This trial is evaluating the safety and effectiveness of fat stem cells in patients following stroke. The trial is being conducted at the Fundación para la Investigación Biomedical del Hospital Clínico San Carlos in Madrid and proposes to recruit 20 patients. All participants will be treated by injections directly into their brains (intracerebral injections) of expanded stem cells from their own fat. Participants will be monitored for complications and assessed for changes in their clinical condition.