The present invention relates to a low profile stabilizer that immobilizes tissue at a surgical site wherein the device includes a stabilizer having a base portion with elongate extending members that surround the sides of an aperture area and a removable end portion which is removable form the base portion and which surrounds the remaining side of the aperture area and wherein the stabilizer is preferably used in combination with a pair of flexible connectors that are threaded through the tissue adjacent to the aperture area to draw the tissue into contact with the aperture area of stabilizer and into contact with a pair of tab members extending from the bottom surface of the stabilizer such that the flow of blood through a blood vessel is occluded by tab members when the flexible connectors are releasably attached to the stabilizer.
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