Analysis of Open Systems of Multiple Pools by Administration of Tracers at a Constant Rate or as a Single Dose as Illustrated by Problems Involving Steroid Hormones

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Abstract
When attempts are made to evaluate the rates of secretion and metabolism of steroid hormones by the application of isotope tracer techniques, compartmental analysis involving pools which represent different related compounds and different spaces of distribution for each compound must be employed. In this paper, new approaches to this form of analysis are presented. Thus, general open systems of multiple pools (in the steady state) into which tracers are introduced at a constant rate have been studied. Mathematical expressions have been derived by which “production rates”, “direct production rates” of each pool, and “transfer factors” between pools can be calculated from isotopic data obtained by sampling the pools at equilibrium. In some more restricted models it was possible to relate the rates of direct transfer between pools to the specific activities of some of the pools. A relationship has been derived between the specific activities of a pool at equilibrium during constant infusion of the tracers and the cumulative specific activities of an end product of that pool after administration of the tracer as a single dose. From this relationship the equations derived assuming constant infusion can be used to calculate rates of production and of metabolism from experiments in which the isotopes are administered as a single dose.