Regulation of PaCO2 during rest and exercise: a modeling study

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 (GL) and closed loop sensitivities SI = delta PaCO2/delta PICO2 and SV = delta PaCO2/delta VCO2 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 VCO2, 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 VCO2. 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.