Research

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

Dan S Karbing^1*, Søren Kjærgaard², Bram W Smith¹, Kurt Espersen³, Charlotte Allerød^1,2, Steen Andreassen¹ and Stephen E Rees¹

• * Corresponding author: Dan S Karbing dank@hst.aau.dk

Author Affiliations

¹ Center for Model-based Medical Decision Support, Department of Health Science and Technology, Aalborg University, Fredrik Bajers Vej 7, E4-215, DK-9220 Aalborg East, Denmark

² Anaesthesia and Intensive Care, Region North Jutland, Aalborg Hospital, Aarhus University, DK-9000 Aalborg, Denmark

³ Department of Intensive Care, Rigshospitalet, University of Copenhagen, DK-2100 Copenhagen East, Denmark

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Critical Care 2007, 11:R118 doi:10.1186/cc6174

See realated letter by El-Khatib and Jamaleddine, http://ccforum.com/12/1/407

Published: 7 November 2007

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.