An optimal control problem in the study of liver kinetics (Q2265965)

The enzyme activities in the liver are described by a system of ordinary differential equations. A certain substance in the blood is transformed twice by different kinds of enzymes. The mathematical problem is to determine the distribution of enzymes along the blood flow so that the outflow concentration of the once-transformed form of the substance is as small as possible. This problem has been considered before and solved for particular types of enzyme kinetics. In this paper, we solve the problem for more general types of kinetics (including substrate-inhibition kinetics). The methods used are also different in that the problem is considered as a problem of optimal control and Pontryagin's maximum principle is applied to derive necessary conditions.