An electrode and / or an optode (40) of the implantable sleeve adapted to surround a practically cylindrical tissue (70), and comprising: a support sheet (43) which, when deployed on a flat surface, comprises a first and second longitudinal edges extending parallel to a transverse axis (X), where the support sheet is non-conductive and wraps around a longitudinal axis (Z), normal to the transverse axis (X), thus forming a sleeve of geometry practically cylindrical or helical that defines a lumen that extends over a length (L), along the longitudinal axis (Z), of practically constant internal diameter (Dc), measured along a radial axis (R), normal to the longitudinal axis (Z), wherein said sleeve comprises, or an internal surface (43d) that forms an interior part of the sleeve, and an external surface (43u) that forms an exterior part of the sleeve, separated from the internal surface by a thickness cuff, or a pair central tee, extending along a length (Ic), of at least 50% of the length (L) of the sleeve, and having a mean central thickness (tc), measured normal to the longitudinal axis (Z) , and wherein the central part is flanked on each side, or a first edge part (43e) extending from a first free edge of the sleeve to the central part along the longitudinal axis (Z), and a second part edge (43e) extending from a second free edge of the sleeve to the central part along the longitudinal axis, wherein the first free edge part has a medium edge thickness (te1), and the second edge part free has a mean edge thickness (te2), at least one first electrode contact (40a) made of a conductive material exposed on the inner surface (43d) of the sleeve, and away from the outer surface (43u) that forms the outside of the sleeve, and / or at least one first optical contact (60, 601a-601c) to guide a beam of light from the inner surface towards the longitudinal axis (Z), characterized in that the mean edge thicknesses (te1, te2) of the first and second edge parts are each less th
