Implant devices for filtering blood flowing through the ostium of an atrial appendage have component structures one or more of which are expandable. Devices with component structures in their unexpanded state have a compact size suitable for intra-cutaneous delivery to an atrial appendage situs. The expandable component structures are expanded in situ to deploy the devices. A device may have sufficiently short axial length so that most or almost all of the device length may fit within the ostium region.