Methods and devices for increasing flow in the left atrial appendage (LAA) include a conduit directing blood flow from a pulmonary artery into the LAA and/or a conduit drawing blood from the LAA by a Bernoulli effect. In one embodiment, a method comprises implanting a conduit in a pulmonary vein, expanding an inlet portion such that the conduit becomes anchored within the vein and directs blood through an outlet portion of the conduit into or toward the left atrial appendage.
