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.