Transluminal methods and apparatus for causing arterial blood to flow through a vein of a mammalian patient, in a direction opposite normal venous blood flow, after an arterial blood containing conduit has been purposely or inadvertently connected to the vein. The method includes the use of a transluminally inserted vessel lumen occluding apparatus to at least partially block (e.g., occlude, embolize or close) the lumen of the vein at a location that is proximal to the location at which the arterial blood containing conduit is connected to the vein. The apparatus comprises a radially expandable lumen blocking device that is implantable in the vein lumen and catheters and other apparatus for implanting the radially expandable lumen blocking device into the lumen of the vein.