Intra-Osseous Co-Transplant of UCB and hMSC

Inclusion Criteria:

* Patients must have one of the following malignancies:

  * Acute myelogenous leukemia (AML): high-risk AML including:

    * Antecedent hematological disease (e.g., myelodysplasia \[MDS\])
    * Treatment-related leukemia
    * Complete remission (first complete remission \[CR1\]) with poor-risk cytogenetics or molecular markers (e.g. fms-related tyrosine kinase 3 \[Flt 3\] mutation, 11q23, del 5, del 7, complex cytogenetics)
    * Second complete remission (CR2) or third complete remission (CR3)
    * Induction failure or first relapse with either

      * ≤ 10% blasts in the marrow and/or
      * ≤ 5% blasts in the peripheral blood
  * Acute lymphoblastic leukemia (ALL)

    * High-risk CR1 including:
    * Poor-risk cytogenetics (e.g., Philadelphia chromosome t(9;22)or 11q23 rearrangements)
    * Presence of minimal disease by flow cytometry after 2 or more cycles of chemotherapy
    * No complete remission (CR) within 4 weeks of initial treatment
    * Induction failure
    * CR2 or CR3 with either:

      * ≤ 10% blasts in the marrow and/or
      * ≤ 5% blasts in the peripheral blood
  * Myelodysplastic syndromes (MDS), Intermediate-1 (INT-1), intermediate-2 (INT-2) or high Revised International Prognostic Scoring System (IPSS-R) score that has failed at least 1 first line therapy
  * Myelofibrosis (MF):

    * Intermediate-2 or high risk by Dynamic International Prognostic Scoring System (DIPSS)-plus
    * Monosomal karyotype
    * Presence of inv(3)/i(17q) abnormalities
    * Other unfavorable karyotype OR leukocytes ≥40 X 10\^9/L AND
    * Circulating blasts ≤ 9%
  * Relapsed or refractory lymphoid malignancies (including non-Hodgkin lymphoma, Hodgkin lymphoma and chronic lymphocytic leukemia) meeting the following criteria:

    * Disease status: stable disease, partial remission or 2nd and 3rd complete remission
  * Chronic myelogenous leukemia (CML) in second chronic phase after accelerated or blast crisis; blast crisis defined as:

    * Blast count ≥ 20% in the peripheral blood or bone marrow
    * Large foci of blasts on bone marrow
    * Presence of extra-medullary blastic infiltrate (myeloid sarcoma or chloroma)
  * Recipients of prior autologous or allogeneic transplant are eligible, as long as at least 3 months have passed since the transplant, and the patient fulfills other eligibility criteria
  * Eastern Cooperative Oncology Group (ECOG) performance status ≤2
  * Candidates for reduced intensity conditioning regimens
  * Patients who do not have HLA-matched (defined as matched in HLA A, B, C, and DRB1) related or unrelated donors, those who elect to undergo UCB even if they have a MRD or MUD, or patients who require a UCB either for emergency indications such as primary graft failure.
  * Cord Blood Units available through NMDP with the following minimal criteria:

    * HLA Match: 4/6 or better match (HLA A, B, DRB1)
    * Cell dose: Minimum of 2.0x107TNC/kg pre thaw
  * Concurrent therapy for extramedullary leukemia or central nervous system (CNS) lymphoma: concurrent therapy or prophylaxis for testicular leukemia, CNS leukemia, and CNS lymphoma including standard intrathecal chemotherapy and/or radiation therapy will be allowed as clinically indicated; such treatment may continue until the planned course is completed; subjects must be in CNS remission at the time of protocol enrollment if there is a history of CNS involvement
  * Subjects must have a back-up umbilical cord on the registry in addition to the umbilical cord being used in this study
  * Subjects must have the ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients with inadequate Organ Function as defined by:

  * Creatinine clearance \< 30 ml/min
  * Bilirubin ≥ 2 x institutional upper limit of normal
  * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≥ 2 x institutional upper limit of normal
  * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≥ 2 x institutional upper limit of normal
  * Corrected diffusing capacity of the lung for carbon monoxide (DLCOcorr) \< 40% normal
* Left ventricular ejection fraction \< 35%
* Patients with uncontrolled inter-current illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant or breastfeeding women are excluded from this study