It has been shown in some scientific studies that the the antibody marker specific for neuromyelitis optica (NMO), known as NMO-Immunoglobulin G (IgG), causes inflammation in brain tissues by activating a substance called complement. Complement can greatly increase the immune attack in the optic nerves (causing optic neuritis (ON)), spinal cords (causing transverse myelitis (TM)) and brains of patients with NMO. Eculizumab has already been shown to be effective in a rare blood disorder known as paroxysmal nocturnal hemoglobinuria (PNH). Attacks of PNH are also mediated through complement. Therefore, the investigators of this study are investigating whether by 'turning off' complement in NMO, further attacks of NMO can be prevented.