How can the lower pressure in a narrowing artery offset..(TBR Non-test question)

[Gauss44]

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There's a comment in TBR that goes, "The lower blood pressure in a narrowing artery can be low enough to do more than offset [the high blood pressure associated with artherosclerosis]."

Can someone please explain this comment?

(You'll notice that I used brackets to summarize a longer quote. If you would like to read the original here it is: "You may have guessed that the pressure should increase because of the high blood pressure associated with artherosclerosis. The heart of one afflicted with atherosclerosis pumps with a greater pressure to keep the blood volumetric flow rate at healthy levels, increasing the total pressure throughout the arteries. However the pressure is lower in an unhealthy section of an artery than it is in a nearby healthy section because of the flow speed increase. This comparison was the thrust of this question. As an aside, the lower pressure in the narrowing artery can be low enough to do more than offset the increased pumping pressure of the heart, making the arterial pressure lower than that in a healthy individual's artery.")

 

[sshah92]

The answer to this question doesn't lie as much in cardiovascular theory as it does in simple fluid mechanics. Think Bernoulli's effect. When you have a pipe that starts off with a small radius and farther down has a much larger radius, you can look at this equation

Psmall + (1/2)rho(vsmall^2) + rho(g)hsmall = Plarge + (1/2)rho(vlarge^2) + rho(g)hlarge

Let's pretend this is a horizontal vessel and there is no height disparity. That eliminates the third item (potential energy). You might remember that velocity is higher in a more occluded vessel than in a dilated vessel. That assumption allows you to rearrange the equation, such that

Psmall/Plarge = (1/2)rho(vlarge^2) / (1/2)rho(vsmall^2)

Again, the velocity in the dilated (large) vessel is smaller than the velocity in the constricted vessel, so the right side of this equation will be a ratio below 1. This means that P large is more than P small (denominator is larger than numerator).

Therefore, the lower blood pressure in a constricted, occluded artery locally offsets the increase in blood pressure (everywhere else) associated with atherosclerosis. Hope this helps!

 

[Gauss44]

The answer to this question doesn't lie as much in cardiovascular theory as it does in simple fluid mechanics. Think Bernoulli's effect. When you have a pipe that starts off with a small radius and farther down has a much larger radius, you can look at this equation

Psmall + (1/2)rho(vsmall^2) + rho(g)hsmall = Plarge + (1/2)rho(vlarge^2) + rho(g)hlarge

Let's pretend this is a horizontal vessel and there is no height disparity. That eliminates the third item (potential energy). You might remember that velocity is higher in a more occluded vessel than in a dilated vessel. That assumption allows you to rearrange the equation, such that

Psmall/Plarge = (1/2)rho(vlarge^2) / (1/2)rho(vsmall^2)

Again, the velocity in the dilated (large) vessel is smaller than the velocity in the constricted vessel, so the right side of this equation will be a ratio below 1. This means that P large is more than P small (denominator is larger than numerator).

Therefore, the lower blood pressure in a constricted, occluded artery locally offsets the increase in blood pressure (everywhere else) associated with atherosclerosis. Hope this helps!

Thank you very much for answering.

Part of my confusion though is figuring out how that squares with this other discussion here: http://forums.studentdoctor.net/showthread.php?t=984414&highlight=kidneys+constrict

And how much does Bernoulli's equation apply to blood?

 

[Gauss44]

I think I might finally understand the question in my topic. A simplification of what they are saying might be, in a system such as a pipe, let's say the pressure is greater toward the beginning and the pressure is smaller toward the end.

Pressure at beginning + Pressure at end = Total Pressure

So, if pressure at the end of the pipe or tube is low enough relative to pressure at the beginning, it has "offset" the high pressure.

Now, the question of how this is possible in the human circulatory system? The answer might lie in laminar versus turbulent flow, and the impact of that on the flow rate and velocity of flow (turbulent flow being slower than laminar). If the plaque in the artery is arranged in such a way that it produces a laminar flow and the blood is reasonably thin, then sure, the velocity and therefore the pressure of the blood in the clogged section of the circulatory system will off set the high pressure in the system before it.

Does this sound correct?