Carotid endarterectomy surgery. Incision is deepened to expose the bifurcation of the carotid artery. The internal jugular vein and cranial nerves are then identified. Silastic slings are placed around the main arteries. Carotid endarterectomy is a surgical procedure to remove a build-up of fatty deposits (plaque), which cause narrowing of a carotid artery. The carotid arteries are the main blood vessels that supply blood to the neck, face and brain.