Trouble understanding basic hemodynamic question

[Daitong]

Hi,

So here is my dilemma. With respect to dP = Q*R (where dP= change in pressure, Q is flow(cardiac output), and R as resistance) and velocity = Q/A with A being cross-sectional area, how do these equations affect perfusion to an area?

When you want to perfusion a region, would the body employ vessel constriction or dilation, and why?

In one hand, you can increase the velocity to an area by vessel constriction (decrease A, greater exchange of nutrients), but then wouldn't that increase resistance so you'd get less flow to the area ultimately? So that's where I have trouble bridging the gap.


For example, when venoconstriction occurs, the venous R increases and more blood is 'pushed' into the right atrium generating greater cardiac output, but at first glance this doesn't make sense to me because intuitively, you always want flow into the regions of lesser resistance so I'd think that the whole system would back-up or something...

Because it seems that you need some degree of constriction to generate velocity (for exchange of nutrients), but then again wouldn't flow decrease through the area since, well, that area is more constricted?

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[mxmd]

generally speaking, vasoconstriction decreases blood flow to an area (well, due to decreasing cross-sectional area). I'm sure there's a tiny bit of increase in velocity as well, but you can't pump a whole lot of blood through a pinhole.

veins have valves that prevent back flow, so regardless of what the pressure differentials are, blood generally flows one-directionally in veins.

 

[HereWeGo21]

P = Q * R really only applies to LAMINAR flow. This basically means that what comes in, comes out.
The simplest example is like a closed system of pipe. You have a pump on one end. That sends fluid through these pipes. The cross-sectional area might vary all over the place, throughout the pipe. But, eventually, the pipe ends, and then, through some tubing, it feeds back to the pump. So, you have a closed loop system. P = QR applies principally to that system.

In the body, this mainly applies to areas of like end circulation, like the coronaries. If the cross-sectional area of the LAD diminishes 7x, then it's pretty safe to say the rate of blood flow will increase ~7x through that area of stenosis. That's because there's just not much space for that blood to back up into. Sure, maybe a bit more would flow into the circumflex. But generally P = QR applies. To formalize this, Q is constant through a "closed system". So, if R increases (narrower lumen) so must P (greater velocity). Note that sometimes it's also written Q = v * A. Once again, Q is constant. if area decreases (narrower lumen) then velocity will have to INCREASE to make up for it. So you have a greater velocity. Velocity and pressure are basically equivalent here, since blood that moves faster exerts more pressure on the surrounding walls.

In systemic circulation, the rule might not apply. Basically, Q is no longer constant. Say you deeply constrict the vessels of the GI. The blood is like, fine. If you constrict those vessels, I'll just go somewhere else. I'll go to the muscle tissue instead, since you're blocking me out, GI. In other words, systemic circulation is highly PARALLEL, so there's always somewhere else to go. So, Q is not constant.

So, once again, you increase resistance in the GI. What happens is that Q will fall, since blood travels to other capillary beds. R obviously is much higher now. The net result might be that PRESSURE is close to equivalent. So, in systemic beds, it might be more accurate to say that PRESSURE Holds constant, as opposed to FLOW.

In one hand, you can increase the velocity to an area by vessel constriction (decrease A, greater exchange of nutrients)

If this is a systemic bed, then increasing R would end up decreasing Q. So, you would decrease flow of nutrients.

For example, when venoconstriction occurs, the venous R increases and more blood is 'pushed' into the right atrium generating greater cardiac output, but at first glance this doesn't make sense to me because intuitively, you always want flow into the regions of lesser resistance so I'd think that the whole system would back-up or something...

Here, venoconstriction can be thought of as more of a series circulation, as opposed to a parallel. If you venoconstrict, well, Q must be constant. So what changes is P within the veins. We already said that P is analogous to v, velocity. So, the blood just moves faster through the veins. This means that the RATE of blood being sent to the heart increases, so the heart has more preload per stroke and has more to deal with.

 

[Daitong]

P = Q * R really only applies to LAMINAR flow. This basically means that what comes in, comes out.
The simplest example is like a closed system of pipe. You have a pump on one end. That sends fluid through these pipes. The cross-sectional area might vary all over the place, throughout the pipe. But, eventually, the pipe ends, and then, through some tubing, it feeds back to the pump. So, you have a closed loop system. P = QR applies principally to that system.

