In a statement released Wednesday afternoon, the clinic said it would continue that effort. At that time there were no signs of rejection. However, several possibilities are to fail, including rejection by the patient’s immune system, infection or a problem with the veins and arteries that were connected to the uterus to provide it with blood flow. Doctors at the University of Gothenburg in Sweden have performed nine uterus transplants, resulting in five births. Only two operations failed. Three other medical centers in the United States are also planning to perform uterus transplants on an experimental basis: Baylor University Medical Center at Dallas, Brigham and Women’s Hospital in Boston and the University of Nebraska Medical Center in Omaha.