= Arterial oxygen partial pressure
{title2=$P_{\mathrm a O_2}$}
\b[Arterial oxygen partial pressure], $P_{\mathrm a O_2}$, is the oxygen tension assessed in an arterial <blood> sample: the oxygen <partial pressure> of a gas phase in equilibrium with that blood. It relates to dissolved <oxygen>, rather than measuring all oxygen bound to <hemoglobin>.<Oxygen partial pressure pO2 by Radiometer>[Definition of pO2]{ref} The arterial qualifier identifies the sampled circulation; a venous measurement answers a different sampling question.
A simple equilibrium model writes dissolved oxygen concentration as
$$
C_{\rm dissolved}=\alpha P_{\mathrm a O_2},
$$
where the solubility coefficient $\alpha$ depends on the specified fluid and temperature. For an original illustration, choose $\alpha=0.003$ mL O$_2$/(dL·mmHg). Pressures 100 and 200 mmHg then correspond to 0.30 and 0.60 mL/dL dissolved oxygen. Those stipulated model concentrations do not include the carrier-bound contribution.
<Oxygen saturation> instead describes occupied binding sites, and <arterial oxygen content> also depends on how much carrier is present. Two samples can therefore have the same $P_{\mathrm a O_2}$ while differing in <hemoglobin> concentration and total oxygen content. A pressure reading alone does not count the available binding sites or determine oxygen delivery by the <blood flow>.
<Blood gas analysis> supplies a sample-specific observation to interpret alongside the inspired gas and respiratory state. The measurement should identify the compartment, temperature convention and sampling conditions. An arterial result, an alveolar estimate and an <inspired oxygen fraction> are related steps in oxygen transport, not three names for the same quantity.
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