On Approach to Equilibrium in Nonlinear Compartmental Systems

Abstract

**Please note that the full text is embargoed** ABSTRACT: A closed compartmental system is a set of nonnegative interdependent functions, [see pdf for notation] such that their sum is constant. The functions can represent populations, masses or concentrations, depending on the particular application. It is convenient to normalize so that [see pdf for notation] in which case the functions are proportions. It is assumed that the (nonnegative) flow rate from j to i has the form fjjxj. Thus, the rate of change, [see pdf for notation] The first term is the inflow to i from the other "compartments" and the second term is the outflow from i to the other compartments. Setting [see pdf for notation] we obtain the system in vector form, [see pdf for notation]

In classical compartmental analysis [1]-[4], which deals mainly with tracer and drug studies, each xi represents the amount of tracer or drug in an organ or a compartment of the human body, hence the term "compartment". Moreover, in classical work, the fij are treated as constants, however, in more recent work [5]-[12], they are functions, [see pdf for notation] Let us consider a classical tracer study.