The sphincter of Oddi is part of your digestive system. A sphincter is a circle of muscle. The sphincter of Oddi surrounds the end of the tubes (ducts) that connect the gallbladder, liver, and pancreas to the first part of the small intestine (duodenum). The sphincter opens to let digestive juices flow through the ducts from the gallbladder, liver, and pancreas into the small intestine. To prevent the juices from leaking back into the ducts, the sphincter squeezes shut.