Hepatic vein

A 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.^[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 iswhere 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,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.