Some embodiments are directed to methods and systems for percutaneously treating dissections in a patient's vasculature, such as, without limitation, the aorta. The method can include deploying a catheter containing a collapsed anchoring element, frame, and cover through a first vessel to an entry point of the dissection. The anchoring element can be secured to the second branch vessel. The frame can be expanded in the first branch vessel. The cover can be unfolded over at least a portion of the entry point. The cover then reduces blood flow into the entry point.
