How does the brain recover consciousness after significant perturbations such as anesthesia? The simplest answer is that as the anesthetic washes out, the brain follows a steady and monotonic path toward consciousness. We show that this simple intuition is incorrect. We varied the anesthetic concentration to parametrically control the magnitude of perturbation to brain dynamics while analyzing the characteristics of neuronal activity during recovery of consciousness. We find that, en route to consciousness, the brain passes through several discrete activity states. Although transitions between certain of these activity states occur spontaneously, transitions between others are not observed. Thus, the network formed by these state transitions gives rise to an ordered sequence of states that mediates recovery of consciousness.

It is not clear how, after a large perturbation, the brain explores the vast space of potential neuronal activity states to recover those compatible with consciousness. Here, we analyze recovery from pharmacologically induced coma to show that neuronal activity en route to consciousness is confined to a low-dimensional subspace. In this subspace, neuronal activity forms discrete metastable states persistent on the scale of minutes. The network of transitions that links these metastable states is structured such that some states form hubs that connect groups of otherwise disconnected states. Although many paths through the network are possible, to ultimately enter the activity state compatible with consciousness, the brain must first pass through these hubs in an orderly fashion. This organization of metastable states, along with dramatic dimensionality reduction, significantly simplifies the task of sampling the parameter space to recover the state consistent with wakefulness on a physiologically relevant timescale.

The brain exhibits a remarkable ability to recover normal function associated with wakefulness, even after large perturbations to its activity. Two well-known examples of this are anesthesia and brain injury (1, 2). How the brain recovers from large perturbations currently is unknown. Given the number of neurons involved, the potential space of activity is huge. Thus, it is not clear how the brain samples the vast parameter space to discover patterns of activity that are consistent with consciousness after a large perturbation.

The simplest possibility for the recovery of consciousness (ROC) is that, driven by noise inherent in many aspects of neuronal activity (3), the brain performs a random walk through the parameter space until it eventually enters the region that is consistent with consciousness. An alternative possibility is that although the motion through the parameter space is not random, the trajectory nonetheless is smooth. Lastly, it is possible that en route to ROC, the brain passes through a set of discrete metastable states—that is, a series of jumps between long-lived activity configurations.

The utility of metastable intermediates to the problem of ROC is well illustrated by analogy with protein folding. Levinthal’s paradox (4) refers to the implausibility of a denatured protein recovering its native fold conformation by random walk alone, as the time required to randomly explore the conformational space will rapidly exceed the age of the universe, even for a small number of residues. However, energetically favorable metastable intermediate states allow denatured proteins to assume their native conformation rapidly. Thus, we hypothesized that after large perturbations, brain dynamics during ROC are structured into discrete metastable intermediate states.

If metastable intermediate states do exist, transitions between them must be considered. It is unclear a priori, for example, whether there will be an obligate intermediate state that must occur en route to consciousness, or if many different routes through intermediate states enable ROC. In this work, we approximate transitions between metastable intermediate states as Markovian–dependent only on the current state of the system—so that characterizing the transition probabilities between states sufficiently characterizes the network of metastable intermediate states. Several examples of possible network structures are (i) an ordered “chain” in which each state connects to only two others; (ii), a “small-world” structure, in which most states are connected only locally whereas a few central hub states connect widely, allowing rapid long-distance travel through the network; and (iii) a lattice structure, in which all states have approximately the same connectivity, allowing multiple routes to ROC.

In this report, we demonstrate that in rats under isoflurane anesthesia, ROC occurs after the brain traverses a series of metastable intermediate activity configurations. We demonstrate that the recovery process is not compatible with a random walk or another continuous process, nor does it occur as a single jump. A low-dimensional subspace allows visualization of key features of the recovery process, including clusters of activity consistent with metastable intermediates. These clusters of activity have structured transition properties such that only certain transitions are observed en route to ROC, suggesting that certain states function as hubs.

Results

To analyze the dynamics of ROC, we simultaneously recorded local field potentials (LFPs) from the anterior cingulate and retrosplenial cortices and the intralaminar thalamus (Fig. S1) in rats (n = 6) during recovery from general anesthesia induced with isoflurane. These interconnected areas are involved in brain arousal and anesthesia (5, 6). The power spectra of the LFPs quantify the distribution of signal power among different frequencies and provide a convenient and statistically robust (7) description of patterns of activity that has been used extensively (e.g., refs. 8, 9) to distinguish neuronal activity in the awake and inactivated brain (e.g., Fig. 1). Thus, in what follows, we chose to quantify brain activity in terms of its spectrum.

