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Alveolar gas equation
The partial pressure of oxygen (pO_{2}) in the pulmonary alveoli is required to calculate both the alveolararterial gradient of oxygen and the amount of righttoleft 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
<math>p_AO_2=F_IO_2(P_{ATM}pH_2O)\frac{p_aCO_2(1F_IO_2[1RER])}{RER}</math>
If F_{I}O_{2} is small, or more specifically if
<math>F_IO_2[1RER] \ll 1</math>
then the equation can be simplified to:
<math>p_AO_2 \approx F_IO_2(P_{ATM}pH_2O)\frac{p_aCO_2}{RER}</math>
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
 ^ CurranEverett D (June 2006). "A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation". Adv Physiol Educ 30 (2): 58–62. PMID 16709734. doi:10.1152/advan.00076.2005.
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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