This research study is being performed to find out more information about the safety and efficacy of autologous bone marrow stem cells transplantation. In patients with myocardial infarction, the heart muscle does not pump well. Over a period of years, this continues to get worse until the patient dies of heart failure. The researchers are trying to find out if the transplantation of these stem cell can make a change in the functioning of these areas of the heart muscle.