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

- Authors
- Journal
- Respiration Physiology 0034-5687
- Publisher
- Elsevier
- Publication Date
- Volume
- 31
- Issue
- 1
- Identifiers
- DOI: 10.1016/0034-5687(77)90069-x
- Keywords
- Disciplines

## Abstract

Abstract A mathematical expression has been developed to describe the ventilatory responses to changes in arterial oxygen saturation (Sa O 2) and arterial carbon dioxide tension (P CO 2). The derivation is based on the experimental observations: (1) that ventilation is a linear function of P CO 2 under isoxic conditions, and (2) that ventilation is a linear function of Sa O 2, under isocapnic conditions. It is assumed that all functions are continuous and single valued, with the implication that for any given Sa O 2, and P co 2 there is a unique ventilatory response. The analysis following from these three assumptions has enabled us to derive the following expression for ventilation: Vi(Sa O 2, p co 2 = α 1·Sa CO 2·P CO 2+α 2·Sa O 2+α 3·P CO 2+α 4 where the α's are constants for an individual. This equation, which follows uniquely from the assumptions stated, is simpler and contains fewer parameters than previous expressions used to describe ventilation.

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