= Hepatic vein
A \b[<hepatic vein>] carries blood out of the <liver> toward the <inferior vena cava>. It is an outflow vessel, whereas the <portal vein> and <hepatic artery> supply the liver through distinct routes.<Anatomy and Physiology 2e by J. Gordon Betts and others>[§20.5, The Inferior Vena Cava and Hepatic Portal System]{ref} The shared word hepatic locates the organ; it does not make these vessels interchangeable.
The two-input arrangement matters to a substance balance. In an original steady-flow model, let portal and arterial inflows be $Q_p,Q_a$, with concentrations $C_p,C_a$, and let hepatic outflow concentration be $C_h$. With negligible fluid accumulation, $Q_h=Q_p+Q_a$. Net production of the substance by the liver is
$$
\dot M_{\mathrm{net}}=(Q_p+Q_a)C_h-Q_pC_p-Q_aC_a,
$$
where positive values denote net release and negative values net removal. The calculation assumes matched sampling, a common concentration basis and negligible storage change over the measurement interval.
For stipulated $Q_p=1.00$ L/min, $Q_a=0.25$ L/min, $C_p=2.00$ mmol/L, $C_a=1.00$ mmol/L and $C_h=1.40$ mmol/L,
$$
\dot M_{\mathrm{net}}=1.25(1.40)-1.00(2.00)-0.25(1.00)
=-0.50\,\mathrm{mmol\,min^{-1}}.
$$
The liver removes the modeled substance overall even though the hepatic-vein concentration exceeds the arterial concentration. Comparing the outflow with only one of two inputs would give a misleading interpretation.
A hepatic-vein measurement thus describes an organ-specific outflow. It need not equal <mixed venous oxygen content> or the composition of every region of the liver. Identifying the drainage territory and allowing for unequal flow among regions are part of interpreting a sample. Anatomy defines the paths; <conservation of mass> defines how the transported quantities must combine.
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