Alveolar gas equation

The partial pressure of oxygen (pO₂) in the pulmonary alveoli is required to calculate both the alveolar-arterial gradient of oxygen and the amount of right-to-left cardiac shunt, which are both clinically useful quantities. However it is not practical to take a sample of gas from the alveoli in order to directly measure the partial pressure of oxygen. The alveolar gas equation allows the calculation of the alveolar partial pressure of oxygen from data that is practically measurable. It was first characterized in 1946.

Assumptions

The equation relies on the following assumptions:

• Inspired gas contains no carbon dioxide (CO₂) or water
• Nitrogen (and any other gases except oxygen) in the inspired gas are in equilibrium with their dissolved states in the blood
• Inspired and alveolar gases obey the ideal gas law
• Carbon dioxide (CO₂) in the alveolar gas is in equilibrium with the arterial blood i.e. that the alveolar and arterial partial pressures are equal
• The alveolar gas is saturated with water

Equation

$p_AO_2=F_IO_2(P_{ATM}-pH_2O)-\frac{p_aCO_2(1-F_IO_2[1-RER])}{RER}$

If F_IO₂ is small, or more specifically if
$F_IO_2[1-RER] \ll 1$
then the equation can be simplified to:
$p_AO_2 \approx F_IO_2(P_{ATM}-pH_2O)-\frac{p_aCO_2}{RER}$ where:

Quantity	Description	Sample value
pAO2	The alveolar partial pressure of oxygen (pO2)	107 mmHg (14.2 kPa)
FIO2	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
PATM	The prevailing atmospheric pressure	760 mmHg (101 kPa)
pH2O	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg (6.25 kPa)
paCO2	The arterial partial pressure of carbon dioxide (pCO2)	40 mmHg (4.79 kPa)
RER	The respiratory exchange ratio	0.8

Sample Values given for air at sea level at 37°C.

See also

• Pulmonary gas pressures

External links

• Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)
• Formula at ucsf.edu
• Derivation and explanation from Continuing Care in Anaesthesia, Critical Care, and Pain
• Online Alveolar Gas Equation and iPhone application by Medfixation.
• A computationally functional Alveolar Gas Equation by vCalc.