Tissue lacerations are closed using a vacuum cup applied to the tissue surface having a tissue-abutting, optically transparent mesh surface that under vacuum conforms with the tissue surface, apposing edges of the wound, and is optionally loaded with a bandage comprising a chitosan film and a collagen backing. An eye tissue surface wound is closed without sutures by closing the wound with a bioadhesive, biocompatible sclera or cornea wound patch comprising a chitosan film and a collagen backing, wherein the backing is bonded to the film without adhesive and protects the film against dissociation when the patch is exposed to a physiological fluid, and the film adheres to the sclera sufficient to retain apposed edges of the wound.