= Venous oxygen content
{title2=$C_v$}
\b[Venous oxygen content] is the amount of oxygen per specified volume of blood sampled from a venous site. The site matters: a local tissue outflow, a <coronary sinus> mixture and a more widely mixed return need not have the same value. Venous describes a circulation route; the <pulmonary vein> carries blood returning from the lungs after oxygen uptake there.<Anatomy and Physiology 2e by J. Gordon Betts and others>[Section 19.1, Chambers and Circulation through the Heart]{ref}
For a matched steady tissue balance,
$$
C_v=C_a-\frac{\dot V_{\mathrm O_2}}{Q}.
$$
A chosen inflow content $C_a=0.20\,\mathrm{mL\ O_2\,mL^{-1}}$, flow $250\,\mathrm{mL\,min^{-1}}$ and uptake $30\,\mathrm{mL\ O_2\,min^{-1}}$ imply $C_v=0.08$. The value depends on uptake relative to flow, not simply on whether the sample is called venous.
Mixing obeys an oxygen-amount balance. For streams with compatible content definitions and negligible exchange during mixing,
$$
C_{v,\rm mix}=\frac{\sum_jQ_jC_{v,j}}{\sum_jQ_j}.
$$
In an original example, flows $100$ and $50\,\mathrm{mL\,min^{-1}}$ have contents $0.05$ and $0.20\,\mathrm{mL\ O_2\,mL^{-1}}$. Their mixture content is $0.10$, not the unweighted mean $0.125$. A <mixed venous oxygen content> is therefore defined by the contributing blood pools and their flows.
Like <arterial oxygen content>, venous content includes oxygen bound to <hemoglobin> and dissolved oxygen. A saturation number alone is not the same amount-per-volume quantity. The primary whole-blood oximeter study measured carrier concentration and saturation separately, illustrating the need to distinguish the inputs to a content calculation.<An oximeter for measuring hemoglobin concentration and oxygen content by A. P. Shepherd and others>[Abstract, separate hemoglobin and saturation measurements]{ref}
The <arteriovenous oxygen content difference> should pair compatible territories and times before it is used to estimate <coronary oxygen uptake>. Comparing an arterial input with an unrelated venous mixture can combine different regions into a number that represents neither intended tissue balance.
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