A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning.
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Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions.This is done 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.
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Affiliation: A*STAR, Singapore Institute of Manufacturing Technology, Singapore, 638075, Singapore. house@SIMTech.a-star.edu.sg.
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 paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-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 and partial state equipartitioning of neural activity without mean field assumptions. This is done 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. No MeSH data available. Related in: MedlinePlus |
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Mentions: For our first example, we demonstrate partial synchronization for the model given by (34) and (35) with three excitatory neurons – and three inhibitory neurons – as shown in Fig. 11. The neural connectivity matrix A is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{aligned} A&= \small{\begin{bmatrix} 0 &1 &0 &-1 &0 &-1 \\ 1 &0 &0 &-1 &-1 &0\\ 0 &1 &0 &-1 &-1 &-1 \\ 0 &0 &1 &0 &-1 &-1\\ 0 &1 &0 &0 &0 &0 \\ 1 &0 &1 &0 &0 &0 \end{bmatrix}} , \end{aligned}$$ \end{document}A=[010−10−1100−1−10010−1−1−10010−1−1010000101000], which implies that the two inhibitory neurons and do not receive inhibitory inputs. Here, we assume that all the excitatory neurons have the same time constant and all the inhibitory neurons have the same prolonged time constant . Furthermore, we assume that , , and the activation functions , , are given by (9). Fig. 11 |
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Affiliation: A*STAR, Singapore Institute of Manufacturing Technology, Singapore, 638075, Singapore. house@SIMTech.a-star.edu.sg.
No MeSH data available.