Static and Dynamic Properties of Blood Pressure

[kbm]

Okay, I have read all the threads on this site that I could find about Bernoulli's equation and blood pressure, but I am still really confused, and the more I think about it the more confused I get.

I get that bernoulli's doesn't take frictional losses into account, but at a short section of an artery, I assume it would still hold.

With bernoulli's equation, I can understand it in terms of energy that if kinetic energy (velocity) goes up, potential (pressure) energy must go down. And with the continuity equation, if radius decreases then velocity increases and so pressure must decrease.

Intuitively I still have a hard time wrapping my head around this - if a fixed volume of fluid was traveling through a pipe, and that pipe's radius got larger, the continuity equation would say that its velocity would decrease, and if velocity decreases, then bernoulli's equation will say that its pressure will increase.

This doesn't really make sense to me though when I think of pressure as the force that the fluid molecules are exerting on the vessel wall. If the same amount of fluid is exerting its force over a dilated vessel with greater surface area, then wouldn't the pressure on the walls decrease compared to a constricted vessel? Or is there a difference in the "fluid pressure" that bernoulli's equation is talking about and the actual pressure on the vessel wall?

Wouldn't something like Boyle's law apply to vessels? I know that blood is incompressible, but if the same amount of blood is contained in a larger volume, then I would think that pressure would decrease, and vice versa for blood contained in a smaller volume. But as soon as fluid starts to flow, then nothing makes sense to me anymore because if the volume gets bigger, velocity goes down and pressure goes up...

On a related note, how can the continuity equation and poiseuille's equation be related? My understanding is that velocity and flow rate aren't quite the same, but they are proportional to each other. With poiseuille's, if radius goes down then flow rate goes way down due to the 4th power relationship, but continuity equation would say that velocity would increase?

Is it ever possible that velocity of the blood would increase but the overall flow rate would decrease?

I hope this makes sense. Blood pressure is much easier to "get" when I think of it purely in terms of how much blood a vessel is holding in relation to its size - a small (constricted) vessel holding a large amount of blood will generate a high pressure on the walls, and a large (dilated) vessel with a small amount of blood will generate a low pressure on the walls. But then bernoulli's equation always jumbles it all up for me and it makes no sense.

 

[Moonbear]

I'm not entirely sure what you're asking, so I think I'll just delve in with a few common misconceptions and see if any of them stick.

First, keep in mind that blood vessels are elastic. Arteries have more muscular walls than veins, so often we refer to arteries as resistance vessels, and veins as capacitance vessels.

Second, when talking about blood pressure, are you talking about local pressure, or are you talking about the arterial pressure measured when someone puts a blood pressure cuff on your arm? They can be different. Also, peripheral resistance can also influence the pressure drop from arterial to venous circulation...it's not a fixed number. In most cases, we disregard peripheral resistance and venous pressure, because it's negligible, but in some pathology, it becomes significant enough to need to measure it. You can also get local changes in vasodilation or vasoconstriction such that organs can regulate blood flow and blood pressure at that organ without altering overall systemic blood pressure.

Another thing to keep in mind is we have a dynamic pump system at the heart. Cardiac output affects blood pressure, so we can compensate for vasodilation by pumping through more blood volume per minute. Likewise, even blood volume is not fixed. This is generally regulated by the kidney that a drop in blood pressure can result in an increase in fluid retention and hence an increase in blood volume to compensate for the pressure drop to restore pressure.

Usually, the misunderstandings come from trying to apply the physics of a closed system of fixed diameter pipes with a fixed fluid volume and pump capacity to cardiovascular physiology, which has more variables.

 

[kbm]

Thanks for the reply. I think my main confusion arose when thinking about the effects of compliance of a vessel on local blood pressure in comparison to what bernoulli's equation would predict. If a vessel had high compliance, then when some volume of blood is injected into it, it would stretch, but pressure would not increase very much. What confused me was that if it stretches, then continuity equation would predict velocity to go down, and bernoulli's would then predict pressure to go up. But I guess if blood is being "added" sort of, then flow isn't constant and bernoulli's and the continuity equation wouldn't really apply then.

Another thing, most resources say that blood flow is constant in each part of the circulatory system, but I don't see how this is the case, since different parts have different resistances, and so wouldn't local flow rates vary? Say if arterioles constricted, wouldn't there be less flow through them, and then blood would "pool up" upstream?

One other thing that has been confusing me recently is how or why the pulmonary circuit operates at a much lower pressure. If stroke volume is the same from the RV and LV, then the same amount of blood is ejected per contraction. I don't know if this is the right way of looking at it, but if each ventricle is ejecting the same amount (mass) of blood at the same rate, then I would think that the force acting on them is the same since f=ma, and since force is proportional to pressure I would think pressure would be the same? To add to that, I am assuming (not totally sure) that the pulmonary circulation is a fair bit lower in volume than the systemic side, and since the pulmonary circuit takes the entire cardiac output, wouldn't pressure be expected to be larger just due to the fact that its the same amount of blood in a smaller space?

Too many questions.. thanks for any feedback