Math 4791/5791 - Problem Set 9
Fall 1998

1. Some two-compartment models. Set up the equations for the two-compartment system shown at the right.

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2. *An inverse problem. Infusion into the blood is often modeled by a two- or three-compartment model such as the one below. Compartment 1 is the central blood plasma, compartments 2 and 3 are auxiliary compartments that account for secondary time scales. Assume that all rate constants are known. For both the two- and three-compartment models solve the following problem: Given a target blood concentration , find, in general terms, the infusion rate that must be used to maintain this concentration for all times. Assume that all initial conditions are zero.

   

means required of graduate students.