This trial is designed to evaluate the use of the patient’s own bone marrow cells for the treatment of Spinal Cord Injury in children. The trial is being conducted by Children's Memorial Hemann Hospital in conjunction with The Institute for Rehabilitation and Research Foundation; The University of Texas Health Science Center; M.D. Anderson Cancer Center and the Baylor College of Medicine. Participants will receive cells from their own bone marrow (Bone Marrow Progenitor Cells) injected directly into the fluid surrounding their spinal cord (intrathecal injection). Participants will be monitored for complications, as well as changes in their clinical condition. The trial expects to enrol 10 subjects by April 2014.