Clinical Ex Vivo Expansion of Human Umbilical Cord Blood Stem and Progenitor Cells

Inclusion Criteria: * Patients will be from the Department of Haematology, Singapore General Hospital, who have the diagnoses listed below and who meet the inclusion criteria. They have to be deemed suitable for trial by the respective attending doctor as well as a panel of at least three hematologists. Suitability will be reassessed by the Principal Investigator again 1. Patients aged 12 years to 60 years. 2. Patient has no currently available HLA-A, B, C, DRB1 and DQB1 matched related or unrelated donor. 3. Patient must have a hematologic malignancy requiring allogeneic haematopoietic stem cell transplantation as further defined below (from National Marrow Donor Program and American Society of Blood and Marrow Transplantation Guidelines) and as further agreed upon by a panel of at least three hematologists specializing in transplantation. * Acute myelogenous leukemia (AML): High-risk AML including: * Antecedent hematological disease (e.g., myelodysplasia (MDS)) * Treatment-related leukemia * Induction failure * 1st complete remission (CR1) with poor-risk cytogenetics or molecular markers (e.g. Flt 3 mutation, 11q23 etc) * 2nd complete remission (CR2) and beyond * Acute lymphoblastic leukemia (ALL) * CR1 up to age 35 * High-risk over age 35 including: * Poor-risk cytogenetics (e.g., Philadelphia chromosome t(9;22)or 11q23 rearrangements) * High white cell count (\> 30,000/mm3) at diagnosis * CNS or testicular leukemia * No CR within 4 weeks of initial treatment * Induction failure * CR2 and beyond * Myelodysplastic syndromes (MDS) * Intermediate-1 (INT-1), intermediate-2 (INT-2) or high IPSS score which includes: * \> 5% marrow blasts * Other than good risk cytogenetics (not 5q- or normal) * \> 1 lineage cytopenia * Chronic myelogenous leukemia (CML) * Disease progression * Accelerated phase * Blast crisis (myeloid or lymphoid) * Follicular lymphoma * Poor response to initial treatment * After second or subsequent relapse * Transformation to diffuse large B-cell lymphoma * Aggressive T-cell or B-Cell lymphoma * After second or subsequent relapse * No CR with initial treatment * Mantle Cell: After second or subsequent relapse * Hodgkin's lymphoma * No initial CR * After second or subsequent relapse * Multiple myeloma: Patients failing autologous transplantation with chromosome 13 abnormalities, first response lasting less than 6 months, or β-2 microglobulin \> 3 mg/L may be considered for this protocol after initial therapy. Exclusion Criteria: 1. Inadequate Organ Function as defined by: * Renal: Creatinine clearance \> 60ml/min * Hepatic: Bilirubin, AST/ALT \< 2x upper limit of normal * Pulmonary function: DLCOcorr \> 50% normal * Cardiac: left ventricular ejection fraction \> 45% 2. Karnofsky score (adults) \< 70% or Lansky score \< 50% (pediatrics)