The various lung models we considered in the previous chapter are all composed of collections of discrete elements, each of which is a resistance, an elastance, or a mass. Such models assume that the dissipative, elastic, and inertive properties of the lung are each lumped together in separate physical locations. Accordingly, these models are known as lumped-parameter models. Most models of lung mechanics that have appeared in the literature over the past century or so have been of this form. The main reason for the prevalence of lumped-parameter models is that they are described by tractable, if sometimes algebraically tortuous, ordinary differential equations. Also, we tend to be comfortable with the idea of associating individual constitutive properties with distinct components in a model. This tendency to make lumped-parameter models may be cultural; probably many of us can remember learning elementary physics at school with the aid of demonstrations of things like weights suspended on springs. It may also reflect an innate need for the human mind to compartmentalize phenomena in order to make sense of a complex world. In any case, lumped-parameter models lead to a rather artificial view of the way the world actually works, and it is now time to revise this view with respect to the modeling of lung mechanics.

Genesis of the constant phase model

Our affinity for linear ordinary differential equations instinctively makes us expect to see exponential-type transient responses in nature.