Disclosed is a pressure sensitive prosthesis that includes a tubular member having a passageway extending therethrough and a sleeve attached about one end of the tubular member. The sleeve functions as a one-way valve to permit fluid flowing through the sleeve lumen in a first, distal direction and under a first pressure, while collapsing in response to fluid flowing in a second direction when the pressure thereof exceeds that of the first direction or pressure. One aspect of the invention includes a first opening and a second opening configured for allowing fluid flow from the passage to the lumen in the first direction.