An apparatus for performing a medical procedure and, in particular, an aortic valvuloplasty, in a vessel for transmitting a flow of fluid. The apparatus includes an inflatable perfusion balloon including an internal passage for permitting the fluid flow in the vessel while the perfusion balloon is in an inflated condition, the balloon including a plurality of cells in a single cross section and a covering for at least partially covering the cells. A valve associated with the balloon controls the fluid flow within the passage, the valve being arranged external to the passage. The valve may form a tubular extension of the covering, or may be separate from the covering, and may comprise flaps. A spiral covering may also form the valve.
