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Optimal control in liver kinetics

Published online by Cambridge University Press:  17 February 2009

A. M. Fink
A. M. Fink
Affiliation:
Mathematics Department, Iowa State University, Ames, Iowa 50011, U. S. A.
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Abstract

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We solve a minimization problem in liver kinetics posed by Bass, et al., in this journal, (1984), pages 538–562. The problem is to choose the density functions for the location of two enzymes, in order to minimize the concentration of an intermediate form of a substance at the outlet of the liver. This form may be toxic to the rest of the body, but the second enzyme renders it harmless. It seems natural that the second enzyme should be downstream from the first. However, we can show that the minimum problem is sometimes solved by an overlap of the supports of the two density functions. Even more surprising is that, for certain forms of the kinetic functions and high levels of transformation of the first enzymatic reaction, some of the first enzyme should be located downstream from all the second enzyme. This suggests that the first reaction should be relatively slow.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 3 , January 1986 , pp. 361 - 369
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Bass, L., Bracken, A. J. and Vyborny, R., “Minimization problems for implicit functionals defined by differential equations of liver kinetics”, J. Austral. Math. Soc. Ser. B 25 (1984), 538–562.CrossRefGoogle Scholar