A therapeutic device for promoting the healing of a wound in a mammal is disclosed. An exemplary device comprises a permeable structure having a plurality of depressions formed in a surface thereof. In use, the surface having the depressions is disposed adjacent a surface of the wound. A method of treating a wound comprises the steps of providing a permeable structure comprising a plurality of randomly disposed fibers and having i) a plurality of wound surface contact elements disposed between end portions of the structure, and ii) a plurality of voids defined by the contact elements; and applying the permeable structure to at least one surface of the wound.