Formulation and Computation of Compartment Models

Abstract

In the formulation of compartment models for describing biological phenomena, two separate approaches have usually been employed for isotope dilution systems and systems for which no tracers are introduced. In the former, steady state is assumed to exist and small perturbations are introduced for solution of the system. In the latter, sets of simultaneous differential equations are solved for the complete time course of the drug kinetic system. For linear systems which can be described by first-order kinetics, it is shown that the isotope dilution problem can be cast into the more general approach of simultaneous linear differential equations and the restriction of steady state removed. Solutions to these equations are shown to be easily obtainable using the state-space approach. For systems in which linearity cannot be assumed, digital computer techniques are presented which greatly facilitate numerical solutions. These concepts are demonstrated with two examples. A third example shows how these concepts and others can be employed with isotope dilution to find the initial pool sizes and rate constants in a six-compartment system.