Stenosis quantification? How do you calculate it?

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Stenosis quantification? How do you calculate it?

Postby AlmostClever » Fri Oct 15, 2010 2:19 pm

Where can you get this percentage?

All I was told was "mild" and "moderate" - no percentages.

Taking measurements from my venogram images, I can determine my vein narrowed down to 5.5 mm from 9 mm so is this about a 50% blockage based on diameter or 70% based on cross section area?

Just wondering what the official ruling on this is...

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Re: Stenosis quantification? How do you calculate it?

Postby patientx » Fri Oct 15, 2010 4:44 pm

AlmostClever wrote:Where can you get this percentage?

All I was told was "mild" and "moderate" - no percentages.

Taking measurements from my venogram images, I can determine my vein narrowed down to 5.5 mm from 9 mm so is this about a 50% blockage based on diameter or 70% based on cross section area?

Just wondering what the official ruling on this is...

A/C


Though it's about arteries, this may shed some light. See, in particular, page 4 of the article:

http://www.allbusiness.com/legal/legal- ... 338-1.html
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Re: Stenosis quantification? How do you calculate it?

Postby 1eye » Tue Jul 23, 2013 2:56 pm

There are a number of considerations which, in arteries at least, simplify this work. However veins are different enough that things like compliance may be factors as well.

From http://www.cvphysiology.com/Hemodynamics/H003.htm

Vessel length does not change appreciably in vivo and, therefore, can generally be considered as a constant. Blood viscosity normally does not change very much; however, it can be significantly altered by changes in hematocrit, temperature, and by low flow states.

If the above expression for resistance is combined with the equation describing the relationship between flow, pressure and resistance (F=ΔP/R), then

This relationship (Poiseuille's equation) was first described by the 19th century French physician Poiseuille. It is a description of how flow is related to perfusion pressure, radius, length, and viscosity. The full equation contains a constant of integration and pi, which are not included in the above proportionality.

In the body, however, flow does not conform exactly to this relationship because this relationship assumes long, straight tubes (blood vessels), a Newtonian fluid (e.g., water, not blood which is non-Newtonian), and steady, laminar flow conditions. Nevertheless, the relationship clearly shows the dominant influence of vessel radius on resistance and flow and therefore serves as an important concept to understand how physiological (e.g., vascular tone) and pathological (e.g., vascular stenosis) changes in vessel radius affect pressure and flow, and how changes in heart valve orifice size (e.g., in valvular stenosis) affect flow and pressure gradients across heart valves.

Although the above discussion is directed toward blood vessels, the factors that determine resistance across a heart valve are the same as described above except that length becomes insignificant because path of blood flow across a valve is extremely short compared to a blood vessel. Therefore, when resistance to flow is described for heart valves, the primary factors considered are radius and blood viscosity.


The best indicator that there is a stenosis seems to be CSA, due to the dominance of vessel diameter or radius with a fourth-power proportionality. Resistance to blood-flow is the quantity directly affected by diameter, but volume flow rate and blood pressure are both linearly proportional to it. A large change in flow value or pressure is a good clue that there is probably a change in CSA. Because of the 4th-power term, a change o a factor of two (50%) changes the linearly related quantities resistance, flow, and pressure by a factor of 16.

Objects (webs, septa, stuck valve leaflets, etc.) in the vessel affect flow and pressure the same way, due again to the dominant influence of CSA, which may be significantly affected by such objects. However such objects' effects are not as predictable as an open, more or less pipe=shaped vessel. When there are no such objects, a visual assessment of CSA is a good predictor of any differences in flow or pressure. CSA can be checked in two dimensions with ultrasound or x-rays, as well as using intra-vascular ultrasound (IVUS). Presence of an object may also cause turbulence, which will raise the resistance to flow even more.

The blood's viscosity also has a linear relationship to the quantities of volumetric flow rate, blood pressure, and blood's resistance to flow. While not as important as CSA, it can also have significant effect.
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Re: Stenosis quantification? How do you calculate it?

Postby Cece » Tue Jul 23, 2013 4:34 pm

Stenosis of 30% or under is mild. Stenosis of 30% - 65% is moderate. Stenosis over 65% is severe. These are just my personal estimates. A 30% stenosis in a vein is equal to a 50% stenosis in an artery approximately. You can get an exact percentage if you go to an IR who uses IVUS. Mine were 78% and 99% which I consider severe! That's using CSA so I'd go by what you are saying is the estimated CSA (70%). Veins are oval not round so the estimate could be off.

What if an upper jugular stenosis causes a greater pressure rise in the venous sinuses than a lower jugular stenosis: would that mean that a 50% upper jugular stenosis is more severe than a 50% lower jugular stenosis? How big is the vein and how flexible is the vein? A 80% stenosis of a large vein allows more flow past than an 80% stenosis of a small vein because of the differences in size of the vein. A more elastic vein might compensate better for the effects of the stenosed area. We need a physicist with equations and access to a flow quantification database and the drive to figure this all out mathematically.

Anyway I don't think the exact percentage of the stenosis matters as much once it gets past the threshold of whether or not it should be treated. Some IRs have considered that threshold to be at 50% stenosis that is standard for arteries but I think that is wrong.

Hope you are well, AlmostClever.
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Re: Stenosis quantification? How do you calculate it?

Postby 1eye » Tue Jul 23, 2013 10:05 pm

I agree re the threshold for treatment, however, CSA is two powers of radius too few. While resistance goes up quickly, and pressure and flow down correspondingly quickly, the amount flow goes down by is not what you'd expect. If you only use a factor of r^4, the percentage of decreased flow for different levels of stenosis is like this:

90% stenosis, < 0.01% of flow
80% stenosis, < 0.16% of flow
70% stenosis, < 0.81% of flow
60% stenosis, < 2.56% of flow
50% stenosis, < 6.25% of flow
40% stenosis, < 12.96% of flow
30% stenosis, < 24.01% of flow
20% stenosis, < 40.96% of flow
10% stenosis, < 65.61% of flow
0% stenosis, < 100% of flow

Since there are a few other factors which more or less linearly affect flow rate, these numbers are on the high side. Non-roundness of veins is one of them.

As you can see, a 50% stenosis probably allows less than 1/16 the flow. Sounds severe enough for me.

That's just for a narrowing. An obstruction (faulty valve, web, septum, etc.) can be far worse.
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Re: Stenosis quantification? How do you calculate it?

Postby MrSuccess » Tue Jul 23, 2013 11:15 pm

patientx .... a good poster ... where have you gone ?

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Re: Stenosis quantification? How do you calculate it?

Postby 1eye » Wed Jul 24, 2013 3:39 pm

What if an upper jugular stenosis causes a greater pressure rise in the venous sinuses than a lower jugular stenosis: would that mean that a 50% upper jugular stenosis is more severe than a 50% lower jugular stenosis? How big is the vein and how flexible is the vein? A 80% stenosis of a large vein allows more flow past than an 80% stenosis of a small vein because of the differences in size of the vein. A more elastic vein might compensate better for the effects of the stenosed area. We need a physicist with equations and access to a flow quantification database and the drive to figure this all out mathematically.


I think you answered your own question about relative sizes of veins. If you are talking percentages, the question is, percent of how much? The diameter of a vein that is not split into two or more remains mostly the same except for obstructions or stenosis, throughout its length.

As for series connections...

The volumetric flow rate is the same everywhere, determined by the sum of all resistances between the left and right sides of the heart. In series-connected blood vessels the flow rate over the entire circuit of blood is the same throughout, determined by the sum of all resistances between the two sides of the heart. It is only when the path splits into two or more parallel ones, that the flow is shared.

What goes down, across a stenosis, or any decrease in the pipe's size, is the pressure.
A piece of the total pressure of the heart is lost every time any significant resistance is encountered.

If blood pressure is higher because of a stenosis, it is because the heart has decided to pump harder, in compensation, to have the same flow rate as it had had earlier before the stenosis appeared. This obviously cannot get worse indefinitely. So, if the heart can't push any harder, the overall flow rate will drop. That means the lower the number of vessels in parallel with one that has a stenosis, the more critical the stenosis is. Because of the way parallel circuits work, if the stenosis is in the largest vein or artery connecting two points, it will affect the overall flow much more. To have the same flow as before the stenosis, the heart will have to work much harder than if a stenosis had appeared in a smaller but parallel vessel.

Elasticity allows a vein to temporarily absorb and store relatively quick changes in pressure. It doesn't affect steady-state unless the vein gets permanently stretched or shrunk.

Ohm's law says V=IR. It's the same with blood. If resistance stays the same, flow and pressure go up and down together.

Resistance (stenosis) cannot ever cause an increase to anything upstream of it (unless the heart compensates by increasing pressure.

It is important to remember cause and effect. Flow is a result of applied pressure. Resistance i.e., stenosis etc., causes a reduction in both pressure and the resulting flow. Flow changes everywhere in the circuit, pressure only drops downstream. Since pressure upstream of a resistance is higher than downstream, and flow does not change from upstream to down, overall flow must decrease as resistance increases. That is because the flow is inversely proportional to it.
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Re: Stenosis quantification? How do you calculate it?

Postby 1eye » Fri Jul 26, 2013 10:26 am

The original poster, back in Oct, 2010, AlmostClever asked about a 9mm vein that was down to 5.5. Using those numbers (presumably diameter), I'd say the radius has gone down by 3.5mm. So the stenosis is 3.5/9 = .3888888, or about a 39% stenosis. If you just round up to 40%, the flow I calculated was <13% of the original flow. How did I get that? I used 1/(pi*r^4). I calculated that factor, based on r=9/2=4.5mm and r=5.5/2=2.75mm. Original 1/r^4 is 0.0024. New 1/r^4 is 0.017. Old 1/((pi)*r^4) is 0.00078. New 1/((pi)*r^4) is 0.0056. This represents a resistance which is higher, so the flow will be reduced. The proportionality of these resulting flows is such that the stenosed vein has at most 14 % of the flow rate it would have had without the stenosis.

This corresponds roughly to the table I posted before, as stenosis is 39%, and flow is down to about 14%. The table is on the liberal side. Actual values will be somewhat smaller (more severe) for flow, because I have tried to find a maximum using no constant of 8 or viscosity factor, which are required in a real calculation, resulting in an impossibly high value for volumetric flow rate. The lesson from this is that a 39% stenosis is already quite severe, having possibly more than 8 times less actual flow than shown in the table above. I imagine it would be quite rare for the smooth muscle layer to reduce a vein's size by so much as 40%. Consequently repairing a stenosis as severe or greater will, if successful, make a large difference to flow.
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