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 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

If is small, or more specifically if then the equation can be simplified to:
where:

Quantity	Description	Sample value
	The alveolar partial pressure of oxygen	107 mmHg
	The fraction of inspired gas that is oxygen.	0.21
	The prevailing atmospheric pressure	760 mmHg
	The saturated vapour pressure of water at body temperature and the prevailing atmospheric pressure	47 mmHg
	The arterial partial pressure of carbon dioxide	40 mmHg
	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.

Abbreviated alveolar air equation

,, 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.

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. 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 O2 that enters the blood and CO2 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 CO2 and O2 molecules were exchanged, in which case the alveolar gas equation would simply be. However in reality the number of CO2 molecules exchanged differs slightly from the number of O2 molecules, according to the respiratory exchange ratio. Hence the alveolar gas equation becomes: