High Dose Therapy and Autologous Stem Cell Transplantation Followed by Infusion of Chimeric Antigen Receptor (CAR) Modified T-Cells Directed Against CD19+ B-Cells for Relapsed and Refractory Aggressive B Cell Non-Hodgkin Lymphoma

Transplant eligible patients will be eligible if criteria met per below. Inclusion Criteria: * Patients ≥ 18 years of age with aggressive B-cell non-Hodgkin lymphoma subtypes including, relapsed or refractory diffused large B-cell lymphoma (DLBCL), and transformed follicular lymphoma meeting at least one of the following criteria: * Bone marrow involvement at the time of relapse or refractory disease and not appropriate for allogeneic transplantation. * PET positive disease outside of one radiation port unless single-port disease treated with prior radiotherapy within the port, following \> or = to 2 cycles of salvage chemotherapy, still achieving chemosensitive status 1999 IWG criteria (section 12.2 and 12.383). * Creatinine ≤ 1.5 mg/100 ml (or measured 24 hour creatinine clearance of ≥ 50 cc/min) * Bilirubin \<2.0 mg/100 ml, AST and ALT \<3x the upper-limit of normal, PT and PTT \< 2x normal outside the setting of stable chronic anticoagulation therapy, * Adequate cardiac function (LVEF\>40%) as assessed by ECHO or MUGA scan performed within 1 month of treatment. * Adequate pulmonary function as assessed by DLCO of \> or = to 45% adjusted for hemoglobin. * Life expectancy of \> 3 months. Exclusion Criteria: * Karnofsky performance status ≤ 70 (see appendix VI). * Patients with other aggressive B-cell malignancies including, but not limited to: Burkitt lymphoma, transformed CLL/SLL and transformed marginal zone lymphoma that are not included in 6.1 inclusion criteria. * Patients previously treated with autologous or allogeneic bone marrow or stem cell transplantation are ineligible. * Other past or current malignancy unless in the opinion of the investigator it does not contraindicate participation in the study. * Uncontrolled bacterial, viral or fungal infection. * Patients with HIV, active hepatitis B or hepatitis C infection.