College Answer

Hypoventilation.

No reason to believe there is parenchymal disease / vasculitis as the A-a gradient is 13 mmHg. This fits with the clinical picture of coma, shallow breathing and hypercapnia

Discussion

This question, though it is a blood gas interprestation question, has been placed into the category of respiratory failure SAQs because there is no complex acid-base disorder to diagnose.

However, it relies on the candidate knowing the alveolar gas equation. Here it is:

PAO₂ = (0.21 x (760 - 47)) - (PaCO₂ x 1.25)

Essentially, at 760mmHg barometric pressure, there should be about 150mmHg occupied by oxygen and carbon dioxide in the alveolus- given that in the alveolus the water vapour pressure is 47mmHg, and FiO₂ remains 21%.

Thus, PAO₂ can be expressed as 150 - (PaCO₂ x 1.25)

Thus, if the PaCO₂ is 80, the O2 should be around 50.

Thus, if the PaO2 is 38, one might surmise that the A-a gradient is 12.

With a normal A-a radient, the only possible explanation for the hypoxia is hypoventilation. Identifying such situations is is almost the only effective use of the A-a gradient in critical care. As with other tension-based indices of oxygenation, this value gives little information about the oxygen content of the blood.