A catheter device is disclosed comprising; an elongate sheath (503) with a lumen and a distal end for positioning at a heart valve (6), an embolic protection device (200) for temporarily positioning in the aortic arch for deflection of embolic debris from the ascending aorta to the descending aorta, said embolic protection device is connectable to a transluminal delivery unit (130) extending proximally from a connection point (131), and having: a frame with a periphery, a blood permeable unit within said periphery for preventing embolic particles from passing therethrough with a blood flow downstream an aortic valve into side vessels of said aortic arch to the brain of a patient, and at least one tissue apposition sustaining unit (300, 350) extending from said catheter, into said aortic arch, and being attached to said embolic protection device at a sustaining point (502), for application of a stabilization force offset to said connection point at said embolic protection device, such as at said periphery, and for providing said stabilization force towards an inner wall of said aortic arch, away from said heart, and in a direction perpendicular to a longitudinal extension of said periphery, when said catheter device is positioned in said aortic arch, such that tissue apposition of said periphery to an inner wall of said aortic arch is supported by said force for improving stability and peripheral sealing. In addition related methods are disclosed.