This trial is designed to evaluate the use of donated spinal cord nerve stem cells for the treatment of Spinal Cord Injury. The trial is being conducted by University of Miami; Shepard Center in Georgia; Thomas Jefferson University Hospital in Philadelphia; and Medical College of Wisconsin, in conjunction with Neuralstem Inc. Participants will receive different doses of human spinal cord stem cells obtained from donated foetal tissue. The cells will be injected into the injured part of the spinal cord as part of a surgical procedure (laminectomy or laminoplasty). Participants will be monitored for complications, as well as changes in their clinical condition. The trial expects to enrol 8 subjects by December 2013 but is not yet accepting participants.