Nonsteady-state Three Compartment Tracer Kinetics. I. Theory

A set of differential equations is derived which describes the four unidirectional fluxes of a substance across the boundaries of the central compartment of a serially arranged three compartment system, and the amount of this substance present in the central compartment. An analytic solution is obtained which yields all of these quantities as functions of time. The analysis is associated with a defined set of repetitive experiments from which the necessary data are obtained and during which the two outer compartments must be subject to experimental control. The solution is applicable to both the initial steady state and a transient, time-dependent state created by making a step change in the initial conditions. It describes the fluxes and compartment size without assuming that constant kinetic coefficients relate the fluxes to compartmental quantities but is limited by the requirement that the response of the system be repeatable in time.