Bone Marrow-derived Mesenchymal Stem Cells (MSC) Administration in Weaning From Left Ventricular Assist Device

INCLUSION CRITERIA: * Postmenopausal female or female who may become pregnant but is using adequate contraceptive precautions with negative pregnancy test, * Severe Left Ventricular dysfunction with Ejection Fraction \< 30% with ischemic cardiomyopathy, * New York Heart Association Class III or IV, * No revascularization options available, * Listed or not for cardiac transplantation, * Clinical indication and accepted candidate for Left Ventricular Assistance Device implantation as a destination therapy or as a bridge to transplantation, * Optimal medical therapy. EXCLUSION CRITERIA: * Cardiothoracic surgery within 30 days prior to study entry, * Myocardial infarction within 3 months prior to study entry, * Prior cardiac transplantation, * Left Ventricular reduction surgery or cardiomyoplasty, * Acute reversible cause of heart failure (e.g. myocarditis, profound hypothyroidism), * Left ventricular aneurysm or wall thickness preventing cell injections, * Anticipated requirement for biventricular mechanical support, * Stroke within 30 days prior to study entry, * Received investigational intervention within 30 days of study entry, * Pregnant or breastfeeding at time of study entry, * Human Imune deficiency Virus, Human T-cell Lymphotrophic Virus, Hepatitis B Virus and Hepatitis C Virus positive within 30 days prior to study entry, * Active systemic infection within 48 hours prior to study entry, * History of cancer in the last 5 years, * Patient participant to other research, * Patient under treatment that may exert an inhibitory or stimulatory effect on the growth and multiplication of cells, or with immunosuppressive properties.