The device comprises a blood vessel engaging portion which is initially disposable in a radially collapsed configuration such that the device may be passed into the lumen of the tapered segment of the blood vessel, and subsequently expandable to an operative configuration where it will frictionally engage the surrounding blood vessel wall to hold the device in fixed position within the blood vessel lumen. It also has a lumen blocking portion which is affixed to the engaging portion. The lumen blocking portion is configured such that, when the engaging portion is in its operative configuration and in contact with the blood vessel wall, the lumen blocking portion will block the flow of blood in at least one direction through the lumen. The blood vessel engaging portion is a wire frame.