Central Pain Study for ABX-1431

Inclusion Criteria: * Patients with chronic central pain, present for at least 3 months due to one of the four following diagnostic groups: NMOSD, LETM, MS, or TM. * Patient has a diagnosis of NMOSD with anti-AQP4 IgG or without AQP4-IgG as defined by the International Panel for NMO Diagnosis at least 3 months prior to the screening visit (IPND 2015) * Patients with idiopathic, LETM, comprising an intramedullary MRI lesion or continuous segments of spinal cord atrophy with a clinical history consistent with acute myelitis, and with chronic pain syndrome consistent with the lesion neuroanatomy may be enrolled. These LETM patients must also demonstrate evidence of acute, inflammatory myelopathy in the past (e.g. clinically acute symptomatic myelitis plus inflammatory CSF analysis (e.g. elevated WBC and IgG index) or imaging consistent with inflammatory myelopathy). LETM must be diagnosed at least 3 months prior to the screening visit. * Patient with MS defined by McDonald criteria \[1\] or Poser criteria \[2\] at least 3 months prior to screening visit. * Patients with post-infectious, autoimmune or idiopathic TM diagnosed by a neurologist at least 6 months prior to the screening visit. * Patient's chronic pain must be neuropathic in nature, and anatomically plausible based on underlying neuropathology. If patient has an additional source of pain (e.g., vascular ischemic pain, transient spasm associated pain, headache, chronic lower back pain or concomitant osteoarthritic joint pain), the central neuropathic pain must be clearly identifiable by the patient, as assessed by the Investigator. * The Investigator determines that the patient can enter daily NRS-11 pain intensity data on an internet connected device such as a smart phone, tablet computer or desktop computer with reliable internet service. Patients that do not have a device will be supplied one for the duration of the study. At the direction of the patient, the patient's caregivers may enter the pain intensity data. * At Visit 2, patient's pain is ≥ 4 on the NRS-11 pain intensity scale, on at least 4 of the 7 days preceding randomization. * Patients taking immunosuppressive therapy (IST) for relapse prevention of NMOSD or TM or taking disease modifying therapy (DMT) for MS must be on a stable maintenance dose(s) of IST or DMT for 30 days prior to screening and must be expected to maintain the IST or DMT regimenduring this study. * Patients taking oral corticosteroids must be on a stable dose of medication for at least one week before study start and must be expected to remain on a stable dose during this study. The dose may be no more than prednisolone 20 mg daily or equivalent. * For patients taking antibody therapy for NMOSD relapse prevention (e.g. rituximab, eculizumab or tocilizumab), therapy must be discontinued at least 6 months prior to screening and patients must be willing to refrain from use during this study. * Patients taking daily neuropathic or central pain medications (e.g. gabapentin, amitriptyline, lamotrigine) must be on a stable dose of medication for 30 days before study start and must be expected to remain on a stable dose during this study. * Patients must give written informed consent. * Patients must be willing and able to comply with the protocol requirements for the duration of the study. * Female patients of child-bearing potential must have a negative pregnancy test \[serum human chorionic gonadotropin (HCG)\]. They must practice a highly effective, reliable and medically approved contraceptive regimen during the study (i.e. theoretical failure rate less than 1% per year including oral or parenteral hormonal contraception, Nuvaring, intrauterine device (IUD) or male condom plus spermicide). Post-menopausal women may enter this study. Post-menopausal women are defined as those without menses in the past 12 months, and with a serum follicle stimulating hormone (FSH) in the post-menopausal range. Women who are surgically sterile may enter this study with historical documentation of surgical procedure and a negative pregnancy test. * Male patients must be willing to use a condom with sexual partners during this study until the poststudy visit. Male patients must be willing to abstain from sperm donation for 3 months after the completion of this study. Exclusion Criteria: * Patients with chronic central pain due to trauma, vascular causes, active infection, neoplasm, radiation, metabolic, toxic or other non-inflammatory brain disease or myelopathy are excluded. Patients with trigeminal neuralgia, either as an isolated condition or with MS are excluded. Patients with a history of encephalitis are excluded. Patients with systemic inflammatory autoimmune disorders associated with TM are excluded (e.g. sarcoidosis, systemic lupus erythematosus, Sjogren's syndrome, Behcet's Syndrome, rheumatoid arthritis). TM secondary to infection of the nervous system is excluded (e.g. herpes virus, Lyme disease). TM associated with HIV infection is excluded. * Patient has an onset of an MS, LETM or TM relapse or NMOSD acute episode within 60 days before the study start. * Patients with unresolved infections, AIDS myelopathy, or degenerative neurological conditions. * Patient has received the following within 60 days before study start: * Intrathecal baclofen. * Injection therapies such a botulinum toxin, anesthetic or nerve block to control pain. * Plasma exchange * Patients taking daily oral opioid drugs are excluded. * Patient is taking carbamazepine or oxcarbazine or eslicarbazepine or other potent cytochrome P450 3A4/5 inducers \[e.g. rifampin, St. John's Wort (Hypericum perforatum), phenytoin\]. Patient is taking strong P450 3A4/5 inhibitors including atazanavir, bocepravir, clarithromycin, grapefruit juice, indinavir, itraconazole, ketoconazole, nefazodone, nelfinavir, posaconazole, ritonavir, saquinavir, telithromycin, or voriconazole. * Patient has evidence of alcohol, drug or chemical abuse, at study start or within 1 year before the study start.