The alveolar gas equation is the method for calculating partial pressure of alveolar oxygen (pAO2).
The equation is used in assessing if the lungs are properly transferring oxygen into the blood.
The alveolar air equation is not widely used in clinical medicine, probably because of the complicated appearance of its classic forms.
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] The equation relies on the following assumptions:
2
(
) −
p
a
2
) )
{\displaystyle p_{A}{\ce {O2}}=F_{I}{\ce {O2}}(P_{{\ce {ATM}}}-p{\ce {H2O}})-{\frac {p_{a}{\ce {CO2}}(1-F_{I}{\ce {O2}}(1-{\ce {RER}}))}{{\ce {RER}}}}}
If FiO2 is small, or more specifically if
2
( 1 −
{\displaystyle F_{I}{\ce {O2}}(1-{\ce {RER}})\ll 1}
then the equation can be simplified to:
{\displaystyle p_{A}{\ce {O2}}\approx F_{I}{\ce {O2}}(P_{{\ce {ATM}}}-p{\ce {H2O}})-{\frac {p_{a}{\ce {CO2}}}{{\ce {RER}}}}}
where: Sample Values given for air at sea level at 37 °C.
Doubling FiO2 will double piO2.
Other possible equations exist to calculate the alveolar air.
{\displaystyle {\begin{aligned}p_{A}{\ce {O2}}&=F_{I}{\ce {O2}}\left(PB-p{\ce {H2O}}\right)-p_{A}{\ce {CO2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\[4pt]&=p_{I}{\ce {O2}}-p_{A}{\ce {CO2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\[4pt]&=p_{I}{\ce {O2}}-{\frac {V_{T}}{V_{T}-V_{D}}}\left(p_{I}{\ce {O2}}-p_{E}{\ce {O2}}\right)\\[4pt]&={\frac {p_{E}{\ce {O2}}-p_{I}{\ce {O2}}\left({\frac {V_{D}}{V_{T}}}\right)}{1-{\frac {V_{D}}{V_{T}}}}}\end{aligned}}}
pAO2, pEO2, and piO2 are the partial pressures of oxygen in alveolar, expired, and inspired gas, respectively, and VD/VT is the ratio of physiologic dead space over tidal volume.