Stability analysis of CO2 control of ventilation

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Abstract
A theoretical analysis of the CO2 control of the respiratory system is presented using both analytic and simulation techniques. A stability index (SI) is obtained by linearizing a dynamic first-order model with a time delay. Analytically, SI values greater than unity predict an unstable response to a disturbance. Because the first-order model is reduced from a higher-order physiological model, SI can be algebraically related to physiological parameters. This relationship shows that SI increases with a decrease in system tissue volume, metabolic rate, or inspired CO2 partial pressure; SI decreases with a decrease in time delay, cardiac output, controller gain, or controller intercept. Analytically, SI distinguishes stable from unstable domains. By simulations of the nonlinear first-order model, three domains are obtained: an unstable domain (sustained oscillations, SI greater than 1.1), an underdamped stable domain (transient oscillations, 0.3 less than SI less than 1.1), and an overdamped stable domain (no oscillations, 0 less than SI less than 0.3). With this classification, disturbances such as change of state (e.g., from awake to asleep) or sigh may produce transient oscillations if the system becomes underdamped even though stable. Potential applications of this work include quantitative distinction of the physiological factors in control disorders associated with short-term periodicities (e.g., Cheyne-Stokes breathing, sleep apnea, breathing at altitude).