Fig. 1. ROC is not attainable by random walk. (A) Cortical LFP exemplifying burst suppression (blue) observed in pathological states (e.g., coma, anesthesia). LFP observed in the awake brain is shown in red. (B) The power spectra for the traces in A and B (blue and red, respectively) distinguish these activity patterns in the frequency domain. Power contained at each frequency is expressed as the fraction of total power. Differences between the spectra are distributed among many frequencies. (C) Cumulative distribution of recovery times of random walk simulations (SI Materials and Methods) shows the improbability of recovery by random walk alone. Red arrows show the experimentally observed recovery times.

We used isoflurane to elicit burst suppression, because its slow pharmacokinetics (10) allowed us to focus on the intrinsic brain dynamics rather than on the kinetics of anesthetic washout. To ensure that all of our experiments began with comparable magnitude perturbation to brain activity, we began each series of experiments with an isoflurane concentration of 1.75%, which reliably produced burst suppression, a pathological pattern of activity seen after trauma (2), anesthesia (11), hypothermia (12), encephalopathy (13), hypoxia (14), and others (e.g., Fig. 1A, blue trace). Burst suppression is defined by episodic low-frequency oscillations (bursts) punctuated by periods of quiescence (suppression) in the electroencephalogram (EEG) and LFPs that correlate with synchronous depolarization of cortical neurons and electrical silence of neuronal membranes (15), respectively. Any further inactivation of the brain results in persistent electrical quiescence. In the awake brain, conversely, persistent high-frequency low-amplitude oscillations (e.g., Fig. 1A, red trace) corresponding to asynchronous neuronal firing (16, 17) are observed.

Animals were maintained at a fixed anesthetic concentration for at least 1 h, after which the concentration was decreased by 0.25% until ROC (usually occurring at 0.75%), defined as the onset of spontaneous movement of the limbs and postural muscles (SI Materials and Methods). Although the onset of movement is an imperfect measure, we chose it as an endpoint for several reasons: (i) Onset of limb movement can be detected readily. (ii) The anesthetic concentration at which humans lose consciousness is correlated closely with the anesthetic concentration at which experimental animals lose their righting reflex (reviewed in ref. 18). (iii) There is no single accepted measure that reliably detects onset of consciousness based on brain activity. (iv) Onset of movement is a conservative estimate of the onset of consciousness in that in the absence of brainstem lesion, it is unlikely that the animal will be awake and not moving during emergence from a pure volatile anesthetic (note that use of an opiate would complicate this, as the animal might be awake but not moving).

The slow titration of isoflurane allowed a prolonged sampling of each anesthetic concentration at steady state. While we controlled inspired anesthetic concentration to make sure that fluctuations in the respiratory dynamics did not result in fluctuations in the brain anesthetic concentration, we monitored respiratory rate (SI Materials and Methods). We could not detect statistically significant changes in respiratory rate during fixed anesthetic exposure (repeated measures ANOVA, df = 19, F = 0.672, P = 0.830). Thus, given no change in tidal volume, the brain anesthetic concentration likely will remain constant for a large fraction of the time exposed to a fixed inspired anesthetic concentration.

ROC Is Not Consistent with a Random Walk—Even with Constraints. Although the characteristics of neuronal activity in the anesthetized and awake brain are well known, how the brain navigates between these states is less clear. Many aspects of neuronal dynamics are stochastic (3). Unsurprisingly, changes in the spectrum from one temporal window to the next are well approximated by multidimensional uncorrelated noise (Fig. S2). This is consistent with the simplest null hypothesis that on a fast time scale (1-s step between consecutive spectral windows), neuronal dynamics perform a random walk. However, even a constrained random walk using the observed pairwise differences between spectra as steps (SI Materials and Methods) fails to reliably reach patterns of activity consistent with wakefulness (Fig. 1C). Considering more aspects of neuronal activity exacerbates this problem, as the return of a random walker is guaranteed in only two dimensions at most (19). Thus, to attain ROC on a physiologically relevant time scale, the neuronal activity must be structured. Indeed, while the anesthetic was decreased slowly and monotonically, neuronal activity switched abruptly between several distinct modes that persisted on the scale of minutes (Fig. 2 spectra; Fig. S3 traces). These fluctuations, evidenced by abrupt changes in power, appear simultaneously in anatomically separated brain regions, signifying a global change in the dynamics of the extended thalamocortical networks. Remarkably, there is no one-to-one correspondence between brain activity and anesthetic concentration—several patterns are seen at a single concentration. These state transitions reveal the essential metastable intermediates produced by the brain en route to ROC. Fig. 2. Time-resolved spectrograms reveal state transitions (A) Diagram of the multielectrode array used to record simultaneous activity in the anterior cingulate (C) and retrosplenial (R) cortices, as well as the intralaminar thalamus (T), superimposed on the sagittal brain section. (B) Time–frequency spectrograms at different anatomical locations during ROC. The power spectral density at each point in time–frequency space indicates the deviation from the mean spectrum on a decibel color scale as the anesthetic concentration is decreased (Bottom) from 1.75% to 0.75% in 0.25% increments until ROC. (C) Data of the kind shown in B pooled across all animals and all anesthetic concentrations were subjected to PCA (SI Materials and Methods). Percent of variance is plotted as a function of the number of PCs. Dynamics of ROC largely are confined to a 3D subspace.

