reliability and subject specificity of personalized whole-brain dynamical models

Dynamical whole-brain models were developed to link structural (SC) and functional connectivity (FC) together into one framework. Nowadays, they are used to investigate the dynamical regimes of the brain and how these relate to behavioral, clinical and demographic traits. However, there is no comprehensive investigation on how reliable and subject specific the modeling results are given the variability of the empirical FC. In this study, we show that the parameters of these models can be fitted with a "poor" to "good" reliability depending on the exact implementation of the modeling paradigm. We find, as a general rule of thumb, that enhanced model personalization leads to increasingly reliable model parameters. In addition, we observe no clear effect of the model complexity evaluated by separately sampling results for linear, phase oscillator and neural mass network models. In fact, the most complex neural mass model often yields modeling results with "poor" reliability comparable to the simple linear model, but demonstrates an enhanced subject specificity of the model similarity maps. Subsequently, we show that the FC simulated by these models can outperform the empirical FC in terms of both reliability and subject specificity. For the structure-function relationship, simulated FC of individual subjects may be identified from the correlations with the empirical SC with an accuracy up to 70%, but not vice versa for non-linear models. We sample all our findings for 8 distinct brain parcellations and 6 modeling conditions and show that the parcellation-induced effect is much more pronounced for the modeling results than for the empirical data. In sum, this study provides an exploratory account on the reliability and subject specificity of dynamical whole-brain models and may be relevant for their further development and application. In particular, our findings suggest that the application of the dynamical whole-brain modeling should be tightly connected with an estimate of the reliability of the results.

Understanding brain states across spacetime informed by whole-brain modelling

In order to survive in a complex environment, the human brain relies on the ability to flexibly adapt ongoing behaviour according to intrinsic and extrinsic signals. This capability has been linked to specific whole-brain activity patterns whose relative stability (order) allows for consistent functioning, supported by sufficient intrinsic instability needed for optimal adaptability. The emergent, spontaneous balance between order and disorder in brain activity over spacetime underpins distinct brain states. For example, depression is characterized by excessively rigid, highly ordered states, while psychedelics can bring about more disordered, sometimes overly flexible states. Recent developments in systems, computational and theoretical neuroscience have started to make inroads into the characterization of such complex dynamics over space and time. Here, we review recent insights drawn from neuroimaging and whole-brain modelling motivating using mechanistic principles from dynamical system theory to study and characterize brain states. We show how different healthy and altered brain states are associated to characteristic spacetime dynamics which in turn may offer insights that in time can inspire new treatments for rebalancing brain states in disease. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

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.

The INSIDEOUT framework provides precise signatures of the balance of intrinsic and extrinsic dynamics in brain states

Finding precise signatures of different brain states is a central, unsolved question in neuroscience. We reformulated the problem to quantify the 'inside out' balance of intrinsic and extrinsic brain dynamics in brain states. The difference in brain state can be described as differences in the detailed causal interactions found in the underlying intrinsic brain dynamics. We used a thermodynamics framework to quantify the breaking of the detailed balance captured by the level of asymmetry in temporal processing, i.e. the arrow of time. Specifically, the temporal asymmetry was computed by the time-shifted correlation matrices for the forward and reversed time series, reflecting the level of non-reversibility/non-equilibrium. We found precise, distinguishing signatures in terms of the reversibility and hierarchy of large-scale dynamics in three radically different brain states (awake, deep sleep and anaesthesia) in electrocorticography data from non-human primates. Significantly lower levels of reversibility were found in deep sleep and anaesthesia compared to wakefulness. Non-wakeful states also showed a flatter hierarchy, reflecting the diversity of the reversibility across the brain. Overall, this provides signatures of the breaking of detailed balance in different brain states, perhaps reflecting levels of conscious awareness.

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.

