Blood flow rate vs pressure

[Monkeymaniac]

When vasoconstrictor constricts, say blood vessels of digestive tracts, then according to this wiki entry, this would decrease the flow rate (Q) of blood and increase the pressure (P). Is this right?

1) But then Poiseuille's Law states that Q=(pi*r^4*P)/(8*mu*L), so when we decrease the flow rate, then the pressure must decrease as well, why is opposite of this actually takes place?

2) In TPRH, it is stated while describing the role of juxtaglomerular cells in controlling the renal blood pressure that

The cells of the macula densa (part of the jg cells) also causes a direct dialation of the afferent arterioel, increasing the blood flow to (and thus blood pressure and filtration rate in) the glomerulus.

In the first example, there is a inverse relationship between Q and P, but in the second example, Q and P are directly related. I know I'm missing something here. What is really going on here?

Thanks in advance!

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[lorenzomicron]

When vasoconstrictor constricts, say blood vessels of digestive tracts, then according to this wiki entry, this would decrease the flow rate (Q) of blood and increase the pressure (P). Is this right?

1) But then Poiseuille's Law states that Q=(pi*r^4*P)/(8*mu*L), so when we decrease the flow rate, then the pressure must decrease as well, why is opposite of this actually takes place?

2) In TPRH, it is stated while describing the role of juxtaglomerular cells in controlling the renal blood pressure that



In the first example, there is a inverse relationship between Q and P, but in the second example, Q and P are directly related. I know I'm missing something here. What is really going on here?

Thanks in advance!

Well, in the first example, you are noting the effect, not the direct cause. If the vasoconstrictor constricts, the radius of the blood vessel must decrease. Thus, that explains that the flow rate decreases. I'm not sure why the pressure increases, but it may be explained perhaps by energy conservation in a closed system.

In the second example, I see no mention of P. The vasodilation increases the radius, which once again causes flow increase.

 

[Monkeymaniac]

Ok, let's think about it for a second.

When blood vessels constrict, the flow of blood is restricted or decreased. - wikipedia

I think "flow" here means (unit volume)/(unt time). Amount of blood that passes a blood vessel per given time decreases becuase body is redirecting the rest of the blood to the other part of the body (e.g. heart).

We can also think of it in terms of liquid flow equivalent of V=IR function. So we instead have P=QR here. Cosntricting the vessel increases vescular resistance (R). But the flow (Q) is decreased due to the constriction. So I think whether P would increase or decrease comes down to whether increase in R is larger than decrease in Q. I think this indeed holds in our case. Could anyone please tell me if this is right?

 

[hockey4496]

how would this correlate to Bernoulli' equation of continuity...doesn't it suggest that radius and pressure are positively correlated, and flow rate inversely? So as the radius increases so does the pressure, which reduces the flow rate...So why is it that with vasoconstriction the pressure is increased and flow rate decreased, when the radius is reduced??

 

[Charles_Carmichael]

The thing about vasoconstriction is that it has different effects on pressure upstream and downstream of region of the vessel that's constricted. Upstream of the vasoconstriction, there will be an increase in pressure. In the example of vasoconstriction of the efferent arterioles of the kidney, an increase in upstream pressure at the glomerulus results in increased GFR.

Downstream of the vasoconstriction, there will be a decrease in pressure. Think of the constriction as an increase in friction which dissipates energy (pressure) as the blood flows through the region. In the case of the afferent arterioles of the kidney, after vasoconstriction, there'll be a decrease in pressure at the glomerulus which results in a decrease in GFR.

Similarly, dilation of the afferent arteriole reduces the "friction" along the vessel. So, there's less energy (pressure) dissipated along it's length. This would increase pressure at the glomerulus. That's why vasodilation of the afferent arteriole increases GFR.

Hope this helps.

 

[Monkeymaniac]

Kaushik, that makes a lot of sense. Thank you for clarifying that point. So I guess that the upstream of where vasodilation happened, the pressure would decrease? since it increases downstream of that point?

 

[Charles_Carmichael]

Kaushik, that makes a lot of sense. Thank you for clarifying that point. So I guess that the upstream of where vasodilation happened, the pressure would decrease? since it increases downstream of that point?

No problem; glad to help. And yes, to your question. That would make sense (there would be less fluid "backed up"). I highly doubt, though, you would be asked a question that would require a high level of understanding of changes in upstream and downstream pressures with regards to vasocontriction/dilation. I would assume (based on practice passages and practice AAMCs, as well as the real MCAT) that if such a question were asked, the answer would be quite obvious from the passage info.

