Relative stability of human respiration during progressive hypoxia

We have systematically studied the relationship between the relative stability (R) of respiration and the loop gain (LG) of the CO2 control system in 15 healthy awake adult males during progressive hypoxia. R was measured by the ventilatory oscillations after brief (less than 10 s) CO2 challenges. Control theory suggests that such oscillations are completely governed by LG. A significant positive correlation was found between R and LG (r = 0.74, P less than 0.01, n = 85). A minimal mathematical model of respiratory control was used to predict R as a function of LG. Serial correlation analysis (r = 0.09, P greater than 0.1) of the residuals indicated statistical agreement between predictions and observations. The mean residual (0.011) was not significantly different from zero (P greater than 0.1). Also, as the model predicted, sustained periodic breathing (PB) occurred whenever the estimated LG was greater than unity. The mean LG breathing room air was 0.51 and for the 13 epochs of PB was 1.17 (range 0.71-1.65). It is concluded that PB is a quantitative extension of the relative stability continuum and corresponds to unstable operation of the CO2 control system. Furthermore, relative stability can be quantitatively predicted for each subject by a minimal mathematical model.