alveolar gas equation

The equation relies on the following assumptions:

• Inspired gas contains no carbon dioxide ({{chem2|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 ({{chem2|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

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 {{chem2|F_{i}O2}} is small, or more specifically if $F\_I\backslash ce\{O2\}(1-\backslash ce\{RER\})\; \backslash ll\; 1$ then the equation can be simplified to:

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 {{chem2|F_{i}O2}} will double {{chem2|p_{i}O2}}.

Other possible equations exist to calculate the alveolar air.Raymond L, Dolan W, Dutton R, et al: Pulmonary function and gas exchange during altitude hypoxia (abstract).

Clin Res 19:147, 1971Spaur 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, 1977Rossier P-H, Blickenstorfer E: Espace mort et hyperventilation. Helv Med Acta 13:328-332, 1946Riley RL, Lilienthal JL Jr, Proemmel DD, et al: On the

determination of the physiologically effective pressures of oxygen and carbon dioxide in alveolar air. Am J Physiol 147:191-198, 1946McNicol MW, Campbell EJM: Severity of respiratory failure: arterial blood gases in untreated patients. Lancet 1:336-338, 1965Begin 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, 1977Suwa K, Geffin B, Pontoppidan H, et al: A nomogram for

deadspace requirement during prolonged artificial ventilation.

Anesthesiology 29:1206-1210, 1968

$$\backslash begin\{align\}$$

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{align}

p_A \ce{O2} = \frac{p_E \ce{O2} - p_i \ce{O2} \frac{V_D}{V_T}}{1- \frac{V_D}{V_T}}

{{chem2|p_{A}O2}}, {{chem2|p_{E}O2}}, and {{chem2|p_{i}O2}} 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.Fenn WO, Rahn H, Otis AB: A theoretical study of the composition of alveolar air at altitude. Am J Physiol 146:637-653, 1946

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})}

== $$$$

\frac{V_D}{V_T} = \frac{p_A \ce{CO2} - p_E \ce{CO2} }{p_A\ce{CO2} }

Intuitive Explanation ==

As 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.

Firstly, the partial pressure of inhaled oxygen is simply the fraction of inhaled oxygen multiplied by the atmospheric pressure $F\_I\backslash ce\{O2\}*P\_\backslash ce\{ATM\}$. Once oxygen enters the airways, we must account for the partial pressure of water vapor which is assumed to reach 100% saturation, hence $F\_I\backslash ce\{O2\}(P\_\backslash ce\{ATM\}\; -\; p\backslash ce\{H2O\})$. Once the humidified atmospheric air reaches the alveoli, gas exchange takes place so we need to consider the amount of O2 that enters the blood and CO2 that leaves the blood. Conveniently, the arterial blood $p\_a\backslash ce\{CO2\}$ equals the alveolar blood $p\_A\backslash ce\{CO2\}$ and so this is a value we know. It would also be convenient if the same number of CO2 and O2 molecules were exchanged, in which case the alveolar gas equation would simply be $p\_A\backslash ce\{O2\}\; \backslash approx\; F\_I\backslash ce\{O2\}(P\_\backslash ce\{ATM\}\; -\; p\backslash ce\{H2O\})\; -\; p\_a\backslash ce\{CO2\}$. However in reality the number of CO2 molecules exchanged differs slightly from the number of O2 molecules, to correct for this the respiratory exchange ratio is used which is the ratio of CO2 produced by the body to O2 consumed by the body. Hence the alveolar gas equation becomes:

p_A\ce{O2} \approx F_I\ce{O2}(P_\ce{ATM} - p\ce{H2O}) - \frac{p_a\ce{CO2}} \ce{RER}

• Pulmonary gas pressures

{{reflist}}

• [http://vam.anest.ufl.edu/simulations/alveolargasequation.php Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)]
• [https://web.archive.org/web/20070418215127/http://www.surgery.ucsf.edu/eastbaytrauma/Protocols/Formulas%20pages/formulasaalvgasequation.htm Formula at ucsf.edu]
• [https://academic.oup.com/bjaed/article-pdf/4/1/24/1021798/mkh008.pdf S. Cruickshank, N. Hirschauer: The alveolar gas equation in Continuing Education in Anaesthesia, Critical Care & Pain, Volume 4 Number 1 2004]
• [http://www.medfixation.com/alveolar-gas-equation-pao2/ Online Alveolar Gas Equation and iPhone application] by Medfixation.
• [https://www.vcalc.com/wiki/vCalc/Alveolar+gas+equation A computationally functional Alveolar Gas Equation by vCalc.]

{{Respiratory physiology}}

{{DEFAULTSORT:Alveolar Gas Equation}}

Category:Respiratory physiology