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.^[1]

1 Assumptions
2 Equation
3 See also
4 References
5 External links

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

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

If F_IO₂ is small then
$F_IO_2[1-RQ]\approx0$
In which case the equation can be simplified to:
$p_AO_2 \approx F_IO_2(P_{ATM}-pH_2O)-\frac{p_aCO_2}{RQ}$ where:

Quantity	Description	Sample value
p_AO₂	The alveolar partial pressure of oxygen (pO₂)	107 mmHg (14.2 kPa)
F_IO₂	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
P_ATM	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)
p_aCO₂	The arterial partial pressure of carbon dioxide (pCO₂)	36 mmHg (4.79 kPa)
RQ (RER)	The respiratory quotient (Respiratory Exchange Ratio)	0.8