The present invention relates to a hydrated, biocompatible tissue-augmentation compound and methodology for its implantation into mammalian tissue. The tissue-augmentation compound is comprised of: living tissue, optionally body derived fluids, and at least one NCO-terminated hydrophilic urethane prepolymer derived from an organic polyisocyanate, and oxyethylene-containing diols or polyols in which essentially all of hydroxyl groups are capped with polyisocyanate.