ApoGraft for the Prevention of Acute Graft Versus Host Disease in Haploidentical Hematopoietic Cell Transplant Recipients

Recipient Inclusion Criteria: * Adult male or female subjects, 18-70 years of age. * Availability of an HLA-haploidentical-HSCT related donor with a minimum match of 5/10 at the HLA A, B, C, DR and DQ loci. * Hematologic malignancy in remission or controlled as below: * Acute myelogenous leukemia (AML) and Acute lymphoblastic leukemia (ALL) in 1st or subsequent complete remission (CR) * Non-Hodgkin's Lymphoma (NHL) in CR by CT or PET/CT * Hodgkin's disease (HD) in 1st or subsequent CR by CT or PET/CT * Intermediate or high risk Myelodysplastic syndrome (MDS) (IPSS-R criteria) * ECOG performance status score 0-1 at time of the screening visit * Cardiac left ventricular ejection fraction ≥ 40% in adults within 90 days of start of lymphodepleting chemotherapy * Pulmonary function test with DLCO, FEV1 and FVC of ≥ 50% within 90 days of start of lymphodepleting chemotherapy. * Oxygen saturation ≥ 90% on room air at screening visit. * Subjects must have adequate organ function as defined below within 2 weeks of Day 0: * AST (SGOT)/ALT (SGPT) ≤ 2.5 × upper limit of normal (ULN). * Serum bilirubin \<3 mg/dL. * Estimated creatinine clearance \>50 * If female of childbearing potential, agree to use an acceptable method of birth control or be surgically sterile, and have a negative pregnancy test. * Available HLA-haploidentical donor * Must be able to receive GvHD prophylaxis with tacrolimus, mycophenolate mofetil, and cyclophosphamide * Able to understand and willing to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Subjects requiring a guardian to sign informed consent will not be included. Recipient Exclusion Criteria: * If a matched related donor is available and able to donate * Participation in an interventional investigational trial within 30 days of Day 0. * Subject suffering from any active or ongoing malignancy (other than the reason for HSCT) in the last 5 years prior to baseline; excluding basal cell carcinoma, in situ malignancy, low-risk prostate cancer, cervix cancer after curative therapy. * Uncontrolled infections (bacterial, viral or fungal including sepsis, pneumonia with hypoxemia, persistent bacteremia, or meningitis within two weeks of the screening visit). * Current known active acute or chronic infection with HBV or HCV. * Known human immunodeficiency virus (HIV) infection or AIDS. * Subjects with severe or symptomatic restrictive or obstructive lung disease or respiratory failure requiring ventilator support. * Subjects with other concurrent severe and/or uncontrolled medical condition, which could compromise participation in the study (i.e. active infection, uncontrolled diabetes, uncontrolled hypertension, congestive cardiac failure, ventricular arrhythmias, and chronic liver or renal disease) * History of any of the following within 12 months prior to screening: Uncontrolled congestive heart failure (New York Heart Association Classification 3 or 4), unstable angina, myocardial infarction, cerebrovascular accident, coronary/peripheral artery bypass graft surgery, transient ischemic attack, or pulmonary embolism. * Any form of substance abuse (including drug or alcohol abuse), psychiatric disorder or any chronic condition susceptible, in the opinion of the investigator, of interfering with the conduct of the study. * Organ allograft transplant recipient. * If female of childbearing potential, agree to use an acceptable method of birth control or be surgically sterile, and have a negative pregnancy test. * Pregnancy or lactation * Must not have undergone a prior allogeneic donor (related, unrelated, or cord) transplant. Prior autologous transplant is not exclusionary. * Presence of donor-specific anti-HLA antibodies. * Must not receive antithymocyte globulin as part of pre-transplant conditioning regimen, plan to receive a T-cell depleted product, or have planned donor leukocyte infusions post-transplant. * Immunosuppressive doses of steroids. Subjects with steroids for adrenal insufficiency will not be excluded. Donor Inclusion Criteria * Adult male or female subjects, 18-65 years of age. * Donor criteria according to standard NMDP criteria for donor selection. * Blood-related family member (sibling (full or half), offspring, parent, cousin, niece or nephew, aunt or uncle, or grandparent). * HLA-haploidentical donor/recipient match by at least low-resolution typing per institutional standards. * In the investigator's opinion, donor is in general good health, and medically able to tolerate leukapheresis required for harvesting HSC. * Fit to receive G-CSF and donate peripheral blood stem cells. * Able to sign written informed consent including consent for 2nd donation in the event of graft failure in the recipient. Donor Exclusion Criteria * HIV, HBV or HCV positive subjects within 30 days prior to day 0. * Pregnant or lactating women. * Uncontrolled intercurrent 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. * Graft donation with less than 0.3% CD34+ cells