Contents

Alveolar gas equation

The equation relies on the following assumptions:

• Inspired gas contains no carbon dioxide (CO₂)
• 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[edit]

${\displaystyle p_{A}{\ce {O2}}=F_{I}{\ce {O2}}(P_{{\ce {ATM}}}-p{\ce {H2O}})-{\frac {p_{a}{\ce {CO2}}(1-F_{I}{\ce {O2}}(1-{\ce {RER}}))}{{\ce {RER}}}}}$

If${\displaystyle F_{I}{\ce {O2}}}$ is small, or more specifically if ${\displaystyle F_{I}{\ce {O2}}(1-{\ce {RER}})\ll 1}$ 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:

Quantity	Description	Sample value
${\displaystyle p_{A}{\ce {O2}}}$	The alveolar partial pressure of oxygen (${\displaystyle p{\ce {O2}}}$)	107 mmHg (14.2 kPa)
${\displaystyle F_{I}{\ce {O2}}}$	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
PATM	The prevailing atmospheric pressure	760 mmHg (101 kPa)
${\displaystyle p{\ce {H2O}}}$	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg (6.25 kPa)
${\displaystyle p_{a}{\ce {CO2}}}$	The arterial partial pressure of carbon dioxide (${\displaystyle p{\ce {CO2}}}$ )	40 mmHg (5.33 kPa)
RER	The respiratory exchange ratio	0.8

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

Doubling ${\displaystyle F_{i}{\ce {O2}}}$ will double ${\displaystyle P_{i}{\ce {O2}}}$.

Other possible equations exist to calculate the alveolar air.^{[2][3][4][5][6][7][8]}

${\displaystyle {\begin{aligned}P_{A}{\ce {O2}}&=F_{I}{\ce {O2}}\left(PB-P{\ce {H2O}}\right)-P_{A}C{\ce {O2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\&=P_{I}{\ce {O2}}-P_{A}C{\ce {O2}}\left(F_{I}{\ce {O2}}+{\frac {1-F_{I}{\ce {O2}}}{R}}\right)\\&=P_{I}{\ce {O2}}-{\frac {V_{T}}{V_{T}-V_{D}}}\left(P_{I}{\ce {O2}}-P_{E}{\ce {O2}}\right)\\&={\frac {P_{E}{\ce {O2}}-P_{I}{\ce {O2}}\left({\frac {V_{D}}{V_{T}}}\right)}{1-{\frac {V_{D}}{V_{T}}}}}\end{aligned}}}$

Abbreviated alveolar air equation[edit]

${\displaystyle P_{A}{\ce {O2}}={\frac {P_{E}{\ce {O2}}-P_{i}{\ce {O2}}{\frac {V_{D}}{V_{T}}}}{1-{\frac {V_{D}}{V_{T}}}}}}$

P_AO₂, P_EO₂, and P_iO₂ 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.^[9]

Respiratory quotient (R)[edit]

${\displaystyle R={\frac {P_{E}{\ce {CO2}}(1-F_{I}{\ce {O2}})}{P_{i}{\ce {O2}}-P_{E}{\ce {O2}}-(P_{E}{\ce {CO2}}*F_{i}{\ce {O2}})}}}$

Physiologic dead space over tidal volume (VD/VT)[edit]

${\displaystyle {\frac {V_{D}}{V_{T}}}={\frac {P_{a}{\ce {CO2}}-P_{E}{\ce {CO2}}}{P_{a}{\ce {CO2}}}}}$

See also[edit]

• Pulmonary gas pressures

References[edit]

External links[edit]

• Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)
• Formula at ucsf.edu
• S. Cruickshank, N. Hirschauer: The alveolar gas equation in Continuing Education in Anaesthesia, Critical Care & Pain, Volume 4 Number 1 2004
• Online Alveolar Gas Equation and iPhone application by Medfixation.
• A computationally functional Alveolar Gas Equation by vCalc.