A system to limit cerebral ischemia occurring as a consequence of aortic valve replacement includes an aortic valve having proximal and distal ends, a sleeve having proximal and distal ends, the proximal end of the sleeve disposed at the distal end of the aortic valve, and a filter attached to the distal end of the sleeve to receive blood and particles passing from the proximal end of the sleeve to the distal end of the sleeve and to separate the particles from the blood. A related method includes introducing a system into a heart of a patient, the system comprising an aortic valve having proximal and distal ends and a sleeve having a proximal end disposed at the distal end of the valve, implanting the valve in an aortic valve annulus, and filtering blood that has passed through the valve into the sleeve.
