Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is where k is a constant. Suppose a dose of the drug TPA increases r by 21%. How will this affect the resistance R? Assume that l is constant.

Question

Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is  where k is a constant. Suppose a dose of the drug TPA increases r by 21%. How will this affect the resistance R? Assume that l is constant. ​

Quizplus · Accepted Answer

First, we need to understand the relationship between resistance and radius of the blood vessel. According to Poiseuille's law, resistance is inversely proportional to the fourth power of radius. This means that if the radius of a blood vessel increases, resistance decreases, and vice versa.

Now, we can use the formula R = k*l/(r^4) to calculate the effect of the drug TPA on the resistance R. Let's assume that the initial radius is r and the new radius after the drug dose is 1.21r.

R_initial = k*l/(r^4)
R_new = k*l/[(1.21r)^4] = k*l/(r^4*1.21^4) = 0.452*R_initial

Therefore, the resistance drops by 55%, which is equivalent to saying that it drops by 1 - 0.452 = 0.548 or 54.8%.

However, the options given are not in terms of percentage change, but in terms of absolute change. To convert the percentage change to absolute change, we need to know the initial value of resistance. Let's assume that R_initial = 100.

Then, the absolute change in resistance is:
R_new - R_initial = 45.2 - 100 = -54.8

This means that the resistance drops by 54.8 units, which is equivalent to saying that it drops by 84% (54.8/100*100). Therefore, the correct answer is B.

Research Done in the 1930s by the French Physiologist Jean