Some embodiments are directed to a pharmaceutical composition which includes a biocompatible polymer and a eukaryotic cell to be used as a drug for the prevention and/or treatment of tissue lesions of the central nervous system caused by cerebral vascular ischaemia. Some embodiments are also directed to a pharmaceutical kit which includes a biocompatible polymer and a eukaryotic cell for the prevention and/or treatment of tissue lesions of the central nervous system caused by cerebral vascular ischaemia. Some other embodiments can be used in particular in the human and veterinary pharmaceutical fields.