This pilot research study is to investigate the safety and effectiveness of stem cell transplantation to treat blood-related (hematopoietic) cancers, using stem cells collected from two different, umbilical cord blood donors. Subjects in this study are receiving a stem cell transplant because other treatments have failed or their disease is unlikely to respond to other treatment options.

Blood-related cancers can be treated and sometimes cured with very high doses of chemotherapy and radiation therapy, given to kill the cancer cells; however, these treatments can prove unsuccessful and can harm normal cells in the bone marrow or a patient's disease may be unlikely to respond to these treatment options.

Hematopoietic stem cells transplantation (HSCT) is a potential cure, but opportunities to perform HSCT are limited by donor availability. Only 20-30% of patients may have matched family donors. In some cases, a mismatched family donor may be suitable. For patients needing a transplant who do not have a suitably matched family donor, blood stem cells from matched unrelated donors can be used. The length of time required to identify a matched unrelated donor presents another obstacle for patients waiting to receive an HSCT.

Blood stem cells are found in umbilical cord blood (UCB), which is blood left over in the placenta (afterbirth) after a baby is born. Usually this blood is discarded with the placenta, but over the past 15 years, we have learned how to collect and freeze cord blood cells to be used for transplants at a later time. A cord blood unit is the cord blood cells collected and stored from a single placenta. More than 6,500 umbilical cord blood stem cell transplants have been done worldwide, mostly in children with leukemia. One important factor affecting the success of a cord blood transplant is the cell dose (number of stem cells in the cord blood unit / recipient's weight). Patients who receive a high cell dose (> 2.5 x 107 cells/kilogram) have better marrow recovery and a higher rate of survival than those who receive a lower cell dose.

In an attempt to make UCB transplantation possible for bigger children, adolescents and adults, researchers have tried giving two cord blood units on the same day for their transplant, one after the other. The data from more than 150 "double cord blood" transplants in adults suggest that the "double cord blood" transplants may allow bone marrow recovery and survival in patients who do not have a single cord blood unit with enough cells for successful transplantation.

This is a pilot study to research the safety and effectiveness of using two UCB units in adult and pediatric UCB transplantation when combined with a conditioning regimen called Flu/Bu4/TLI (consisting of fludarabine, busulfan and total lymphoid irradiation).

Inclusion Criteria:

• The candidate must have an incurable hematological malignancy or non-malignant hematological disorder and be eligible for transplant by the University of Michigan program.
• The candidate must have a life expectancy of less than one year without transplantation.
• The candidate must have two partially HLA-matched UCB (cord blood) units.Units must be HLA-matched minimally at 4 of 6 HLA-A and B (at intermediate resolution by molecular typing) and DRB1 (at high resolution by molecular typing) loci. Units must be HLA-matched at 3 of 6 HLA- A, B, DRB1 loci with each other (using same resolution of molecular typing as indicated above).
• The candidate must have access to two appropriately HLA-matched units that are available such that one unit delivers a pre-cryopreserved nucleated cell dose of at least 2.5 x 107 per kilogram and the second unit at least 2.0 x 107 per kilogram.

Exclusion Criteria:

• The candidate is an adult or pediatric patient who has a suitable related or unrelated donor available for transplant. Suitable donors include 8/8 (HLA-A,B,C and DR, with all loci high-resolution typing) or 7/8 related or unrelated donor available within 42 days of search initiation.
• The candidate has a Karnofsky (Adult) or Lansky (Pediatrics) performance status of < 70% at the time of admission for HSCT.
• The candidate is a patient with evidence of HIV infection.
• The candidate is a patient with active bacterial, fungal or viral infection not responding to treatment. Non-response to treatment is determined by body temperature, blood culture results, and radiographic findings as applicable.
• The candidate is pregnant.
• The candidate has any medical comorbidities/conditions that, in the opinion of the transplant team, would keep the patient from complying with the needs of the protocol and/or would markedly increase the morbidity and mortality from the procedure.
• The candidate has any conditions, in the opinion of the transplant team, such as substance abuse, or severe personality disorder that would keep the patient from complying with the needs of the protocol and would markedly increase the morbidity and mortality from the procedure.