The Alveolar Gas Equation

Derivation of the alveolar gas equation

The alveolar-gas equation (AGE) illustrates the relationship between the partial pressure of inspired O₂ (PIO₂) and the partial pressure of oxygen in the alveoli (PAO₂; Figure 1). The reason that there is a difference between inspired air and alveolar air is that the CO₂ the body produces takes up some "room" (partial pressure). If you're already lost, the gas basics page might be worth a visit.

Figure 1: The alveolar gas equation plots the relationship between the partial pressure of inhaled O₂ (PIO₂) and the partial pressure of O₂ in the alveoli (PAO₂). While PAO₂ is difficult to determine without specialised equipment, it can be estimated using this equation, based on an arterial blood gas analysis. If someone has a low PaO₂, just add what’s missing in terms of kPa of O₂: room air has a PIO₂ of 21 kPa; if the patient is 10 kPa low then add 10 kPa O₂ (+10%, at sea level).

This is the simplified version of the AGE and is more than adequate for our needs.

If you’re not mathematically minded, that equation reads pretty much as: “The partial pressure of O₂ in the alveoli (PAO₂) is whatever fraction of O₂ is being inhaled (FIO₂) multiplied by the atmospheric pressure (PB). Take away from that the amount of CO₂ being produced (and hence taking up partial pressure in the alveoli) by taking metabolism into account”. There’s an explanation of the respiratory exchange ratio here. Even if you don’t really understand the maths, if you can remember how to use this simple equation, you’ll find disturbances in respiratory physiology a lot easier to unpick.

Using the AGE in practice

Why is it useful to be able to calculate PAO₂? Because PAO₂ should be within a kPa or two of PaO₂ if the lungs are doing their job properly. You generally perform an arterial blood gas analysis when you should be thinking about the PAO₂-PaO₂ difference (O₂ sats under 92%), and when you do the readout gives you all the information you need to do a quick AGE calculation. It looks like a bulky bit of algebra to carry around, but it’s rather simple around sea level, if someone is breathing room air:

So, in that example you’d expect a PaO₂ of at least 13-14 if the lungs are working. If that’s not what the arterial blood gas (ABG) analysis tells you, something is wrong. Note also, that if you don't have a good estimate of FIO₂ (and often you may not), then the AGE isn't much use.

An example: hypoventilation

Say a patient presents at A&E following a heroin overdose. Opioids like heroin cause respiratory depression (by inhibiting the central respiratory pattern generator), and this is a serious risk with such a patient. An ABG from such a patient might look a bit hypoxaemic and hypercapnic as CO₂ accumulates and insufficient breathing doesn’t bring enough O₂ into the alveoli to keep up with metabolic demand. An ABG might look something like this:

If we do a quick AGE calculation, we can establish whether the problem here is simple hypoventilation or something more serious:

So, the patient’s PaO₂ is close to the predicted PAO₂, based on metabolism and the degree of CO₂ accumulation. There’s nothing wrong with their lungs, they just need to breathe appropriately. You could intubate and ventilate them or give O₂; both would improve oxygenation. Only intubating them and increasingly ventilation would fix the quite serious hypercapnia though, so it’s the better option.

An example: asthma

Asthma is an obstructive disease where airflow is limited by bronchoconstriction, making it difficult to ventilate many of the alveoli. Bronchoconstriction tends to be patchy, so some regions of the lung are more affected than others. An asthmatic (like Emily) presenting with severe shortness of breath will be hypoxaemic and will probably give an ABG reading like this:

A quick AGE calculation shows that something more complicated than hypoventilation is going on here:

These lungs are not working well at all: the PAO₂-PaO₂ difference is greater than 10 kPa! The problem here isn't hypoventilation. In fact, the PaCO₂ reading tells us that hyperventilation is part of the complex pathophysiology going on here. See the case of Emily for more on this!