An Optimization for Biological Compartment System

Hirofumi HIRAYAMA; Norio TAKEUCHI; Yuzou FUKUYAMA

An Optimization for Biological Compartment System

Hirofumi HIRAYAMA, Norio TAKEUCHI, Yuzou FUKUYAMA

Full Text Views

0

Cite this

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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.11 pp.1896-1903

Publication Date: 1994/11/25

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section LETTER (Special Section of Letters Selected from the 1994 IEICE Spring Conference)

Category

Cite this

Copy

Hirofumi HIRAYAMA, Norio TAKEUCHI, Yuzou FUKUYAMA, "An Optimization for Biological Compartment System" in IEICE TRANSACTIONS on Fundamentals, vol. E77-A, no. 11, pp. 1896-1903, November 1994, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_11_1896/_p

Copy

@ARTICLE{e77-a_11_1896,
author={Hirofumi HIRAYAMA, Norio TAKEUCHI, Yuzou FUKUYAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Optimization for Biological Compartment System},
year={1994},
volume={E77-A},
number={11},
pages={1896-1903},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={November},}

Copy

TY - JOUR
TI - An Optimization for Biological Compartment System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1896
EP - 1903
AU - Hirofumi HIRAYAMA
AU - Norio TAKEUCHI
AU - Yuzou FUKUYAMA
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1994
AB - 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.
ER -