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Nonsteady-state three compartment tracer kinetics. I. Theory.

T L Schwartz, F M Snell

Biophysical Journal

|July 1, 1968

Summary

This study presents a mathematical model for substance transport in a three-compartment system, offering an analytic solution for fluxes and amounts over time. The model is applicable to both steady and transient states in repeatable experimental setups.

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Area of Science:

Pharmacokinetics and Systems Biology
Mathematical Modeling
Chemical Kinetics

Background:

Understanding substance distribution in biological systems is crucial for drug development and physiological studies.
Compartmental models are widely used to represent complex biological systems.
Previous models often rely on assumptions of constant kinetic coefficients, limiting their applicability.

Purpose of the Study:

To derive and solve a set of differential equations describing unidirectional fluxes and substance amounts in a three-compartment system.
To provide an analytic solution applicable to both steady-state and transient conditions.
To develop a model that does not assume constant kinetic coefficients.

Main Methods:

Derivation of differential equations for a serially arranged three-compartment system.
Obtaining an analytic solution for fluxes and compartment quantities as functions of time.
Utilizing data from repetitive experiments with controlled outer compartments.

Main Results:

An analytic solution was obtained for the four unidirectional fluxes and the central compartment's substance amount.
The solution accurately describes the system's behavior in both initial steady state and transient states.
The model successfully describes fluxes and compartment size without assuming constant kinetic coefficients.

Conclusions:

The derived analytic solution provides a robust method for analyzing substance transport in three-compartment systems.
The model's applicability to transient states and its independence from constant kinetic coefficient assumptions enhance its utility.
Repeatable experimental conditions are essential for the model's successful application.

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