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

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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.