A mathematical expression to describe the ventilatory response to hypoxia and hypercapnia

A mathematical expression has been developed to describe the ventilatory responses to changes in arterial oxygen saturation (SaO2) and arterial carbon dioxide tension (PCO2). The derivation is based on the experimental observations: (1) that ventilation is a linear function of PCO2 under isoxic conditions, and (2) that ventilation is a linear function of SaO2 under isocapnic conditions. It is assumed that all functions are continuous and single valued, with the implication that for any given SaO2 and PCO2 there is a unique ventilatory response. The analysis following from these three assumptions has enabled us to derive the following expression for ventilation: VI(SaO2, PCO2) = alpha1 - SaO2 - PCO2 + alpha2 - SaO2 + alpha3 - PCO2 + alpha4 where the alpha's are constants for an individual. This equation, which follows uniquely from the assumption stated, is simpler and contains fewer parameters than previous expressions used to describe ventilation.