After numerous studies it has been determined that dissection (separation of the

Question

After numerous studies it has been determined that dissection (separation of the layers of the artery wall) occurred in 43% of the patients when the radius of the artery was expanding more rapidly than 0.01 mm/s the stent you are testing has a radius of 4 mm when fully expanded the artery is under the greatest stress as the stent reaches its full expansion It is desired to have an even rate of expansion so the safe rate should be the rate considered safe when the stent reaches full expansion The length of the stent is 20 mm Assume a cylindrical shape for the balloon and stent Determine the rate at which the fluid should be pumped into the stent to achieve the optimal radial expansion rate of 0.01 mm/s when the radius is 4 mm. Your answer should be in cubic mm/sec. Use this to determine how long it will take to fully inflate the stent. When blood flows along a blood vessel, the volume of blood per unit time that flows past a given point is called the flux F. Poiseuilles Law says that flux is proportional to the fourth power of the radius r of the blood vessel so F = kr^4 If after performing angioplasty, the radius of the artery was increased 0.5 mm to 4 mm, by what percent did this procedure increase blood flow? Also, to figure percent increase of the flux, youd need to take the change in flux divided by the original flux. For r make sure you use the original arterial size before expansion.

Explanation / Answer

1. hp = volume / time [q(m3/s)]2

Since the pump equation

hp = 0.01 + 20×103q2 = 0.2x103 q2

Q = 0.2 mm3/s

2. The change in relative of Fis given by DFF and the relative change in R is given by DRR. F = kr4 DF DR = 4kr3

So DF= 4kr3dr because we want the relative change in F, we divide by f to get DF F = 4kr3 f DR DF F = 4kr3 kr4 DR DF F = 4 r DR DF F = 4 · DR R

and, the relative change of the flux F is 4 times relatively change in the radius R.

A 5% increasing in the radius relates to a 20% increase in blood flow rate.

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