A Neural Field Theory for Loss of Consciousness: Synaptic Drive Dynamics, System Stability, Attractors, Partial Synchronization, and Hopf Bifurcations Characterizing the Anesthetic Cascade

Abstract

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state-that is, lack of responsiveness to noxious stimuli. In this chapter we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the anesthetic cascade. The proposed synaptic drive firing rate model predicts the conscious-unconscious transition as the implied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincar-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization of neural activity without mean field assumptions. We do this by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.