The present invention relates to apparatus and methods tor providing embolic protection in a patient's vascular system, in particular, it relates to an embolic protection device comprising, in one embodiment, braided mesh-like tubular embolus collection structure or structures that can be deployed in a patient's aorta to protect the aortic arch vessels and downstream organs from, embolus formation by collecting and removing emboli from the blood stream. This embolic protection device can be used acutely, for example for embolic protection during cardiac surgery and interventional cardiology procedures, or it can be implanted for chronic embolic protection, for example from cardiogenic emboli or emboli front ruptured or vulnerable aortic plaque. In one coaxial embodiment, multiple i.e., 20 or more, braided, mesh-like tubular structures are used. In a farther embodiment multiple coaxial braided mesh-like tubular structures are used having varying degrees of porosity, the inner-most tubular structure being most porous and the outer-most tubular structure being the last porous.