A membrane applied to the ostium of an atrial appendage for blocking blood from entering the atrial appendage which can form blood clots therein is disclosed. The membrane also prevents blood clots in the atrial appendage from escaping therefrom and entering the blood stream which can result in a blocked blood vessel, leading to strokes and heart attacks. The membranes are percutaneously installed in patients experiencing atrial fibrillations and other heart conditions where thrombosis may form in the atrial appendages. A variety of means for securing the membranes in place are disclosed. The membranes may be held in place over the ostium of the atrial appendage or fill the inside of the atrial appendage. The means for holding the membranes in place over the ostium of the atrial appendages include prongs, stents, anchors with tethers or springs, disks with tethers or springs, umbrellas, spiral springs filling the atrial appendages, and adhesives. After the membrane is in place a filler substance may be added inside the atrial appendage to reduce the volume, help seal the membrane against the ostium or clot the blood in the atrial appendage. The membranes may have anticoagulants to help prevent thrombosis. The membranes be porous such that endothelial cells cover the membrane presenting a living membrane wall to prevent thrombosis. The membranes may have means to center the membranes over the ostium. Sensors may be attached to the membrane to provide information about the patient.