The purpose of this study is to evaluate the effectiveness of giving stem cells from the umbilical cord blood of two newborn infants to patients with hematological cancers that are advanced or at high risk of relapse. Patients will first receive a combination of chemotherapy drugs (cyclophosphamide and fludarabine) and whole-body irradiation to further treat their cancer. The goal of the transplanted stem cells is to repopulate the patient’s bone marrow with healthy cells, and create a new donor immune system to protect against relapse.
However, a single donor cord blood transplant may not contain enough cells to ensure recovery of the patient’s bone marrow after chemotherapy. Therefore, in this study two cord blood collections will be used to increase the number of cord blood cells patients receive. This approach is called a “double unit” cord blood transplant. A previous study suggests double unit cord blood transplantation may be more effective than a single-cord transplant.