A packaged bioprosthetic heart valve comprising a bioprosthetic heart valve, an adaptive seal and a package. The bioprosthetic heart valve comprises an at least partially dehydrated biological tissue leaflet structure coupled to a supporting frame. The bioprosthetic heart valve has a periphery, an inflow portion, and an outflow portion. The adaptive seal is coupled to the bioprosthetic heart valve around at least a portion of the periphery. The adaptive seal comprises an expandable material that expands after exposure to an initiating condition. The bioprosthetic heart valve and the adaptive seal is stored and contained within the package, which does not contain a liquid storage solution in contact with the bioprosthetic heart valve and the adaptive seal.