Basically, fat in your blood travels as lipoproteins along with cholesterol, proteins, and phospholipids.  In order for the artery to be "clogged", a plaque must first appear on its inner wall.  They can be triggered by stress, smoking, etc. In order for the walls to be normal and thus prevent "clogging", it is necessary to take vitamin E. Being a fat-soluble vitamin, it needs fat for better absorption by the body.  Thus, consuming fat can help your arteries heal themselves and thus prevent them from clogging up.