## Document Type

Report

## Source Publication Title

Technical Report 149

## 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.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

2-1-1981

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Eisenfeld, Jerome, "On Approach to Equilibrium in Nonlinear Compartmental Systems" (1981). *Mathematics Technical Papers*. 2.

https://mavmatrix.uta.edu/math_technicalpapers/2