In the body, this mainly applies to areas of like end circulation, like the coronaries. If the cross-sectional area of the LAD diminishes 7x, then it's pretty safe to say the rate of blood flow will increase ~7x through that area of stenosis. That's because there's just not much space for that blood to back up into. Sure, maybe a bit more would flow into the circumflex. But generally P = QR applies. To formalize this, Q is constant through a "closed system". So, if R increases (narrower lumen) so must P (greater velocity). Note that sometimes it's also written Q = v * A. Once again, Q is constant. if area decreases (narrower lumen) then velocity will have to INCREASE to make up for it. So you have a greater velocity. Velocity and pressure are basically equivalent here, since blood that moves faster exerts more pressure on the surrounding walls.

Thanks, to follow up, wouldn't this violate Bernoulli's principle though? When you decrease vessel radius with same flow Q, the velocity increases but wouldn't the pressure decrease since total energy (P1+.5pv^2=P2+.5pv^2) must be maintained?

 

[DrPicard]

The body wants to control blood flow, not velocity, so its more intuitive to place Q on one side of the equation.

Since Q = P1-P2 / R, the body can increase flow to an organ either by increasing dP (the perfusion pressure), or decreasing R. Remember that the control point for vessel diameter are the arterioles which lie before the organ. So when you constrict the arterioles for organ X, this increases the R and hence decreases flow through the organ (same as our discussion on shock). While the cross sectional area has decreased, so has flow, and when we consider V = Q/A, I would guess in such a physiological state, there shouldn't be much difference in the velocity of the blood. (Or maybe there is, but its not something I've ever come across, so if a difference does exist its probably inconsequential).

Keep in mind that vasoconstriction for organ X has two effects: first, it decreases flow through itself, and second, it functions to increase TPR. Since MAP = TPR X CO, and since the body has mechanisms in place to maintain the MAP, the increase in TPR in this case will be accompanied by a decrease in CO. This decrement in CO is equal to the the amount organ X isn't receiving anymore (due to vasoconstricting its arterioles). Blood to other organs will remain unaffected.

As you discontinue excercising the vessels in your musculature lose their state of vasodilation, which decreases flow through them. The muscles don't require enhanced flow anymore. This blood doesn't get shunted through different organs; rather, like I explained in the paragraph before, CO simply decreases by the appropriate amount to find a new setpoint where organs are perfused as per their requirement.

The discussion you've made above involves understanding the circulatory system as a parallel circuit, since we're talking about flow through one organ relative to others. The next question you've posed, about venoconstriction, is taking a look at it as a series circuit. What you're saying is that venous pressure, as a whole, has increased, thus increasing the dP driving blood into the RA. Venous blood doesn't have anywhere to go but the right heart. By the time blood reaches the right atrium, almost all the pressure has dissipated overcoming resistance, and is close to 0mmHg. The RV then generates pressure by actively contracting. This is the dP that pushes blood through the pulmonary circulation. And in similar fashion, the LV contracts to generate the dP that pushes blood through the systemic pressure, and dissipates by the time it reaches the right heart.

Blood won't back up because of valves. When you get incompetent valves, this does happen, and you get a fluid/volume overloaded state.

The contraction of the heart generates the pressure to drive blood through the vasculature with whatever velocity. Organ blood flow is controlled by altering the diameter of arterioles. Velocity isn't something the body cares to actively control.

 

[worldbeater]

Sorry, but why is there so much writing on this thread? If you want to increase the amount of perfusion (delivery of blood to tissue) you need to vasodilate the vessel. If you vasodilate a vessel, you increase the flow (amount of blood delivered to the tissue).

 

[wjs010]

Perfusion works best at lower velocity I thought. The lower the laminar velocity in capillaries, the more time you have for diffusion across the capillary.

 

[Daitong]

Perfusion works best at lower velocity I thought. The lower the laminar velocity in capillaries, the more time you have for diffusion across the capillary.

True. Not only do you have more time for diffusion, but also you have increased perfusion pressure into the ECF space due to Bernoulli's. Lower velocity => higher P

 

[worldbeater]

Perfusion works best at lower velocity I thought. The lower the laminar velocity in capillaries, the more time you have for diffusion across the capillary.

Correct, when you vasodilate, the walls of the vessel expand outwards and the velocity decreases. This slows down the speed of the blood and increases the amount of perfusion/flow/amount of blood/diffusion to the cells.

Remember that velocity and flow are inversely proportional, it's a really common mistake.