Alveolar gas equation

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The alveolar gas equation is a simple way to estimate the oxygen level in the air inside the lungs (alveolar oxygen, pAO2). It helps doctors evaluate how well oxygen moves from the lungs into the blood, without needing to sample alveolar gas directly. The idea is to use measurements that are easy to obtain.

The basic idea
- Alveolar oxygen (pAO2) depends on how much oxygen you breathe in, how humidified that air becomes in the lungs, and how much CO2 is left in the blood after gas exchange.
- The common formula (in plain terms) is:
pAO2 ≈ FiO2 × (Patm − PH2O) − PaCO2 ÷ RER
Where:
- FiO2 is the fraction of inspired oxygen (room air is about 0.21)
- Patm is atmospheric pressure (about 760 mmHg at sea level)
- PH2O is the water vapor pressure when air is humidified (about 47 mmHg at body temperature)
- PaCO2 is the arterial CO2 partial pressure (roughly equal to alveolar CO2)
- RER is the respiratory exchange ratio (about 0.8; CO2 produced per O2 consumed)

A simpler version
- If FiO2 is small, the equation can be simplified to:
pAO2 ≈ FiO2 × (Patm − PH2O) − PaCO2 ÷ RER

Why this helps
- pAO2 is used to calculate the alveolar-arterial oxygen gradient and to check for abnormal blood flow or shunts.
- Since taking a direct alveolar gas sample is impractical, this equation gives a practical estimate from measurable data.

A quick example (sea level, 37°C)
- FiO2 = 0.21, Patm ≈ 760 mmHg, PH2O ≈ 47 mmHg, PaCO2 ≈ 40 mmHg, RER ≈ 0.8
- pAO2 ≈ 0.21 × (760 − 47) − 40 ÷ 0.8 ≈ 0.21 × 713 − 50 ≈ 100 mmHg

The concept was described in medical literature around 1946.