A mathematical model of the ventilatory control system to carbon dioxide with special reference to athletes and nonathletes.

The ventilatory response curve (VRC) as a function of alveolar and arterial pCO2 was recorded in 6 high-performance athletes and 6 nonathletes. The best fit to the data points could be found for an equation of the form (see article) showing that the results are strongly related to a Gaussian probability density function (PDF). After normalizing the equation to a form (see article) (M = mean value of PDF), sigma, A and M could be determined for both groups. Sigma and A are smaller in the athletic group, whereas M did not show any systematic difference. Regarding the respiratory center consisting of functional "elements" responding indirectly to variable pCO2 it can be concluded that the frequency distribution of the different active elements is greater and spread over a wider pCO2 range in the nonathletes with the same mean value in both groups. Using Loeschcke's model (1960), the open loop gain factor for different V CO2 as a function of p(A)CO2 was computed; the gain factor showed a maximum in the physiological range of pCO2.