The Hopf whole-brain model and its linear approximation.

Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transmission delays. Multiple choices for the local dynamics have been proposed. Among them, nonlinear oscillators corresponding to a supercritical Hopf bifurcation have been used to link brain connectivity and collective phase and amplitude dynamics in different brain states. Here, we studied the linear fluctuations of this model to estimate its stationary statistics, i.e., the instantaneous and lagged covariances and the power spectral densities. This linear approximation-that holds in the case of heterogeneous parameters and time-delays-allows analytical estimation of the statistics and it can be used for fast parameter explorations to study changes in brain state, changes in brain activity due to alterations in structural connectivity, and modulations of parameter due to non-equilibrium dynamics.

A view-based decision mechanism for rewards in the primate amygdala.

Primates make decisions visually by shifting their view from one object to the next, comparing values between objects, and choosing the best reward, even before acting. Here, we show that when monkeys make value-guided choices, amygdala neurons encode their decisions in an abstract, purely internal representation defined by the monkey's current view but not by specific object or reward properties. Across amygdala subdivisions, recorded activity patterns evolved gradually from an object-specific value code to a transient, object-independent code in which currently viewed and last-viewed objects competed to reflect the emerging view-based choice. Using neural-network modeling, we identified a sequence of computations by which amygdala neurons implemented view-based decision making and eventually recovered the chosen object's identity when the monkeys acted on their choice. These findings reveal a neural mechanism in the amygdala that derives object choices from abstract, view-based computations, suggesting an efficient solution for decision problems with many objects.

Critical scaling of whole-brain resting-state dynamics.

Scale invariance is a characteristic of neural activity. How this property emerges from neural interactions remains a fundamental question. Here, we studied the relation between scale-invariant brain dynamics and structural connectivity by analyzing human resting-state (rs-) fMRI signals, together with diffusion MRI (dMRI) connectivity and its approximation as an exponentially decaying function of the distance between brain regions. We analyzed the rs-fMRI dynamics using functional connectivity and a recently proposed phenomenological renormalization group (PRG) method that tracks the change of collective activity after successive coarse-graining at different scales. We found that brain dynamics display power-law correlations and power-law scaling as a function of PRG coarse-graining based on functional or structural connectivity. Moreover, we modeled the brain activity using a network of spins interacting through large-scale connectivity and presenting a phase transition between ordered and disordered phases. Within this simple model, we found that the observed scaling features were likely to emerge from critical dynamics and connections exponentially decaying with distance. In conclusion, our study tests the PRG method using large-scale brain activity and theoretical models and suggests that scaling of rs-fMRI activity relates to criticality.

One ring to rule them all: The unifying role of prefrontal cortex in steering task-related brain dynamics.

Surviving and thriving in a complex world require intricate balancing of higher order brain functions with essential survival-related behaviours. Exactly how this is achieved is not fully understood but a large body of work has shown that different regions in the prefrontal cortex (PFC) play key roles for diverse cognitive and emotional tasks including emotion, control, response inhibition, mental set shifting and working memory. We hypothesised that the key regions are hierarchically organised and we developed a framework for discovering the driving brain regions at the top of the hierarchy, responsible for steering the brain dynamics of higher brain function. We fitted a time-dependent whole-brain model to the neuroimaging data from large-scale Human Connectome Project with over 1000 participants and computed the entropy production for rest and seven tasks (covering the main domains of cognition). This thermodynamics framework allowed us to identify the main common, unifying drivers steering the orchestration of brain dynamics during difficult tasks; located in key regions of the PFC (inferior frontal gyrus, lateral orbitofrontal cortex, rostral and caudal frontal cortex and rostral anterior cingulate cortex). Selectively lesioning these regions in the whole-brain model demonstrated their causal mechanistic importance. Overall, this shows the existence of a 'ring' of specific PFC regions ruling over the orchestration of higher brain function.

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.

Macroscopic Quantities of Collective Brain Activity during Wakefulness and Anesthesia.

The study of states of arousal is key to understand the principles of consciousness. Yet, how different brain states emerge from the collective activity of brain regions remains unknown. Here, we studied the fMRI brain activity of monkeys during wakefulness and anesthesia-induced loss of consciousness. We showed that the coupling between each brain region and the rest of the cortex provides an efficient statistic to classify the two brain states. Based on this and other statistics, we estimated maximum entropy models to derive collective, macroscopic properties that quantify the system's capabilities to produce work, to contain information, and to transmit it, which were all maximized in the awake state. The differences in these properties were consistent with a phase transition from critical dynamics in the awake state to supercritical dynamics in the anesthetized state. Moreover, information-theoretic measures identified those parameters that impacted the most the network dynamics. We found that changes in the state of consciousness primarily depended on changes in network couplings of insular, cingulate, and parietal cortices. Our findings suggest that the brain state transition underlying the loss of consciousness is predominantly driven by the uncoupling of specific brain regions from the rest of the network.