 

[lord_jeebus]

We can also think of it in terms of liquid flow equivalent of V=IR function. So we instead have P=QR here. Cosntricting the vessel increases vescular resistance (R). But the flow (Q) is decreased due to the constriction. So I think whether P would increase or decrease comes down to whether increase in R is larger than decrease in Q. I think this indeed holds in our case. Could anyone please tell me if this is right?

V = IR

V = delta(pressure) = Mean arterial pressure - central venous pressure. CVP is low and fairly constant so let's just say V = Mean Arterial Pressure (MAP)

I = flow = cardiac output

R = systemic vascular resistance (SVR)

Constricting a vessel increases SVR. Flow (cardiac output) is dependent on multiple factors (contractility, preload, afterload) and the SVR increase will not change it significantly. Hence MAP (V) must increase.

 

[lord_jeebus]

For the second example, imagine several resistors in parallel, each representing an organ. Dilation of any vessels going to or coming from the kidneys decreases their resistance. When the resistance at one resistor decreases, flow through that resistor increases compared to those others in parallel.

The question of afferent vs. efferent renal vessels (ie. resistors in series) determines the pressure between them (at the glomerulus). If afferents dilate, renal blood flow increases (because overall renal resistance decreases), and pressure at the glomerulus also increases (because there is less pressure drop prior to the glomerulus). If efferents dilate, renal blood flow still increases (overal renal resistance is still decreased), but the glomerulus sees lower pressure. It is this pressure, and not renal blood flow, that determines GFR.

 

[Phantastic]

Thank you Kaushik and lord_jeebus, between both your replies I have finally figured out wtf is going on with GFR in relation to blood pressure and flow. I was curious if anyone knows the common motifs for presenting this material? e.g. free standing? passage based drug mechanism? hormonal response to homeostasis restoration?

 

[BerkReviewTeach]

When vasoconstrictor constricts, say blood vessels of digestive tracts, then according to this wiki, this would decrease the flow rate (Q) of blood and increase the pressure (P). Is this right?

1) But then Poiseuille's Law states that Q=(pi*r^4*P)/(8*mu*L), so when we decrease the flow rate, then the pressure must decrease as well, why is opposite of this actually takes place?

With these questions, you need to ask which pressure are they talking about, pressure against the inside of the vessel walls, or the pressure difference between the ends of the pipe. It is my belief that they are asking about the pressure against the insides of the vessel walls, which is governed by Bernoulli's principle and not Poiseuille's law.

In general, this concept causes a great deal of confusion, I believe because they (physicists) don't specify that the pressure difference between the two ends of the pipe in Poiseuille's Law (deltaP) is different from the pressure against the insides of the wall which is what is being referred to in Bernoulli's principle.

To help distinguish the difference, first consider a simple system, where a single pipe of uniform radius experiences an increase in pressure at the end with higher pressure. This would be synonimous with a greater cardiac output. The result is a greater deltaP, which will cause the fluid to flow at a greater volume flow rate. This could only be possible if the average speed of the fluid particles increases. The faster the particles flow down the pipe, the less frequently they will randomly collide with the walls, resulting in a reduced pressure against the insides of the walls of the vessel. This is why according to Bernoulli, k = Pagainst walls + 1/2rho(v^2) + rho(g)(h), as speed goes up, pressure goes down.

So the result is that as deltaP between the ends of the pipe increases, the pressure against the insides of the wall decreases. So if I were to ask, "what happens to the pressure as the result of a greater average flow speed for the particles in a fluid?", the correct answer could be that it must have increased (if we are asking about pressure difference and Poiseuille's law) or it is decreasing, because of greater particle speed (if we are asking about pressure against the walls and Bernoulli's principle). There is an ambiguity caused by me not specifying what pressure we are talking about.

The physiology insights and physics anaology listed above are great for this specific system, and explain it quite well. My response is more generic for these types of questions. If you start by asking "what pressure are they asking about?", then you'll have a little less confusion.

 

[UIUCstudent]

When we measure blood pressure we refer to the difference in blood pressure (poiiseuille)?

 

[jphwki82]

When we measure blood pressure we refer to the difference in blood pressure (poiiseuille)?

