This will be a tricenter randomized double blind sham controlled trial with stratified randomization based on the area of pain. Patients will first undergo MRI of the skull to determine the exact position of the coil of the motor cortex for neuronavigation with conventional rTMS. After providing informed consent, they will be randomly assigned to one of 2 treatment groups: active rTMS and Hcoil or sham rTMS and sham Hcoil, according to a 2 : 1 ratio (2 for active, 1 for placebo). For each treatment group (active or sham), the order of sessions will be again randomized according to a crossover design : thus each patient will receive successively either active rTMS followed by active H coil or active H coil followed by active rTMS or two sham stimulations (rTMS and H coil). Each treatment will be applied by an independent investigator not involved in the assessment or selection of patients. The treatment protocol will include 2 periods separated by an interval of 5 to 6 weeks depending on the potential residual analgesic effects to avoid carryover effects (patients whose pain intensity remains minimal after 6 weeks, eg less than 4 /10 on NRS, will not participate in the second crossover period of the study). Each session will consist of 5 consecutive stimulation visits of (active or sham) rTMS and H coil over 5 consecutive days. Each patient will thus receive a total of 10 stimulations (2 series of 5 active rTMS or H coil or 2 series of 5 sham rTMS or H coils) and will have a total of 15 visits, including one screening visit (V1), 10 stimulation visits (V2-V5 and V8-V13), and 4 poststimulation visits 1 and 3 weeks after each treatment period (V6, V7, V14, V15). Conventional magnetic stimulations will be applied with a MacPROX100 machine using neuronavigation system and sessions will consist of 30 series of 10 second pulses with a frequency of 10 Hz and an interval of 20 seconds between each. The stimulation intensity used will be 80 % of the resting motor threshold. Conventional rTMS stimulations will target the primary motor cortex contralateral to the painful area or left side in case of bilateral pain and sham stimulation will be carried out with the opposite face of the coil (biface coil) of identical size, color and shape emitting a sound similar to that emitted by the active coil. H-coil rTMS will be delivered with the Brainsway H-coil (Brainsway, Jerusalem, Israel) applied via a helmet placed on the head corresponding to the primary motor cortex (H10 coil) and connected to a Masgtim Rapid2 stimulatior (Mastim, Whitland, UK), while sham stimulation will be delivered with a sham coil placed in the helmet encasing the active rTMS coil. Active rTMS sessions with H-coil will use exactly the same parameters of stimulation as conventional rTMS, e.g. 30 consecutive trains of stimuli delivered at 10 Hz, at 80 % resting motor threshold (RMT), separated by intertrain intervals of 20 seconds.
