Flow and Resistance

[plzNOCarribbean]

The equation delta P = Q x R

where delta P = (i think) is the pressure difference between two points in the vessel
Q= flow
R= Resistance

So, I was wondering, does delta P mean what I describe above? Also, I know this may sound stupid but I am kinda confused after doing some passages and i want to make sure I understand the relationships correctly, so please don't laugh/ridicule my questions.

1) Does this equation say that as we keep the pressure constant in the vessel, that by increasing the resistance we will decrease flow?

I remember reading a passage similar to this where a guy was running on the treadmill, and despite him exercising, his BP was constant. Is this even possible? (if you exercise, CO increases, which means your pumping more blood per minute, and since theirs more blood in the arterioles wouldn't the pressure have to increase since arteriole vasoconstriction is what diverts blood to specific tissues that need it (ie exercising muscle).

2) Does increasing the pressure within the vessel increase flow? (assuming that resistance is constant)

^I'm really confused about the delta P term, because I believe that pressure differences are what drive flow. Fluids flow from an area of high pressure to lower pressure. So, thats why I am wondering if increasing the delta P term means there is either (1) a greater pressure difference between two points within the vessel OR (2) the pressure just increased because we reduced the diameter of the vessel due to constriction of the vessel (but then in this case R could not be constant since resistance would increase if we reduced the vessel diameter)

lastly, is this an analog to Ohm's law? I tried thinking about it that way to see if I could relate similarities. Would the delta P term be analogous to voltage, since a potential difference is what drives current, which would be analogous to a pressure difference within the vessel driving the movement of fluid. And Q is analogous to I, the current. And resistance, R is well, equal to the resistance within the circuit, which is why when we increase resistance we reduce current, so when when increase resistance we would reduce Q in this case.

basically, am I correct in thinking that this equation states on 2 things about flow. Its saying that flow, Q can only be affected by either changing the resistance within the vessel or by changing the pressure? and any time we change one variable, do we have to assume that the other is constant? <this always trips me up. Thanks guys for sharing

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[BMEN]

So this equation can be seen as a fluid analog to Ohm's law. If you lower the resistance or up the flow of fluid/electrons you get a larger potential difference.

What delta P means here is that there is a pressure gradient or a change in pressure from one area to another. Now i know you are saying "BP is constant" and sure while that is true, there are branches of vessels with lower pressure which are driving this pressure gradient. This is ultimately what is driving this lower pressure. Then once the blood gets to the veins, the veins will have vasomotion to pump blood, as well as having veins to prevent fluid back flow. You also have to remember BP is two numbers, diastolic and systolic. The difference in these two is your pulse pressure, which is a pressure gradient

On vascular resistance, R here is acting as peripheral resistance, or the resistance of the smaller vessels(mainly arterioles). Resistance includes the factors of density, blood viscosity, diameter. Individual resistance can have local blood flow affects but in the larger picture, peripheral resistance is what is usually applied to in that equation.

So with all that said you are kinda correct in assuming that flow can only be changed by resistance and changes in pressure gradient. However in the larger picture its a little more complex than that.

If this seems a little incomplete i apologize. Im at work and ill get back to this ASAP

Edit1: During exercise BP does increase. Systolic will go up thanks to an increase in cardiac output from the heart and vaso constriction.

 

[gabdolce]

So it looks to me that you are indeed thinking about these relationships correctly. The P=QR equation (usually found in the context of the CV system) is IDENTICAL to ohm's law. I repeat, IDENTICAL.

If you haven't already taken a CV physiology course, many questions and concepts of flow distribution throughout the body can be modelled as a electric circuit, e.g. the effects of a fistula in the leg that came from a laceration or trauma.

Point 1 is correct. I think it's more important that you consider everything that may happening in the exercising scenario:

1) The sympathetic response would increase your rate of fire and your heart's ionotropy (CO) [beta1 adrenergic receptors].
2) As another consequence of the sympathetic response, yes, epinephrine and norepinephrine will be working on various alpha and beta adrenergic receptors, diverting blood flow away from unnecessary organs (vasoconstriction). Some of these adrenergic receptors also vasodilate such as the beta2 (skeletal bronchioles/muscle/liver). I assume that this concomitant dilation and constriction could feasibly maintain the same pressure.. But I am like you still a little confused because it is hard to tell exactly what's going on here. Two of your terms, Q and R are fluctuating in opposite directions and consequently, yes, you COULD have a situation where BP doesn't change, but I think it is also possible (and more likely) that the BP does change.

