The extrahepatic bile ducts consists of the right and left hepatic ducts the common hepatic duct the cystic duct and the common bile duct these structures are the system of the biliary channels
The common bile duct is about 7-11 cm in length and 5-10 mm in diameter the common bile duct enters the second part of the duodenum through a muscular structure called the sphincter of Oddi which consists of a thick coat of circular smooth muscle surrounds the common bile duct at the ampulla of vatar it is regulate flow of the bile and pancreatic juice into the duodenum and prevent the regurigitation of duodenal contents into the biliary channels and diverts bile into the gallbladder

The common bile duct divided into three thirds
 The upper third is the part above the duodenum
supraduodenal portion) which passes downward in the free edge of the hepatoduodenal ligament to the right of the hepatic artery and anterior to the portal vein
The middle third of the common bile duct  is the part present behind the duodenum (retroduodenal portion) which curves behind the first part of the duodenum and diverges laterally from the portal vein and the hepatic arteries
The lower third of the common bile duct is the part which present behind the pancreatic head( pancreatic portion ) which curves behind the head of pancreas in a groove or traverses through it and enters the second part of the duodenum where the pancreatic duct frequently joint it
The common bile duct  runs obliquely downward within the wall of the duodenum for 1 to 2 cm before opening on a papilla of the mucous membrane called ampulla of vater which lies about 10 cm distal to the pylorus of the stomach
 The union of the common bile duct and the main pancreatic duct may take one of these features most of the people these ducts unite outside the duodenal wall as a single duct in some people they join within the duodenal wall and have or no common duct in rare people they may exit by separate opening into the duodenum
 The common hepatic duct is 1 to 4 cm in length and it is diameter about 4 mm  it is lies in the front of the portal vein and to the right of the hepatic artery
 The common hepatic formed by union of right and left hepatic duct close to their emergence from the liver the left hepatic duct is longer than the right
The common hepatic duct is joined at an acute angle by the cystic duct to form the common bile duct
The length of cystic duct variable it may be to short or absent and may join the hepatic duct in high position or long and runs parallel  behind or spiral to the main hepatic duct before joining it
These variation of cystic duct very important to be in mind during removal of gallbladder by cholecystecomy operation
 These variation such as the cystic duct may joined the common hepatic duct at low level  or it may become adherent to the common hepatic duct
Or may joined common hepatic duct at high level or the cystic duct may open into the right hepatic duct instead of common hepatic duct the cystic duct may be long that joined the common hepatic duct behind the duodenum
Or it may cross behind the common hepatic duct and joined it anteriorly the cystic duct may be absent  or it may courses anterior to the common hepatic duct and joint it posteriorly

the segment of the cystic duct adjacent to the gallbladder neck have mucosal folds called the spiral valves of Heister
 Blood supply
The arterial supply of the bile duct is derived from the gastroduodenal and the right hepatic arteries with major trunks running along the medial and lateral walls of the common bile duct referred to as 3 o`clock and 9 o`clock these arteries anastomose within the duct walls venous drainage following their arterial supply
Nerve supply
Same as gall bladder see here but the density of the nerve fibers and ganglia increase near the sphincter of Oddi

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