1) The heart is filled with blood, so why does the heart muscle need a special artery to supply it with food and oxygen? What is this blood vessel called? 2) Why is the subclavian vein and artery are positioned where they are relative to one another? 3) How many capillary beds would a red blood cell in the mesenteric artery pass through to reach the left atrium if it traveled by the shortest path? 4) How many capillary beds would a red blood cell in an atery in your big toe pass through to reach the right atrium if it traveled by the shortest path? Solution the heart is filled with blood but the blood is deoxygenated as well, the heart is blood pumping machine and therefore its muscles should function tirelessly to maintain blood flow thorughout the body. the heart contains deoxygenated blood that contains waste material that is why the heart muscles need a special artery to supply it with food and oxygen, these arteries are called coronary arteries. there is one blood vessel known as pulmonary vein that takes oxygenated blood from the lungs to the heart..