Vessels on the outside of the heart called coronary arteries supply the heart with blood. Fatty matter (cholesterol), calcium, proteins and inflammatory cells can build up in the coronary arteries to form plaques of different sizes. Plaques harden over time, causing your arteries to narrow (a condition known as coronary artery disease), and block or slow the flow of blood to your heart. This is the most common cause of a heart attack. However, heart attacks can also occur when the coronary artery suffers a spasm, cutting off blood flow to the heart.