Functional network antagonism and consciousness.

Spontaneous brain activity changes across states of consciousness. A particular consciousness-mediated configuration is the anticorrelations between the default mode network and other brain regions. What this antagonistic organization implies about consciousness to date remains inconclusive. In this Perspective Article, we propose that anticorrelations are the physiological expression of the concept of segregation, namely the brain's capacity to show selectivity in the way areas will be functionally connected. We postulate that this effect is mediated by the process of neural inhibition, by regulating global and local inhibitory activity. While recognizing that this effect can also result from other mechanisms, neural inhibition helps the understanding of how network metastability is affected after disrupting local and global neural balance. In combination with relevant theories of consciousness, we suggest that anticorrelations are a physiological prior that can work as a marker of preserved consciousness. We predict that if the brain is not in a state to host anticorrelations, then most likely the individual does not entertain subjective experience. We believe that this link between anticorrelations and the underlying physiology will help not only to comprehend how consciousness happens, but also conceptualize effective interventions for treating consciousness disorders in which anticorrelations seem particularly affected.

The fMRI resting paradigm can quantify brain function by surpassing communication and sophisticated setups, hence helping to infer consciousness in individuals who are unable to communicate with their environment. A particular consciousness-mediated rsfMRI configuration is that of functional anticorrelations, that is, the antagonistic relationship between a specific set of brain regions. We suggest that anticorrelations are a key physiological prior, without which consciousness cannot be supported, because the brain cannot segregate how regions get connected. We postulate that segregation is possible thanks to neural inhibition, by regulating global and local inhibitory activity. We believe that the link between anticorrelations and the underlying physiology can help not only to comprehend how consciousness happens, but also conceptualize effective interventions for treating its disorders.

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.

Circuit mechanisms for the chemical modulation of cortex-wide network interactions and behavioral variability.

Influential theories postulate distinct roles of catecholamines and acetylcholine in cognition and behavior. However, previous physiological work reported similar effects of these neuromodulators on the response properties (specifically, the gain) of individual cortical neurons. Here, we show a double dissociation between the effects of catecholamines and acetylcholine at the level of large-scale interactions between cortical areas in humans. A pharmacological boost of catecholamine levels increased cortex-wide interactions during a visual task, but not rest. An acetylcholine boost decreased interactions during rest, but not task. Cortical circuit modeling explained this dissociation by differential changes in two circuit properties: the local excitation-inhibition balance (more strongly increased by catecholamines) and intracortical transmission (more strongly reduced by acetylcholine). The inferred catecholaminergic mechanism also predicted noisier decision-making, which we confirmed for both perceptual and value-based choice behavior. Our work highlights specific circuit mechanisms for shaping cortical network interactions and behavioral variability by key neuromodulatory systems.

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

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.

Memory reactivation in rat medial prefrontal cortex occurs in a subtype of cortical UP state during slow-wave sleep.

Interaction between hippocampal sharp-wave ripples (SWRs) and UP states, possibly by coordinated reactivation of memory traces, is conjectured to play an important role in memory consolidation. Recently, it was reported that SWRs were differentiated into multiple subtypes. However, whether cortical UP states can also be classified into subtypes is not known. Here, we analysed neural ensemble activity from the medial prefrontal cortex from rats trained to run a spatial sequence-memory task. Application of the hidden Markov model (HMM) with three states to epochs of UP-DOWN oscillations identified DOWN states and two subtypes of UP state (UP-1 and UP-2). The two UP subtypes were distinguished by differences in duration, with UP-1 having a longer duration than UP-2, as well as differences in the speed of population vector (PV) decorrelation, with UP-1 decorrelating more slowly than UP-2. Reactivation of recent memory sequences predominantly occurred in UP-2. Short-duration reactivating UP states were dominated by UP-2 whereas long-duration ones exhibit transitions from UP-1 to UP-2. Thus, recent memory reactivation, if it occurred within long-duration UP states, typically was preceded by a period of slow PV evolution not related to recent experience, and which we speculate may be related to previously encoded information. If that is the case, then the transition from UP-1 to UP-2 subtypes may help gradual integration of recent experience with pre-existing cortical memories by interleaving the two in the same UP state. This article is part of the Theo Murphy meeting issue 'Memory reactivation: replaying events past, present and future'.

Cortical state transitions and stimulus response evolve along stiff and sloppy parameter dimensions, respectively.