Explosive Synchronization-Based Brain Modulation Reduces Hypersensitivity in the Brain Network: A Computational Model Study

Fibromyalgia (FM) is a chronic pain condition that is characterized by hypersensitivity to multimodal sensory stimuli, widespread pain, and fatigue. We have previously proposed explosive synchronization (ES), a phenomenon wherein a small perturbation to a network can lead to an abrupt state transition, as a potential mechanism of the hypersensitive FM brain. Therefore, we hypothesized that converting a brain network from ES to general synchronization (GS) may reduce the hypersensitivity of FM brain. To find an effective brain network modulation to convert ES into GS, we constructed a large-scale brain network model near criticality (i.e., an optimally balanced state between order and disorders), which reflects brain dynamics in conscious wakefulness, and adjusted two parameters: local structural connectivity and signal randomness of target brain regions. The network sensitivity to global stimuli was compared between the brain networks before and after the modulation. We found that only increasing the local connectivity of hubs (nodes with intense connections) changes ES to GS, reducing the sensitivity, whereas other types of modulation such as decreasing local connectivity, increasing and decreasing signal randomness are not effective. This study would help to develop a network mechanism-based brain modulation method to reduce the hypersensitivity in FM.

Criticality Creates a Functional Platform for Network Transitions Between Internal and External Processing Modes in the Human Brain

Continuous switching between internal and external modes in the brain appears important for generating models of the self and the world. However, how the brain transitions between these two modes remains unknown. We propose that a large synchronization fluctuation of brain networks, emerging only near criticality (i.e., a balanced state between order and disorder), spontaneously creates temporal windows with distinct preferences for integrating the network's internal information or for processing external stimuli. Using a computational model, electroencephalography (EEG) analysis, and functional magnetic resonance imaging (fMRI) analysis during alterations of consciousness in humans, we report that synchronized and incoherent networks, respectively, bias toward internal and external information with specific network configurations. In the brain network model and EEG-based network, the network preferences are the most prominent at criticality and in conscious states associated with the bandwidth 4-12 Hz, with alternating functional network configurations. However, these network configurations are selectively disrupted in different states of consciousness such as general anesthesia, psychedelic states, minimally conscious states, and unresponsive wakefulness syndrome. The network preference for internal information integration is only significant in conscious states and psychedelic states, but not in other unconscious states, suggesting the importance of internal information integration in maintaining consciousness. The fMRI co-activation pattern analysis shows that functional networks that are sensitive to external stimuli-such as default mode, dorsal attentional, and frontoparietal networks-are activated in incoherent states, while insensitive networks, such as global activation and deactivation networks, are dominated in highly synchronized states. We suggest that criticality produces a functional platform for the brain's capability for continuous switching between two modes, which is crucial for the emergence of consciousness.

Parcellation-induced variation of empirical and simulated brain connectomes at group and subject levels

Recent developments of whole-brain models have demonstrated their potential when investigating resting-state brain activity. However, it has not been systematically investigated how alternating derivations of the empirical structural and functional connectivity, serving as the model input, from MRI data influence modeling results. Here, we study the influence from one major element: the brain parcellation scheme that reduces the dimensionality of brain networks by grouping thousands of voxels into a few hundred brain regions. We show graph-theoretical statistics derived from the empirical data and modeling results exhibiting a high heterogeneity across parcellations. Furthermore, the network properties of empirical brain connectomes explain the lion’s share of the variance in the modeling results with respect to the parcellation variation. Such a clear-cut relationship is not observed at the subject-resolved level per parcellation. Finally, the graph-theoretical statistics of the simulated connectome correlate with those of the empirical functional connectivity across parcellations. However, this relation is not one-to-one, and its precision can vary between models. Our results imply that network properties of both empirical connectomes can explain the goodness-of-fit of whole-brain models to empirical data at a global group level but not at a single-subject level, which provides further insights into the personalization of whole-brain models.

The structural and functional connectivities of the brain, which reflect the anatomical connections of axonal bundles and the amount of coactivation between brain regions, respectively, only weakly correlate with each other. In order to enhance and investigate this relationship, large-scale whole-brain dynamical models were involved in this branch of research. However, how the definitions of the brain regions parcellated according to a so-called brain atlas influence these models has so far not been systematically assessed. In this article, we show that this influence can be large, and link group-averaged, atlas-induced deviations to network properties extracted from both types of connectivity. Additionally, we demonstrate that the same association does not apply to subject-specific variations. These results may contribute to the further personalization of the whole-brain models.