Your statement 2 is also correct. Simple analysis of the equation above mentions this. Pressure does indeed dictate flow. Also, if you KNOW blood is flowing at a certain amount and you have a total resistance of a certain degree, you must also KNOW that the pressure across the region must be a certain amount. You presented two separate situations. In the first, YOU increase pressure across a region, do not alter the resistances, and consequently you have greater flow. In your second example, you are relating transmembranal pressure according to pressure which is described by P=2*(surface tension)/radius. Looking at that equation, the *transmembranal* pressure does increase with the decreased radius. Also, according to Pouiselle's law, decreasing radius also increased resistance by a LOT. Assuming you keep flow constant, pressure ACROSS your region also increases (if you didn't assume flow constant, you get multiple possible scenarios like we discussed above).

To determine absolute outcomes, you must keep one variable constant. Otherwise, you get competing effects and must determine which one has greater effect. So for P=QR, a directly correlating relationship (rather than inversely correlated) if you had flow decreasing, and resistance increasing, which one is going to affect P more? If you can't determine this, or don't have the information to, then certainly, you cannot determine the fate of P either.

Do note: if Q and R had been going in the SAME direction, then you could prove that P will also increase.

Ultimately, it sounds like you've got the right idea.

 

[plzNOCarribbean]

So it looks to me that you are indeed thinking about these relationships correctly. The P=QR equation (usually found in the context of the CV system) is IDENTICAL to ohm's law. I repeat, IDENTICAL.

If you haven't already taken a CV physiology course, many questions and concepts of flow distribution throughout the body can be modelled as a electric circuit, e.g. the effects of a fistula in the leg that came from a laceration or trauma.

Point 1 is correct. I think it's more important that you consider everything that may happening in the exercising scenario:

1) The sympathetic response would increase your rate of fire and your heart's ionotropy (CO) [beta1 adrenergic receptors].
2) As another consequence of the sympathetic response, yes, epinephrine and norepinephrine will be working on various alpha and beta adrenergic receptors, diverting blood flow away from unnecessary organs (vasoconstriction). Some of these adrenergic receptors also vasodilate such as the beta2 (skeletal bronchioles/muscle/liver). I assume that this concomitant dilation and constriction could feasibly maintain the same pressure.. But I am like you still a little confused because it is hard to tell exactly what's going on here. Two of your terms, Q and R are fluctuating in opposite directions and consequently, yes, you COULD have a situation where BP doesn't change, but I think it is also possible (and more likely) that the BP does change.

Your statement 2 is also correct. Simple analysis of the equation above mentions this. Pressure does indeed dictate flow. Also, if you KNOW blood is flowing at a certain amount and you have a total resistance of a certain degree, you must also KNOW that the pressure across the region must be a certain amount. You presented two separate situations. In the first, YOU increase pressure across a region, do not alter the resistances, and consequently you have greater flow. In your second example, you are relating transmembranal pressure according to pressure which is described by P=2*(surface tension)/radius. Looking at that equation, the *transmembranal* pressure does increase with the decreased radius. Also, according to Pouiselle's law, decreasing radius also increased resistance by a LOT. Assuming you keep flow constant, pressure ACROSS your region also increases (if you didn't assume flow constant, you get multiple possible scenarios like we discussed above).

To determine absolute outcomes, you must keep one variable constant. Otherwise, you get competing effects and must determine which one has greater effect. So for P=QR, a directly correlating relationship (rather than inversely correlated) if you had flow decreasing, and resistance increasing, which one is going to affect P more? If you can't determine this, or don't have the information to, then certainly, you cannot determine the fate of P either.

Do note: if Q and R had been going in the SAME direction, then you could prove that P will also increase.

Ultimately, it sounds like you've got the right idea.

Great! thank you for the thorough explanation I think I got it down.

