Method and apparatus for effecting an aortic valve bypass, including the provision and use of a t-stent for effecting a distal anastomosis for the same

A method for joining a first hollow structure to the side wall of a second hollow structure, the method comprising:

• providing a connector comprising:
• a fluid-constraining tube having a fluid-constraining neck extending therefrom, wherein the tube comprises a lumen having a first opening and a second opening and the neck comprises a lumen having a first opening and a second opening, the neck being joined to the tube so that the neck is in fluid communication with the tube intermediate the length of the tube, such that fluid entering the first opening of the tube can exit the second opening of the tube, and fluid entering the first opening of the neck can exit the second opening of the tube;
• at least the portions of the tube adjacent to the first opening of the tube and second opening of the tube being biased radially outwardly so that they normally assume a radially-expanded configuration, but being capable of being restrained in a radially-contracted configuration, wherein the tube is sized so that, when it is in its radially-expanded configuration, it has an outer diameter which is larger than the inner diameter of the second hollow structure;
• restraining the tube in its radially-contracted configuration;
• selecting a location on the side wall of the second hollow structure;
• forming an opening in the side wall of the second hollow structure at the selected location;
• positioning the connector so that the tube resides within the interior of the second hollow structure and the neck extends out of the side wall of the second hollow structure;
• allowing the tube to expand back into its radially-expanded configuration;
• and
• connecting the neck to the first hollow structure.