## The alveolar air equation

If we wish to determine the alveolar concentration of a gas X, it is clear that:

alveolar concentrationX = FiX   -   uptakeX/ A
In other words, the final alveolar concentration depends on the inspired concentration less the change in concentration due to removal of the gas. As the alveolar ventilation ( A) increases, so will the change in concentration due to removal decrease, because more of the gas is being provided in the inhaled air. Similarly, if a gas (such as CO2) is being added, the above version of the alveolar air equation will allow us to calculate the alveolar concentration, given inspired concentration, output of the gas, and A. (We must of course change the sign to "+" as the amount will be greater than the inspired concentration).

1. An alternative, convenient but inaccurate way of estimating PAO2 is to assume that the amount of oxygen absorbed is almost the same as the amount of CO2 produced! If we do this, then we can estimate that:

PAO2    ~    PiO2 - PACO2

2. Using the knowledge that carbon dioxide rapidly diffuses across the membranes of the alveolus into the blood, we can say that
PAO2    ~    PiO2 - PaCO2

In other words, we can substitute arterial PCO2 (PaCO2) for the more-difficult-to-measure PACO2, without much loss of accuracy. This is more than a trifle inaccurate, as in most people the ratio of CO2 production to oxygen consumption (respiratory quotient or RQ) is about 0.8 to one. We can compensate for this by:

3.      PAO2    ~    PiO2 - PaCO2 / RQ

4. This is still not quite right, because the volume of inspired gas will also change if the RQ is not one. We can compensate for this by:

PAO2    ~    PiO2 - PaCO2 / RQ * (1 - FiO2(1-RQ) )