Traumatic brain injuries (TBI) are one of the leading causes of death and disability worldwide. These patients are burdened by physical, cognitive, and psychosocial deficits, leading to an important economic impact for society. Treatments for TBI patients are limited and none has been shown to provide prolonged and long-term neuroprotective or neurorestorative effects. TBI related disability is linked to the severity of the initial injury but also to the following neuroinflammatory response which may persist long after the initial injury. Moreover, a growing body of evidence suggests a link between TBI-induced neuro-inflammation and neurodegenerative post traumatic disorders. Consequently, new therapies triggering immunomodulation and promoting neurological recovery are the subject of major research efforts. In this context, mesenchymal cell-based therapies are currently investigated to treat various neurological disorders due to their ability to modulate neuroinflammation and to promote simultaneous neurogenesis, angiogenesis, and neuroprotection. Clinical trials using intravenous MSC have been conducted for various pathologies, all these studies showing a good safety profile. The hypothesis of the study is that intravenous repeated treatment with MSC derived from Wharton's Jelly of the umbilical cord may be associated with a significant decrease of post-TBI neuroinflammation and improvement of neuroclinical status. The main objective of the study is to evaluate the effect of iterative IV injections of MSC on post-traumatic neuroinflammation measured in corpus callosum by PET-MRI at 6 months in severe brain injured patients unresponsive to simple verbal commands 5 days after sedation discontinuation.