Contradictions between fluid motion physics and blood flow in bio

[Trayshawn]

I am having some serious difficulties understanding the physics behind vasoconstriction/dilation. The affects don't seem to line up with what I understand about hydrodynamics.


First, let me see if I got the basics right.

- Blood pressure is the hydrostatic pressure of blood against the walls of vessels.
- Resistance is the opposition to fluid flow by the cells of the blood vessels.
- Vasoconstriction is the decrease in diameter of primarily arterioles (mainly arterioles, right?) due to the contraction of nearby smooth muscle cells.
- Vasodilation is the increase in diameter of primarily arterioles due to the inhibition of nearby smooth muscle cell contraction.
- Vasoconstriction increases resistance since the space available for blood flow is decreased.
- Vasodilation decreases resistance since the space available for blood flow is increased.

But from here on is where I get confused.
Vasoconstriction is supposed to increase blood pressure right?
But the law of continuity says that a fluid increases in velocity when the cross sectional area is smaller. Vasoconstriction leads to a smaller cross sectional area and so should increase velocity. But an increase in velocity indicates an acceleration. Since accelerations are only due to forces, there must be a net force acting on the blood. This force must be from a difference in pressure - higher before the constricted arteriole, lower after it. This this implies that blood pressure DECREASES during constriction.
But this is not the case, why not?

When I asked this to someone before, they mentioned the formula blood pressure = cardiac output x resistance (or BP = CO x R).
Vasoconstriction increases resistance, fine. But it shouldn't necessarily follow that blood pressure should increase as a result of this. Thats assuming that cardiac output is constant. But if cardiac output decreased more than R increased, then BP would decrease.

This brings up another point. How is cardiac output affected in vasoconstriction. I would think that since there is more resistance, there is slower blood velocity and thus a lower CO. But isn't the CO generated in the heart (stroke volume x heart rate)? The heart shouldn't care whether vessels outside of it are constricted or not, it should be the one to generate the CO regardless of vasoconstriction or vasodilation.

I also don't understand the analogy that the formula tries to make to batteries in circuits. The pressure is supposed to equal the voltage drop, the cardiac output translates to the current, and the resistance is..well..the resistance.

But in the case of a battery with one resistor, there is NO way to change the voltage drop without changing the battery. Changing the resistance will only affect the current.
If you consider one particular artery running to an organ and back to the heart (as a vein), then this should resemble the one resistor circuit I mentioned. However, here increasing the resistor somehow DOES increase the voltage-equivalent aka pressure. This makes no sense!

And how does vasoconstriction limit blood flow to certain organs? Again, by the law of continuity, the volume of blood passing through any cross sectional area should be constant. Blood should simply move faster if the area is smaller. This would suggest that vasoconstriction does NOT limit blood flow to any area, it just makes the same amount of blood move by faster.

AHHH SO MANY CONTRADICTIONS!!!!


Please help! My test in in a week and this is the ONE concept that I don't get. I can help explain anything else to any of you if you need it as a thanks lol.

Thanks!

---

Members don't see this ad.

 

[MangoPlant]

During vasoconstriction the force acting on the blood comes from the walls of the blood vessel, but remember by newtons third law that the blood produces a reaction force on the walls of the blood vessel. This reaction force is blood pressure. Also note that there is acceleration only WHILE the blood vessel is constricting. Once the vessel reaches its shorter diameter the acceleration goes back to 0 and the new, higher velocity remains constant. The force/acceleration is only present DURING constriction.

 

[Trayshawn]

Really? I don't see why acceleration would only be when the vessel is contracting.
All that seems to be necessary for acceleration is a point where the areas are different for the reasons I mentioned before.
That area exists during the actual contraction and throughout the sustained contracted state.

In any case, the increaed velocity and acceleration (no matter how brief) indicate a pressure difference. So it still doesn't follow why the blood in the constricted vessel is at a higher pressure instead of a lower one.

 

[curt656]

I am by no means an expert and you obviously have a better grasp on the entirety of the concept than I do. My test is in 2 weeks, so I want to understand as much as you do and will try to help talk through it, lol.

In vasoconstriction, blood pressure increases proportionally as resistance increases while blood flow decreases. To me that says that velocity (and cardiac output for that matter) does not change and there is no acceleration. If velocity increased, then flow would increase right? But velocity doesn't increase and isn't a part of the equation. The question is why?

As far as the heart and CO is concerned, increased resistance requires an increase in CO to move the same volume of blood as a result of increased BP. If resistance is increased, the heart is going to have to work harder to keep CO at the same level. So I think CO would decrease somewhat in the presence of resistance. If I am not mistaken (I do not know for sure), the heart can only work faster, not harder (more forcefully). So, if the heart rate is unchanged, the vessels are constricted, and resistance increases then CO should decrease an response to an increase in BP, and blood flow decreases as a result of all three factors.

My feeling is that the resistance increase is compensated by BOTH an increase in BP and a decrease in CO resulting in a decrease of blood flow. It would have to work this way or velocity would increase, right?

