equilibrium - Measure of partial pressure on blood

Here is the issue of blood gases partial pressure.

On medical reports is common to see partial pressure of gas on blood, usually oxygen, but there is no gas in equilibrium with blood, so it is confusing. What they mean with partial pressure of a gas on blood is, according to this answer:

the partial pressure which would prevail in a gas phase in equilibrium with the liquid [blood] at the same temperature.

I suppose they use a partially filled vessel with blood and a manometer or something like that, but I would like to know the way they measure it.

Question

How do they measure $p(\mathrm{O}_2)$?

Answer

In principle you could measure it by getting a sample of blood and putting it in contact with gaseous O₂ at various pressures. Whatever external pressure of O₂ results in the amount of O₂ dissolved in the blood neither increasing nor decreasing would equal p(O₂) in the blood.

As for how it's actually measured, I believe the usual answer these days is spectroscopically. That is, you shine light through a sample of blood and look for the absorption at certain frequencies which are typical of hemoglobin with O₂ bound to it. The amount of absorption is proportional to the concentration of oxygenated hemoglobin, and your software has some internal chart that converts that to partial pressure.

As for why it's measured that way, in part it's probably just tradition, and medicine changes very slowly and conservatively, for obvious reasons (you're experimenting with health and life). In part, though, it may be that it directly relates to something important: the partial pressure of O₂ in the atmosphere, which is about 160 mmHg. That's the concentration of O₂ in the lungs. What fraction of that reaches the blood at various points in the circulation is a natural indicator of how well oxygen is being taken up, transported, and delivered. That is, you can directly relate this particular measure of O₂ concentration to the form of concentration usually used to describe a mixture of gases, in this case the air you breathe, which is the origin and destination of the blood gases.