A mathematical analysis of the Grodins model of respiratory control

Abstract

The classical Grodins model of chemical respiratory control is analysed. Scaling and asymptotic analysis are used to reduce the model drastically to a much simplified form. In essence, the model consists of two separate controllers due to oxygen and carbon dioxide. The authors focus on the carbon dioxide controller, and show that it can be considered as two coupled delay recruitment equations. While, in normal circumstances, steady ventilation is stable, it is shown that, by varying controlling parameters, periodic and chaotic solutions may be obtained.

respiratory control, mathematical modelling, asymptotic analysis, delay recruitment equations, chaos