Percolation Model of Sensory Transmission and Loss of Consciousness Under General Anesthesia

Neurons communicate with each other dynamically; how such communications lead to consciousness remains unclear. Here, we present a theoretical model to understand the dynamic nature of sensory activity and information integration in a hierarchical network, in which edges are stochastically defined by a single parameter $p$ representing the percolation probability of information transmission. We validate the model by comparing the transmitted and original signal distributions, and we show that a basic version of this model can reproduce key spectral features clinically observed in electroencephalographic recordings of transitions from conscious to unconscious brain activities during general anesthesia. As $p$ decreases, a steep divergence of the transmitted signal from the original was observed, along with a loss of signal synchrony and a sharp increase in information entropy in a critical manner; this resembles the precipitous loss of consciousness during anesthesia. The model offers mechanistic insights into the emergence of information integration from a stochastic process, laying the foundation for understanding the origin of cognition.

Figure 1

Information percolation in a neural network. (a) Output activities are plotted for various $p$ on a randomly selected node in a one-to-four fractalization network. Input amplitude was scaled to $p=1$. The output reproduces several clinical EEG features. At $p=0.2$, burst suppression is observed. (b) Fourier analysis, averaged from 40 replicas on randomly selected output nodes, reveals a frequency shift upon network inhibition. Around $p=0.7$, frequency shifts from the $\beta$ to $\alpha$ range. Power concentrates toward the $\alpha$ and $\delta$ ranges with decreasing $p$. (c) Burst suppressions become evident at low $p$. Corresponding time-domain activities are superimposed onto spectrograms depicting frequency components of the bursts. Without losing generality, 50% random noises were added to a 115-Hz sinusoidal signal as input.

Figure 2

Thalamocortical and corticocortical coherence. (a) Thalamocortical coherence, measured as cross-spectral density averaged from 40 replicas on randomly selected posterior nodes, is plotted as a function of $p$. Patterns for anterior nodes are similar. Until $p\approx 0.8$, no coherent activity is dominant at any frequency. With further inhibition, thalamocortical coherence appears in the $\beta$ range, and it lowers to the $\alpha$ range at $p\approx 0.6$. Between $p\approx 0.5–0.3$, a band of $\gamma$ coherence is visible. (b) Corticocortical coherence between two randomly selected nodes in the output layer appears in the $\alpha$ and $\delta$ ranges for $p<0.6$. Coherence frequencies further decrease with $p$. To maximize test stringency, simulations were performed using random noise as input.

Figure 3

Anteriorization of cortical activity. Fourier analyses of output node activity for the indicated edge probabilities are shown. Output nodes are arranged 1 to 256 in groups of 16 from posterior to anterior. Higher power in the $\alpha$ and $\delta$ bands shifts to the anterior (higher number) nodes with decreasing $p$ until $p=0.3$, when anteriorization effects dissipate.

Figure 4

Emergence of correlative signal cohesion. (a) Output information entropy, measured by the KL divergence [$\mathrm{KL}(P\parallel Q)-{\mathrm{KL}}_c$] as an order parameter, is plotted as a function of $p$. Each value represents bits lost in the output from 8 bits of maximum information. A phase transition is revealed at $p\approx 0.3$. (b) KL divergence plotted as a function of pixel intensity for $p=0$ (purple), 0.15 (red), 0.20 (orange), 0.25 (yellow), 0.30 (black), 0.35 (green), 0.40 (cyan), 0.45 (blue), and 1 (dark blue). Similar to (a), a clear dichotomy in information entropy occurs around $p=0.3$. Information content is lost more rapidly from high-intensity signals. (c) Graphic illustration of transitions revealed in (a) and (b): Reconstructions of an 8-bit gray scale image at $p=0.00$, 0.30, 0.32, 0.34, 0.38, and 1.00, respectively. The original image features emerge sharply, becoming recognizable between $p=0.32$ and $p=0.34$.