Neuropathic pain is a public health problem with less than 50% of patients being relieved by drug treatments.

Surgically implanted motor cortex stimulation represents an invasive therapeutic solution capable of relieving a significant proportion of drug-resistant patients (1 in 2); it cannot, however, be offered to all patients, and is not morbidity-free.

Non-invasive motor cortex stimulation techniques have been refined over the last decade, in particular transcranial repetitive magnetic stimulation (rTMS) and transcranial direct current stimulation (tDCS), which provide pain relief among almost half of drug-resistant patients with few or no side effects.

To be efficient, cortical stimulation requires the activation of multiple distant networks involved in the cognitive and motivational response to pain; stimulation frequency is a crucial parameter for activating these mechanisms. The match between cortical stimulation frequency and the intrinsic neuronal frequency of the stimulated cortex has recently been suggested as a key determinant of clinical effect. Indeed, the transmission efficiency of an oscillatory network increases when its intrinsic frequency matches that of the stimulus applied to it. Given that human sensorimotor networks spontaneously oscillate at frequencies around 10 and 20 Hertz (Hz), this match could underlie the superior efficacy of transcranial stimulation at these frequencies.

The hypothesis of the study is that the analgesic effect of cortical stimulation will be enhanced if the stimulation frequency resonates with the spontaneous oscillations of the underlying cortex, thus facilitating its connectivity with the remote structures involved in pain control. The investigators propose to test this hypothesis in a population of patients with drug-resistant neuropathic pain, referred to the Pain Evaluation and Treatment Center (CETD) of the Neurological hospital, at the Hospices Civils de Lyon. The overall aim of the project is to compare the efficacy of stimulation at each individual's own rate of oscillation of the motor cortex, against a "classic" stimulation protocol, and against placebo stimulation.

Inclusion Criteria:

• Aged 18 to 80 years
• Neuropathic pain of more than one year's duration1
• Failed treatment with tricyclic or tetracyclic antidepressants, antiepileptics and a combination of morphine and a serotonin (5HT) norepinephrine (NA2) reuptake inhibitor, in the absence of contraindication.
• Average pain intensity of at least 4/10 in the month preceding the inclusion visit.
• Recipient or beneficiary of a social security scheme-

Exclusion Criteria:

• Chronic non-neuropathic pain or pain associated with progressive pathology, active epilepsy, unhealed scalp wound, impaired comprehension or communication that prevents subjective daily and weekly assessments.
• Active epilepsy, treated or not
• Unhealed scalp wound adjacent to EEG recording electrodes or transcranial stimulation application (contraindication to Medical Device (DM) use)
• Pregnant or breast-feeding women
• Inability to understand or follow the ins and outs of the study, in particular the need to assess pain intensity on a daily basis or to trace it, possibly with the help of a third party (comprehension or communication disorders).
• People under guardianship, curatorship or legal protection
• Persons deprived of their liberty, persons under psychiatric care and persons admitted to a health or social establishment for purposes other than clinical investigation
• Participation in other research interfering with the present study.