Alveolar Gas Equation

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.

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

$p_A\ce = F_I\ce(P_\ce - p\ce) - \frac \ce$

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

$p_A\ce \approx F_I\ce(P_\ce - p\ce) - \frac \ce$

where:

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

Doubling will double .

Other possible equations exist to calculate the alveolar air.

\begin
p_A \ce & = F_I \ce \left(PB - p\ce\right) - p_A \ce \left(F_I \ce + \frac\right) \\ pt & = p_I \ce - p_A \ce \left(F_I \ce + \frac\right) \\ pt & = p_I \ce - \frac\left(p_I \ce - p_E \ce\right) \\ pt & = \frac
\end

Abbreviated alveolar air equation

$p_A \ce = \frac$
, , 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.Fenn WO, Rahn H, Otis AB: A theoretical study of the composition of alveolar air at altitude. Am J Physiol 146:637-653, 1946

Respiratory quotient (R)

$R = \frac$

Physiologic dead space over tidal volume (VD/VT)

$\frac = \frac$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 $F_I\ce*P_\ce$. Once oxygen enters the airways, we must account for the partial pressure of water vapor which is assumed to reach 100% saturation, hence $F_I\ce(P_\ce - p\ce)$. 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 $p_a\ce$ equals the alveolar blood $p_A\ce$ 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 $p_A\ce \approx F_I\ce(P_\ce - p\ce) - p_a\ce$. 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:

$p_A\ce \approx F_I\ce(P_\ce - p\ce) - \frac \ce$

See also

* Pulmonary gas pressures

References

External links

Free interactive model of the simplified and complete versions of the alveolar gas equation (AGE)



S. Cruickshank, N. Hirschauer: ''The alveolar gas equation'' in Continuing Education in Anaesthesia, Critical Care & Pain, Volume 4 Number 1 2004Online Alveolar Gas Equation and iPhone application
by Medfixation.

A computationally functional Alveolar Gas Equation by vCalc.

{{DEFAULTSORT:Alveolar Gas Equation
Respiratory physiology