The device comprises a dressing made from a porous material (11) intended for placing against tissues, for example skin, the material being synthetic or organic and being distinguished by communicating cavities in the form of open pores, interdigitating gaps in particle material or communicating cavities in capillary structures. The dressing (11) can, by layers, have different cavity qualities and is provided with a dense, sealing shell (10) or layer in which is disposed at least one fluid supply connection (12) and at least one fluid removal connection (13) in spaced apart relationship. Conduits are coupled to the connections (12, 13) and permit the establishment of treatment fluid flow from the supply connection (12), through the cell material dressing (11) in contact with the tissue, to the removal connection (13). Fluid supply can be effected under pressure and/or fluid removal under suction. Electrodes can be disposed in the cell material dressing (11) for sensing the fluid saturation degree, and with the possibility of registering and/or regulating this saturation degree by means of valves. Temperature sensors may be provided in the supply conduit or in the cell material dressing (11) and may be connected to a temperature regulator. Fluid-impervious walls may be provided in the cell material dressing (11) for guiding the treatment fluid flow. The cell material dressing may have one or several replaceable layers.