Neurophysiologic Complexity in Children Increases with Developmental Age and Is Reduced by General Anesthesia

BACKGROUND

Neurophysiologic complexity in the cortex has been shown to reflect changes in the level of consciousness in adults but remains incompletely understood in the developing brain. This study aimed to address changes in cortical complexity related to age and anesthetic state transitions. This study tested the hypotheses that cortical complexity would (1) increase with developmental age and (2) decrease during general anesthesia.

METHODS

This was a single-center, prospective, cross-sectional study of healthy (American Society of Anesthesiologists physical status I or II) children (n = 50) of age 8 to 16 undergoing surgery with general anesthesia at Michigan Medicine. This age range was chosen because it reflects a period of substantial brain network maturation. Whole scalp (16-channel), wireless electroencephalographic data were collected from the preoperative period through the recovery of consciousness. Cortical complexity was measured using the Lempel-Ziv algorithm and analyzed during the baseline, premedication, maintenance of general anesthesia, and clinical recovery periods. The effect of spectral power on Lempel-Ziv complexity was analyzed by comparing the original complexity value with those of surrogate time series generated through phase randomization that preserves power spectrum.

RESULTS

Baseline spatiotemporal Lempel-Ziv complexity increased with age (yr; slope [95% CI], 0.010 [0.004, 0.016]; P < 0.001); when normalized to account for spectral power, there was no significant age effect on cortical complexity (0.001 [-0.004, 0.005]; P = 0.737). General anesthesia was associated with a significant decrease in spatiotemporal complexity (median [25th, 75th]; baseline, 0.660 [0.620, 0.690] vs. maintenance, 0.459 [0.402, 0.527]; P < 0.001), and spatiotemporal complexity exceeded baseline levels during postoperative recovery (0.704 [0.642, 0.745]; P = 0.009). When normalized, there was a similar reduction in complexity during general anesthesia (baseline, 0.913 [0.887, 0.923] vs. maintenance 0.851 [0.823, 0.877]; P < 0.001), but complexity remained significantly reduced during recovery (0.873 [0.840, 0.902], P < 0.001).

CONCLUSIONS

Cortical complexity increased with developmental age and decreased during general anesthesia. This association remained significant when controlling for spectral changes during anesthetic-induced perturbations in consciousness but not with developmental age.

EDITOR’S PERSPECTIVE

Loss of consciousness reduces the stability of brain hubs and the heterogeneity of brain dynamics

Low-level states of consciousness are characterized by disruptions of brain activity that sustain arousal and awareness. Yet, how structural, dynamical, local and network brain properties interplay in the different levels of consciousness is unknown. Here, we study fMRI brain dynamics from patients that suffered brain injuries leading to a disorder of consciousness and from healthy subjects undergoing propofol-induced sedation. We show that pathological and pharmacological low-level states of consciousness display less recurrent, less connected and more segregated synchronization patterns than conscious state. We use whole-brain models built upon healthy and injured structural connectivity to interpret these dynamical effects. We found that low-level states of consciousness were associated with reduced network interactions, together with more homogeneous and more structurally constrained local dynamics. Notably, these changes lead the structural hub regions to lose their stability during low-level states of consciousness, thus attenuating the differences between hubs and non-hubs brain dynamics.

López-González et al study the fMRI brain dynamics and their underlying mechanism from patients that suffered brain injuries leading to a disorder of consciousness as well as from healthy subjects undergoing propofol-induced sedation. They show that pathological and pharmacological low-level states of consciousness display disrupted synchronization patterns, higher constraint to the anatomy and a loss of heterogeneity and stability in the structural hubs compared to conscious states.

