The illustrative embodiments described herein are directed to apparatuses, systems, and methods for applying reduced pressure to a subcutaneous tissue site. In one illustrative embodiment, the apparatus includes a membrane having a substantially uniform membrane wall thickness and a first, tissue-facing surface. The membrane may be shaped to form a plurality of protrusions on the tissue-facing surface. The plurality of protrusions at least partially defines at least one channel operable to transfer the reduced pressure along the tissue-facing surface.