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Inclusion Criteria Adults 18 years of age and older. Must be able to care for self. Organ Function Permitted: Serum Creatinine normal, or estimated creatinine clearance greater than 60 ml/min Liver Function tests less than 5 times uppper limit of normal Bilirubin less than 2.0 mg/dl Left ventricular ejection fraction greater than 45% Patients who have undergone stem cell transplantation (autologous or allogeneic) are eligible if greater than 4 weeks from transplant and have no active GVHD Patients who fail primary induction therapy or relapse after achieving complete remission (CR) are eligible if they have undergone no more than 3 prior cytotoxic regimen, greater than 3 weeks off cytotoxic chemotherapy, and greater than 2 weeks radiation therapy. Patients must be off biologic therapies including hematopoietic growth factors greater than 1 week. If using hydroxyurea (HU), steroids, imatinib, arsenic, interferon, or other non-cytotoxics for blast count control, patient must be off for greater than 24 hrs before starting ABT-888. Exclusion: Hyperleukocytosis with greater than 50,000 blasts/uL (If using HU, steroids, imatinib, arsenic, interferon or leukopheresis for blast count control, patient must be off those agents for 24 hours prior to beginning ABT-888) Acute Progranulocytic Leukemia (APL, M3) Active disseminated intravascular coagulation (DIC) Active CNS leukemia Active, uncontrolled infection. Patients with infection under active treatment and controlled with antibiotics are eligible. Pregnant women are excluded from this study because ABT-888 is PARP inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ABT-888, breastfeeding should be discontinued if the mother is treated with ABT-888. These potential risks may also apply to other agents used in this study. Previous history or current seizure disorder HIV-positive patients receiving anti-retroviral therapy