An intervertebral cage for arthrodesis, composed of: (a) an upper face and a lower face comprising, respectively, an upper contact zone and a lower contact zone which are intended to contact, respectively, a first vertebra and a second vertebra consecutive to the first vertebra, each of these faces comprising an orifice ; (b) a part connecting the upper face and the lower face , with continuity of material, and configured to form a cavity intended to receive a bone graft, where said cavity opens out at the orifices of each of the upper and lower faces; characterized in that (c) at least part of the upper and/or lower contact zone is made of a porous titanium material with a thickness of at least 1 mm and with a porosity of between 50% and 90%; (d) the diameter of the pores (DP) is between 200 μm and 1 mm; (e) the pores have an aperiodic distribution; (f) the porous titanium material is a continuous material composed of a plurality of filaments of dense titanium material which are interlaced and in part join each other that join each other at some places and are separated by an empty space at other places; (g) the pores are formed by the space between these filaments ; (h) the material is a "branched" type material, according to a three-dimensional structure; (i) the filaments are of a substantially circular cross section with a diameter DF of between 100 and 300 μm; (j) the porous titanium material is produced by additive manufacturing; (k) the titanium material is of substantially constant chemical composition; (l) the density of the titanium material differs between at least two parts of the cage. (a) an upper face and a lower face comprising, respectively, an upper contact zone and a lower contact zone which are intended to contact, respectively, a first vertebra and a second vertebra consecutive to the first vertebra, each of these faces comprising an orifice ; (b) a part connecting the upper face and the lower face , with continuity of material, and configured to form a cavity intended to receive a bone graft, where said cavity opens out at the orifices of each of the upper and lower faces; characterized in that (c) at least part of the upper and/or lower contact zone is made of a porous titanium material with a thickness of at least 1 mm and with a porosity of between 50% and 90%; (d) the diameter of the pores (DP) is between 200 μm and 1 mm; (e) the pores have an aperiodic distribution; (f) the porous titanium material is a continuous material composed of a plurality of filaments of dense titanium material which are interlaced and in part join each other that join each other at some places and are separated by an empty space at other places; (g) the pores are formed by the space between these filaments ; (h) the material is a "branched" type material, according to a three-dimensional structure; (i) the filaments are of a substantially circular cross section with a diameter DF of between 100 and 300 μm; (j) the porous titanium material is produced by additive manufacturing; (k) the titanium material is of substantially constant chemical composition; (l) the density of the titanium material differs between at least two parts of the cage. <EOS>