Hemodynamics Question

[masterchiefk57]

So based on the equation Velocity = Blood flow / cross sectional area, the overall speed of capillaries is much lower than other vasculature groups due to its immense total areas.

However if you examine an individual capillary, would this still hold true? I know the area is tiny, but wouldn’t the blood flow (mL/s) in each individual capillary be as well?

Also, when evaluating pressure, we use the equation: Delta P = Blood flow / resistance, with resistance largely based on the radius to the 4th power. Is this a measurement from the perspective of an individual vessel or overall...or both?

---

Members don't see this ad.

 

[OnePunchBiopsy]

I'll take a crack at it.

However if you examine an individual capillary, would this still hold true? I know the area is tiny, but wouldn’t the blood flow (mL/s) in each individual capillary be as well?

If Velocity = Blood flow / cross sectional area, we assume blood flow (volume) is constant, and cross sectional area increases as all the blood volume moves from the aorta to capillaries. Higher denominator means lower velocity. Examining an individual capillary is a snapshot of this system at work, and does not show ALL the blood at once. Furthermore, all blood volume does not drain into a single capillary.

Also, when evaluating pressure, we use the equation: Delta P = Blood flow / resistance, with resistance largely based on the radius to the 4th power. Is this a measurement from the perspective of an individual vessel or overall...or both?

It can be a measurement across BOTH a single vessel of the whole system at work. Delta P is simply where you choose to set your beginning and end point pressures. For the whole body, beginning would be the left ventricle and end would be the right atrium.

 

[aldol16]

However if you examine an individual capillary, would this still hold true? I know the area is tiny, but wouldn’t the blood flow (mL/s) in each individual capillary be as well?

Blood flow in capillaries are necessarily slower. This is because there has to be time for the cells to extract all the nutrients. But it can't be too tiny either. If it's too small, then the cells can't get rid of their waste products fast enough. So there's a balance. But in either case, remember that the cross sectional area varies with the square of radius. So as your vessel radius goes down, your cross sectional area decreases very dramatically.

Also, when evaluating pressure, we use the equation: Delta P = Blood flow / resistance, with resistance largely based on the radius to the 4th power. Is this a measurement from the perspective of an individual vessel or overall...or both?

I do believe you meant to say change in pressure = flow times resistance. Because this is just Ohm's law stated for blood flow instead of circuits.

Now your question is actually a nuanced one. First and foremost, you can apply Ohm's law to one blood vessel or multiple. Doesn't matter because all operate under the same laws of physics. The nuance comes with what happens when you apply it to multiple.

Recall from general physics that resistances add differently when they're in series vs in parallel. When resistances are in series, you can sum the individual resistances. But when they're in parallel, the inverse of the combined resistance is equal to the sum of the inverse resistances. So in other words, when vessels are added in parallel, the overall resistance actually drops, leading to a drop in blood pressure. This is why your BP is highest coming out of the LV but then drops sharply as blood starts entering more and more tributaries and finally the capillaries.

 

[masterchiefk57]

Blood flow in capillaries are necessarily slower. This is because there has to be time for the cells to extract all the nutrients.

Would this decreased blood flow be due to significantly reduced diameter of the capillary? Assuming it’s diameter is much smaller than other capillaries, the amount of blood flowing through a single capillary must be tiny, correct?

 

[masterchiefk57]

Examining an individual capillary is a snapshot of this system at work, and does not show ALL the blood at once. Furthermore, all blood volume does not drain into a single capillary.

I guess if we were examining a single individually capillary, in which some, not all, blood was flowing through...within that single capillary would we see a super fast velocity, or would velocity be slowed because of the significantly reduced blood flow in that individual capillary?

 

[aldol16]

Would this decreased blood flow be due to significantly reduced diameter of the capillary? Assuming it’s diameter is much smaller than other capillaries, the amount of blood flowing through a single capillary must be tiny, correct?

I said blood slows down, i.e. velocity slows down. It has to do with the combined capillaries. All the capillaries together have a huge collective diameter. Recall the continuity equation, which is basically another statement of conservation of mass. Area times velocity is a constant in a closed system. Blood flow through the entire system remains constant at each point in the circuit, i.e. through the sum of all the capillaries.

If you're asking about blood flow through individual capillaries vs the sum of all capillaries, then the question is a simple arithmetic one. Say a system consisted of a single tube is flowing at 10 mL/s. Then the system splits into 10 tubes. Thus, the 10 mL has to be divided into the 10 tubes. Just like how the sum of currents flowing through parallel paths is equal to the total current from the source.

 

[OrgoCoop]

Think about it as a circuit in physics. The capillaries are in parallel to the system. The velocity through each capillary is low but the overall series adds up to be high blood flow.

 

[masterchiefk57]

Recall from general physics that resistances add differently when they're in series vs in parallel. When resistances are in series, you can sum the individual resistances. But when they're in parallel, the inverse of the combined resistance is equal to the sum of the inverse resistances. So in other words, when vessels are added in parallel, the overall resistance actually drops, leading to a drop in blood pressure. This is why your BP is highest coming out of the LV but then drops sharply as blood starts entering more and more tributaries and finally the capillaries.

Hmmm...I am still a bit confused and maybe that's simply due to the semantics by the textbook I am using. It states this relationship in terms of delta Pressure, the difference in pressure, and states:

"Increasing resistance (e.g., by arteriolar vasoconstriction) decreases flow, and decreasing resistance (e.g., by arteriolar vasodilation) increases flow."

If we rearrange the equation to be: Delta P = Blood Flow x Resistance, wouldn't an increase in overall resistance lead to a greater difference between the blood pressures from beginning to end of the circulation, rather than a decrease in the resistance?

 

[aldol16]

"Increasing resistance (e.g., by arteriolar vasoconstriction) decreases flow, and decreasing resistance (e.g., by arteriolar vasodilation) increases flow."

If we rearrange the equation to be: Delta P = Blood Flow x Resistance, wouldn't an increase in overall resistance lead to a greater difference between the blood pressures from beginning to end of the circulation, rather than a decrease in the resistance?

Ignore what I said. The pressure drop is biggest when you have the most resistance. Instead, it's best to conceptualize resistance via Poiseuille's law. As radius of blood vessel drops, resistance increases to the fourth power.

 

[WheezyBaby]

So based on the equation Velocity = Blood flow / cross sectional area, the overall speed of capillaries is much lower than other vasculature groups due to its immense total areas.

However if you examine an individual capillary, would this still hold true? I know the area is tiny, but wouldn’t the blood flow (mL/s) in each individual capillary be as well?

Also, when evaluating pressure, we use the equation: Delta P = Blood flow / resistance, with resistance largely based on the radius to the 4th power. Is this a measurement from the perspective of an individual vessel or overall...or both?

I wouldn't expect traditional fluid dynamics to hold entirely true at capillary level given relative size of rbcs flowing through, it's just a useful way to think about flow at a more global level, eg capillary bed, not single capillary