The anterior pontomesencephalic vein, made up of the anterior mesencephalic and anterior pontine veins, makes up a portion of the longitudinal venous system running on the anterior surface of the brainstem, extending from the mesencephalon to the cervical spinal cord.
It is not a term of the terminologia anatomica, but is commonly used and composing the anterior longitudinal group.
Rhoton calls the anterior pontomesencephalic vein the “Medial anterior pontomesencephalic vein”. The anterior medullary vein is named “medial anterior medullary vein”. Rhoton’s terminology is important in recognising that the anterior group is sometimes made up of “Lateral anterior pontomesencephalic vein” and “lateral anterior medullary vein” — reflecting the fact that these veins often don’t run exactly in midline, and may even be paired on the anterior surface.
In terminologia anatomica, veins of brainstem are subdivised in pontomesencephalic vein (no reference to anterior position), pontine veins and veins of medulla oblongata
Source : neuroangio.org