The treatment consists of laminectomy or laminoplasty of approximately two to three vertebral segments overlying either L2 through L4 (for Group E only) or C3 through C5 cord segments (for all Groups) in order to allow intraspinal injections of HSSC. Each injection will administer approximately 2, 3, or 4 x 105 cells in approximately 8.5 - 10 µL volume. The subjects will receive 5 or 10 injections at approximately 4 to 5mm intervals on each side of the cord, in total 10 or 20 injections. Each injection is completed in approximately 3 minutes. The total surgical time is expected to be approximately 3 to 5 hours. After the surgery, subjects will receive routine standard of care for laminectomy subjects who undergo an intradural procedure. Prior to and after the transplant, subjects will be required to remain on immunosuppressive therapy. Immunosuppressive therapy will consist of: 1) basiliximab (Simulect®) 20mg intravenously (IV) when the dura is opened, then again at day 4 post transplantation; 2) tacrolimus (Prograf®) initially dosed at a maximum of 0.1 mg/kg divided approximately every 12 hours by mouth (po) on post transplant day 1, and then maintained at a dose that provides a trough serum level of 4 to 8 ng/ml (adjusted for IV use as necessary); and 3) mycophenolate mofetil (CellCept®) started on post transplant day 1 at 500 mg approximately every 12 hours and progressively increased over 2 weeks to 1.0 gram by mouth (po) twice a day as tolerated. Dose escalation may be modified at the discretion of the site Principal Investigator (PI). Subjects will also receive an initial bolus dose of methylprednisolone 125 mg IV approximately 2 hours prior to the first injection. Beginning on post-operative day 1, the subject will receive oral prednisone 60 mg po daily (QD) for 7 days postoperatively, then progressively decreased over the next 21 days as follows: 40 mg/day for 7 days, 20 mg/day for 7 days, then 10 mg/day for 7 days. At 28 days, prednisone will be discontinued. All pre- and post-surgery immunosuppressive drugs will be administered as noted above, at the discretion of the site PI. If these subjects have previously discontinued mycophenolate mofetil and/or tacrolimus, they may be re-challenged as per the dosing described above, at the discretion of the site PI.