Mesenchymal Stem Cell Infusion as Treatment for Steroid-Resistant Acute Graft Versus Host Disease (GVHD) or Poor Graft Function

Inclusion Criteria: Patient eligibility criteria 1. Male or female of any age. 2. Previous allogeneic transplantation (related or unrelated donor, any degree of HLA matching) or autologous transplantation (for part 2 only) of HSC at any time before. 3. Any source of HSC (marrow, PBSC, cord blood) and any conditioning regimen. 4. Informed consent given by donor or his/her guardian if of minor age. 5. Additional criteria for each part of the protocol: Part 1: MSC for steroid-refractory grade II-IV acute GVHD 1. Allogeneic transplantation. 2. Grade II-IV acute GVHD (see appendix A for acute GVHD grading) de novo or following DLI. 3. Acute GVHD refractory to mPDN 2 mg/kg/day or equivalent, defined as * progression of GVHD on day 3 after initiation of steroids * no improvement of GVHD on day 7 after initiation of steroids * absence of complete resolution of acute GVHD on day 14 after initiation of steroids * relapse of acute GVHD during or after steroid taper. 4. Ongoing therapy with Ciclosporine or Tacrolimus at therapeutic doses. 5. Patient may have received previously any other form of treatment for acute GVHD, but no new treatment started within 1 month of study entry. Part 2: MSC for poor graft function (PGF) 1. Allogeneic or autologous transplantation. 2. Cytopenia in 2 or 3 lineages: * Hb \< 8.0 g/dL and reticulocytes \< 1%, with or without transfusion * Plt \< 20,000/µL without transfusion * Neutrophils \< 500/µL, without G-CSF administration OR severe cytopenia in 1 lineage: * RBC transfusion dependent (if autologous transplantation; despite EPO administration if allogeneic transplantation) * Plt transfusion dependent * Neutrophils \< 500/µL despite G-CSF administration 3. Cytopenia duration ≥ 2 weeks beyond day 28 after autologous HCT, or day 42 (day 60 for cord blood transplantation) after allogeneic HCT. 4. Cytopenia is not related to CMV or other infection, myelosuppressive/toxic drugs, renal failure, peripheral cell destruction or other identifiable cause. 5. In case of HLA-identical related donor and full donor chimerism, patient can only be included if a boost of donor CD34+ cells has been unsuccessful or is not feasible. Part 3: MSC + DLI for poor donor T-cell chimerism 1. Nonmyeloablative allogeneic transplantation. 2. Donor T-cell chimerism \< 50% for at least 2 consecutive weeks beyond day 21 after HCT OR * 20% decrease in donor T-cell chimerism with the second value \< 50%. MSC donor inclusion criteria 1. Related to the recipient (sibling, parent or child) or unrelated. 2. Male or female. 3. Age \> 16 yrs (no age limit if same as HSC donor). 4. No HLA matching required. 5. Fulfills generally accepted criteria for allogeneic HSC donation. 6. Informed consent given by donor or his/her guardian if of minor age. Exclusion Criteria: Patient exclusion criteria 1. HIV positive. 2. Active uncontrolled infection at time of scheduled MSC infusion. 3. Relapsing or progressing malignancy. MSC donor exclusion criteria 1. HIV positive 2. Known allergy to Lidocaine 3. If donor other than HSC donor : any risk factor for transmissible infectious diseases.