 

[plzNOCarribbean]

@ gabdolce; I understand what you saying about having to keep one variable constant if we want an absolute outcome; Specifically regarding the issue of decreasing vessel diameter, which would increase pressure and increase resistance, it would be hard to tell what happens to flow since Q = delta P/ R. Since vasoconstriction increases pressure, you'd expect flow to increase; at the same time, vasoconstriction increases resistance, which reduced pressure. so which is it? like you said, we can't know unless data/extra info is given in the passage since both variables are changing and nothing is constant


However, I just did a passage in TBR and this exact situation came up. Their explanation and reasoning was as follows, which I find interesting. They said that by reducing the diameter, we would be increasing resistance, and this increase in resistance would reduce blow flow. They reasoned that since flow is reduced, there is less blood traveling in the vessel, and less blood means less Force/ per unit area exerted on the blood vessel walls, so pressure decreases. Again, nothing is being held constant, and two variables are changing (higher resistance, lower flow) and this leads to reduced pressure.

So basically, given delta P = Q X R , the changes described above in the TBR scenario (higher resistance, lower flow) which are both proportional to Pressure, would have competing results. Apparently, the Resistance value trumps the flow value when determining pressure, which I guess makes since since flow is proportional to the 4th power of the radius of the vessel. Does that makes sense? I just hate how nothing is definitive. I can totally see myself trying to overanalyze these situations on the test, specially if they don't specify if any conditions are kept constant.

 

[BMEN]

if that were the case the pressure gradient would go way up. Diameter is on the bottom of the fraction for poiseuille.

Heres the thing plzNOCar:

On the actual exam things wont be so wonky.

In real physiological conditions, the equations are much more complex, and take into account a multitude of factors depending on various situations. Just understand the concept of fluid flow in the CV system and know how some of the physics works.

 

[gabdolce]

@ gabdolce; I understand what you saying about having to keep one variable constant if we want an absolute outcome; Specifically regarding the issue of decreasing vessel diameter, which would increase pressure and increase resistance, it would be hard to tell what happens to flow since Q = delta P/ R. Since vasoconstriction increases pressure, you'd expect flow to increase; at the same time, vasoconstriction increases resistance, which reduced pressure. so which is it? like you said, we can't know unless data/extra info is given in the passage since both variables are changing and nothing is constant


However, I just did a passage in TBR and this exact situation came up. Their explanation and reasoning was as follows, which I find interesting. They said that by reducing the diameter, we would be increasing resistance, and this increase in resistance would reduce blow flow. They reasoned that since flow is reduced, there is less blood traveling in the vessel, and less blood means less Force/ per unit area exerted on the blood vessel walls, so pressure decreases. Again, nothing is being held constant, and two variables are changing (higher resistance, lower flow) and this leads to reduced pressure.

So basically, given delta P = Q X R , the changes described above in the TBR scenario (higher resistance, lower flow) which are both proportional to Pressure, would have competing results. Apparently, the Resistance value trumps the flow value when determining pressure, which I guess makes since since flow is proportional to the 4th power of the radius of the vessel. Does that makes sense? I just hate how nothing is definitive. I can totally see myself trying to overanalyze these situations on the test, specially if they don't specify if any conditions are kept constant.

You are again confusing two distinct pressures. The pressure according to laplace (the one with surface tension and radius) is the *transmembranal* pressure. Decreasing radius has NO DIRECT implication on the pressure drop driving the blood within the vessels (what I was referring to as the pressure "across a region"). So in this case, you are increasing resistance, and barring other unusual circumstances, the driving pressure (the pumping of the heart - ionotropy) remains the same. Thus flow does decrease. This is what you want: consider the sympathetic response - the vessels to your GI tract vasoconstrict to divert blood flow from these nonessential organs.

Let's look at it another way: let's consider a branch of two arteries that split at a junction. Artery A is the one that vasoconstricts and the other one, artery B, let's just say doesn't change too much. When A vasoconstricts, the pressure upstream increases and the pressure downstream decreases. This greater pressure upstream now pushes more blood through artery B, the expected physiological response to increased oxygen needs.

Many different things to consider all at once within the human body - but like I said before, it sounds like you've got a good grasp on the concepts and you're thinking critically.