This trial aims to investigate the effect of stem cells from the patient's own bone marrow in treating multiple sclerosis. The trial is being conducted by the Karolinska Institute and the Karolinska University Hospital Solna in Stockholm and proposes to recruit 15 subjects between February 2013 and December 2015. Participants will be divided into two groups. The first group will receive an injection of their own bone marrow stem cells at the beginning of the trial. The second group will receive the injection of their own stem cells 24 weeks later. All participants will be monitored for complications and changes in clinical condition at our-week intervals for 48 weeks.