Edit 1: The heart can work harder only after a prolonged period of time in which the walls of the heart muscle get thicker as to maintain CO with a larger force of contraction. So, I think I may be correct. The increased resistance and BP results in a lower CO which maintains velocity thus reducing blood flow in the presence of smaller vessel area.

 

[MangoPlant]

But from here on is where I get confused.
Vasoconstriction is supposed to increase blood pressure right?
But the law of continuity says that a fluid increases in velocity when the cross sectional area is smaller. Vasoconstriction leads to a smaller cross sectional area and so should increase velocity. But an increase in velocity indicates an acceleration. Since accelerations are only due to forces, there must be a net force acting on the blood. This force must be from a difference in pressure - higher before the constricted arteriole, lower after it. This this implies that blood pressure DECREASES during constriction.
But this is not the case, why not?

In regards to the bold part above, the higher pressure is not before the arteriole constricts but AFTER it constricts. This would mean that blood pressure increases during constriction as observed and maybe you have the difference in pressure backwards? I might be misinterpreting what you wrote but maybe this is the case.

 

[Trayshawn]

@mangoplant - thats just bad wording on my part. I meant like WHILE the arteriole is contricted, the pressure within the arteriole is lower than the artery that is immediately before it (before in terms of location, not time)

@curt656 - Hmm.. I think a good place to start would be here:
Does changing blood pressure and resistance (by vasodilation or vasoconstriction) alter cardiac output?
Because cardiac output seems to be a property dependent on the state of the heart and NOT on the vessels at all.

It may be something like the resistance of a resistor in a circuit. While R = V/I (ohms law), changing V and/or I will NOT change the value of R. R is dependent on a different set of variables intrinsic to the resistor. Namely, R = rho*length/area.

Is this the same thing for cardiac output? Because CO also = stroke volume x heart rate which are, indeed, independent of vessel size and intrinsic to the state of the heart

 

[curt656]

@curt656 - Hmm.. I think a good place to start would be here:
Does changing blood pressure and resistance (by vasodilation or vasoconstriction) alter cardiac output?
Because cardiac output seems to be a property dependent on the state of the heart and NOT on the vessels at all.

It may be something like the resistance of a resistor in a circuit. While R = V/I (ohms law), changing V and/or I will NOT change the value of R. R is dependent on a different set of variables intrinsic to the resistor. Namely, R = rho*length/area.

Is this the same thing for cardiac output? Because CO also = stroke volume x heart rate which are, indeed, independent of vessel size and intrinsic to the state of the heart

I feel ya. I just can't imagine any other way to explain why flow decreases.

Blood flow is inversely proportional to resistance which is inversely proportional to the 4th power of the vessel radius (Poiseuille's Law) so flow is proportional to radius. So if the vessel radius decreases by half, resistance is increased by a factor of 16 and flow decreases by the same amount.

Cardiac output is a measure of blood flow. Flow = pressure/resistance (CO = BP/R) or heart rate x stroke volume.

I'm afraid this is the best my research can determine. Sorry if it doesn't help, lol. Good luck next week!!

 

[Eastfolding]

Blood pressure increases because resistance to flow increases.

Water flow is analagous to electrical current.

 

[richkaj]

Also, think about why there is vasoconstriction and vasodilation. This usually occurs together in seperate parts of the body... during flight and fight response... blood is shunted from the digestive system and more towards the muscles that need more oxygen (i.e. leg muscles)... there is a increase and decrease but when the response is over, the system goes back to equilibrium... Just wanted to explain that vasoconstriction is not a boxed in situation, blood flow must go somewhere else so that the voltage/cardiac output can stay the same...

 

[richkaj]

I am just imagining if all blood vessels (arterioles) constricted... I wonder if that would lead to a heart attack

 

[docelh]

Trayshawn, there is no contradiction. You're just framing the problem incorrectly.

One flaw in your analysis is that you're framing the problem of looking at one arteriole. The constant flow equation requires that you look at all arterioles in the aggregate when comparing to the aorta in the aggregate or the capillaries in the aggregate. For example, it would appear that the velocity and pressure is higher in the aorta than in the capillary based on what appears to be true. What appears to be true is not necessarily true. That is true for an individual capillary, but not true for all capillaries taken as a whole. Aggregate pressure is higher in the capillaries than in the aorta. This makes sense when you consider that net pressure is fundamental in the exchange of nutrients/waste between vessels/tissue, and that diffusion takes up energy that can't be used to accelerate the aggregate velocity of the fluid through the capillary. I used the example of the capillary, but you can easily extend this analysis to the flaws of looking at metarterioles individually as opposed to the aggregate.

A second flaw in your analysis is that you are applying the wrong physics laws. You are using laws based on constant fluid flow to a situation where that is not true. With metarteriole constriction, the body is clearly trying to change fluid flow in some parts of the body. The proper framework to apply here is the Bernoulli equation where blood is flowing from point 1 (artery) to point 2 (capillary), but metarteriole constriction is now adding pressure at point 2.

Hope this helps.

P.S. - Venuous return drives cardiac output. Thus, output is completely dependent on the vessels (blood inflow) and secondarily on the heart itself. The heart does the work, but it only works on what is coming in. This is what the Frank-Starling theory states.