= Arteriovenous oxygen content difference
{title2=$C_a-C_v$}
The \b[arteriovenous oxygen content difference] is <arterial oxygen content> minus the <venous oxygen content> leaving the same tissue bed:
$$
\Delta C_{\mathrm O_2}=C_a-C_v.
$$
It measures <oxygen> removed per unit volume of <blood>. For the whole body, the venous term is <mixed venous oxygen content>; for <coronary oxygen uptake>, the arterial and venous sampling sites must represent the <coronary circulation>. Oxygen content includes both <hemoglobin>-bound and dissolved <oxygen>, so this quantity is not simply the difference between two <oxygen saturation> readings.<Hemoglobin by Radiometer>[Total hemoglobin species and oxygen-binding capacity]{ref}
If $C_a=20$ and $C_v=15$ mL/dL, then $\Delta C_{\mathrm O_2}=5$ mL/dL. With <blood flow> $Q=50$ dL/min, the <Fick principle> gives <oxygen consumption> $Q\Delta C_{\mathrm O_2}=250$ mL/min. The same content difference at half the <blood flow> gives half the oxygen transfer. Conversely, at fixed oxygen transfer, a fall in <blood flow> requires a larger content difference in the steady-state balance.
Subtraction also has a useful <measurement uncertainty> structure. If $u_a,u_v$ are the standard uncertainties of the two content measurements, then
$$
u_{\Delta C}^2=u_a^2+u_v^2-2\operatorname{Cov}(C_a,C_v).
$$
The <covariance> term accounts for shared errors.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[§§5.1–5.2, correlated input quantities]{ref} A common additive offset cancels in the difference, whereas a common multiplicative gain error scales the difference. Matched sampling and knowledge of shared <measurement calibration> errors can therefore matter as much as the repeatability of either measurement separately.
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