This Is MS Multiple Sclerosis Community: Knowledge & Support

Dear Malden,

I see a number of flaws in your argument.



This argument makes absolultely no sense. The scenario you suggest of a large tube that is narrowed is the exact same as mine. What counts is the cross sectional area of empty space through whic fluid could pass or inner diameter. If your argument was correct, I could get more flow through a tube if I increase the thickness of its walls. Think of your pumbing. Would increasing the thickness of the pipes while leaving the inner diameter change anything?? Undoubtedly not.

The following argument also does not make any sense.



From your argument, velocity of flow in a vertical tube is a function of just gravity (9. and DH. The diameter of the tube should therefore not affect velocity. In the scenario of the two buckets, velocity through the larger and smaller tubes would be the same.

You also mention that both tubes have the same cross sectional area, as you are using outer diameter. This is not correct as you need to use inner diameter. If you use inner diamter your formula will state that flow is reduced in the smaller tube.

I will make one last attempt to convince you that flow is reduced in the face of a stenosis. Here is another model:

Imaginge a closed loop system with a heart pumping blood at a certain cardiac output of lets of litres per minute. This closed loop system consists of a tube coming out or the heart and then going back into it. Let us assume that this cardiac output stays constant even in the face of a stenosis. In this scenario, as you would predict, there would be no reduced flow if you compare the system of the stenosis vs the system with no stenosis. What differs however is that velocity is higher through the stenotic portion. Another difference is that pressure would be higher before the stenosis and lower afterward.

Now take this system and modify it a bit. After the tube comes out of the heart, have it split into two tubes. Then have the tubes join together to form one tube which then goes back into the heart. What happens if you create a stenosis in one of these tubes? What will happen is that more blood will go down the tube without stenosis and less blood through the stenotic tube. As stenosis increases, less and less blood will get through this tube. When stenosis reaches 100% no more blood will go through the blocked tube and all of it will go through the patent tube. This scenario is closer to what happens in reality. It is common sense, intuitive and make sense from a mechanics point of view.

North

From your argument, velocity of flow in a vertical tube is a function of just gravity ( 9.81 m/s ) and DH.

- no, I wrote "exit flow speed" not "velocity of flow in a vertical tube". Exit flow speed (velocity) is at the and of the tube, where flow runs free out in the air. And only at this particular place flow velocity is function of just gravity constant and dH. And this exit velocity we use with exit cross section to calculate exit flow. And that flow is constant along the whole tube. Only velocities changes along the tube if cross section changes too (narrowing, widening).

The diameter of the tube should therefore not affect velocity. In the scenario of the two buckets, velocity through the larger and smaller tubes would be the same.

- No, diametar does not effect exit velocity, inner diameter of a tube just affect flow as a component of a cross section area.

You also mention that both tubes have the same cross sectional area, as you are using outer diameter. This is not correct as you need to use inner diameter.

- I don't specify neither inner or outher diameter, It's obious that inner counts (flow cross section).

If you use inner diamter your formula will state that flow is reduced in the smaller tube.

- tubes are the same size at exit cross section area.

I will make one last attempt to convince you that flow is reduced in the face of a stenosis. Here is another model:

Imaginge a closed loop system with a heart pumping blood at a certain cardiac output of lets of litres per minute. This closed loop system consists of a tube coming out or the heart and then going back into it. Let us assume that this cardiac output stays constant even in the face of a stenosis.

- correct, cardiac output stays constant if hart rate stays constant.

In this scenario, as you would predict, there would be no reduced flow if you compare the system of the stenosis vs the system with no stenosis.

- yes, flow is generated by hart (pump) only.

What differs however is that velocity is higher through the stenotic portion.

- correct.

Another difference is that pressure would be higher before the stenosis and lower afterward.

- yes, total preasure decrease constantly during blood trip through this closed loop system. Decreasing is from resistence from tube walls roughness and from local flow resistence (narowing, widening, turning, etc).

Now take this system and modify it a bit. After the tube comes out of the heart, have it split into two tubes. Then have the tubes join together to form one tube which then goes back into the heart. What happens if you create a stenosis in one of these tubes? What will happen is that more blood will go down the tube without stenosis and less blood through the stenotic tube. As stenosis increases, less and less blood will get through this tube. When stenosis reaches 100% no more blood will go through the blocked tube and all of it will go through the patent tube. This scenario is closer to what happens in reality. It is common sense, intuitive and make sense from a mechanics point of view.

- Yes, at start flow will be distributed through two paralel tubes, according to tubes resistance. 50:50 flow, for example, for the same branch cross sections and the same branch resistence. When one branch start to cloth and narrowing, ratio changes for eg. 80:20. When one branch it's totaly closed ratio is 100:0.

Everything you said is correct, but the flow is reduced just in one branch, total flow in the loop (hart-brain-hart) is still 100% -not reduced at all!

Best regards, M.

Dear Mladen,

Sorry for the late response. I agree with what you had written in your last posting. I think you misunderstood, or perhaps I did not explain the bucket model as I should have, and I think this led to some confusion. I won't go through this again as I think it will get too complicated. I want to concentrate on the second part of your posting that comments on the heart pumping model.

First, though, I want to say that this back and forth has allowed me to scrutinize point number 2) of my model and I can see where your criticisms were correct regarding velocity of flow. I will restate point 2 here:

"2) This obstruction of the larger veins in turn results in reduced rate and velocity of flow in the microvasculature (capillaries and post capillary venules) upstream from the stenosis or obstruction. This deduction is supported by simple hemodynamic principals. "

I mention that obstruction will result in both reduced rate of flow and velocity of flow. It was incorrect to assume velocity of flow would necessarily be reduced as velocity of flow would also be a function of how many capillaries the body decides to keep open.

What is important, though, in my model is not velocity of blood flow in the capillaries but the rate rate of flow (volume per unit time). It is this rate of blood flow that will in the end determine the level of oxygen that gets to the brain and this is what is important. My point 2 should state that it is the rate of flow (not velocity) that is decreased. I should also have pointed out that the rate of flow is decreased regionally, specifically in the capillaries that eventually feed into the stenosis. As you pointed out in the heart model, total flow in the system will be the same (There will be greater flow on the side that has no stenosis). In the brain, however, venous obstruction will result in greater vascular resistance for blood trying to pass through the brain. This will result in blood flowing preferentially to areas other than the brain and therefore in a global hypoperfusion of the brain.

The key point I want to emphasize here is that rate of flow in certain capillaries (microvasculature) can be decreased because of stenosis in a larger vein. This is what leads to adverse neurologic consequences. If this is correct, my point 2 is not disproven.

North

I can't comment on the finer points, but would it not be more analogous to visualize hoses (arteries) pumping fluid into a sponge within a membrane (the brain), with the outlet hoses (veins)? You are considering a free-flowing system, without perfusion resistance, in using the bucket analogy.

There is a problem with that though, in that my brain parynchema is shrinking, or atrophying, rather than swelling like a saturated sponge - and I use my brain a lot (admittedly, it is becoming progressively more useless!).

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My name is not really Johnson. MSed up since 1993