Non-dimensional quantification of the interactions between hypoxia, hypercapnia and exercise on ventilation in humans

The purpose of this study was to develop a non-dimensional approach towards the description of interaction between the three respiratory stimuli of hypoxia, hypercapnia and exercise and to use this approach to quantify the relative strengths of their interactions. Only a part of the study related to the overall interaction of the three stimuli is presented here. Nine volunteers took part in the study and their ventilatory responses to hypoxia were measured under four different conditions of rest-eucapnia, rest-hypercapnia, exercise-eucapnia and exercise-hypercapnia. Non-dimensional linear functions of hypercapnia (x), hypoxia (y) and exercise (z) were defined such that a value of one would double the resting ventilation. Non-dimensional ventilation v was derived as: v(x,y,z) = 1+ x + y + z + g1xy + g2xz + g3yz + g4xyz, where g1, g2, g3 and g4 provide non-dimensional measures of the strength of stimulus interaction. These interactions were calculated from the parameters obtained by fitting simple respiratory models to the data. The values for g1, g3 and g4 were significantly different from zero (p < 0.05, t-test). An intriguing result of this study is the overall negative interaction of the three stimuli, which may suggest that the linear, stimulus-response models commonly used to describe respiratory data may not be adequate for describing these complex interactions.