Antigen Specific Adoptive T Cell Therapy for Adenovirus Infection After Hematopoietic Stem Cell Transplantation

The purpose of this study is to determine if it is possible to treat an infection with a cell-based immunotherapy (therapy that uses the patient's own immune system to treat the infection). This treatment is called adoptive T cell therapy. Another purpose is to learn about the side effects and toxicities of adoptive T cell therapy. Adoptive T cell therapy is an investigational (experimental) therapy that works by using the blood of a donor that has immunity against the virus. The donor cells are collected and then the cells, called T cells, that are capable of defending against the virus are selected out. These selected T cells are then infused back into the patient, to try to give the immune system the ability to fight the infection. Adoptive T cell therapy is experimental because it is not approved by the Food and Drug Administration (FDA).

Inclusion Criteria: * Patients must have received allogeneic HSCT and be greater than 30 days post-HSCT at the time of registration. * Patients must have evidence of documented HAdV infection/reactivation. Patients may be: * Symptomatic with any detectable viral load OR * Asymptomatic with viral load that is: \>1000 copies/ml in peripheral blood OR qualitative detection in stool, urine and/or other specimens * Patients must have poor response and/or contraindication to therapy: * Absence of an improvement of viral load (decrease by at least 1 log, i.e. 10-fold) after ≥ 14 days of antiviral therapy with ganciclovir, valganciclovir and/or foscarnet. OR * New, persistent and/or worsening HAdV-related symptoms, signs and/or markers of end organ compromise while on antiviral therapy with ganciclovir, valganciclovir or foscarnet. OR * Have contraindications or experience adverse effects of antiviral therapy with ganciclovir, valganciclovir, cidofovir or foscarnet. * Performance Score: Eastern Cooperative Oncology Group (ECOG) Performance Score ≤ 3. Karnofsky (≥ 16 years) or Lansky (\0.5 mg/kg/day prednisone or its equivalent) as treatment. * Treatment with antithymocyte globulin within 28 days of planned infusion of virus - specific, antigen selected T cells. * Treatment with virus - specific T cells within 6 weeks (42 days) of planned infusion.