Brain Activity During ROC Exhibits Clusters Consistent with Metastable Intermediate States. Brain activity during ROC does not evenly occupy the volume spanned by the first three PCs, as evidenced by distinct peaks in the probability distribution shown in Fig. 3B. Consistent with abrupt fluctuations in spectral power (Fig. 2B), the data projected onto the first three PCs form eight distinct clusters (SI Materials and Methods), the approximate locations of which are shown in Fig. 3C. Although clustering was performed on the data concatenated across all experiments, the distribution of data from each experiment taken individually also was multimodal (Fig. S5 A and B). Furthermore, the concordance of clustering between individual experiments is statistically significant (SI Materials and Methods, Figs. S5 and S6). Thus, the clusters represent reproducible and distinct states distinguished by the distribution of spectral power across brain regions. Three lines of evidence indicate that these clusters represent attractor states of the thalamocortical dynamics: (i) The transitions between states are abrupt (e.g., Fig. S3), and the paucity of points between the peaks of the probability distribution (Fig. 3B group data, Fig. S5 individual experiments) suggests that the system does not spend a significant amount of time between the densely occupied states. (ii) Dwell times within each state may last up to several minutes (Fig. S7A). (iii) Fluctuations die down when the system arrives into the clusters and increase between clusters (Fig. S8). The decrease in the amplitude of fluctuations associated with the arrival into densely populated regions of the parameter space suggests stabilization of neuronal activity. In this view, the multimodal distribution of brain activity in PCA space may be seen as an anesthetic–concentration-dependent energy landscape in which the location of local energy minima gives rise to densely occupied states and local maxima demarcate boundaries between them. Note that the stabilization is not enough to trap the brain in any one state permanently, and spontaneous state transitions are observed readily at many anesthetic concentrations. Thus, we refer to the densely occupied regions of the parameter space as metastable states. The characteristic spectral profile for each state (Fig. 4A) reveals that they can be grouped further into three distinct categories. Although each group of states exhibits a consistent increase in power at distinct frequency bands observed across all anatomical sites, individual members of each group are distinguished by the anatomical distribution of power in the high-frequency range. This suggests that fluctuations observed between clusters within the same group correspond to state-dependent fluctuations in thalamocortical coupling en route to awakening. Fig. 4. The network linking the metastable states contains hubs; arrival into the hubs is essential for ROC. (A) Characteristic spectral density for each cluster (labels as in Fig. 3C). Clusters are grouped based upon the frequency range [blue, burst suppression; green, δ (1–4 Hz); red, θ (4–8 Hz)] that has consistently increased power in all electrodes. (B) The trajectory of a single experiment through the clusters suggests that certain state transitions are more likely than others. (C) A sphere centered at the cluster centroid shows each cluster. The radius of the sphere is proportional to the total time spent in the cluster. Arrow color shows transition probability. The network of transition probabilities reveals two hubs (blue and green asterisks in A–C) defined as the targets of multiple convergent transitions. Awakening was observed in the cluster shown by red asterisks ∼95% of the time. Note that all paths into the “awake” cluster (red asterisks) from burst suppression (any one of the blue spheres) must involve passage first through the burst suppression hub state (blue asterisk) then through the δ-dominant hub (green asterisk). See also Movie S2 for better visualization of the network structure. Clustering allows us to simplify ROC further as a sequence of states, starting from burst suppression and ultimately leading to wakefulness (Fig. 4B). The observed sequences of states reveal an additional element of the structure—some state transitions appear more frequently than others. Note, for instance, that although burst suppression is exhibited in all blue states, transitions to δ-dominant states (green) are observed from only one of them. Likewise, transitions to θ-dominant states (red) are observed from a single δ-dominant state. Although certain transitions appeared more frequently than others, to a good approximation the specific sequence of states appears stochastic. Thus, we assumed that the system is Markovian and computed transition probabilities between all pairs of states.