An inflatable structure for use in biological lumens and methods of making and using the same are disclosed. The structure can have an inflatable balloon encircled by a shell. The shell can have proximal and distal tapered necks, longitudinally-oriented flutes, and apertures at the proximal and distal ends of the shell. The apertures can be recessed in the flutes in the necks. The shell can also have fiber reinforced walls.