Two-compartment models do a good job of accounting for the behavior of the normal lung over a modest range of ventilation frequencies or stress-adaptation time scales. Of course, these models do not come close to representing the structural complexities of a real lung, so one can easily imagine that a model with more than two compartments might provide an improved account of lung mechanical behavior. This is particularly true for behavior pertaining to extended scales of time or frequency, or when the lungs become heterogeneous in disease. In principle, there is no limit to the number of compartments such a model could possess. Dealing with such models might sound like a daunting prospect, given the algebraic machinations presented in the previous chapter for models with only two compartments. Fortunately, the tools of linear systems theory, and the fast Fourier transform (FFT) in particular, come to the rescue. These tools apply so long as the lung can be considered to behave as a collection of linear compartments, each behaving like the model in Fig. 3.1. In this chapter, we examine the principal tools of linear systems theory and see how they apply to the study of lung mechanics.

Linear systems theory

A system is a set of components that have some kind of collective identity. Systems interact with their environments by receiving inputs and producing outputs. The relationships between these inputs and outputs are determined by processes within the system.