Alveolar gas equation explained

The alveolar gas equation is the method for calculating partial pressure of alveolar oxygen . 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 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
• 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 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

$$p\_A\backslash ce\; =\; F\_I\backslash ce(P\_\backslash ce\; -\; p\backslash ce)\; -\; \backslash frac\; \backslash ce$$

If is small, or more specifically if $F\_I\backslash ce(1-\backslash ce)\; \backslash ll\; 1$ then the equation can be simplified to:

$$p\_A\backslash ce\; \backslash approx\; F\_I\backslash ce(P\_\backslash ce\; -\; p\backslash ce)\; -\; \backslash frac\; \backslash ce$$

where:

Quantity	Description	Sample value
$p\_A\backslash ce$	The alveolar partial pressure of oxygen ($p\backslash ce$)	107 mmHg (14.2 kPa)
$F\_I\backslash ce$	The fraction of inspired gas that is oxygen (expressed as a decimal).	0.21
P _{ATM}	The prevailing atmospheric pressure	760 mmHg (101 kPa)
$p\backslash ce$	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg (6.25 kPa)
$p\_a\backslash ce$	The arterial partial pressure of carbon dioxide ($p\backslash ce$)	40 mmHg (5.33 kPa)
RER	The respiratory exchange ratio	0.8

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

Doubling will double .

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

Abbreviated alveolar air equation

$$p\_A\; \backslash ce\; =\; \backslash frac$$,, and 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)

$$R\; =\; \backslash frac$$

Physiologic dead space over tidal volume (VD/VT)

$$\backslash frac\; =\; \backslash frac$$

See also

• Pulmonary gas pressures

External links

• 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.

Notes and References

1. Curran-Everett D . A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation . Adv Physiol Educ . 30 . 2 . 58–62 . June 2006 . 16709734 . 10.1152/advan.00076.2005 . 42010762 .
2. Raymond L, Dolan W, Dutton R, et al: Pulmonary function and gas exchange during altitude hypoxia (abstract).Clin Res 19:147, 1971
3. Spaur WH, Raymond LW, Knott MM, et al: Dyspnea in divers at 49.5 ATA: Mechanical not chemical in origin. Undersea Biomed Res 4:183-198, 1977
4. Rossier P-H, Blickenstorfer E: Espace mort et hyperventilation. Helv Med Acta 13:328-332, 1946
5. Riley RL, Lilienthal JL Jr, Proemmel DD, et al: On thedetermination of the physiologically effective pressures of oxygen and carbon dioxide in alveolar air. Am J Physiol 147:191-198, 1946
6. McNicol MW, Campbell EJM: Severity of respiratory failure: arterial blood gases in untreated patients. Lancet 1:336-338, 1965
7. Begin R, Renzetti AD Jr: Alveolar-arterial oxygen pressure gradient: I. Comparison between an assumed and actual respiratory quotient in stable chronic pulmonary disease; Relationship to aging and closing volume in normal subjects. Respir Care 22:491-500, 1977
8. Suwa K, Geffin B, Pontoppidan H, et al: A nomogram fordeadspace requirement during prolonged artificial ventilation.Anesthesiology 29:1206-1210, 1968
9. Fenn WO, Rahn H, Otis AB: A theoretical study of the composition of alveolar air at altitude. Am J Physiol 146:637-653, 1946