An embolic protection device for use in a patient's blood vessel, such as the aorta, has an approximately cylindrical outer structure made of a filter mesh material and an approximately conical inner structure also made of a filter mesh material. On the downstream end of the embolic protection device, the wider end of the conical inner structure is joined to the cylindrical outer structure. The upstream end of the embolic protection device is open for blood to flow between the conical inner structure and the cylindrical outer structure. The space between the conical inner structure and the cylindrical outer structure defines a collection chamber for captured emboli. The narrow upstream end of the conical inner structure has a catheter port with a resilient seal that is sized for passage of a catheter shaft. The filter mesh material may be self-supporting or it may be supported on a resilient-framework or an inflatable framework.