Pain affects up to 30% of the general population. In particular, neuropathic pain (NeP) is caused by lesion or desease affecting peripheral or central somatosensory pathways and affects 7% of the adult population. Despite the availability of evidence based pharmacological and surgical treatment for NeP, about 50% of patients remais symptomatic despite best medical treatment. Some neuropathic pain syndromes are specially refractory. In particular, central NeP is caused by disease or lesion to central structures involves in somatosensory integration of nociceptive information is non-responsive to drugs usually employed in other NeP syndromes. Classical neuromodulatory techniques such as conventional repetitive Transcranial Magnetic Stimulation aiming at the motor of prefrontal cortices are ineffective to relieve pain in this population. Recently new technology advances have made possible non-invasive stimulation of deeper cortical targets. Some of them are activelly involved in the integration of the perception of pain, such as the anterior cingulate cortex or the posterior insula. The aim this study is to treat 90 patients with central pain (post stroke pain, spinal cord lesions after trauma or demyelinizating diseases) under best medical pharmacological treatment in three different conditions: AAC (n= 30 with the H-Coil), Superior Posterior Insula (SPI) n=30 cooled double cone coil double cool coil, and sham(n=30). Each patients will undergo daily stimulation for a week, then weekly stimulations for 3 months (total of 17 sessions). The main study outcome is pain relief at the last stimulation week (visual-analogic scale). Secondary end-points are changes in the McGill Pain Questionnaire, Neuropathic Pain Symptom Inventory, DN4 questionnaire, SF -36, brief pain inventory and cognitive assessment including the trail making test A and B, Strrop color interference test, and subscalles from the CERAD. All patients will undergo quantitative sensory test and measurements of cortical excitability over M1 before and after to treatment.

Inclusion Criteria:

• Signed term of informed consent
• central pain

Exclusion Criteria:

• Trauma of Skull, epilepsy don't treated,
• Use of medications decrease the seizure threshold
• Patients in use of drugs, how cocaine and alcohol
• neurosurgical clips, pacemakers, increased intracranial pressure (risk of sequelae after seizure)
• Pregnant or lacting women