1–5. a. Saying that the diameter of a vessel increases by 10% is equivalent to saying that its radius increases by 10%; that is, the radius after the change is 1.1 times the radius before the change. The Poiseuille equation says that, other factors equal, resistance is proportional to 1 over radius to the fourth power:
R ∝ 1/r4
Rbefore ∝ 1/(rbefore)4
Rafter ∝ 1/(1.1rbefore)4 = [1/(1.1)4][1/(rbefore)4] = (1/1.46)Rbefore = 0.68 Rbefore
Therefore, a 10% increase in vessel radius will reduce its resistance by 32%.
b. Because Q̇ = ΔP/R, and Rafter = 0.68 Rbefore
Q̇after = ΔP/0.68 Rbefore
… and for a given ΔP…
Q̇after = 1/0.68 Rbefore = 1.46 Q̇before
Therefore, for a given ΔP, a 10% increase in vessel diameter will increase flow by 46%.
[Note: One must always use change factors NOT percentage changes in these equations.]1–6. a. Wrong! The pulmonary and systemic circuits are arranged in series and therefore must have the same through-flow.
b. Wrong! The right and left hearts are served by a common electrical excitation system and therefore beat at the same rate.
c. Wrong! Although it is true that the right ventricle is less muscular than the left, that fact does not explain why pulmonary pressure is so low. Actually, it is the other way around: because pulmonary arterial pressure is low, the right ventricle does not have to be very muscular to pump blood into the lungs.
d. Right! ΔP = Q̇ × R. Because Q̇ is the same (= CO) through the lungs and the systemic circulation, the only way pulmonary arterial pressure could be relatively low is for pulmonary vascular resistance to be relatively low.
e. Wrong! CO = HR × SV. CO and HR are the same for both the right ...