The researchers in this study are aiming to develop methods to measure the mass of insulin producing cells. A method (positron emission tomography, PET) previously used for the diagnosis of tumors of insulin producing cells may also be used to measure the amount of insulin producing cells in patients with type I diabetes. They plan to evaluate participants with type 1 diabetes that have undergone islet transplantation, to evaluate if PET can be used to measure the beta cell mass after islet transplantation.