The infundibulum describes the portion of the hair shaft that extends from the sebaceous gland up toward the opening of the skin. It is lined by epithelium and can be the source for skin regeneration in cases in which the skin is partially lost like in laser skin resurfacing. The infundibulum and the isthmus immediately below it (See Isthmus) constitute the upper portion of the hair shaft which is considered the permanent part of the hair shaft that does not change during the hair cycle.
See:
Hair Anatomy