Compartmental models: Theory and practice using the saam II software system

Abstract

Understanding in vivo the functioning of metabolic systems at the whole- body or regional level requires one to make some assumptions on how the system works and to describe them mathematically, that is, to postulate a model of the system. Models of systems can have different characteristics depending on the properties of the system and the database available for their study; they can be deterministic or stochastic, dynamic or static, with lumped or distributed parameters. Metabolic systems are dynamic systems and we focus here on the most widely used class of dynamic (differential equation) models: compartmental models. This is a class of models for which the governing law is conservation of mass. It is a very attractive class to users because it formalizes physical intuition in a simple and reasonable way. Compartmental models are lumped parameter models, in that the events in the system are described by a finite number of changing variables, and are thus described by ordinary differential equations. While stochastic compartment models can also be defined, we discuss here the deterministic versions - those that can work with exact relationships between model variables. These are the models most widely used in discussions of endocrinology and metabolism. In this chapter, we will discuss the theory of compartmental models, and then discuss how the SAAM II software system, a system designed specifically to aid in the development and testing of multicompartmental models, can be used.