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

Nonsteady-State Three Compartment Tracer Kinetics: II. Sodium Flux Transients in the Toad Urinary Bladder in Response to Short Circuit

The theoretical approach presented in the previous paper provides an analytical method for determining the unidirectional, nonsteady-state fluxes in a three compartment system. Based on this a study was made of the sodium flux transients in the toad urinary bladder. A transient time-dependent state was generated by suddenly short-circuiting a bladder previously maintained in an open-circuited steady state. The sequence of experiments suggested by the theory provided the data required for the analysis. The results of these tracer experiments were consistent with the complex non-three compartmental structure of this tissue. As a result both of the inadequacy of the three compartment model in representing the tissue and of certain experimental difficulties, attempts at a quantitative solution were not entirely successful. Useful information was nevertheless obtained through a careful use of this model, and a qualitative analysis implied that the sodium influxes into the tissue at both of its surfaces are sensitive to changes in electrical potential while both effluxes are insensitive to this change. This suggests that both of the effluxes result from active processes while both influxes are associated with passive processes. The net transepithelial transport of sodium would then necessarily result from a more complex polarization than that proposed by Koefoed-Johnsen and Ussing