In patients with Type 1 Diabetes Mellitus, hypoglycemia (low blood sugar) is the rate-limiting step to achieve glucose level control. As a result, understanding the body's responses (including the brain's response) to hypoglycemia is essential for the effective treatment of patients with T1DM. The purpose of this research is to determine whether pancreatic islet cell allotransplantation to restore normoglycemia (normal blood glucose levels) in Type 1 Diabetic patients with hypoglycemia unawareness alters brain fuel utilization and cognitive performance under euglycemic (blood sugar at 100 mg/dl) and hypoglycemic (blood sugar at 50 mg/dl) conditions. Three groups of subjects will be studied: (1) T1DM patients with a history of severe hypoglycemia and/or hypoglycemia unawareness who have been selected for pancreatic islet cell allotransplantation; (2) T1DM patients who also have a history of severe hypoglycemia and/or hypoglycemia unawareness; (3) nondiabetic subjects. All subjects will undergo identical testing including: (a) screening; (b) neuropsychological testing; (c) and functional magnetic resonance imaging (fMRI) during euglycemic and hypoglycemic conditions.