The valves of Heister are spiral folds of mucous membrane in the wall of the cystic duct. Their function is unknown; it is believed that they prevent sudden distention of the cystic duct when pressure in the gallbladder or cystic duct rises.
Hartmann's pouch is a sacculation of the neck of the gallbladder; it is a common site for gallstones to lodge in this pouch, also known as the infundibulum of the gallbladder.1
February 2001. Arch Surg. 2001;136(2):146. doi:10.1001/archsurg.136.2.146