Umbilical Cord Blood Transplant With Added Sugar and Chemotherapy and Radiation Therapy in Treating Patients With Leukemia or Lymphoma

PRIMARY OBJECTIVES: I. To evaluate the safety and feasibility of transplantation of cord blood which is expanded in mesenchymal precursor cell (MPC) co-cultures then fucosylated with fucosyltransferase (FT)-VI and guanosine diphosphate (GDP) fucose prior to infusion in patients with hematologic malignancies following high-dose therapy. II. To evaluate the time to engraftment using expanded fucosylated cord blood. SECONDARY OBJECTIVES: I. To evaluate the rate and severity of graft versus host disease. II. To evaluate the rates of infectious complications. III. To evaluate the rates of disease-free and overall survival. Summary: All patients receive Busulfan as per standard of care. Busulfan test dose can be administered either as an outpatient prior to admission or as an inpatient on Day -10. Busulfan pharmacokinetics will be performed with the test dose and the first dose on Day -7 per standard of care. The doses of Days -6, -5, and -4 will be subsequently adjusted to target an AUC of 4,000 microMol.min-1. In the event that PK adjusting were not possible a dose of busulfan of 130 mg/m2 will be administered. GVHD PROPHYLAXIS: All patients receive mycofenolate mofetil IV over 2 hours or orally (PO) twice daily (BID) on days -3 with a taper beginning on day 100 in the absence of GVHD, tacrolimus IV or PO starting on day -2 for 6 months in the absence of GVHD, and filgrastim-sndz subcutaneously (SC) once daily (QD) starting on day 0 until white blood count begins to recover. After completion of study treatment, patients are followed up at months 1, 3, 6, and 12.