Abstract: Apparatus and methods for interconnecting an artery and a vein by means of a graft of biocompatible material and a catheter of biocompatible material. The graft has an end configured for attachment to the artery and another end configured for interconnection with the catheter. The catheter has an end configured for interconnection with the graft and has at least one hole spaced axially therefrom that is positionable within the interior of the vein and spaced from an opening of the vein through which the catheter passes into the vein. The at least one hole provides an outlet within the interior of the vein for blood from the artery that passes through the graft and the catheter. The catheter and graft may be provided as a combined assembly, or the catheter may be inserted through the wall of an existing graft in order to salvage the existing graft.