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.

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.

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.

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.

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.

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.

Spontaneous cortical activity is transiently poised close to criticality.

Brain activity displays a large repertoire of dynamics across the sleep-wake cycle and even during anesthesia. It was suggested that criticality could serve as a unifying principle underlying the diversity of dynamics. This view has been supported by the observation of spontaneous bursts of cortical activity with scale-invariant sizes and durations, known as neuronal avalanches, in recordings of mesoscopic cortical signals. However, the existence of neuronal avalanches in spiking activity has been equivocal with studies reporting both its presence and absence. Here, we show that signs of criticality in spiking activity can change between synchronized and desynchronized cortical states. We analyzed the spontaneous activity in the primary visual cortex of the anesthetized cat and the awake monkey, and found that neuronal avalanches and thermodynamic indicators of criticality strongly depend on collective synchrony among neurons, LFP fluctuations, and behavioral state. We found that synchronized states are associated to criticality, large dynamical repertoire and prolonged epochs of eye closure, while desynchronized states are associated to sub-criticality, reduced dynamical repertoire, and eyes open conditions. Our results show that criticality in cortical dynamics is not stationary, but fluctuates during anesthesia and between different vigilance states.

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.

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome.

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.

Task-Driven Activity Reduces the Cortical Activity Space of the Brain: Experiment and Whole-Brain Modeling.

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model's prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.

Resting-state temporal synchronization networks emerge from connectivity topology and heterogeneity.

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain's anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.

Stimulus-dependent variability and noise correlations in cortical MT neurons.

Population codes assume that neural systems represent sensory inputs through the firing rates of populations of differently tuned neurons. However, trial-by-trial variability and noise correlations are known to affect the information capacity of neural codes. Although recent studies have shown that stimulus presentation reduces both variability and rate correlations with respect to their spontaneous level, possibly improving the encoding accuracy, whether these second order statistics are tuned is unknown. If so, second-order statistics could themselves carry information, rather than being invariably detrimental. Here we show that rate variability and noise correlation vary systematically with stimulus direction in directionally selective middle temporal (MT) neurons, leading to characteristic tuning curves. We show that such tuning emerges in a stochastic recurrent network, for a set of connectivity parameters that overlaps with a single-state scenario and multistability. Information theoretic analysis shows that second-order statistics carry information that can improve the accuracy of the population code.

How local excitation-inhibition ratio impacts the whole brain dynamics.

The spontaneous activity of the brain shows different features at different scales. On one hand, neuroimaging studies show that long-range correlations are highly structured in spatiotemporal patterns, known as resting-state networks, on the other hand, neurophysiological reports show that short-range correlations between neighboring neurons are low, despite a large amount of shared presynaptic inputs. Different dynamical mechanisms of local decorrelation have been proposed, among which is feedback inhibition. Here, we investigated the effect of locally regulating the feedback inhibition on the global dynamics of a large-scale brain model, in which the long-range connections are given by diffusion imaging data of human subjects. We used simulations and analytical methods to show that locally constraining the feedback inhibition to compensate for the excess of long-range excitatory connectivity, to preserve the asynchronous state, crucially changes the characteristics of the emergent resting and evoked activity. First, it significantly improves the model's prediction of the empirical human functional connectivity. Second, relaxing this constraint leads to an unrealistic network evoked activity, with systematic coactivation of cortical areas which are components of the default-mode network, whereas regulation of feedback inhibition prevents this. Finally, information theoretic analysis shows that regulation of the local feedback inhibition increases both the entropy and the Fisher information of the network evoked responses. Hence, it enhances the information capacity and the discrimination accuracy of the global network. In conclusion, the local excitation-inhibition ratio impacts the structure of the spontaneous activity and the information transmission at the large-scale brain level.

Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations.

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

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.

On the anticipatory precue activity in motor cortex.

Motor cortical neurons are activated during movement preparation and execution, and in response to task-relevant visual cues. A few studies also report activation before the expected presentation of cues. Here, we study specifically this anticipatory activity preceding visual cues in motor cortical areas. We recorded the activity of 1215 neurons in the motor cortex of two macaque monkeys while they performed a center-out reaching task, including two consecutive delays of equal duration, known in advance. During the first delay (D1), they had to await the spatial cue and only reach to the cued target after the second delay (D2). Forty-two percent of the neurons displayed anticipatory activity during D1. Among these anticipatory neurons, 59% increased (D1up) their activity and the remaining decreased (D1down) their activity. By classifying the neurons according to these firing rate profiles during D1, we found that the activity during D2 differed in a systematic way. The D1up neurons were more likely to discharge phasically soon after the spatial cue and were less active during movement execution, whereas the D1down neurons showed the opposite pattern. But, regardless of their temporal activity profiles, the two categories seemed equally involved in early and late motor preparation, as reflected in their directional selectivity. This precue activity in motor cortex may reflect two complementary, coexisting processes: the facilitation of incoming spatial information in parallel with the downregulation of corticospinal excitability to prevent a premature response.

Dynamics of cortical neuronal ensembles transit from decision making to storage for later report.

Decisions based on sensory evaluation during single trials may depend on the collective activity of neurons distributed across brain circuits. Previous studies have deepened our understanding of how the activity of individual neurons relates to the formation of a decision and its storage for later report. However, little is known about how decision-making and decision maintenance processes evolve in single trials. We addressed this problem by studying the activity of simultaneously recorded neurons from different somatosensory and frontal lobe cortices of monkeys performing a vibrotactile discrimination task. We used the hidden Markov model to describe the spatiotemporal pattern of activity in single trials as a sequence of firing rate states. We show that the animal's decision was reliably maintained in frontal lobe activity through a selective state sequence, initiated by an abrupt state transition, during which many neurons changed their activity in a concomitant way, and for which both latency and variability depended on task difficulty. Indeed, transitions were more delayed and more variable for difficult trials compared with easy trials. In contrast, state sequences in somatosensory cortices were weakly decision related, had less variable transitions, and were not affected by the difficulty of the task. In summary, our results suggest that the decision process and its subsequent maintenance are dynamically linked by a cascade of transient events in frontal lobe cortices.

Context-related frequency modulations of macaque motor cortical LFP beta oscillations.

The local field potential (LFP) is a population measure, mainly reflecting local synaptic activity. Beta oscillations (12-40 Hz) occur in motor cortical LFPs, but their functional relevance remains controversial. Power modulation studies have related beta oscillations to a "resting" motor cortex, postural maintenance, attention, sensorimotor binding and planning. Frequency modulations were largely overlooked. We here describe context-related beta frequency modulations in motor cortical LFPs. Two monkeys performed a reaching task with 2 delays. The first delay demanded attention in time in expectation of the visual spatial cue, whereas the second delay involved visuomotor integration and movement preparation. The frequency in 2 beta bands (around 20 and 30 Hz) was systematically 2-5 Hz lower during cue expectancy than during visuomotor integration and preparation. Furthermore, the frequency was directionally selective during preparation, with about 3 Hz difference between preferred and nonpreferred directions. Direction decoding with frequency gave similar accuracy as with beta power, and decoding accuracy improved significantly when combining power and frequency, suggesting that frequency might provide an additional signal for brain-machine interfaces. In conclusion, multiple beta bands coexist in motor cortex, and frequency modulations within each band are as behaviorally meaningful as power modulations, reflecting the changing behavioral context and the movement direction during preparation.

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.