Previous research showed that spontaneous neuronal activity presents sloppiness: the collective behavior is strongly determined by a small number of parameter combinations, defined as 'stiff' dimensions, while it is insensitive to many others ('sloppy' dimensions). Here, we analyzed neural population activity from the auditory cortex of anesthetized rats while the brain spontaneously transited through different synchronized and desynchronized states and intermittently received sensory inputs. We showed that cortical state transitions were determined by changes in stiff parameters associated with the activity of a core of neurons with low responses to stimuli and high centrality within the observed network. In contrast, stimulus-evoked responses evolved along sloppy dimensions associated with the activity of neurons with low centrality and displaying large ongoing and stimulus-evoked fluctuations without affecting the integrity of the network. Our results shed light on the interplay among stability, flexibility, and responsiveness of neuronal collective dynamics during intrinsic and induced activity.

Distinct modes of functional connectivity induced by movie-watching.

A fundamental question in systems neuroscience is how endogenous neuronal activity self-organizes during particular brain states. Recent neuroimaging studies have demonstrated systematic relationships between resting-state and task-induced functional connectivity (FC). In particular, continuous task studies, such as movie watching, speak to alterations in coupling among cortical regions and enhanced fluctuations in FC compared to the resting-state. This suggests that FC may reflect systematic and large-scale reorganization of functionally integrated responses while subjects are watching movies. In this study, we characterized fluctuations in FC during resting-state and movie-watching conditions. We found that the FC patterns induced systematically by movie-watching can be explained with a single principal component. These condition-specific FC fluctuations overlapped with inter-subject synchronization patterns in occipital and temporal brain regions. However, unlike inter-subject synchronization, condition-specific FC patterns were characterized by increased correlations within frontal brain regions and reduced correlations between frontal-parietal brain regions. We investigated these condition-specific functional variations as a shorter time scale, using time-resolved FC. The time-resolved FC showed condition-specificity over time; notably when subjects watched both the same and different movies. To explain self-organisation of global FC through the alterations in local dynamics, we used a large-scale computational model. We found that condition-specific reorganization of FC could be explained by local changes that engendered changes in FC among higher-order association regions, mainly in frontal and parietal cortices.

Portraits of communication in neuronal networks.

The brain is organized as a network of highly specialized networks of spiking neurons. To exploit such a modular architecture for computation, the brain has to be able to regulate the flow of spiking activity between these specialized networks. In this Opinion article, we review various prominent mechanisms that may underlie communication between neuronal networks. We show that communication between neuronal networks can be understood as trajectories in a two-dimensional state space, spanned by the properties of the input. Thus, we propose a common framework to understand neuronal communication mediated by seemingly different mechanisms. We also suggest that the nesting of slow (for example, alpha-band and theta-band) oscillations and fast (gamma-band) oscillations can serve as an important control mechanism that allows or prevents spiking signals to be routed between specific networks. We argue that slow oscillations can modulate the time required to establish network resonance or entrainment and, thereby, regulate communication between neuronal networks.

Whole-Brain Neuronal Activity Displays Crackling Noise Dynamics.

Previous studies suggest that the brain operates at a critical point in which phases of order and disorder coexist, producing emergent patterned dynamics at all scales and optimizing several brain functions. Here, we combined light-sheet microscopy with GCaMP zebrafish larvae to study whole-brain dynamics in vivo at near single-cell resolution. We show that spontaneous activity propagates in the brain's three-dimensional space, generating scale-invariant neuronal avalanches with time courses and recurrence times that exhibit statistical self-similarity at different magnitude, temporal, and frequency scales. This suggests that the nervous system operates close to a non-equilibrium phase transition, where a large repertoire of spatial, temporal, and interactive modes can be supported. Finally, we show that gap junctions contribute to the maintenance of criticality and that, during interactions with the environment (sensory inputs and self-generated behaviors), the system is transiently displaced to a more ordered regime, conceivably to limit the potential sensory representations and motor outcomes.

Stereotypical modulations in dynamic functional connectivity explained by changes in BOLD variance.

Spontaneous activity measured in human subject under the absence of any task exhibits complex patterns of correlation that largely correspond to large-scale functional topographies obtained with a wide variety of cognitive and perceptual tasks. These "resting state networks" (RSNs) fluctuate over time, forming and dissolving on the scale of seconds to minutes. While these fluctuations, most prominently those of the default mode network, have been linked to cognitive function, it remains unclear whether they result from random noise or whether they index a nonstationary process which could be described as state switching. In this study, we use a sliding windows-approach to relate temporal dynamics of RSNs to global modulations in correlation and BOLD variance. We compare empirical data, phase-randomized surrogate data, and data simulated with a stationary model. We find that RSN time courses exhibit a large amount of coactivation in all three cases, and that the modulations in their activity are closely linked to global dynamics of the underlying BOLD signal. We find that many properties of the observed fluctuations in FC and BOLD, including their ranges and their correlations amongst each other, are explained by fluctuations around the average FC structure. However, we also report some interesting characteristics that clearly support nonstationary features in the data. In particular, we find that the brain spends more time in the troughs of modulations than can be expected from stationary dynamics.

