lactiferous ampulla
lactiferous sinus

However new research suggests that lactiferous sinus does not exist.

Lactiferous sinuses do not, in fact, exist.

Within the areola, the lactiferous duct were thought to dilate to form the lactiferous sinus in which supposedly milk accumulates between breastfeeding sessions.

The injection of coloured wax into milk duct openings at the nipple inflated those ducts, giving the impression that near the nipple they expand into milk storage sacs called lactiferous sinuses.