Mathematical techniques for solving analytically large compartmental systems

Abstract

The flow of radioactive particles inside the body from internally deposited radioisotopes in people exposed to inhalation, ingestion, injection, or other ways is usually evaluated using compartmental models. The biokinetic models included in the documents of the International Commission on Radiological Protection such as International Commission on Radiological Protection 66 and 78 involve many compartments. Usually numeric methods are applied. Very often analytical solutions are not possible. New computer programs that include symbolic capability can be used to solve compartmental systems. In this paper some techniques are developed in order to make feasible a computer program that gives not only faster and more accurate solutions, but also analytic solutions for these kind of models. The main idea is to make a partition of subsystems and solve them sequentially. The concept of pseudotrap compartments in a subsystem is crucial at this point. Impulse (acute), constant, and continuous (such as exponential) intakes are considered. This technique has been applied to develop a computer code called Humorap to solve the International Commission on Radiological Protection 66 and 78 models.