CO2 control of the respiratory system: Plant dynamics and stability analysis

A stability analysis of respiratory chemical control is developed using a mathematical model of CO₂ mass transport dynamics. Starting with a 3-compartment model of CO₂ stores that distinguishes alveolar, muscle, and other tissue, model reduction techniques are applied to obtain a first-order representation of the respiratory plant. This model contains an effective tissue volume for CO₂, whose derived value is much smaller than previously predicted. To investigate oscillatory instabilities, a controller which incorporates only peripheral chemoreceptor responses was added to the first-order plant model. An explicit stability index (SI) is obtained analytically from a linearized version of this model. SI varies directly with the controller gain and circulation delay time and inversely with the effective tissue volume and inspired CO₂ concentration. Numerical simulations using the first-order nonlinear model show that SI is a good predictor of system stability. According to the linearized model, the system is stable for SI<1; from the nonlinear model, the system is stable for SI<1.1. For typical normal adults, the SI value is well within the stable region. Ahmed ElHefnawy is supported in part by a fellowship from the Egyptian Ministry of Higher Education; he is currently on leave of absence from Cairo University.