= Inferior vena cava
The \b[<inferior vena cava>] is a major <vein> returning blood from most regions below the <diaphragm> to the <right atrium>. It forms from the joining <common iliac veins> and receives abdominal tributaries, including the <hepatic veins>.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§20.5, The Inferior Vena Cava; Veins Draining the Lower Limbs]{ref} Inferior describes its anatomical relationship to the upper return channel, not a ranking of its physiological importance.
The <inferior vena cava> carries a mixture of regional returns. The <hepatic vein> connection brings blood that has passed through the liver; other tributaries represent other tissues. The composition at one location can therefore depend on which tributaries have joined and how their streams mix. Sampling a large return vessel is not automatically the same as measuring fully <mixed venous oxygen content>.
For an original mixing example, suppose two tributary groups deliver 2 and 1 litres per minute with oxygen contents 0.12 and $0.06\,\mathrm{mL\ O_2\,mL^{-1}}$. After complete mixing without oxygen exchange,
$$
C_{\mathrm{IVC}}=\frac{2(0.12)+1(0.06)}{3}=0.10\,\mathrm{mL\ O_2\,mL^{-1}}.
$$
An equal-weight average would give 0.09 and would ignore how much blood each group contributes. If a sampling location has not yet mixed the two streams, even the flow-weighted calculation need not describe a local sample.
The vessel also participates in venous storage and return under changing <pressure>. Its volume change obeys inflow minus outflow, so temporary changes in return need not imply that a tissue suddenly changed oxygen use. Anatomy identifies the contributing routes; <conservation of mass>, flow and adequate mixing determine how their transported substances combine.
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