Mathematical study of periodic breathing as an instability of the respiratory system

A theoretical study of respiratory stability, based on a simple CO2 model of the respiratory system, investigates each component of respiration: the plant system and the central and peripheral controller systems. Analysis of the dynamic properties of the plant leads to a simplified respiratory model for the study of the influence of the central and peripheral controller components on stability. It is shown that the central component is not involved in respiratory instability phenomena such as periodic breathing whereas the peripheral component plays a major role. The explicit analytical index of stability obtained allows definition of the conditions of occurrence of periodic breathing in terms of the fundamental respiratory parameters. Moreover, this index can be used to evaluate the influence of various respiratory parameters on the stability of respiration.