The present invention is directed to implantable bioabsorbable non-woven self-cohered web materials having a very high degree of porosity. The web materials are very supple and soft, while exhibiting proportionally increased mechanical strength in one or more directions. The web materials often possess a high degree of loft. The web materials can be formed into a variety of shapes and forms suitable for use as implantable medical devices or components thereof. In some embodiments, the web materials exhibit significant thrombogenic properties.