Linear Systems Analysis of Blood Clotting System

Hirohumi HIRAYAMA  Kiyono YOSHII  Hidetomo OJIMA  Norikazu KAWAI  Shintaro GOTOH  Yuzo FUKUYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.10   pp.1419-1431
Publication Date: 1995/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Systems and Control
Keyword: 
blood coagulation,  cascade of activation reactions,  controllability,  stability,  

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Summary: 
The controllability and the stability of the blood clotting system are examined with the linear system analysis. The dynamic behavior of the clotting system consisting of a cascade of ten proteolytic reactions of the clotting factors with multiple positive feed back and feed forward loops is represented by the rate equations in a system of non linear ordinary differential equations with 35 variables. The time courses of concentration change in every factor are revealed by numerical integration of the rate equations. Linearization of the rate equations based on the dynamic behavior of the chemical species relevant to the nonlinear terms leads to the linear systems analysis of the clotting system to clarify the essential features of blood coagulation. It follows from the analysis that the clotting system is uncontrollable regardless of changes in any system parameters and control input and that all the chemical species of the system are uncontrollable so that the sequential reactions in the cascade proceed irreversibly, once they are activated. More over by the analysis of the eigen values, the clotting reaction as a total system was shown to be unstable which was insensitive to changes in the system parameters. These characteristic natures of clotting system must be derived in the sequential cascade reaction pattern and the inherent multiple positive feed back and feed forward regulation.