Variation in the PaO2/FiO2 ratio with FiO2: mathematical and experimental description, and clinical relevance

Abstract
Introduction
Previous studies have shown through theoretical analyses that the ratio of the partial pressure of oxygen in arterial blood (PaO2) to the inspired oxygen fraction (FiO2) varies with the FiO2 level. The aim of the present study was to evaluate the relevance of this variation both theoretically and experimentally using mathematical model simulations, comparing these ratio simulations with PaO2/FiO2 ratios measured in a range of different patients.

Methods
The study was designed as a retrospective study using data from 36 mechanically ventilated patients and 57 spontaneously breathing patients studied on one or more occasions. Patients were classified into four disease groups (normal, mild hypoxemia, acute lung injury and acute respiratory distress syndrome) according to their PaO2/FiO2 ratio. On each occasion the patients were studied using four to eight different FiO2 values, achieving arterial oxygen saturations in the range 85–100%. At each FiO2 level, measurements were taken of ventilation, of arterial acid–base and of oxygenation status. Two mathematical models were fitted to the data: a one-parameter 'effective shunt' model, and a two-parameter shunt and ventilation/perfusion model. These models and patient data were used to investigate the variation in the PaO2/FiO2 ratio with FiO2, and to quantify how many patients changed disease classification due to variation in the PaO2/FiO2 ratio. An F test was used to assess the statistical difference between the two models' fit to the data. A confusion matrix was used to quantify the number of patients changing disease classification.

Results
The two-parameter model gave a statistically better fit to patient data (P < 0.005). When using this model to simulate variation in the PaO2/FiO2 ratio, disease classification changed in 30% of the patients when changing the FiO2 level.

Conclusion
The PaO2/FiO2 ratio depends on both the FiO2 level and the arterial oxygen saturation level. As a minimum, the FiO2 level at which the PaO2/FiO2 ratio is measured should be defined when quantifying the effects of therapeutic interventions or when specifying diagnostic criteria for acute lung injury and acute respiratory distress syndrome. Alternatively, oxygenation problems could be described using parameters describing shunt and ventilation/perfusion mismatch.