Anorexia nervosa is an eating disorder characterized by intense fear of becoming fat despite the obvious thinness and extreme behaviors for weight loss. The result is a massive weight loss and / or pathological thinness. The care of anorexia is difficult and few treatments have proved to be effective in adults.

Transcranial direct current stimulation (tDCS) is a neuromodulation technique that uses an electrical current of low intensity. It allows to modulate the corticospinal excitability: two electrodes, an anode (excitatory) and a cathode (inhibitory), are positioned on the skull according to the region which is desired to influence the operation.

Although tDCS was shown to no noticeable side effects, it is first necessary to assess the feasibility and safety of this technique in these physically frail patients. A recent pilot study suggests the acceptability, safety and efficacy of tDCS program in patients with anorexia nervosa.

Given these preliminary data and the extreme seriousness and vulnerability of patients with resistant anorexia, the investigators want to assess the risk / benefit ratio for the use of this technique in patients suffering from resistant anorexia nervosa. The current data are too preliminary to consider a randomized controlled trial, the investigators hope, initially, replicate the data from this pilot study in a second sample with a more rigorous and comprehensive assessment methodology .

During stimulation, the anode will be placed over the left dorsolateral prefrontal cortex and the cathode on the right dorsolateral prefrontal cortex. Stimulation of 2 milli-Ampere is applied for 25 minutes each session.

20 sessions will be conducted twice a day respecting a period of four hours between sessions.

The tDCS sessions will start maximum 15 days after the inclusion visit.

Two intermediate control visits will be conducted. One after the first week of tDCS, the other immediately after the last session of tDCS.

The main assessment visit will be carried out one month (+/- 5 days) after the last session of tDCS. Finally a reminder visit will be performed 6 months (+/- 3 weeks) after the last session of tDCS to assess the stability over time of the potential effects observed.

Inclusion Criteria:

• Present a current anorexia nervosa (according to Diagnostic and Statistical Manual of Mental Disorders (DSM V)) ,severe, for at least 3 years
• Attest to the failure of at least one outpatient treatment conducted by a specialized team (Level 2/3) for the management of patients with eating disorders according to the criteria of French Association for the Development of Specialized Approaches of eating disorders and General Direction of the care
• Have an effective mean of contraception throughout the study
• Being able to understand the nature, purpose and methodology of the study
• Being affiliated to a social security scheme or being the beneficiary of such a scheme.
• Having signed the informed consent

Exclusion Criteria:

• Refusal to participate
• Present a body mass index lower than 13.5
• Present a history of seizures or epilepsy
• Presenting a head injury and / or brain pathology
• Presenting an unstabilized serious physical illness
• Present pregnancy (attested by a blood test Beta-HCG) or breastfeeding
• Present physical disease that may affect cognitive abilities and brain structures (eg HIV infection, multiple sclerosis, lupus, Parkinson's disease, epilepsy, dementia ...)
• Deprived of liberty subject (judicial or administrative decision)
• People protected by law