Vein-style air pumping tube and tire system and method of assembly

A method of assembling an air maintenance tire system comprising:

• forming an elongate tire groove into a flexing region of a tire sidewall, the groove having a profiled internal geometry;
• forming an elongate air pumping tube, the air pumping tube having an internal elongate air passageway and an external geometric shape substantially complementing the tire groove internal geometry for operably enabling a close receipt of the air pumping tube into the tire groove;
• forming at least one access shaft within the air pumping tube extending from an outward tube surface to a check valve seat positioned at a depth within the air pumping tube substantially in line with the air passageway;
• seating a check valve device through the access shaft to engage the check valve seat in an alignment with the air passageway;
• filling the access shaft by a plug component to a depth of the check valve device whereby the plug component occupies the access shaft.