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

Abstract

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

Fig. 1. Capturing signatures of brain states estimating the inside out balance of intrinsic and extrinsic dynamics.

The arrow of time in brain signals contains a precise signature of the reversibility, reflecting how the brain is driven by the level of interaction with the environment. a In thermodynamics, the arrow of time in physical systems can be precisely estimated to provide a measure of non-reversibility and non-equilibrium, i.e. how the system is driven by external forces. The subpanel shows an example of a non-equilibrium system given by a Brownian particle in a moving potential, whose position is controlled externally, moving from one position to another in the forward process. The top of the subpanel shows examples the forward evolving trajectories (light grey lines) with the average (solid grey line). The average trajectory lags behind the centre of the potential (grey dashed line). In contrast (bottom of right subpanel) shows sample backward trajectories (light red lines) and their average (solid red line). Here the average trajectory leads the potential’s centre (red dashed line). This asymmetry in time of forward and backward trajectories (i.e. the differences between the lines for average and the potential’s centre) provides the exact level of non-reversibility/non-equilibrium of the system [adapted from]. b The present framework uses this key idea from thermodynamics to extract the arrow of time in brain signals in order to capture the level of interaction between the brain and the environment. c The framework estimates the asymmetry by using pairwise comparisons of forward signals across the whole brain. d This is accomplished by constructing the backward brain signal from the forward signal by creating a reversal of the backward time series in each brain region. The panel shows the notation used for describing this process for a pair of regions. e The panel shows the main principle of the framework for measuring the level of non-reversibility/non-equilibrium through the pairwise level of asymmetry using a time-shifted measure of their correlation. The subpanels show how the shifted correlation captures the causal interactions between two time series where the top example shows strong time dependency while the bottom example shows weak time dependency. This is clearly seen by how the shifted correlation (as a function of the time shift, ∆t) decays more rapidly for signals with weak compared to strong time dependency. The middle subpanels show the same method but now used for comparing forward and reversed regionals pairs of brain signals. The right subpanel shows examples of the time series for a given shift ∆t = T and how the level of non-reversibility is computed as the absolute quadratic difference between the time-shifted correlations between forward and the reversal time series averaged over all pairs. f We applied this framework to the multidimensional time series covering the whole brain. g We created two time-shifted correlation matrices for the forward and reversed time series (at a given shift time point ∆t = T). h The level of non-reversibility/non-equilibrium is given exactly by the distance between the two matrices (see Methods).

Fig. 2. Experimental paradigm with different brain states in the same environment.

a We leveraged the power of an existing dataset from four non-human primates in different brain states (wake, sleep and four different forms of anaesthesia, see Methods for detailed description). The experimental paradigm consisted of two main manipulations of brain state measuring sleep and anaesthesia. For the sleep condition in the upper row, the non-human primate was awakened from sleep, leading to three sessions with sleep, awake with eyes closed and awake with eyes opened. For the anaesthesia conditions, the lower rows show the protocol with the injection of one of four pharmacological agents (propofol, medetomidine (MD), ketamine+MD and ketamine). The five sessions consisted of (1) awake eyes open, (2) awake eyes closed, (3) anaesthesia, (4) recovery eyes closed and (5) recovery eyes open. For the results reported here, only sessions with eyes closed were used. b The data from the sessions were recorded with electrocorticography (ECOG) from 128 electrodes covering one hemisphere in each of the non-human primates, with the combined locations shown in the subpanel and the locations in each individual shown in the other four subpanels.

Fig. 3. Estimating the arrow of time in brain signals provides significantly different signatures of brain state.

The figure summarises the results of analysing all the available (eyes closed) data from the non-human primates in sleep and four different states of anaesthesia (see Methods and Fig. 2). a The column shows individual examples of the functional connectivity matrices across the 128 electrodes and a scatter plot of the correlation between each condition. As can be seen, this conventional method is unable to distinguish between the very different brain states. b In contrast, the central panel shows the application of the thermodynamic framework of estimating the arrow of time on the same individual time series, which is clearly distinguishing brain states. c The column shows the significant group level results (across all non-human primates with all sessions belonging to the specific brain state) which provides a clear signature able to distinguish between different brain states (Wilcoxon rank-sum, p < 0.001).

Fig. 4. Hierarchical signature of different brain states.

We constructed a measure of hierarchy by estimating the variability of the non-equilibrium/non-reversibility of different brain states across space. For each condition, the row shows example renderings of the electrode-level non-equilibrium/non-reversibility for the two non-human primates (George and Chibi) who participated in all experimental conditions. The smaller inserts show how the level of reversibility is associated with the causal driving of the incoming ${\mathrm{FC}}_{\mathrm{in}}\left(\mathrm{\tau }\right)$ and outgoing ${\mathrm{FC}}_{\mathrm{out}}\left(\mathrm{\tau }\right)$ information captured by the shifted correlation (see Fig. 1 and Methods). The column shows the significant group-level results for the hierarchy of the inside out balance of intrinsic and extrinsic balance for all non-human primates with all sessions belonging to the specific brain state (Wilcoxon rank-sum, p < 0.001).