# Alveolar gas equation

The partial pressure of oxygen (pO_{2}) 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]}

## Assumptions

The equation relies on the following assumptions:

- Inspired gas contains no carbon dioxide (CO
_{2}) 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 (CO
_{2}) 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

If F_{I}O_{2} is small, or more specifically if

then the equation can be simplified to:

where:

Quantity | Description | Sample value |
---|---|---|

p_{A}O_{2} |
The alveolar partial pressure of oxygen (pO_{2}) |
107 mmHg (14.2 kPa) |

F_{I}O_{2} |
The fraction of inspired gas that is oxygen (expressed as a decimal). | 0.21 |

P_{ATM} |
The prevailing atmospheric pressure | 760 mmHg (101 kPa) |

pH_{2}O |
The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure | 47 mmHg (6.25 kPa) |

p_{a}CO_{2} |
The arterial partial pressure of carbon dioxide (pCO_{2}) |
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

## References

- ↑ Curran-Everett D (June 2006). "A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation".
*Adv Physiol Educ*.**30**(2): 58–62. doi:10.1152/advan.00076.2005. PMID 16709734.

## 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.

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