On a Multicompartment Migration Model with Chronic Feeding

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Abstract
In uptake and retention studies involving radioactive tracer materials, the biosystem can often be thought of as comprising K distinct compartments with constant rates of passage of particles from any compartment to a different compartment. Before the theoretical uptake and retention curve for any compartment can be plotted and compared with the sequence of experimental points for the same compartment, it must be possible to estimate these rates from the data of the experiment. A mathematical model of such a system is deduced which is sufficiently general to comprehend both the chronic and acute feeding situations. To estimate the migration rate constants a method which does not require the explicit solution of the system of differential equations is presented. The method depends solely on the use of matrix techniques applied directly to the system of differential equations. No large sample properties of the estimates are considered, but a conjecture concerning improvement of the accuracy of the estimates is offered.

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