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.

Figure 1

Mathematical models of pulmonary gas exchange. (a) The 'effective shunt' model. (b) The two-parameter shunt and ventilation/perfusion mismatch model. Data describing oxygen transport in the models are indicated: oxygen partial pressure in alveolar air (P_AO₂), oxygen partial pressure in capillary blood (P_cO₂), oxygen partial pressure in arterial blood (P_aO₂), concentration of oxygen in venous blood (C_vO₂), concentration of oxygen in capillary blood (C_cO₂), concentration of oxygen in arterial blood (C_aO₂), cardiac output (Q), shunt parameter (shunt), and parameters describing ventilation/perfusion mismatch (fA2, ΔPO₂).

Figure 2

Model simulations of arterial oxygen saturation and arterial oxygen partial pressure/inspired oxygen fraction ratio. (a) Inspired oxygen fraction (FiO₂) versus arterial oxygen saturation (SaO₂). (b) FiO₂ versus the partial pressure of oxygen in arterial blood (PaO₂)/FiO₂ ratio. Simulations performed using shunt = 0–30%, parameter ΔPO₂ (fA2) = 0 kPa (0.9), oxygen consumption = 0.26 l/min, alveolar minute volume = 5.25 l. Points a and b, the PaO₂/FiO₂ ratios for FiO₂ = 0.19 (point a) and FiO₂ = 0.57 (point b) – corresponding to the extremes of the relevant range of FiO₂ (thick solid line).

Figure 3

Model simulations of arterial oxygen saturation and arterial oxygen partial pressure/inspired oxygen fraction ratio. (a) Inspired oxygen fraction (FiO₂) versus arterial oxygen saturation (SaO₂). (b) FiO₂ versus the partial pressure of oxygen in arterial blood (PaO₂)/FiO₂ ratio. Simulations performed using shunt = 5%, parameter ΔPO₂ (fA2) = 0–30 kPa (0.9–0.11), oxygen consumption = 0.26 l/min, alveolar minute volume = 5.25 l. Points a and b, the PaO₂/FiO₂ ratios for FiO₂ = 0.26 (point a) and FiO₂ = 0.35 (point b) – corresponding to the extremes of the relevant range of FiO₂ (thick solid line).

Figure 4

Model simulations and measured data for six patients selected to represent typical cases. Model fitted simulations (curves) and measured data (crosses) describing (i) inspired oxygen fraction (FiO₂) versus arterial oxygen saturation (SaO₂) and (ii) FiO₂ versus the partial pressure of oxygen in arterial blood (PaO₂)/FiO₂ ratio. (a) Normal subject [14], (b) cardiac incompensation patient [14], (c) gynaecological laparotomy patient [14], (d) cardiac surgery patient [15], (e) intensive care patient [14], and (f) previously unpublished intensive care data. Curves, parameter values and fitting residuals (root mean square (RMS)) for the 'effective shunt' model (dashed lines, 'effective shunt' parameter) and for the two-parameter model (solid lines, shunt and ΔPO₂ parameters). Thick lines, range of FiO₂ giving a SaO₂ of 92–98%.