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 less than 1; from the nonlinear model, the system is stable for SI less than 1.1. For typical normal adults, the SI value is well within the stable region.