biliary. pertaining to the bile, to the bile ducts, or to the gallbladder. biliary catheter (biliary decompression catheter) a catheter inserted via a skin incision through the liver and common bile duct into the duodenum.Its purpose is to provide for drainage of bile past obstructed bile ducts and into the small intestine, where it aids digestion. Called also transhepatic biliary catheter.iliary. pertaining to the bile, to the bile ducts, or to the gallbladder. See also bile duct. biliary excretion. removal in the bile of substances including drugs, toxins, hormones or pigments, or their breakdown products. These are delivered to the duodenum and removed in the feces.