Unrelated Umbilical Cord Blood Transplantation Augmented With ALDHbr Umbilical Cord Blood Cells

The main purpose of this investigational (not approved by the FDA) Phase I research is to test whether transplantation of umbilical cord blood cells can be safely supplemented with a transfusion of a portion of these cells that have been sorted (collected from a special machine called a cell sorter) and then either infused a few hours after the standard transplant or for some patients grown in a special system in the laboratory prior to the transplant, designed to increase the number of stem cells transplanted. This system is currently in the early phases of testing.