Linking Entropy at Rest with the Underlying Structural Connectivity in the Healthy and Lesioned Brain.

The brain is a network that mediates information processing through a wide range of states. The extent of state diversity is a reflection of the entropy of the network. Here we measured the entropy of brain regions (nodes) in empirical and modeled functional networks reconstructed from resting state fMRI to address the connection of entropy at rest with the underlying structure measured through diffusion spectrum imaging. Using 18 empirical and 18 modeled stroke networks, we also investigated the effect that focal lesions have on node entropy and information diffusion. Overall, positive correlations between node entropy and structure were observed, especially between node entropy and node strength in both empirical and modeled data. Although lesions were restricted to one hemisphere in all stroke patients, entropy reduction was not only present in nodes from the damaged hemisphere, but also in nodes from the contralesioned hemisphere, an effect replicated in modeled stroke networks. Globally, information diffusion was also affected in empirical and modeled strokes compared with healthy controls. This is the first study showing that artificial lesions affect local and global network aspects in very similar ways compared with empirical strokes, shedding new light into the functional nature of stroke.

Resting state networks in empirical and simulated dynamic functional connectivity.

It is well-established that patterns of functional connectivity (FC) - measures of correlated activity between pairs of voxels or regions observed in the human brain using neuroimaging - are robustly expressed in spontaneous activity during rest. These patterns are not static, but exhibit complex spatio-temporal dynamics. Over the last years, a multitude of methods have been proposed to reveal these dynamics on the level of the whole brain. One finding is that the brain transitions through different FC configurations over time, and substantial effort has been put into characterizing these configurations. However, the dynamics governing these transitions are more elusive, specifically, the contribution of stationary vs. non-stationary dynamics is an active field of inquiry. In this study, we use a whole-brain approach, considering FC dynamics between 66 ROIs covering the entire cortex. We combine an innovative dimensionality reduction technique, tensor decomposition, with a mean field model which possesses stationary dynamics. It has been shown to explain resting state FC averaged over time and multiple subjects, however, this average FC summarizes the spatial distribution of correlations while hiding their temporal dynamics. First, we apply tensor decomposition to resting state scans from 24 healthy controls in order to characterize spatio-temporal dynamics present in the data. We simultaneously utilize temporal and spatial information by creating tensors that are subsequently decomposed into sets of brain regions ("communities") that share similar temporal dynamics, and their associated time courses. The tensors contain pairwise FC computed inside of overlapping sliding windows. Communities are discovered by clustering features pooled from all subjects, thereby ensuring that they generalize. We find that, on the group level, the data give rise to four distinct communities that resemble known resting state networks (RSNs): default mode network, visual network, control networks, and somatomotor network. Second, we simulate data with our stationary mean field model whose nodes are connected according to results from DTI and fiber tracking. In this model, all spatio-temporal structure is due to noisy fluctuations around the average FC. We analyze the simulated data in the same way as the empirical data in order to determine whether stationary dynamics can explain the emergence of distinct FC patterns (RSNs) which have their own time courses. We find that this is the case for all four networks using the spatio-temporal information revealed by tensor decomposition if nodes in the simulation are connected according to model-based effective connectivity. Furthermore, we find that these results require only a small part of the FC values, namely the highest values that occur across time and ROI pair. Our findings show that stationary dynamics can account for the emergence of RSNs. We provide an innovative method that does not make strong assumptions about the underlying data and is generally applicable to resting state or task data from different subject populations.

Increased Stability and Breakdown of Brain Effective Connectivity During Slow-Wave Sleep: Mechanistic Insights from Whole-Brain Computational Modelling.

Recent research has found that the human sleep cycle is characterised by changes in spatiotemporal patterns of brain activity. Yet, we are still missing a mechanistic explanation of the local neuronal dynamics underlying these changes. We used whole-brain computational modelling to study the differences in global brain functional connectivity and synchrony of fMRI activity in healthy humans during wakefulness and slow-wave sleep. We applied a whole-brain model based on the normal form of a supercritical Hopf bifurcation and studied the dynamical changes when adapting the bifurcation parameter for all brain nodes to best match wakefulness and slow-wave sleep. Furthermore, we analysed differences in effective connectivity between the two states. In addition to significant changes in functional connectivity, synchrony and metastability, this analysis revealed a significant shift of the global dynamic working point of brain dynamics, from the edge of the transition between damped to sustained oscillations during wakefulness, to a stable focus during slow-wave sleep. Moreover, we identified a significant global decrease in effective interactions during slow-wave sleep. These results suggest a mechanism for the empirical functional changes observed during slow-wave sleep, namely a global shift of the brain's dynamic working point leading to increased stability and decreased effective connectivity.