What use is the alveolar gas equation?
None! Just kidding; it’s useful for evaluating hypoxia because it can easily rule out hypoventilation as the cause.
For background, the alveolar gas equation is a way of calculating what the level of oxygen is in the alveoli, given the atmospheric pressure (pATM, usually 760mmHg), the fraction of inspired oxygen (FIO2, which is 21% for room air and increases if they’re on supplemental oxygen), the pressure of water vapour in the lungs (pH2O, usually 47mmHg), the arterial CO2 (paCO2, taken from your ABG), and the respiratory exchange ratio (RER, the amount of oxygen exchanged for carbon dioxide in one breath, usually 0.8). The equation is:
pAO2 = FIO2(PATM – pH2O) – paCO2(1 – FIO2[1 – RER]) / RER
The use of the alveolar gas equation is in the A-a gradient, the difference between what the alveolar gas equation says your alveolar oxygen is and what your ABG says your arterial oxygen is. If there’s lots of oxygen getting to the alveoli, then you should have lots of oxygen in the blood. A normal A-a gradient is approximately (age / 4) + 4, so it should be about 9 for a healthy young 20-year old and 24 for an 80-year old.
How is the A-a gradient useful? Well, there are only two things that cause hypoxia with a normal A-a gradient: hypoventilation (not moving enough air), and decreased PiO2 (that is, high altitude). Since I’m rarely doing my ABGs on a mountaintop, the A-a gradient is basically a quick and easy way to rule out hypoventilation as the cause of their hypoxia.
Read more: Adequacy of Ventilation in Chapter 306e: Disturbances in Respiratory Function, Harrison’s Principles of Internal Medicine 19e.