Perturbations in dynamical models of whole-brain activity dissociate between the level and stability of consciousness

Consciousness transiently fades away during deep sleep, more stably under anesthesia, and sometimes permanently due to brain injury. The development of an index to quantify the level of consciousness across these different states is regarded as a key problem both in basic and clinical neuroscience. We argue that this problem is ill-defined since such an index would not exhaust all the relevant information about a given state of consciousness. While the level of consciousness can be taken to describe the actual brain state, a complete characterization should also include its potential behavior against external perturbations. We developed and analyzed whole-brain computational models to show that the stability of conscious states provides information complementary to their similarity to conscious wakefulness. Our work leads to a novel methodological framework to sort out different brain states by their stability and reversibility, and illustrates its usefulness to dissociate between physiological (sleep), pathological (brain-injured patients), and pharmacologically-induced (anesthesia) loss of consciousness.

Revisiting the global workspace orchestrating the hierarchical organization of the human brain

A central challenge in neuroscience is how the brain organizes the information necessary to orchestrate behaviour. Arguably, this whole-brain orchestration is carried out by a core subset of integrative brain regions, a 'global workspace', but its constitutive regions remain unclear. We quantified the global workspace as the common regions across seven tasks as well as rest, in a common 'functional rich club'. To identify this functional rich club, we determined the information flow between brain regions by means of a normalized directed transfer entropy framework applied to multimodal neuroimaging data from 1,003 healthy participants and validated in participants with retest data. This revealed a set of regions orchestrating information from perceptual, long-term memory, evaluative and attentional systems. We confirmed the causal significance and robustness of our results by systematically lesioning a generative whole-brain model. Overall, this framework describes a complex choreography of the functional hierarchical organization of the human brain.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity

An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart-Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.

Increased sensitivity to strong perturbations in a whole-brain model of LSD

•

Novel offline perturbational method applied on functional magnetic resonance imaging (fMRI) data under the effect of lysergic acid diethylamide (LSD).

•

Shift of brain's global working point to more complex dynamics after LSD intake.

•

Consistently longer recovery time after model perturbation under LSD influence.

•

Strongest effects in resting state networks relevant for psychedelic experience.

•

Higher response diversity across brain regions under LSD influence after an external in silico perturbation.

Lysergic acid diethylamide (LSD) is a potent psychedelic drug, which has seen a revival in clinical and pharmacological research within recent years. Human neuroimaging studies have shown fundamental changes in brain-wide functional connectivity and an expansion of dynamical brain states, thus raising the question about a mechanistic explanation of the dynamics underlying these alterations. Here, we applied a novel perturbational approach based on a whole-brain computational model, which opens up the possibility to externally perturb different brain regions in silico and investigate differences in dynamical stability of different brain states, i.e. the dynamical response of a certain brain region to an external perturbation. After adjusting the whole-brain model parameters to reflect the dynamics of functional magnetic resonance imaging (fMRI) BOLD signals recorded under the influence of LSD or placebo, perturbations of different brain areas were simulated by either promoting or disrupting synchronization in the regarding brain region. After perturbation offset, we quantified the recovery characteristics of the brain area to its basal dynamical state with the Perturbational Integration Latency Index (PILI) and used this measure to distinguish between the two brain states. We found significant changes in dynamical complexity with consistently higher PILI values after LSD intake on a global level, which indicates a shift of the brain's global working point further away from a stable equilibrium as compared to normal conditions. On a local level, we found that the largest differences were measured within the limbic network, the visual network and the default mode network. Additionally, we found a higher variability of PILI values across different brain regions after LSD intake, indicating higher response diversity under LSD after an external perturbation. Our results provide important new insights into the brain-wide dynamical changes underlying the psychedelic state - here provoked by LSD intake - and underline possible future clinical applications of psychedelic drugs in particular psychiatric disorders.

Turbulent-like Dynamics in the Human Brain

Turbulence facilitates fast energy/information transfer across scales in physical systems. These qualities are important for brain function, but it is currently unknown if the dynamic intrinsic backbone of the brain also exhibits turbulence. Using large-scale neuroimaging empirical data from 1,003 healthy participants, we demonstrate turbulent-like human brain dynamics. Furthermore, we build a whole-brain model with coupled oscillators to demonstrate that the best fit to the data corresponds to a region of maximally developed turbulent-like dynamics, which also corresponds to maximal sensitivity to the processing of external stimulations (information capability). The model shows the economy of anatomy by following the exponential distance rule of anatomical connections as a cost-of-wiring principle. This establishes a firm link between turbulent-like brain activity and optimal brain function. Overall, our results reveal a way of analyzing and modeling whole-brain dynamics that suggests a turbulent-like dynamic intrinsic backbone facilitating large-scale network communication.

