Participants in this study have been diagnosed with aggressive B-Cell lymphoma. The purpose of this research study is to compare the good and/or bad effects of an experimental approach to treating the disease. Approximately 9 people will take part in this study conducted by investigators at the University of Iowa. Involvement in the chemotherapy regimen, may last between 9 to 24 weeks. After completing the study treatment portion, the study doctor will ask participants to schedule follow-up exams for at least 5 years.