Question

Let’s say an arteriole dilates to 50% greater than its original size (i.e., the new radius of the arteriole is 1.5 times the original radius). How does the blood flow rate through the arteriole change after dilation? (Hint: You do not need to know the exact values for viscosity, arteriole length, or pressure gradient in order to answer this question.)

Answer 1

The blood flow is given by the equation:

Flow = ΔP/ R where ΔP = pressure difference (mm Hg); and R = resistance to flow (mm Hg x time/volume)

The resistance to blood flow (R) is given by:

R = 8 L η/ π r⁴ where r = inside radius of the vessel, L = vessel length, and η = blood viscosity.

Here it is clear from the equation that a small change in vessel radius will have a very large influence (4th power) on its resistance to flow.

Here the radius is increasing by 50% which means the radius is increased by 1.5 times and thus blood flow will be increased by 4th power of 1.5 i.e blood flow will be increased by (1.5 x 1.5 x 1.5 x 1.5 = 5.06) almost 5 times.