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Physiology · Cardiovascular: haemodynamics
Sample itemA vasodilator drug doubles the radius of a systemic arteriole while the pressure gradient across it and the blood viscosity stay constant. By what factor does flow through that arteriole change?
Original practice item, not a recalled exam question. Nothing here is recorded.
The answer and the reasoning
D. It increases 16-fold
According to Poiseuille's law, flow is proportional to the fourth power of the vessel radius, and resistance is inversely proportional to r to the power 4. Doubling the radius therefore gives 2 x 2 x 2 x 2 = 16 times the flow. This is why small changes in arteriolar calibre have such a large effect on peripheral resistance.
Option by option
A. It increases 8-fold
An 8-fold change would follow a cubic relationship, which does not describe laminar flow in a tube.
B. It increases 2-fold
A 2-fold change would occur only if flow were directly proportional to radius.
C. It increases 4-fold
A 4-fold change would occur if flow depended on the square of the radius, which is the cross-sectional area.
D. It increases 16-fold (correct)
Correct. Flow varies with r4, so 2 to the power 4 gives 16.
Source note: Original NextPrep sample item — pending expert review. This item is original practice material awaiting independent expert review, so confirm important facts in a standard textbook.
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