This trial aims to investigate the use of stem cells obtained from the patient's fat in treating Critical Limb Ischaemia. The trial is sponsored by the Fundación Pública Andaluza Progreso y Salud, in conjunction with Iniciativa Andaluza en Terapias Avanzadas, and proposes to recruit 33 patients between February 2011 and July 2013. Participants will be treated at the University Hospital and the Hospital San Lazaro in Seville. Participants will be randomly divided into three groups. The control group will receive a placebo injection. The two experimental groups will receive different doses of their own stem cells. All participants will be monitored for up to one year for complications following the transfusion, and changes in clinical condition including changes in perfusion and ulceration.