An Optimization for Biological Compartment System

Hirofumi HIRAYAMA  Norio TAKEUCHI  Yuzou FUKUYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.11   pp.1896-1903
Publication Date: 1994/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1994 IEICE Spring Conference)
Category: 
Keyword: 
optimal control,  biological compartments model,  trasfer rate,  anesthesia,  Rapid Inhalation Induction,  

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Summary: 
An optimal control theory has been applied to a biological compartment system to show a method to analyze the control principle of biological system represented by compartments. Present theory has been proposed to afford a theoretical back ground and validity for the strategy of drug administration or control of the anesthetic agent in practical medicine. The instantaneous change of the concentration of a given material within a biological system has been expressed by differential equations. Each compartment has been set to be transferred a material from all other compartments and conversely each compartment sends it to all other compartments. The control input was restricted to be one kind. The performance function involved the deviation from the target value, the rate of change in concentration and the amount of the control variables. The biological system was defined to operate optimally only when the performance function has been minimized during a given time period. By the optimal control theory of Pontoriagin, above biological problem has been converted to a mathematical problem and was solved numerically by multiple shooting method. The calculated trajectory of the optimal control has been asymmetric parabolic one with the maximum at its initiation and the minimum at the middle of total reaction time. This pattern has been consistent with that of probable transient change of the concentration of anesthetic agent when it has been inhalated under the most up to date "Rapid Inhalation Induction" method. The optimal trasient change of the concentration at each compartment has beeb affected by the difference in time dependent nature and the magnitude of the transfer rate. Present theory afforded a method to analyze the control strategy of biological system expressed by compartments model and showed an availability for actual clinical medicine. The optimal control principle must be a most adequate one to describe the Homeostasis in biological system.