Regulation of PaCO₂ during rest and exercise: A modeling study

Abstract

A nonlinear mathematical model of the CO₂ control system was used to examine a number of issues concerning the regulation of PaCO₂ during rest and exercise. To gain insight to the regulatory properties of the respiratory system, the open loop gain (G_l) and closed loop sensitivities S_i=ξPaCO₂/ξPiCO₂ and$Sv = \partial PaCO_2 /\partial \dot Vco_2$ were calculated. Gl indicates the ability of a control system to regulate the controlled variable, PaCO₂ in the model. Si and Sv represent the change in PaCO₂ to unit changes in PiCO₂ and$\dot Vco_2$, respectively. Model predications were obtained for rest and various intensities of exercise for the following challenges to the respiratory system: (a) CO₂ inhalation, (b) i.v. CO₂ loading, (c) application of an external dead space, and (d) a shift in the resting operating point. Increasing exercise intensity produced a substantial decrease in Gl and increase in Si consistent with the hypothesis that exercise degrades the ability of the respiratory system to regulate PaCO₂. However, Sv decreased indicating that the respiratory system would actually be better able to regulate PaCO₂ if there were fluctuations in$\dot Vco_2$. Thus, Gl does not completely describe the regulatory characteristics of the respiratory control system. It is demonstrated that the regulatory characteristics of the respiratory system as described by Gl, Si, and Sv are complex and depend on the nature of the challenge. Techniques for systematically describing the regulatory properties of the CO₂ control system are described.