Papillary stenosis is a disturbance of the sphincter of Oddi, a muscular valve, that prevents the opening and release of bile or pancreatic fluids into the duodenum in response to food entering the duodenum. Papillary stenosis is a disturbance of the sphincter of Oddi, a muscular valve, that prevents the opening and release of bile or pancreatic fluids into the duodenum in response to food entering the duodenum.