Like the arteries that supply blood to the heart -- the coronary arteries -- the carotid arteries can also develop atherosclerosis or âhardening of the arteriesâ on the inside of the vessels. Over time, the buildup of fatty substances and cholesterol narrows the carotid arteries.n this article. Carotid artery disease is also called carotid artery stenosis. The term refers to the narrowing of the carotid arteries. This narrowing is usually caused by the buildup of fatty substances and cholesterol deposits, called plaque. Carotid artery occlusion refers to complete blockage of the artery.