# Question 3.1

A 49-year-old female, with a history of pulmonary vasculitis is found collapsed in the ward with shallow breathing and a GCS of 6.

An initial arterial blood gas on room air (FiO2 0.21) reveals:

 Parameter Result Normal Range Barometric pressure 760 mmHg (100 kPa) pH 7.13* PCO2 80 mmHg (10.5 kPa)* 35– 45 (4.6 – 6.0) PO2 38 mmHg (5.0 kPa) Bicarbonate 26 mmol/L 22 – 27 Base Excess +2 mmol/L -2 – +2

What is the cause of the hypoxia?

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.

## References

Here is an intersting digression about the alveolar gas equation:

Cruickshank, Steven, and Nicola Hirschauer. "The alveolar gas equation."Continuing Education in Anaesthesia, Critical Care & Pain 4.1 (2004): 24-27.