Apparatus for permanent placement across an ostium of a left atrial appendage in a patient, which includes a filtering membrane configured to extend across the ostium of the left atrial appendage. The filtering membrane has a permeable structure which allows blood to flow through but substantially inhibits thrombus from passing therethrough. The apparatus also includes a support structure attached to the filtering membrane which retains the filtering membrane in position across the ostium of the left atrial appendage by permanently engaging a portion of the interior wall of the left atrial appendage. The support structure may be radially expandable from a first configuration to a second configuration which engages the ostium or the interior wall of the left atrial appendage. The filtering membrane may define an opening therethrough that is configured to expand from a first size which inhibits the passage of thrombus therethrough to a second size which allows an interventional device, e.g., an expansion balloon, to pass therethrough, and wherein the opening is resiliently biased towards the first size.