Resistance to blood flow

Definitions & Key takeaways

Resistance to blood flow refers to the opposition that the circulatory system presents to the flow of blood. It plays a critical role in regulating blood pressure and blood flow to different organs and tissues. This resistance is directly proportional to blood viscosity (η) and the blood vessel's length (L); and inversely proportional to the radius of the vessel (r). This resistance (R) is represented as R=8Lr4

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Introduction0:00–0:27

Blood flow refers to the volume of blood travelling through a blood vessel, an organ, or the entire body over a period of time, and it can be measured as liters per minute.
As blood flows, it encounters various factors that resist flow and movement of blood, known as the vascular resistance. The first factor to contribute to vascular resistance is blood viscosity, where you can think of viscosity as the fluid’s thickness, or how sticky it is.

Blood viscosity0:27–2:00

The relationship is directly proportional, which can be represented as resistance ∝ η which is the greek letter eta and represents viscosity.
So this means that as viscosity goes up, it’s harder it is for the liquid’s molecules to slide past each other, and the resistance goes up.
Think about a heaping stack o’ pancakes, then picture some maple syrup. Even on flipping the syrup upside down it doesn’t really come out right away and resists moving right away; slowly it gloops out and doesn’t splash but just coats those pancakes in a delicious film of sugary goodness, oh right.
Now, with another stack, grab some orange juice and pour...it immediately comes out and pretty goes everywhere. This is because the juice is less viscous than the syrup, so there’s going to be less resistance to movement.
Because blood is full of large proteins and cells, it’s pretty viscous and moves much more slowly than just plain water, or orange juice.
Blood viscosity doesn’t change much over time, but certain conditions like polycythemia, where the person has too many red blood cells, can increase viscosity, and conditions like anemia, where the person doesn’t have enough red blood cells, can decrease viscosity.

Blood vessel length2:00–2:29

A second factor that affects resistance is total blood vessel length. Just like with viscosity, the relationship is directly proportional, and this can be represented as resistance ∝ L, so, simply put, shorter vessels have less resistance and longer vessels have more resistance because there’s more friction resisting flow.
This means that as a child grows into an adult, their blood vessels will get longer, and their peripheral resistance will go up.
A third factor that affects resistance is blood vessel radius, which in this case is inversely proportional to resistance...to the fourth power!

Blood vessel radius2:29–3:08

Meaning that as a vessel’s radius goes down, its resistance really goes up. Unlike viscosity and length, the radius can change from minute to minute, especially the radius of arterioles, which can vasoconstrict like when you’re lying at home on the couch, which would decrease diameter and increase resistance, or vasodilate like when you’re running outside playing frisbee, which would increase diameter and decrease resistance.
Now, the equation relating all these variables is resistance R is equal to 8 times viscosity eta times length L divided by pi times radius r to the fourth power.

Resistance3:08–4:34

Now keep in mind that resistance is also related to blood pressure and blood flow by the relationship: Q = P / R. So let’s apply this to a real-life situation, let’s say a person has a blood flow of 300 ml/min going through their carotid artery and they suddenly develop a blockage of exactly half of the artery, which can happen in a stroke, what would happen to the blood flow?
Well, a 50% blockage means that the radius is now ½ of what it was, and looking at our equation, since nothing else has changed, plugging in 1/2r for our original r, we get ½ r to the fourth or 1/16 r, meaning resistance goes up by 16 times!
iAssuming that the blood pressure doesn’t change right away, subbing in this new 16 times greater resistance, we see that the blood flow drops by 16 times,i from 300 ml/min to 300 ml/min / 16 = 19 ml/min, which is a huge drop!
So that’s how resistance works for a single vessel. Now, what if you have a bunch of different sized vessels in a row, each with their own resistance, and you wanted to figure out the total resistance?

Serial resistance4:34–5:54

Well since, they’re in a row one after another, we say they’re in series, and you simply add the individual resistances all together to get a total resistance.
That’s called the serial resistance. As an example, let’s think about blood heading out to a cell in your toe and back.
After leaving your heart, It has to go through an artery, then through an arteriole, then through a capillary alongside that toe cell, then back through a venule, and finally through a vein to reach the heart.
If we add up all of those individual resistances, our total will equal the total resistance faced by the blood flow going to the toe cell and then back to the heart, assuming there are no branches in the system and no other cells to worry about.
When we arrange resistance in series like this, the blood flow through each part of the system is the same, but the resistance at each level will differ mostly based on the length and radius of each vessel.
So far, so good. Of course, this doesn’t account for the millions of branch points in the circulatory system, and for that we have to think about the concept of parallel resistance.
In short, it’s when two vessels branch and move blood in parallel and then meet up again, which is exactly what happens in the circulatory system since there is a lot of branching and ultimately all of the blood meets up again in the right atrium.

Parallel resistance5:54–6:25

To calculate the total resistance for these portions where the vessels split, we use 1/Rtotal = 1/R1 + 1/R2 + etc. So to apply these two equations, let’s say that we want to figure out the total resistance here.

Total resistance6:25–8:49

In this case we have five different resistances to worry about. Now let’s give these some numbers, Let’s say we’ve got a larger but longer blood vessel with a resistance of 6, and then it branches into three.
The very thin blood vessel in the middle has a resistance of 10, and the slightly larger ones on either side both have a resistance of 5.
Then all the branches come back together and connect to a short wide vessel with a resistance of 2. Now, these resistances do have units, but for simplicity’s sake I’m not showing them, but in case you’re curious resistance is measured as mmHg・minutes/Liter.
To figure out the total resistance we need to break this down into two parts, and we’re going to add up the parallel resistance of the three vessels in the middle first.
So that’s ⅕ + 1/10 + ⅕, which is 2/10 + 1/10 + 2/10, which is 5/10, which remember is equal to 1 over R total. So if we flip 1/Rtotal and 5 over 10, we get Rtotal equals 10 over 5 which equals 2.
So this is the resistance of this chunk of parallel vessels. That makes sense, because with parallel resistance, the total is always less than the resistance of any one component.
Now that we have the combined resistance of the parallel guys, the remaining are just in series, so we just add up 6 + 2 + 2, and that’s 10 or 10 mmHg・minutes/Liter, which just happens to be right around the actual resistance you see in the entire systemic circulation, by comparison, the pulmonary circulation has only 1/10th of that resistance, it’s closer to 1 mmHg・minutes/Liter.
It’s also worth mentioning quick that, just like before, the flow through these bits in series is the same, along with the total flow through this whole parallel system.
The flow through each of these parallel vessels though, is not the same, since the blood has to split flow through each of the vessels, although, the sum of these three flows must equal the total flow!
All right, as a quick recap: vascular resistance is a measure of the resistance that must be overcome to push blood through the vessels, and can be represented by the equation 8 times viscosity eta times length L divided by pi times r^4i, so it’s directly proportional to the viscosity and the length, and inversely proportional to the radius to the fourth power.

Review8:49–10:28

Resistance in series is equal to the sum of each resistance, and one over the resistance in parallel is equal to the sum of the inverse of each resistance.