When you measure blood pressure using the blood pressure cuff, you are measuring the pressure during the systolic phase of the cardiac cycle and the diastolic phase during the cardiac cycle. Systole corresponds to the Left Ventricular pressure derived from the contraction of the myocardium in order to eject blood into the aorta. During systole, the aortic valve opens, allowing ejection of blood from the LV. This occurs because the left ventricle begins to contract, increasing the pressure in the left ventricle, closing the mitral valve. While contracting, the pressure inside the LV will exceed that in the aorta, and the aortic valve will open to allow blood to eject into the aorta. Diastole is the phase of the cardiac cycle that corresponds to the time after systole, where blood flows from the left atrium into the relaxed left ventricle. So the mitral valve will be open, and the aortic valve will be closed. During diastole, pressure in the left atrium slightly exceeds that of the relaxed ventricle, and blood will flow into the left ventricle.

So when taking the BP of the brachial artery, you are gathering measurements of the pressure of that vessel during the beginning (systolic) and end (diastolic) of the cardiac cycle. These can vary with stress, hypertension, hypotension and etc. On another note, the difference between systolic and diastolic pressures will give you the pulse pressure. Pulse pressure is proportional to stroke volume, the amount of blood ejected from the heart during systole. Stroke Volume = End Systolic Volume - End Diastolic Volume.

This is all stuff that will be covered at length once you get into medical school. Hope this covered your question. Good luck with your studying.

Poiseuille's equation is emphasizing factors that alter the resistance in blood vessels. Resistance will be directly proportional to the blood viscosity and length of the vessel, and inversely related to radius to the 4th power of that blood vessel. The pressure drop you are referring to is the mean arterial pressure - right atrial pressure. You can calculate the mean arterial pressure from Systolic and Diastolic pressure, which would be Mean Arterial Pressure = (Syst + 2 x Diast.)/3.

 

[UIUCstudent]

Sweet thanks for the great explanation. Just a bit confused on why the pressure drop relies on mean pulmonary artery pressure, since the right ventricle gives it another push.

Why isn't the pressure drop = mean arterial pressure at the aorta - mean venous pressure at the vena cavae?

Then again I'm looking at it at the perspective of those plumbing tubes where P1 at one end - P2 at the other end (which might be the wrong way to go about this).

 

[jphwki82]

Sweet thanks for the great explanation. Just a bit confused on why the pressure drop relies on mean pulmonary artery pressure, since the right ventricle gives it another push.

Why isn't the pressure drop = mean arterial pressure at the aorta - mean venous pressure at the vena cavae?

Then again I'm looking at it at the perspective of those plumbing tubes where P1 at one end - P2 at the other end (which might be the wrong way to go about this).

Sorry, I meant to say Right Atrial Pressure. I went back to re-edit that comment. Ill chalk that mistake up to spring break.

The mean arterial pressure is based on the systolic and diastolic pressure of the left ventricle during the cardiac cycle, like I mentioned. Also, they use the right atrial pressure because that is the end point in the system, where the blood re-enters the heart. The pressure drop across the systemic vasculature represents cardiac output. You can approximate that the mean arterial pressure will be equal to CO x Systemic Vascular Resistance, since the right atrial pressure will be close to 0 mmHg.

 

[Polycherry]

Nice reading through the posts above. Felt like there are many with the same dilemma as mine
During vasconstriction, there is a decrease in the diameter of the arteriole. So how do the following parameters change.

• Pressure on the walls
• Pressure drop across
• Volume Flow rate
• Velocity of blood flow
• Systemic blood pressure
• Resistance to flow

And how to come about with these logically. I suppose we can not use Bernoulli’s because the system is actually changing (tube is narrowing) and Poisueille’s, the net resistance is changing. Please clarify what is to be used. There was also a mention that Bernoulli’s can’t be used because this is a non ideal condition. But i guess we can definitely include a term for dissipative loss and apply Bernoulli’s too as in the Bernoulli’s - Poisueille’s equation.
Desperate for a clarification

 

[Polycherry]

Sweet thanks for the great explanation. Just a bit confused on why the pressure drop relies on mean pulmonary artery pressure, since the right ventricle gives it another push.

Why isn't the pressure drop = mean arterial pressure at the aorta - mean venous pressure at the vena cavae?

Then again I'm looking at it at the perspective of those plumbing tubes where P1 at one end - P2 at the other end (which might be the wrong way to go about this).

The blood pressure we measure is the pressure at the walls of the brachial artery. Makes sense, bcoz we're varying the pressure on the cuff. The flow will stop only when pressure in the cuff exceeds that in the artery. This as we all know, can be heard as differences in sound. The pressure we measure varies with the cardiac cycle - systolic and diastolic. Although these are pressures at the heart, the BP measured at the brachial artery will be more or less the same since the pressure drop from heart to the hand in the artery is negligible as major resistance is offered by the arterioles and not the artery. Correct me if I'm wrong