EEG microstate periodicity explained by rotating phase patterns of resting-state alpha oscillations

Spatio-temporal patterns in electroencephalography (EEG) can be described by microstate analysis, a discrete approximation of the continuous electric field patterns produced by the cerebral cortex. Resting-state EEG microstates are largely determined by alpha frequencies (8-12 Hz) and we recently demonstrated that microstates occur periodically with twice the alpha frequency. To understand the origin of microstate periodicity, we analyzed the analytic amplitude and the analytic phase of resting-state alpha oscillations independently. In continuous EEG data we found rotating phase patterns organized around a small number of phase singularities which varied in number and location. The spatial rotation of phase patterns occurred with the underlying alpha frequency. Phase rotors coincided with periodic microstate motifs involving the four canonical microstate maps. The analytic amplitude showed no oscillatory behaviour and was almost static across time intervals of 1-2 alpha cycles, resulting in the global pattern of a standing wave. In n=23 healthy adults, time-lagged mutual information analysis of microstate sequences derived from amplitude and phase signals of awake eyes-closed EEG records showed that only the phase component contributed to the periodicity of microstate sequences. Phase sequences showed mutual information peaks at multiples of 50 ms and the group average had a main peak at 100 ms (10 Hz), whereas amplitude sequences had a slow and monotonous information decay. This result was confirmed by an independent approach combining temporal principal component analysis (tPCA) and autocorrelation analysis. We reproduced our observations in a generic model of EEG oscillations composed of coupled non-linear oscillators (Stuart-Landau model). Phase-amplitude dynamics similar to experimental EEG occurred when the oscillators underwent a supercritical Hopf bifurcation, a common feature of many computational models of the alpha rhythm. These findings explain our previous description of periodic microstate recurrence and its relation to the time scale of alpha oscillations. Moreover, our results corroborate the predictions of computational models and connect experimentally observed EEG patterns to properties of critical oscillator networks.

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.

Modeling regional changes in dynamic stability during sleep and wakefulness

Global brain states are frequently placed within a unidimensional continuum by correlational studies, ranging from states of deep unconsciousness to ordinary wakefulness. An alternative is their multidimensional and mechanistic characterization in terms of different cognitive capacities, using computational models to reproduce the underlying neural dynamics. We explore this alternative by introducing a semi-empirical model linking regional activation and long-range functional connectivity in the different brain states visited during the natural wake-sleep cycle. Our model combines functional magnetic resonance imaging (fMRI) data, in vivo estimates of structural connectivity, and anatomically-informed priors to constrain the independent variation of regional activation. The best fit to empirical data was achieved using priors based on functionally coherent networks, with the resulting model parameters dividing the cortex into regions presenting opposite dynamical behavior. Frontoparietal regions approached a bifurcation from dynamics at a fixed point governed by noise, while sensorimotor regions approached a bifurcation from oscillatory dynamics. In agreement with human electrophysiological experiments, sleep onset induced subcortical deactivation with low correlation, which was subsequently reversed for deeper stages. Finally, we introduced periodic forcing of variable intensity to simulate external perturbations, and identified the key regions relevant for the recovery of wakefulness from deep sleep. Our model represents sleep as a state with diminished perceptual gating and the latent capacity for global accessibility that is required for rapid arousals. To the extent that the qualitative characterization of local dynamics is exhausted by the dichotomy between unstable and stable behavior, our work highlights how expanding the model parameter space can describe states of consciousness in terms of multiple dimensions with interpretations given by the choice of anatomically-informed priors.

