Hou Saing Paul, Haddad Wassim M, Meskin Nader, Bailey James M
A*STAR, Singapore Institute of Manufacturing Technology, Singapore, 638075, Singapore.
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA.
J Math Neurosci. 2015 Dec;5(1):20. doi: 10.1186/s13408-015-0032-7. Epub 2015 Oct 5.
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.
随着生物化学、分子生物学和神经化学的发展，在理解麻醉剂的分子特性方面取得了令人瞩目的进展。然而，对于麻醉剂的分子特性如何导致所观察到的定义麻醉状态的宏观特性，即对有害刺激无反应性，却很少有人关注。在本文中，我们使用动力系统理论来开发一个用于神经活动的机械平均场模型，以研究随着麻醉剂浓度增加，从意识状态到无意识状态的突然转变。所提出的突触驱动发放率模型预测，随着施加的麻醉剂浓度增加，会发生意识 - 无意识转变，其中兴奋性神经活动的特征是一个庞加莱 - 安德罗诺夫 - 霍普夫分岔，清醒状态转变为一个稳定极限环，随后转变为一个渐近稳定的无意识平衡状态。此外，我们在没有平均场假设的情况下，解决了神经活动同步和部分状态均分的更一般问题。这是通过关注一个假定的抑制性神经元子集来实现的，这些抑制性神经元本身不与其他抑制性神经元相连。最后，给出了几个数值实验来说明所提出理论的不同方面。
