Response function as a quantitative measure of consciousness in brain dynamics

TL;DR

The paper tackles the problem of quantifying consciousness from brain dynamics by fitting a data-driven continuous-time RNN to intracranial ECoG data from a non-human primate across wakefulness, anesthesia, and recovery. It introduces and measures a neural response function $\chi(t)$, derived from small perturbations to the network, to capture nonequilibrium dynamical sensitivity and its relation to consciousness. The results show that wakefulness and recovery exhibit strong, distributed, high-dimensional couplings with larger $\chi(t)$, while anesthesia suppresses responsiveness and simplifies network structure; the dynamics align with edge-of-chaos theories. This work provides a mechanistic, dynamical framework for assessing levels of consciousness and motivates future translations to human data and clinical monitoring.

Abstract

Understanding the neural correlates of consciousness remains a central challenge in neuroscience. In this study, we investigate the relationship between consciousness and neural responsiveness by analyzing intracranial ECoG recordings from non-human primates across three distinct states: wakefulness, anesthesia, and recovery. Using a nonequilibrium recurrent neural network (RNN) model, we fit state-dependent cortical dynamics to extract the neural response function as a dynamics complexity indicator. Our findings demonstrate that the amplitude of the neural response function serves as a robust dynamical indicator of conscious state, consistent with the role of a linear response function in statistical physics. Notably, this aligns with our previous theoretical results showing that the response function in RNNs peaks near the transition between ordered and chaotic regimes -- highlighting criticality as a potential principle for sustaining flexible and responsive cortical dynamics. Empirically, we find that during wakefulness, neural responsiveness is strong, widely distributed, and consistent with rich nonequilibrium fluctuations. Under anesthesia, response amplitudes are significantly suppressed, and the network dynamics become more chaotic, indicating a loss of dynamical sensitivity. During recovery, the neural response function is elevated, supporting the gradual re-establishment of flexible and responsive activity that parallels the restoration of conscious processing. Our work suggests that a robust, brain-state-dependent neural response function may be a necessary dynamical condition for consciousness, providing a principled framework for quantifying levels of consciousness in terms of nonequilibrium responsiveness in the brain.

Figures (9)

• Figure 1: Sketch of experimental data: 2D ECoG electrode array and neural activity signals for Monkey George tycho. Left: Spatial layout of the $128$‑channel ECoG grid covering frontal, parietal, and temporal cortices (image adapted from tycho). This map serves as the anatomical reference for interpreting the fitted RNN dynamics across cortical regions. Right: Representative neural activity traces from channels $1$ and $128$ during three behavioral states---wakefulness, anesthesia, and recovery. The purple shaded region marks the time window used for model fitting in this study (up to $200$ s).
• Figure 2: Fitted RNN results across three brain states: awake, anesthesia, and recovery. (a-c) Each panel shows the average training loss within $100$-second fitting windows (models were fitted every two seconds). Insets compare the reconstructed and target trajectories. At the $1800$-th time step (indicated by the vertical dashed line), the reconstructed RNN initialized from the target trajectory runs for the next $200$ time steps, in order to evaluate the prediction accuracy. (d-f) The measured mean population activity $\langle \phi(\mathbf{x}(t)) \rangle$ as a function of perturbation amplitude $h$ (applied at $t=0.005$ s, i.e., $5$ time steps away from the moment when the perturbation is applied) for the three different brain states. The results are average over all inferred recurrent neural networks [see (a-c)]. The corresponding slope reflects the strength of the neural response function defined in the main text.
• Figure 3: Distribution of the learned recurrent weight matrix $\mathbf{J}$ across the three brain states: awake, anesthesia, and recovery. All learned coupling weights obtained from $100$-second fitting windows (as in Fig. \ref{['fig2']}) are combined and shown in a single plot, with different colors representing different brain states. The inset provides an enlarged view that highlights subtle differences in the weight distributions among the three states.
• Figure 4: Connection pattern of $\mathbf{J}$ for the three brain states: awake, anesthesia, and recovery. Results are shown for the first two-second segment from the $100$-second fitting window. Shown are the strongest 1% of connections in absolute value among the $128$ channels. Positive weights are shown in red and negative weights in blue. The first row displays the upper-triangular part of $\mathbf{J}$, and the second row shows the lower-triangular part, highlighting how coupling patterns evolve across different cortical conditions.
• Figure 5: Full recurrent weight matrices $\mathbf{J}$ for the three brain states: awake, anesthesia, and recovery. Each panel shows the entire structured $\mathbf{J}$ matrix (including all elements) corresponding to the same fitted segment as in Fig. \ref{['fig4']}, visualized as a heat map. Positive weights are shown in red and negative weights in blue.