Assessing someone's level of consciousness is a complex matter, and attempts have been made to aid clinicians in these assessments through metrics based on neuroimaging data. Many studies have empirically investigated measures related to the complexity elicited after the brain is stimulated to quantify the level of consciousness across different states. Here we hypothesized that the level of non-equilibrium dynamics of the unperturbed brain already contains the information needed to know how the system will react to an external stimulus. We created personalized whole-brain models fitted to resting state fMRI data recorded in participants in altered states of consciousness (e.g., deep sleep, disorders of consciousness) to infer the effective connections underlying their brain dynamics. We then measured the out-of-equilibrium nature of the unperturbed brain by evaluating the level of asymmetry of the inferred connectivity, the time irreversibility in each model and compared this with the elicited complexity generated after in silico perturbations, using a simulated fMRI-based version of the Perturbational Complexity Index, a measure that has been shown to distinguish different levels of consciousness in in vivo settings. Crucially, we found that states of consciousness involving lower arousal and/or lower awareness had a lower level of asymmetry in their effective connectivities, a lower level of irreversibility in their simulated dynamics, and a lower complexity compared to control subjects. We show that the asymmetry in the underlying connections drives the nonequilibrium state of the system and in turn the differences in complexity as a response to the external stimuli.

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.

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.

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.

[This corrects the article DOI: 10.1371/journal.pcbi.1008310.].

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.

The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, most efforts of capturing the causal mechanistic generating principles have supposed underlying stationarity, being unable to describe the non-stationarity of brain dynamics, i.e. time-dependent changes. Here, we present a novel framework able to characterise brain states with high specificity, precisely by modelling the time-dependent dynamics. Through describing a topological structure associated to the brain state at each moment in time (its attractor or 'information structure'), we are able to classify different brain states by using the statistics across time of these structures hitherto hidden in the neuroimaging dynamics. Proving the strong potential of this framework, we were able to classify resting-state BOLD fMRI signals from two classes of post-comatose patients (minimally conscious state and unresponsive wakefulness syndrome) compared with healthy controls with very high precision.

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

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.

Human social behaviour is complex, and the biological and neural mechanisms underpinning it remain debated. A particularly interesting social phenomenon is our ability and tendency to fall into synchronization with other humans. Our ability to coordinate actions and goals relies on the ability to distinguish between and integrate self and other, which when impaired can lead to devastating consequences. Interpersonal synchronization has been a widely used framework for studying action coordination and self-other integration, showing that even in simple interactions, such as joint finger tapping, complex interpersonal dynamics emerge. Here we propose a computational model of self-other integration via within- and between-person action-perception links, implemented as a simple Kuramoto model with four oscillators. The model abstracts each member of a dyad as a unit consisting of two connected oscillators, representing intrinsic processes of perception and action. By fitting this model to data from two separate experiments we show that interpersonal synchronization strategies rely on the relationship between within- and between-unit coupling. Specifically, mutual adaptation exhibits a higher between-unit coupling than within-unit coupling; leading-following requires that the follower unit has a low within-unit coupling; and leading-leading occurs when two units jointly exhibit a low between-unit coupling. These findings are consistent with the theory of interpersonal synchronization emerging through self-other integration mediated by processes of action-perception coupling. Hence, our results show that chaotic human behaviour occurring on a millisecond scale may be modelled using coupled oscillators.

In this paper, we demonstrate a new approach for the fusion of multichannel signals. We show how this method can be used to combine signals from magnetometer and gradiometer sensors used in magnetoencephalography (MEG). This approach works by assuming that the lead-fields have multiplicative errors which in turn leads to an under-determined problem. To solve this problem, we impose two constraints that result in closed-from solutions: i) one set of sensors is error-free, ii) the norm of the multiplicative error is bounded. These prior assumptions to estimate the error are used in the linearly constraint minimum variance (LCMV) spatial filter to improve the optimisation. Although we focus on the fusion of MEG sensors, this approach can be employed for multimodal fusion of other multichannel signals such as MEG and EEG signals.

Evidence suggests that magnetoencephalogram (MEG) data have characteristics with non-Gaussian distribution, however, standard methods for source localisation assume Gaussian behaviour. We present a new general method for non-Gaussian source estimation of stationary signals for localising brain activity in the MEG data. By providing a Bayesian formulation for linearly constraint minimum variance (LCMV) beamformer, we extend this approach and show that how the source probability density function (pdf), which is not necessarily Gaussian, can be estimated. The proposed non-Gaussian beamformer is shown to give better spatial estimates than the LCMV beamformer, in both simulations incorporating non-Gaussian signal and in real MEG measurements.

In this study, a robust minimum variance beam-former (RMVB) is employed for source reconstruction in simultaneous MEG and local field potential (LFP) measurements. RMVB selects the electrical activity only from a specified volume of the brain while suppressing the rest. To improve imaging we added two more terms to the RMVB: the first term minimises the mean squared error (i.e. maximises the correlation) between the recorded LFP and reconstructed time courses from MEG data, the second term nulls the large inference induced by deep brain stimulation (DBS) device. A solution of this problem, relevant both with and without extra terms, is presented using the Lagrange multiplier method. This solution-if we ignore the new terms-has a simpler secular equation compared to its original solution and therefore is faster. The method is validated using both simulated and real data to show its potential use in practical applications.