Activity-dependent myelination: A glial mechanism of oscillatory self-organization in large-scale brain networks

Communication and oscillatory synchrony between distributed neural populations are believed to play a key role in multiple cognitive and neural functions. These interactions are mediated by long-range myelinated axonal fiber bundles, collectively termed as white matter. While traditionally considered to be static after development, white matter properties have been shown to change in an activity-dependent way through learning and behavior-a phenomenon known as white matter plasticity. In the central nervous system, this plasticity stems from oligodendroglia, which form myelin sheaths to regulate the conduction of nerve impulses across the brain, hence critically impacting neural communication. We here shift the focus from neural to glial contribution to brain synchronization and examine the impact of adaptive, activity-dependent changes in conduction velocity on the large-scale phase synchronization of neural oscillators. Using a network model based on primate large-scale white matter neuroanatomy, our computational and mathematical results show that such plasticity endows white matter with self-organizing properties, where conduction delay statistics are autonomously adjusted to ensure efficient neural communication. Our analysis shows that this mechanism stabilizes oscillatory neural activity across a wide range of connectivity gain and frequency bands, making phase-locked states more resilient to damage as reflected by diffuse decreases in connectivity. Critically, our work suggests that adaptive myelination may be a mechanism that enables brain networks with a means of temporal self-organization, resilience, and homeostasis.

Brain network constraints and recurrent neural networks reproduce unique trajectories and state transitions seen over the span of minutes in resting-state fMRI

Large-scale patterns of spontaneous whole-brain activity seen in resting-state functional magnetic resonance imaging (rs-fMRI) are in part believed to arise from neural populations interacting through the structural network (Honey, Kötter, Breakspear, & Sporns, 2007). Generative models that simulate this network activity, called brain network models (BNM), are able to reproduce global averaged properties of empirical rs-fMRI activity such as functional connectivity (FC) but perform poorly in reproducing unique trajectories and state transitions that are observed over the span of minutes in whole-brain data (Cabral, Kringelbach, & Deco, 2017; Kashyap & Keilholz, 2019). The manuscript demonstrates that by using recurrent neural networks, it can fit the BNM in a novel way to the rs-fMRI data and predict large amounts of variance between subsequent measures of rs-fMRI data. Simulated data also contain unique repeating trajectories observed in rs-fMRI, called quasiperiodic patterns (QPP), that span 20 s and complex state transitions observed using k-means analysis on windowed FC matrices (Allen et al., 2012; Majeed et al., 2011). Our approach is able to estimate the manifold of rs-fMRI dynamics by training on generating subsequent time points, and it can simulate complex resting-state trajectories better than the traditional generative approaches.

Brain network models have become a promising theoretical framework for simulating signals that are representative of whole-brain activity such as resting-state fMRI. However, it has been difficult to compare the complex brain activity obtained from simulations with empirical data. Previous studies have used simple metrics to characterize coordination between regions such as functional connectivity. In this manuscript, we extend this work by utilizing modern machine learning techniques to fit the brain network models to observed data and train on the mismatch between the model and observed signal. Our results show that our system training on these new metrics generalizes to a system that is able to reproduce trajectories and complex state transitions seen in rs-fMRI over the span of minutes. Our results will be useful in constraining and developing more realistic simulations of whole-brain activity.

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.

Concurrent human TMS-EEG-fMRI enables monitoring of oscillatory brain state-dependent gating of cortico-subcortical network activity

Despite growing interest, the causal mechanisms underlying human neural network dynamics remain elusive. Transcranial Magnetic Stimulation (TMS) allows to noninvasively probe neural excitability, while concurrent fMRI can log the induced activity propagation through connected network nodes. However, this approach ignores ongoing oscillatory fluctuations which strongly affect network excitability and concomitant behavior. Here, we show that concurrent TMS-EEG-fMRI enables precise and direct monitoring of causal dependencies between oscillatory states and signal propagation throughout cortico-subcortical networks. To demonstrate the utility of this multimodal triad, we assessed how pre-TMS EEG power fluctuations influenced motor network activations induced by subthreshold TMS to right dorsal premotor cortex. In participants with adequate motor network reactivity, strong pre-TMS alpha power reduced TMS-evoked hemodynamic activations throughout the bilateral cortico-subcortical motor system (including striatum and thalamus), suggesting shunted network connectivity. Concurrent TMS-EEG-fMRI opens an exciting noninvasive avenue of subject-tailored network research into dynamic cognitive circuits and their dysfunction.

