Distally-narrowed vascular grafts and methods of using same for making artery-to-vein and artery-to-artery connections

A method, comprising:

• making an incision in the wall of a preselected target blood vessel;
• providing a vascular graft defining a lumen for passage of blood, the graft including:
• a distal end adapted for placement in the blood vessel through the incision and defining a first orifice having a first diameter;
• a proximal end adapted for attachment to an artery;
• a first tubular section between the distal and proximal ends, the first tubular section defining a portion of the lumen having a second, generally constant diameter greater than the first diameter;
• and
• a first taper section between said first tubular section and said distal end, and having a generally gradually decreasing diameter along the first taper section;
• inserting the distal end through the incision into the blood vessel such that the distal end passes to a point downstream of the incision;
• securing the graft to the blood vessel wall;
• and
• anastomosing the proximal end of the graft to a preselected target artery site.

A method comprising:

• anastomosing a first end of a vascular graft to a first blood vessel;
• anastomosing a second end of the graft to a second blood vessel;
• removing a medial portion of the graft by clipping the graft at two locations between the first end and the second end, thereby providing a first graft piece comprising the first end and a second graft piece comprising the second end;
• providing a generally tubular connector device defining a lumen therethrough, the device having a first end segment configured for insertion into the lumen of the first graft piece;
• and a second end segment configured for insertion into the lumen of the second graft piece;
• and
• connecting the first and second graft pieces to the first and second portions of the connector device.

A generally tubular connector device defining a lumen therethrough, the device comprising:

• a first end segment configured for insertion into the lumen of a first graft piece;
• a second end segment configured for insertion into the lumen of a second graft piece;
• and
• a middle segment configured to maintain the graft piece ends in a spaced apart relationship.

A generally tubular connector device defining a lumen therethrough, the device comprising:

• a first end segment configured for insertion into the lumen of a first graft piece;
• and
• a second end segment configured for insertion into the lumen of a second graft piece;
• wherein each of the first and second end segments defines a groove for receiving a suture for attachment of the segments to the first and second graft pieces.