A low swell, long-lived hydrogel sealant formed by reacting a highly oxidized polysaccharide containing aldehyde groups with a multi-arm amine is described. The hydrogel sealant may be particularly suitable for applications requiring low swell and slow degradation, for example, ophthalmic applications such as sealing wounds resulting from trauma such as corneal lacerations, or from surgical procedures such as vitrectomy procedures, cataract surgery, LASIK surgery, glaucoma surgery, and corneal transplants neurosurgery applications, such as sealing the dura and as a plug to seal a fistula or the punctum. The low swell, long-lived hydrogel sealant may also be useful as a tissue sealant and adhesive, and as an anti-adhesion barrier.