A common cause of cardiovascular disease is atherosclerosis, the hardening and narrowing of arteries due to a buildup of plaque. For instance, significant narrowing in the coronary arteries, which bring oxygenated blood to the heart, can produce symptoms such as chest pain, dizziness, and breathlessness. Heart muscle Coronary artery (supplies blood and oxygen to heart muscle) Healthy heart muscle Blood clot blocks artery Blocked blood flow Plaque Coronary artery buildup in artery Dead heart muscle Image by NIH: National Heart, Lung and Blood Institute [Public domain], via Wikimedia Commons The chart provides typical values for blood flow through a coronary artery. 1060 kg/m³ Density (blood) P Viscosity (blood) 0.004 Pa*s Flow rate Q 0.8 mL/s Length (artery) L 3 cm Radius (artery) r 0.18 cm (a) Using Poiseuille's Law, calculate the pressure drop across this artery. (Things to think about: How does the pressure drop calculated in this part compare to mean arterial pressure?) Use 1 mL = 106 m³. AP= Pa (b) Calculate the velocity of blood through this artery. Hint: How is velocity of the flow related to flow rate? v= m ES (c) If the artery forms blockages, the pressure drop might remain the same as above, since the heart supplies a constant pressure. Assuming the pressure drop in a healthy coronary artery is the same as calculated in part (a), calculate the flow rate for this artery if the radius experiences an 9% reduction. Q= mL S (d) Similar to the question above: Assuming the pressure drop in a healthy coronary artery is same as part (a), calculate the flow rate for this artery if the radius experiences an 90% reduction. Q= mL S Significance: Parts (c) and (d) show us what happens to the flow rate of the blood for the same pressure across the artery for different amounts of blockage. How much does the flow rate drop from (c) to (d). What implications can this have? (e) The body quite readily accommodates to the reduction in coronary artery radius by increasing the radius of blood vessels downstream (via auto-regulation), which reduces the overall resistance of the circulatory system and raises the local flow rate in the coronary artery to an acceptable value. However, as the numbers in the previous parts suggest, an 90% reduction severely reduces the flow rate (over 99%). What if the body could maintain a flow rate of 0.8 mL/s in the 90% occluded vessel by raising the pressure? What pressure drop occurs across an 90% occluded artery at a flow rate of 0.8 mL/s? Significance: When the blockage increases significantly, the flow rate of the blood through the vessels decreases by a large amount. If the heart wants to restore the flow rate to the healthy flow rate, how much pressure difference is required across the artery. Does this pressure put strain on the heart? AP= Pa