A method for reducing or stopping flow through a tubular structure of a patient can include positioning an elongate member within a lumen of the tubular structure. The elongate member can be arranged to form a frame having a distal opening and a proximal opening. The elongate member can substantially reduce or totally obstruct, with a flow reducing member coupled to the frame, flow of at least one of emboli and fluid flowing through the lumen. The flow reducing member can comprise a one-way valve that moves in response to fluid flow to substantially prevent distal flow through the distal opening and to allow proximal flow through the distal opening.
