I found this on the web and I wanted to pass this along. I thought this was a really good explanation about Vasodilation and decreased pressure, but I think we can project this to Vasoconstriction as well.
Bernoulli's Principle and Vasodilation
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Question: So from what I understand vasoconstriction causes an increased blood pressure and vasodilation decreases blood pressure. This makes sense to me in the intuitive sense. However, from what I also understand of Bernouli's equation, this doesn't make sense. I'll try and explain with the vasodilation example. I feel as if one of these statements might be incorrect which is why I might be confused...
1. Vasodilation --> increased cross-sectional area
2. Increased cross-sectional area --> decreased velocity (A1V1=A2V2)
3. Decreased velocity --> Increased pressure (Bernouli's equation)
4. Therefore vasodilation --> increased blood pressure
Yet vasodilation is supposed to decrease blood pressure...
So I feel like I might be mistaken at either step 1 or step 3, but I really don't know where.. could you perhaps help explain this concept to me?
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Answer: First of all, all of the statements you provided there are correct when we're talking about physics. Vasodilation by definition means that we have an increased radius of small blood vessels due to one of many triggers. From the continuity equation, as you wrote, an increase in A, the cross-sectional area, will correspond to a decreased v, velocity. All else being equal (density of fluid, height, etc.), a decreased velocity corresponds to increased pressure.
And yet vasodilation does decrease blood pressure.
First, there are a number of assumptions that are true when we're talking about MCAT physics that don't apply in the human body:
1. The continuity equation assumes that the flow rate is constant; indeed, the very point of the continuity equation stems from the idea that if the flow is constant, then decreasing the cross-sectional area means the fluid has to come out faster. In biology, this is not necessarily true. In many cases, for example, vasoconstriction is caused by an outpouring of epinephrine (the idea being that in a fight-or-flight response, you don't want a bleeding risk and so the blood flow, especially to injured areas, decreases by vasoconstriction). At the same time, however, epinephrine increases heart rate and stroke volume. This leads to a much larger cardiac output, and therefore the continuity equation doesn't really apply. We're putting through a faster flow rate, so that partially increases the pressure.
2. MCAT physics assumes that the tubes are made of an inelastic material. While this may seem insignificant at first, it's actually a critical difference between what makes the pressure in a concrete tube, and what makes pressure in blood vessels. Pressure for a rigid surface is really just based on the force of the fluid over a cross-sectional area. We assume the tube to be rigid so that recoil doesn't really play a role. In the human body, however, this is a key part to how blood vessels work. In the intimal layer of arteries and arterioles (less so venules and veins), there are proteins that are designed to stretch when the artery is filled with blood, and recoil during the other half of the cardiac cycle. These proteins, called elastins (hence the name), act much like a balloon. As the vessel is dilated, they aren't able to provide as much recoil (think about how a balloon gets much easier to inflate once you've gotten it started). This is why aneurysms can occur - as the vessel stretches, it becomes easier to continue stretching and can blow out. In looking at vasoconstriction, the wall will have much more recoil. This causes a lot more pressure within that vessel.
3. One last assumption is that the volume of the fluid stays the same. When vessels vasodilate, they tend to lose some of their fluid into the interstitium. This "extravasation" of fluid explains why people can get very swollen when they're sunburnt - the vasodilated vessels, trying to give off heat and bring white blood cells to the affected area, allow fluid leakage. This causes a decrease in pressure in the remaining vessels as blood volume goes down.
Hopefully these two points help explain this connection. Vasodilation causes a decrease in blood pressure, and vasoconstriction causes an increase in blood pressure. The specifics are outside the scope of the MCAT, but hopefully it helped put together some points from physics and biology! There may be even more to answer this question, and if I hear anything about it when we start cardiology next week, I'll make sure to share.
-Alex
