Study of Unrelated Cord Blood Transplantation Using Tacrolimus and Sirolimus

Inclusion Criteria: Patients with hematologic malignancies for whom allogeneic stem cell transplantation is deemed clinically appropriate Non-Hodgkin's lymphoma, or Hodgkin's lymphoma: in Complete Remission >2 (second complete remission, third complete remission, etc) or in partial remission Multiple myeloma: relapsed Chronic lymphocytic leukemia, Rai stage III or IV, or lymphocyte doubling time of 6 months, or stage I-II, having progressed after > 2 chemotherapy regimens, in partial remission. Acute myelogenous or lymphoblastic leukemia in second or subsequent remission or in first remission with adverse cytogenetic or antecedent hematologic disorder Chronic myelogenous leukemia in accelerated or second stable phase, or imatinib resistant and not eligible for an ablative transplant Myelodysplasia, previously treated or not eligible for ablative transplant Age 18-65 years. ECOG performance status of 0, 1, or 2. Lack of 6/6 or 5/6 HLA-matched related, 10/10 matched unrelated donor, or unrelated donor not available within the time frame necessary to perform a potentially curative stem cell transplant. Exclusion Criteria: Cardiac disease: symptomatic congestive heart failure or radionuclide ventriculogram (RVG) or echocardiogram determined left ventricular ejection fraction of < 40%, active angina pectoris, or uncontrolled hypertension. Pulmonary disease: severe chronic obstructive lung disease, or symptomatic restrictive lung disease, or corrected DLCO of < 50% of predicted. Renal disease: serum creatinine > 2.0 mg/dl. Hepatic disease: serum bilirubin > 2.0 mg/dl (except in the case of Gilbert's syndrome or hemolytic anemia in which the bilirubin can be elevated greater than 2.0mg/dl), SGOT or SGPT > 3 x normal. Neurologic disease: symptomatic leukoencephalopathy, active central nervous system (CNS) malignancy or other neuropsychiatric abnormalities believed to preclude transplantation (previous CNS malignancy, presently in complete remission [CR] is not exclusion). HIV antibody. Uncontrolled infection. Pregnancy or breast feeding mother.