What's in A-a Gradient?

Sam Nunn – 24 August 2024

bsod_abg

So, you’ve just collected an ABG.

Now the machine wants to know the patient’s FiO2. They had a non-rebreather on… 50% seems right. Right?

You plug in the number and the machine goes about its business. Finally, moment to think…

Why did it ask for the FiO2?

The Case of Mr Puff 📋

Imagine the machine reported a PaO2 of 68 mmHg. The normal range is 60-100 mmHg, so that seems fine. No concerns at all, right?

❌ WRONG ❌

Their PaO2 is just in the normal range despite getting more than double the normal concentration of oxygen in the atmosphere.

Forget the “normal” PaO2. Something is very wrong in their lungs.

Oxygen gets into the arteries by diffusing across the alveolar membrane, driven by a pressure gradient. A high partial pressure of alveolar oxygen should produce a similarly high partial pressure in the arterial blood.

Alveolus diffusing

When that doesn’t happen, we call it an A-a gradient. A very high A-a gradient means the lungs are not absorbing oxygen properly. That might be due to:

If you want to know more about hypoxia and its causes, check out this article.

Quantify

So, how do we measure the A-a gradient?

Arterial O2 is easy: just use the ABG machine. Alveolar O2 isn’t directly measured, but we can guesstimate it using the alveolar gas equation:

\[ P_{A_{O_{2}}}= F_{IO_{2}} \times (P_{ATM} - P_{H_{2}O}) - \frac{P_{aCO_{2}}}{RQ} \]

It’s not the most approachable specimen. Rather than taking out a pad and pencil for every gas, most of the time we can make these assumptions:

We can plug these assumptions into our equation like so:

\[ P_{A_{O_{2}}}= F_{IO_{2}} \times (760mmHg - 47mmHg) - \frac{40}{0.8} \]

Which yields a much simpler, if similarly impractical:

\[ P_{A_{O_{2}}}= F_{IO_{2}} \times 713 - 50 \]

Which is conventionally simplified to this rule of thumb:

\[ P_{A_{O_{2}}}= F_{IO_{2}} (\%) \times 5 \]

The Case of Mr Puff 📋

Let’s go back to our example. That PaO2 seems low, but how low?

We can work out his predicted PaO2 using the formula we just learned:

\[ P_{A_{O_{2}}}= F_{IO_{2}} (\%) \times 5 \] \[ P_{A_{O_{2}}}= 50 \times 5 \] \[ P_{A_{O_{2}}}= 250\ mmHg \]

If his actual PaO2 was 68 mmHg and his predicted PaO2 was 250 mmHg, that means there is an A-a gradient of 182 mmHg.

Such a large gradient is always pathological, but smaller gradients can be normal. Lung function deteriorates with age so we can reasonably expect to find a small A-a gradient in the elderly. One commonly-used formula is:

\[ Acceptable\ A–a\ gradient = \frac{Age}{5} + 5 \]

The Case of Mr Puff 📋

Mr Puff is 65 years old. Let’s work out his normal A-a gradient using our new formula:

\[ Acceptable\ A–a\ gradient = \frac{Age}{5} + 5 \] \[ = \frac{65}{5} + 5 \] \[ = 18\ mmHg \]

That means his current A-a gradient is more than ten times the upper limit of normal for his age.

Practical Implications

You can’t trust a normal (or high) PaO2 in isolation. You must know the FiO2 when the gas was taken and you must use that information to identify a raised A-a gradient when you see one.

If you’d like to play around with ABGs in a needle-free environment, check out the Gas Notes ABG Machine now:

  1. The human respiratory tract is remarkably effective at humidification, so alveolar PH2O is quite consistently 47 mmHg.