A stochastic basis for neural inertia in emergence from general anaesthesia

Transitions into and out of the anaesthetised state exhibit resistance to state transitions known as neural inertia. As a consequence, emergence from anaesthesia occurs at a consistently lower anaesthetic concentration than induction. Motivated by stochastic switching between discrete activity patterns observed at constant anaesthetic concentration, we investigated the consequences of such switching for neural inertia.

We simulated stochastic switching in MATLAB as Brownian motion on an energy landscape or equivalently as a discrete Markov process. Effects of anaesthetics were modelled as changing stability of the awake and the anaesthetised states. Simulation results were compared with re-analysed neural inertia data from mice and Drosophila.

Diffusion on a two-well energy landscape gives rise to hysteresis. With additive noise, hysteresis collapses. This collapse occurs over a mixing time that is independent from pharmacokinetics. The two-well potential gives rise to the leftward shift for the emergence dose-response curve. Yet, from in vivo data, ΔEC₅₀ and Δ Hill slope are strongly negatively correlated (R²=0.45, P<1.7×10^-15). This correlation is not explained by a two-well potential. The extension of the diffusion model to a Markov process with 10 states (three awake, seven unconscious) reproduces both the left shift and the shallower Hill slope for emergence.

Stochastic state switching accounts for all known features of neural inertia. More than two states are required to explain the consistent increase observed in variability of recovery from general anaesthesia. This model predicts that hysteresis should collapse with a time scale independent of anaesthetic drug pharmacokinetics.