Neural network based mathematical model and the concentration-response curve of inhalation anesthetics.

吸入麻醉药的浓度-反应曲线在ED50和GT；值附近变得非常陡峭，通常用Logistic曲线图进行分析。临床麻醉的希尔系数在两位数范围内，约为20到30。相比之下，离子通道和酶的麻醉剂浓度-反应曲线是渐变的；通常不到3。这种陡度上的差异可能是解决麻醉机制的关键。本研究建立了麻醉神经网络的数学模型，并研究了麻醉剂对其的影响。模型：假设网络中有m条传导通路(多通路)，每条传导通路中有n个传导单元(多通路)。麻醉被定义为失去传导的状态(多单元多路径系统：腮腺炎)。结果与讨论：1.剂量-反应曲线的构象变化：临床麻醉的陡坡(Hill系数=20)不能通过单独增加神经网络的n或m值来实现。2.模型参数的影响：随着n个数的增加，麻醉剂的表观效力(如MAC)降低，受试者对麻醉药的敏感性变弱。参数n是漏洞参数。当传导路径的数目(M)增加时，表观电势降低。参数m是冗余参数。3.MAC的年龄依赖性：我们成功地证明了MAC的年龄依赖性与传导通路数目的减少有关。4.优先麻醉的脑和脊髓的MAC：我们发现，脊髓麻醉效应的夸大与脑和脊髓神经网络结构的差异有关。5.药物相互作用：目前我们开始研究神经网络结构与药物相互作用之间的关系。

The concentration-response curves of inhalation anesthetics become extremely steep around ED_<50> values, and are often analyzed by logistic plot. The Hill coefficients of clinical anesthesia are in the two-digit ranges about 20 to 30. Contrastingly, the anesthetic concentration-response curves of ion channels and enzymes are gradual ; usually less than three. This discrepancy in the steepness may be a key to solve the anesthesia mechanisms. The present research project deals with the derivation of a mathematical model for the nervous network of anesthesia, and examines the effect of anesthetic on it. Model : It is assumed that there are m conduction pathways (Multi-Path) in the network, and n conduction units (Multi-Unit) in each conduction pathway. Anesthesia is defined as the state where the conduction is lost (Multi-Unit and Multi-Path System : MUMPS). Results and Discussions : 1.The conformational change of dose-response curve : The steep slope (Hill coefficient = 20) of clinical anesthesia can not be achieved by independent increase of n or m values of neural network. 2.The effect of model parameters: When the number of n increases, the apparent anesthetic potency, such as MAC, decreases and the subject becomes weak to the anesthetics. The parameter, n, is the vulnerability parameter. When the number of conduction pathways (m) increases, the apparent potency decreases. The parameter, m, is the redundancy parameter. 3.The age dependency of MAC : We successfully demonstrated that the age dependency of MAC is related to the decreased number of the conduction pathways. 4.The MAC of preferentially anesthetized brain and spinal cord : We showed that the exaggerated anesthetic effects on the spinal cord were related to the structural difference of the neural network between the brain and spinal cord. 5.The interaction of drug : We currently start to investigate the relation between the structures of neural network and the drug interaction.