Aneurysms are treated by filling at least one double-walled filling structure with a filling medium within the aneurysm, such as filling structures having a membrane that allows water molecules to permeate across the membrane in response to a water potential differential across the membrane. The transport of fluid across the membrane allows the bag to expand or shrink to accommodate changes in the size or shape of the aneurysm, thereby maintaining a seal between the filling structure against the vessel wall and maintaining apposition of the filling structure against the inside surface of the aneurysm. Transport of water molecules into or out of the filling structure is controlled by adjusting for the osmolarity of the filling fluid medium. The filling structures may be delivered over balloon deployment mechanisms in order to shape occlude the aneurysm and open a tubular lumen for flow of blood through the filling structure.