This is an open-label, dose-escalating clinical trial. Three groups of four patients will receive transplants of increasing doses of HLA-matched umbilical cord blood mononuclear cell into the spinal cord. In the fourth group, we will transplant the highest volume of cells that did not increase neurological deficits along with a single bolus of 30mg/kg methylprednisolone sodium succinate. In the fifth group of four subjects, we will inject that volume of cells plus a bolus intravenous dose of 30mg/kg methylprednisolone sodium succinate and a 6-week course of oral lithium carbonate titrated to 0.6-1.0 mM serum levels. All the subjects are encouraged to stand or walk for one hour a day after the cell transplantation.