Abstract: In some implementations, a radially self-expanding endograft prosthesis is provided that includes (i) distal flange that is self-expanding and configured to flip generally perpendicularly with respect to a body of the prosthesis to help seat the prosthesis against a tissue wall, (ii) a distal segment extending proximally from the distal flange that has sufficient stiffness to maintain a puncture open that is formed through a vessel wall (iii) a compliant middle segment extending proximally from the distal segment, the middle segment being more compliant than the distal segment, and having independently movable undulating strut rings attached to a tubular fabric, the combined structure providing flexibility and compliance to allow for full patency while flexed, the segment being configured to accommodate up to a 90 degree bend, (iv) a proximal segment having a plurality of adjacent undulating strut rings that are connected to each other.