An apparatus includes a first stent graft that is at least partially insertable into a first blood vessel. The first stent graft has a first end, a second end, an inside surface, and an outside surface. The apparatus also includes an inflatable fill structure fixed to a portion of the outside surface of the first stent graft. The inflatable fill structure includes an outer membrane that is configured to extend beyond the first end of the first stent graft when the inflatable fill structure is in a filled state.
