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.
The equation relies on the following assumptions:
If is small, or more specifically if then the equation can be simplified to:
where:
Sample Values given for air at sea level at 37 ðC.
Doubling will double .
Other possible equations exist to calculate the alveolar air.
, , 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.
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 . Once oxygen enters the airways, we must account for the partial pressure of water vapor which is assumed to reach 100% saturation, hence . Once the humidified atmospheric air reaches the alveoli, gas exchange takes place so we need to consider the amount of <chem> O2 </chem> that enters the blood and <chem> CO2 </chem> that leaves the blood. Conveniently, the arterial blood equals the alveolar blood and so this is a value we know. It would also be convenient if the same number of <chem> CO2 </chem> and <chem> O2 </chem> molecules were exchanged, in which case the alveolar gas equation would simply be . However in reality the number of <chem> CO2 </chem> molecules exchanged differs slightly from the number of <chem> O2 </chem> molecules, according to the respiratory exchange ratio. Hence the alveolar gas equation becomes: