What the hell is going on here?

[TallScrubs]

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Ok, I come to you guys as my last resort--I'm frustrated as hell and I have spent way too much time on this one subject.

Q = dP / R

Equation should be easy for me, right? Wrong.

Costanzo says the following:

"[referring to blood going from aorta to large arteries to arterioles, etc] This decrease in pressure occurs as blood flows through the vasculature because energy is consumed in overcoming the frictional resistances"

"Since total blood flow is constant at all levels of the CV system, as resistance increases, downstream pressure must necessarily decrease, Q = dP/R or dP = Q x R"

This does not make any sense to me. If you constrict a blood vessel, you would increase the pressure. using the dP = Q x R, wouldn't an increase in R necessitate an increase in P?

Whoever explains this disparity to me will make my day

-TS

 

[loveoforganic]

Ok, I come to you guys as my last resort--I'm frustrated as hell and I have spent way too much time on this one subject.

Q = dP / R

Equation should be easy for me, right? Wrong.

Costanzo says the following:

"[referring to blood going from aorta to large arteries to arterioles, etc] This decrease in pressure occurs as blood flows through the vasculature because energy is consumed in overcoming the frictional resistances"

"Since total blood flow is constant at all levels of the CV system, as resistance increases, downstream pressure must necessarily decrease, Q = dP/R or dP = Q x R"

This does not make any sense to me. If you constrict a blood vessel, you would increase the pressure. using the dP = Q x R, wouldn't an increase in R necessitate an increase in P?

Whoever explains this disparity to me will make my day

-TS

You're making an assumption that applies to the system as a whole and applying it to a single vessel. Flow through that vessel must by no means be a constant or vary in any concordance with cardiac output. Picture just two pipes in parallel with one another, with a single pipe leading into them and a single pipe leading out. If both the parallel pipes are identical, you have the same flow through each. If one of the parallel pipes has markedly higher resistance than the other, the majority of the flow will go through the low resistance pipe. Now add on some parallel pipes coming off downstream of each of the original two parallel pipes. Which set of downstream parallel pipes would have lower pressure? The ones with less flow through them (i.e. the ones coming from the high resistance pipe)

 

[TallScrubs]

Loveoforganic, I really like your explanation--I just would like some further clarification.

The equation Q = dP / R is only really applicable to the entire CV system, and not an individual blood vessel?

Or in other words, I'm not being totally ******ed in saying that if you increased the resistance of a vessel/pipe (by decreasing a diameter), you would increase the pressure.

But, as you increase the resistance in that pipe, because there is now less flow thru that vessel, there is less flow to subsequent vessels which would lead to decreased pressure. Am I saying that right?

 

[ToldYouSo]

What you're saying would make sense if the entire output from the aorta were going to a single capillary, the pressure would increase dramatically. But since the capillary system as a whole has the largest surface area (and Pressure = force/area) you actually end up with a much decreased pressure.

 

[loveoforganic]

Loveoforganic, I really like your explanation--I just would like some further clarification.

The equation Q = dP / R is only really applicable to the entire CV system, and not an individual blood vessel?

It's applicable to both, but you have to define what your system is. If your system is arteriole -> capillary -> venule, then that equation will apply (that's how I came to the conclusion that there would be less pressure following the higher resistance vessel). I don't know how long ago you took physics, but try to remember how you had to sum resistors to be able to figure out where the current actually went through the system. It's the same principle

 

[adaptation1]

You can also think of it in terms of math.

Q= dP/R. Assuming Q is constant, if R increases, dP must increase, right?

But remember, dP is the_change_in pressure! So dP= Upstream pressure minus downstream pressure. That is, P1 minus P2.

And so if we want to increase dP, the downstream pressure, P2, must decrease -- as costanza stated.

The pipe analogy above is ace, as well.

 

[TallScrubs]

To whom it may concern,

I figured it out. Here was my problem (not that any of you really care)--I was concentrating on ABSOLUTE pressure and not the pressure difference.

thank you to all who helped.

 

[Rothbard]

nm

 

[TallScrubs]

New question

Now I can't understand why increased TPR decreases flow to the venous side. Didn't we conclude in our earlier argument that when you crank up the resistance at one part, you created a bigger deltaP, and thus increase flow?

I feel like that just undid everything I just learned.

 

[scotchtapetest]

Ok, I come to you guys as my last resort--I'm frustrated as hell and I have spent way too much time on this one subject.

Q = dP / R

Equation should be easy for me, right? Wrong.

Costanzo says the following:

"[referring to blood going from aorta to large arteries to arterioles, etc] This decrease in pressure occurs as blood flows through the vasculature because energy is consumed in overcoming the frictional resistances"

"Since total blood flow is constant at all levels of the CV system, as resistance increases, downstream pressure must necessarily decrease, Q = dP/R or dP = Q x R"

This does not make any sense to me. If you constrict a blood vessel, you would increase the pressure. using the dP = Q x R, wouldn't an increase in R necessitate an increase in P?

Whoever explains this disparity to me will make my day

-TS

I don't understand your question....

If you increase R, you increase dP which means you increase the CHANGE in pressure (that's where that little "d" comes into play). Therefore if you have higher resistance you require higher CHANGE in P resulting in a smaller P downstream.

Sorry if I totally missed your question or my answer is totally unrelated/doesn't make sense...

Think about the aorta. The aorta is arranged in series with the source of pressure (heart) lying upstream, and the tissues lying downstream. To maintain a constant flow in the face of increasing resistance (for example, the aorta becomes stenotic), you must have a simultaneous increase in pressure difference.

That's incorrect. In fact the aorta is arranged in parallel with tissue/organs lying downstream!

 

[scotchtapetest]

New question

Now I can't understand why increased TPR decreases flow to the venous side. Didn't we conclude in our earlier argument that when you crank up the resistance at one part, you created a bigger deltaP, and thus increase flow?

I feel like that just undid everything I just learned.

Your conclusion is incorrect.

If you increase R, then you have to decrease Q and/or increase dP such that dP=Q*R remains true. So, based on your question, if you just increase dP in response to increase R, then there will be NO change in Q and Q should never increase to compensate for increased R, because that makes the inequality larger then requiring more increase in dP creating an unstable situation.

Also, unless there is increased tissue demand, there is no reason to increase Q, therefore, increased resistance can be compensated for by decreasing Q.

 

[TallScrubs]

Your conclusion is incorrect.

If you increase R, then you have to decrease Q and/or increase dP such that dP=Q*R remains true. So, based on your question, if you just increase dP in response to increase R, then there will be NO change in Q and Q should never increase to compensate for increased R, because that makes the inequality larger then requiring more increase in dP creating an unstable situation.

Also, unless there is increased tissue demand, there is no reason to increase Q, therefore, increased resistance can be compensated for by decreasing Q.

Thank you.

 

[loveoforganic]

In fact the aorta is arranged in parallel with tissue/organs lying downstream!

How is that exactly?

 

[scotchtapetest]

How is that exactly?

Look at the anatomy of blood vessels and apply what you learned in Physics....

But to help you out (just in case you forgot everything from physics):

Series: Flow (I or Q in this case) must be equal through each element (regardless of R or C) in series with one another. I think you'd agree that the arteriole in your left large toe doesn't get the same flow that your femoral artery gets or the flow that your aorta gets.... Therefore, by definition they can not be in series...

 

[loveoforganic]

All the systemic blood comes from the aorta... so everything systemic is in series with the aorta

 

[scotchtapetest]

All the systemic blood comes from the aorta... so everything systemic is in series with the aorta

Yes, the ENTIRE systemic circulation as a whole is in series with the aorta... but each individual segment/tissue/organ is NOT in series with the aorta.

I truly hope this is what you meant or (with all due respect) you have some major reviewing to do!

 

[loveoforganic]

You would say that the top path (the one at the top of the black wall) is in parallel with the 30 ohm and 10 ohm down slopes? That's not what I remember as the definition of parallel paths

 

[scotchtapetest]

You would say that the top path (the one at the top of the black wall) is in parallel with the 30 ohm and 10 ohm down slopes? That's not what I remember as the definition of parallel paths

No, the top path to the left of the 30 ohm (before you get to 30 ohm) is in parallel with the 30 and 10 ohm slopes. The top path to the right of 30 ohm (passed the 30 ohm) is just part of the 10 ohm slope.

Dude, I don't mean to disrespect you or anything but I don't even feel like it's worth arguing this with you... It is a pretty settled issue from Year 1, day 5....

I'm just going to give you a hint by telling you the physiologic consequence and then you should definitely go review this stuff....

Pregnancy causes a drop in BP... Why? Because the placenta like everything else is in parallel with the aorta/LV therefore using the equation for equivalent Resistance for parallel circuits, it decreases the overall resistance thereby decreasing the Pressure (BP); if it was in series, given the increased Q in pregnancy and the R due to placenta, BP would've increased.

Same thing applies to amputees... Losing a limb results in loss of a parallel pathway therefore increasing R resulting in increased BP... If the limb was in series, it would've decreased BP 2/2 loss a limb/resistance.

Just out of curiosity what year are you?

 

[loveoforganic]

That's right, sorry. I'm sure you can find it in your heart to forgive a brain fart from a 1st year stuck learning how fats are put together 😉

 

[scotchtapetest]

That's right, sorry. I'm sure you can find it in your heart to forgive a brain fart from a 1st year stuck learning how fats are put together 😉

No worries 🙂... Anything for the future of Medicine 😉

 

[SpecterGT260]

Ok, I come to you guys as my last resort--I'm frustrated as hell and I have spent way too much time on this one subject.

Q = dP / R

Equation should be easy for me, right? Wrong.

Costanzo says the following:

"[referring to blood going from aorta to large arteries to arterioles, etc] This decrease in pressure occurs as blood flows through the vasculature because energy is consumed in overcoming the frictional resistances"

"Since total blood flow is constant at all levels of the CV system, as resistance increases, downstream pressure must necessarily decrease, Q = dP/R or dP = Q x R"

This does not make any sense to me. If you constrict a blood vessel, you would increase the pressure. using the dP = Q x R, wouldn't an increase in R necessitate an increase in P?

Whoever explains this disparity to me will make my day

-TS

P is useless here because the equation is dP. dP = P(upstream)-P(downstream). Pu may increase but depends on the scope of the question. Pd will always decrease.

The levels are going to be key to understanding this. "equal at all levels" is a broad scope approach. Net flow through aorta = net flow through muscular arteries = net flow through caps = net flow through vena cava.

However on the individual vascular bed scale this is no longer true. Net flow changes in individual beds based on pressure and resistance.

If you constrict 1 arteriole, the systemic pressure is unaffected. Think about traffic, if cars are units of pressure, if 1 minor road clogs in a city you do not affect net traffic flow in the city. What happens downstream of the gridlock? you get a trickle of cars coming out of it i.e. decreased downstream pressure. The analogy falls apart a little because you get a buildup within the street lol. But a street only hold so many cars and the rest of them take other routes.

if that didnt help just think about pouring a bucket of water into a funnel with a hose. The pull of gravity represents a functional driving pressure. If you pinch the hose the flow out will decrease due to increased resistance. The pressure this downstream flow exerts will be less. The backed up flow does not generate higher pressure, it just flows out an around of the funnel. Fun fact with this - when I was a kid and had a need to fill a bucket with water (as kids usually do 😕) I used to like to find the spray attachment and tighten it down into a jet thinking i was filling faster. This is wrong. Even tough the speed of the flow is greater, the volume of material is reduced by the increased resistance so total flow is also reduced. Also the total pressure at the release is lower, which may be counterintuitive but remember the speed of ejection is due to pressure relative to cross section and the size of dP, and remember from above, dP is relative of up and downstream. an arterial BP of 600mmHg and venous BP of 550mmHg will produce the same net flow theoretically as 51mmHg and 1mmHg respectively.


a 3rd way to think about this (and my favorite for thought experiments) think extremes.

Pinch off the aorta. What is the pressure in the illiac arteries? zero. All of these things function on a continuum so if we go to the extreme, we know that less extremes will have an effect in the same direction. And this is also talking about downstream pressures. Sure arterial BP will raise with application of a systemic vasoconstrictor. But any point "B" downstream from any point "A" has a lower pressure than point A. Increased resistance will amplify this.

so just remember to determine if we are talking systemic constriction or an individual vascular bed.

 

[SpecterGT260]

To whom it may concern,

I figured it out. Here was my problem (not that any of you really care)--I was concentrating on ABSOLUTE pressure and not the pressure difference.

thank you to all who helped.

damn... missed it lol

 

[SpecterGT260]

Look at the anatomy of blood vessels and apply what you learned in Physics....

But to help you out (just in case you forgot everything from physics):

Series: Flow (I or Q in this case) must be equal through each element (regardless of R or C) in series with one another. I think you'd agree that the arteriole in your left large toe doesn't get the same flow that your femoral artery gets or the flow that your aorta gets.... Therefore, by definition they can not be in series...

you are both kind of right depending on what you are looking at.

The CV is in series if we talk about net flow in the various levels of organization. Aorta > total arteriole > total cap flow > total venous flow. The blood going out of the aorta must equal the blood returning in the vena cava.

The individual organs are in parallel. i.e. the spleen and stomach are both in parallel configuration. They receive independent blood supply from the same source and deposit blood back into a communal source (portal system). Blood flow through spleen does not have to equal blood flow through stomach.

It is useful to think about the CV system is both ways and constantly remind yourself and re-orient yourself on what you are looking at. All med students should play pipe dream on a regular basis lol.

 

[scotchtapetest]

you are both kind of right depending on what you are looking at.

The CV is in series if we talk about net flow in the various levels of organization. Aorta > total arteriole > total cap flow > total venous flow. The blood going out of the aorta must equal the blood returning in the vena cava.

The individual organs are in parallel. i.e. the spleen and stomach are both in parallel configuration. They receive independent blood supply from the same source and deposit blood back into a communal source (portal system). Blood flow through spleen does not have to equal blood flow through stomach.

It is useful to think about the CV system is both ways and constantly remind yourself and re-orient yourself on what you are looking at. All med students should play pipe dream on a regular basis lol.

I think we both agree on the big picture (see below).... not much to argue about.... and my original post was in response to another post which said tissues/organs are in series with the aorta which is completely false.

Although to be a purist, even at various levels, especially at the level of arteriole/capillary, levels are not in series with the aorta because of shunting. Therefore, the only physiologically accurate statement would be what I posted previously which is re-posted below...

Yes, the ENTIRE systemic circulation as a whole is in series with the aorta... but each individual segment/tissue/organ is NOT in series with the aorta.

 

[SpecterGT260]

I know what you mean. Honestly I've worked with those systems enough that it is second nature and the equations confuse me as i try to re-orient what it is that the variables all mean lol.

 

[Rothbard]

nm

 

[SpecterGT260]

Guys, the aorta most certainly is in series with the rest of the circulation. Starting from the LV (the source of pressure), any blood that reaches the arterioles of the legs, placenta, or any other organ had to first pass through the aorta. That's what it means for two paths to be connected in series.

I was trying not to be nitpicky. While you are technically correct, I think the language above just got a little clumsy.
If we dumb it down, the aorta is more closely related to the non-resistor parts of any diagram

(solid non-zigzaggy line)
IRL a circuit with resistors will have resistance in the wire itself. This resistance would be dwarfed by the resistors and therefore excluded from consideration - much like the aorta and the capillary beds.

But if we want to get REALLY nit picky and include aortic resistance...
Technically we are only really talking about the segment immediately past the aortic valve because the coronary arteries branch off about 1cm or so after the valve. This system is is parallel with the ascending, descending aorta, and aortic arch. In addition, the entire blood supply to the head and neck and upper limb is in parallel with the descending aorta. Segmental branches of the thorax are all parallel to more distal aorta....

we get the concepts here.... but the context of previous statements implied there was confusion about how to handle the system in general. For all practical purposes it is only useful to consider the system in parallel when considering total flow through a vessel TYPE and not vessel bed. unless we want to look at 1 vessel and think about occlusive lesions..... but that is the only other time I can think of where consideration as parallel makes sense. in general the aorta need not be considered as a contributor of resistance and therefore any talk of it being parallel or series is beside the point. it is the conduit - and parallel vessel beds within the conduit control how blood flows within it.

 

[scotchtapetest]

Guys, the aorta most certainly is in series with the rest of the circulation. Starting from the LV (the source of pressure), any blood that reaches the arterioles of the legs, placenta, or any other organ had to first pass through the aorta. That's what it means for two paths to be connected in series.



This is not true. If the aorta were in parallel with the tissues, then there would exist a path by which blood could go from the heart to the tissues without passing through the aorta.

When two resistors are arranged in parallel, neither one is downstream of the other - they're both in "parallel".



Pregnancy reduces the resistance of the vasculature distal to the aorta, and so total resistance is reduced.

Look at this diagram

R3 is the aorta, and let's say R2 and R1 are the arms and legs. R2 and R1 are in parallel with each other and in series with R3. Adding another resistor R4 in parallel with R1 and R2 (like the placenta) will reduce total resistance and increase current (or flow, just like in pregnancy). It should be obvious that R1 is not in parallel with any other resistor.

In the example that you provided neither R1 nor R2 is individually in series with R3. What is in series with R3 is the parallel combination of R1 + R2.

Or in other words, the flow/current through R1 or R2 is NOT equal to flow/current through R3 and therefore neither R1 nor R2 is in series with R3. However, The flow/current through R1 + R2 is equal to flow/current through R3 and therefore, R3 is in series with the parallel combination of R1 + R2 (same applies to individual organs/tissue of the body and the aorta).

Therefore, the only resistance downstream of the aorta that is in series with the aorta is the equivalent resistance of the ENTIRE systemic circulation. Individual segments/organs alone are NOT in series with the aorta.

However, I do agree that if you consider the resistance of the aorta, then technically the aorta is not in parallel with the systemic circulation (that was my poor use of language to describe the physics in this case), however the aorta is certainly not in series with any individual organ/tissue. As I alluded to in the above post, the appropriate description of this circuit would be that the aorta is in series with the parallel combination of resistances of the different levels of organization/organs/tissue (i.e. ENTIRE systemic resistance)....

 

[SpecterGT260]

lame... the dude read my post and copied the resister image idea.... 👎 now my point looks much less clever

 

[Rothbard]

nm

 

[SpecterGT260]

In the example that you provided neither R1 nor R2 is individually in series with R3. What is in series with R3 is the parallel combination of R1 + R2.

Or in other words, the flow/current through R1 or R2 is NOT equal to flow/current through R3 and therefore neither R1 nor R2 is in series with R3. However, The flow/current through R1 + R2 is equal to flow/current through R3 and therefore, R3 is in series with the parallel combination of R1 + R2 (same applies to individual organs/tissue of the body and the aorta).

Therefore, the only resistance downstream of the aorta that is in series with the aorta is the equivalent resistance of the ENTIRE systemic circulation. Individual segments/organs alone are NOT in series with the aorta.

However, I do agree that if you consider the resistance of the aorta, then technically the aorta is not in parallel with the systemic circulation (that was my poor use of language to describe the physics in this case), however the aorta is certainly not in series with any individual organ/tissue. As I alluded to in the above post, the appropriate description of this circuit would be that the aorta is in series with the parallel combination of resistances of the different levels of organization/organs/tissue (i.e. ENTIRE systemic resistance)....

This is true.

To be series 2 things must be true - flow through each resister must remain equal, and voltage drops between resisters changes

to be parallel 2 things are true - flow changes with each resister and voltage drop across each resister varies.

none of these statements apply to 3 vs 1 or 3 vs 2 so neither R1 or R2 can be said to be in series with R3. Rather, R3 is in series with sum(R1,R2).

 

[scotchtapetest]

This is true.

To be series 2 things must be true - flow through each resister must remain equal, and voltage drops between resisters changes

to be parallel 2 things are true - flow changes with each resister and voltage drop across each resister varies.

none of these statements apply to 3 vs 1 or 3 vs 2 so neither R1 or R2 can be said to be in series with R3. Rather, R3 is in series with sum(R1,R2).

Almost..... (your description of parallel circuit is only partially correct)!

Series: Same current/flow; Different delta voltage/pressure...

Parallel: Different current/flow; Same delta voltage/pressure....

 

[SpecterGT260]

oh crap. i knew that. it was late and brain cells were dedicated to immunology.... I was reading it straight off of the website and just crossed my B's and dotted my Q's where I shouldnt have