A-a gradient

This is another classic formula.

• It is still used a lot, but new studies indicate that there may be other methods that work better.
• It predicts the degree of shunt by comparing the partial pressure of O2 in the (A) alveoli to that in the (a) artery.
• The difference between them gives us an idea how well the oxygen is moving from the alveoli to the arterial blood.
• The PaO2 is obtained from the ABG
• The PAO2 is obtained from the Alveolar Gas equation: (PAO2 - PaO2)
• Alveolar Gas equation:
• Daltons law says the total pressure of gases in a mixture is equal to the sum of the partial pressures of the constituent gases.
• 2 + 2 + 2 = 6 (easy enough?)
• Now work that backwards. If we know the total and all but one of the constituents, we can find the partial pressure of the last one.
• 6 - 2 - 2 = 2 (still easy.)
• We start with:
• the pressure of the inspired air (760 mm Hg at sea level),
• subtract water vapor pressure (47 mm Hg), and
• PaCO2 (value from your ABG).
• We also have to take into account how much oxygen was in the inhaled air, (FiO2) and a "respiratory quotient" ( 0.8 or if patient is on 100% FiO2, it's 1.0)
• Translated into the language of mathematics it looks like this:

PAO2 = ( 760 - 47 ) x FiO2 - PaCO2 /0.8 (or 1)

Normal A-a gradient is 20 in a health young person.

### a/A Ratio

• In this formula, the same values as A-a gradient are divided, rather than subtracted.

(PaO2 /PAO2)

### PaO2 / FiO2 Ratio or "P/F" Ratio

• Another much friendlier method ( because it doesn't use the alveolar gas equation) used to predict shunt.
• Just like the name says, PaO2 is divided by FiO2
• Normal is 286; lower indicates a shunt.

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