Criticality as a Determinant of Integrated Information Φ in Human Brain Networks

Integrated information theory (IIT) describes consciousness as information integrated across highly differentiated but irreducible constituent parts in a system. However, in a complex dynamic system such as the brain, the optimal conditions for large integrated information systems have not been elucidated. In this study, we hypothesized that network criticality, a balanced state between a large variation in functional network configuration and a large constraint on structural network configuration, may be the basis of the emergence of a large Φ¯, a surrogate of integrated information. We also hypothesized that as consciousness diminishes, the brain loses network criticality and Φ¯ decreases. We tested these hypotheses with a large-scale brain network model and high-density electroencephalography (EEG) acquired during various levels of human consciousness under general anesthesia. In the modeling study, maximal criticality coincided with maximal Φ¯. The EEG study demonstrated an explicit relationship between Φ¯, criticality, and level of consciousness. The conscious resting state showed the largest Φ¯ and criticality, whereas the balance between variation and constraint in the brain network broke down as the response rate dwindled. The results suggest network criticality as a necessary condition of a large Φ¯ in the human brain.

Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates

Whole-brain computational modeling based on structural connectivity has shown great promise in successfully simulating fMRI BOLD signals with temporal coactivation patterns that are highly similar to empirical functional connectivity patterns during resting state. Importantly, previous studies have shown that spontaneous fluctuations in coactivation patterns of distributed brain regions have an inherent dynamic nature with regard to the frequency spectrum of intrinsic brain oscillations. In this modeling study, we introduced frequency dynamics into a system of coupled oscillators, where each oscillator represents the local mean-field model of a brain region. We first showed that the collective behavior of interacting oscillators reproduces previously shown features of brain dynamics. Second, we examined the effect of simulated lesions in gray matter by applying an in silico perturbation protocol to the brain model. We present a new approach to map the effects of vulnerability in brain networks and introduce a measure of regional hazardousness based on mapping of the degree of divergence in a feature space.

Awakening: Predicting external stimulation to force transitions between different brain states

We describe a quantitative and robust definition of a brain state as an ensemble of “metastable substates,” each with a probabilistic stability and occurrence frequency. Fitting this to a generative whole-brain model provides an innovative avenue for predicting where simulated brain stimulation can force transitions between different brain states. We provide proof-of-concept by systematically applying this model framework to neuroimaging data of the human sleep cycle and show where to stimulate to awaken the human sleeping brain and vice versa. These results suggest an avenue for using causal whole-brain models to discover in silico where to force a transition between brain states, which may potentially support recovery in disease.

A fundamental problem in systems neuroscience is how to force a transition from one brain state to another by external driven stimulation in, for example, wakefulness, sleep, coma, or neuropsychiatric diseases. This requires a quantitative and robust definition of a brain state, which has so far proven elusive. Here, we provide such a definition, which, together with whole-brain modeling, permits the systematic study in silico of how simulated brain stimulation can force transitions between different brain states in humans. Specifically, we use a unique neuroimaging dataset of human sleep to systematically investigate where to stimulate the brain to force an awakening of the human sleeping brain and vice versa. We show where this is possible using a definition of a brain state as an ensemble of “metastable substates,” each with a probabilistic stability and occurrence frequency fitted by a generative whole-brain model, fine-tuned on the basis of the effective connectivity. Given the biophysical limitations of direct electrical stimulation (DES) of microcircuits, this opens exciting possibilities for discovering stimulation targets and selecting connectivity patterns that can ensure propagation of DES-induced neural excitation, potentially making it possible to create awakenings from complex cases of brain injury.

A fast and general method to empirically estimate the complexity of brain responses to transcranial and intracranial stimulations

BACKGROUND

The Perturbational Complexity Index (PCI) was recently introduced to assess the capacity of thalamocortical circuits to engage in complex patterns of causal interactions. While showing high accuracy in detecting consciousness in brain-injured patients, PCI depends on elaborate experimental setups and offline processing, and has restricted applicability to other types of brain signals beyond transcranial magnetic stimulation and high-density EEG (TMS/hd-EEG) recordings.

