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Page history last edited by Joe Redish 1 year, 7 months ago



Your body reduces blood flow to a region by vasoconstriction – contracting the smooth muscles that wrap around the artery. This reduces the artery’s radius. The drawing shows a piece of an artery with a part of it cut away so you can see the inside. Below that is another drawing showing the forces on just the top half of the artery. Model the artery as a cylinder with radiusand a length and consider only forces from pressure and tension forces in the muscle.  

A. Briefly give a reason why the body would need to change blood flow to some particular region. How do you know about this? (Where did you learn about it, for example.) If you aren’t sure, make a hypothesis and state why you think it might be true.


B. Suppose the blood in the artery has pressure P0+ΔP, where Pis the pressure outside the artery. Write an equation for the net force from pressure on the top half of the artery as a function of (possibly) P0, ΔPRL. A view of the forces on the top half of the artery is shown below the drawing. (Hint: If you prefer to simplify the shape of the artery to make calculations simpler, you are welcome to do so.) 



C. Suppose that an artery constricts and Δremains the same. Do the tension forces in the muscles around the blood vessel increase or decrease? How do you know? (In reality, the blood pressure would usually increase in this scenario, but we will ignore that complication here.) 


D.Suppose Δ= 10 kPa. Suppose we model the tension forces a muscle can create as γ= στ where τ is the thickness of the muscle. A typical smooth muscle has a σ of about 200 kPa. The thinnest possible muscle in a blood vessel wall would be a layer one muscle cell thick, about 10 microns. What is the largest blood vessel for which a muscle one cell thick could still constrict the blood vessel? 



Mark Eichenlaub & Joe Redish  12/15/17

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