OBJECTIVE

We aim to address these limitations by introducing PCI^ST, a fast method for estimating perturbational complexity of any given brain response signal.

METHODS

PCI^ST is based on dimensionality reduction and state transitions (ST) quantification of evoked potentials. The index was validated on a large dataset of TMS/hd-EEG recordings obtained from 108 healthy subjects and 108 brain-injured patients, and tested on sparse intracranial recordings (SEEG) of 9 patients undergoing intracranial single-pulse electrical stimulation (SPES) during wakefulness and sleep.

RESULTS

When calculated on TMS/hd-EEG potentials, PCI^ST performed with the same accuracy as the original PCI, while improving on the previous method by being computed in less than a second and requiring a simpler set-up. In SPES/SEEG signals, the index was able to quantify a systematic reduction of intracranial complexity during sleep, confirming the occurrence of state-dependent changes in the effective connectivity of thalamocortical circuits, as originally assessed through TMS/hd-EEG.

CONCLUSIONS

PCI^ST represents a fundamental advancement towards the implementation of a reliable and fast clinical tool for the bedside assessment of consciousness as well as a general measure to explore the neuronal mechanisms of loss/recovery of brain complexity across scales and models.

Sleep Modelling across Physiological Levels

Sleep and circadian rhythms are regulated across multiple functional, spatial and temporal levels: from genes to networks of coupled neurons and glial cells, to large scale brain dynamics and behaviour. The dynamics at each of these levels are complex and the interaction between the levels is even more so, so research have mostly focused on interactions within the levels to understand the underlying mechanisms—the so-called reductionist approach. Mathematical models were developed to test theories of sleep regulation and guide new experiments at each of these levels and have become an integral part of the field. The advantage of modelling, however, is that it allows us to simulate and test the dynamics of complex biological systems and thus provides a tool to investigate the connections between the different levels and study the system as a whole. In this paper I review key models of sleep developed at different physiological levels and discuss the potential for an integrated systems biology approach for sleep regulation across these levels. I also highlight the necessity of building mechanistic connections between models of sleep and circadian rhythms across these levels.

Brain songs framework used for discovering the relevant timescale of the human brain

A key unresolved problem in neuroscience is to determine the relevant timescale for understanding spatiotemporal dynamics across the whole brain. While resting state fMRI reveals networks at an ultraslow timescale (below 0.1 Hz), other neuroimaging modalities such as MEG and EEG suggest that much faster timescales may be equally or more relevant for discovering spatiotemporal structure. Here, we introduce a novel way to generate whole-brain neural dynamical activity at the millisecond scale from fMRI signals. This method allows us to study the different timescales through binning the output of the model. These timescales can then be investigated using a method (poetically named brain songs) to extract the spacetime motifs at a given timescale. Using independent measures of entropy and hierarchy to characterize the richness of the dynamical repertoire, we show that both methods find a similar optimum at a timescale of around 200 ms in resting state and in task data.

Dynamic properties of simulated brain network models and empirical resting-state data

Brain network models (BNMs) have become a promising theoretical framework for simulating signals that are representative of whole-brain activity such as resting-state fMRI. However, it has been difficult to compare the complex brain activity obtained from simulations to empirical data. Previous studies have used simple metrics to characterize coordination between regions such as functional connectivity. We extend this by applying various different dynamic analysis tools that are currently used to understand empirical resting-state fMRI (rs-fMRI) to the simulated data. We show that certain properties correspond to the structural connectivity input that is shared between the models, and certain dynamic properties relate more to the mathematical description of the brain network model. We conclude that the dynamic properties that explicitly examine patterns of signal as a function of time rather than spatial coordination between different brain regions in the rs-fMRI signal seem to provide the largest contrasts between different BNMs and the unknown empirical dynamical system. Our results will be useful in constraining and developing more realistic simulations of whole-brain activity.