Peripheral Resistance Formula

And I’m going to talk to you about pressure, resistance, and flow. We’re going to try to make sure you feel real comfortable with all three of these things by the time we’re done. So we start with the heart, and off of the heart is the aorta. This is the largest artery in the body. And this is one branch of the aorta. I didn’t draw a lot of the other ones. This is the brachial artery. And the blood is flowing from the aorta into the brachial artery. And let’s say that the blood is trying to make its way out.

To a fingertip, for example. So on its way out there, it makes its way to an arterial. And the blood continues flowing, and it goes into the capillary bed, and the vessels are too small to draw, so I just kind of do that thing. And it then goes into the other half of the capillary bed, where now the blood is deoxygenated. So I’m going to draw that as blue. That’s the part where now the blood is without oxygen. And then it continues to go and get collected.

Into a venule, which sounds a little bit like the arterial on the other side, right And we’ve got a vein over here. And then finally, the blood gets collected in a large vein called the vena cava. And there are actually two vena cavas, so this’ll be the superior vena cava. There’s also an inferior vena cava. And the blood flow through this half is, as you would guess, continues to go around. And if I was to try to figure out the pressures, the blood pressures, at different points along the system,.

Putting it all together Pressure, flow, and resistance

I’m going to choose some points that I think would be interesting ones to check. So it would be good probably to check what the pressure is right at the beginning. And then maybe at all the branch points. So what the pressure is as the blood goes from the aorta to the brachial artery. Maybe as it ends the brachial artery and enters the arterial. Maybe the beginning and the end of the capillaries. Also from the venue to a vein, and also, wrapping it up, what the pressure is at the end.

Now, these numbers, or these pressures, can be represented as numbers, right Like what is the millimeters of mercury that the blood is exerting on the wall at that particular point in the system And earlier, we talked about systolic versus diastolic pressure, and there we wanted to use two numbers, because that’s kind of the range, the upper and the lower range of pressure. But now I’m going to do it with one number. And the reason I’m using one number instead of two, is that this is the average pressure over time.

So the average pressure over time, for me keep in mind my blood pressure is pretty normal. It’s somewhere around 120 over 80 in my arm. So the average pressure in the aorta kind of coming out would be somewhere around 95, and in the artery in the arm, probably somewhere around 90. Again, that’s what you would expect somewhere between 80 and 120. So 90 is the average, because it’s going to be not exactly 100, because remember, it’s spending more time in diastole and relaxation than in systole. So it’s going to be closer to 80 for that reason.

And then if you check the pressure over here by this x, it’d probably be something like, let’s say 80. And then as you cross the arterial, the pressure falls dramatically. So it’s somewhere closer to 30. And then here it’s about 20. Here it’s about 15. Let’s say 10 over here. And then at the very end, it’s going to be close to a 5 or so. So here. Let me just write that again. 10 and 5. And the units here are millimeters of mercury. So I should just write that.

Pressure in millimeters of mercury. That’s the units that we’re talking about. So the pressure falls dramatically, right So from 95 all the way to five, and the heart is a pump, so it’s going to instill a lot of pressure in that blood again and pump it around and around. And that’s what keeps the blood flowing in one direction. So now let me ask you a question. Let’s see if we can figure this out. Let’s see if we can figure out what the resistance is in all of the vessels in our body combined.

So we talked about resistance before, but now I want to pose this question. See if we can figure it out. So what is total body resistance And that’s really the key question I want to try to figure out with you. We know that there is some relationship between radius and resistance, and we talked about vessels and tubes and things like that. But let’s really figure this out and make this a little bit more intuitive for us. So to do that, let’s start with an equation. And this equation is really going.

To walk us through this puzzle. So we’ve got pressure, P, equals Q times R. Really easy to remember, because the letters follow each other in the alphabet. And here actually, instead of P, let me put delta P, which is really change in pressure. So this is change in pressure. And a little doodle that I always keep in my mind to remember what the heck that means is if you have a little tube, the pressure at the beginning let me say start S is for start and the pressure at the end can be subtracted from one another.

And that gives you PS minus PE equals delta P. The change in pressure is really the change from one part of tube the end of the tube. And that’s the first part of the equation. So next we’ve got Q. So what is Q This is flow, and more specifically it’s blood flow. And this can be thought of in terms of a volume of blood over time. So let’s say minutes. So how much volume how many liters of blood are flowing in a minute Or two minutes Or whatever number of minutes you decide.

And that’s kind of a hard thing to figure out actually. But what we can figure out is that Q, the flow, will equal the stroke volume, and I’ll tell you what this is just after I write it. The stroke volume times the heart rate. So what that means is that basically, if you can know how much blood is in each heartbeat so if you know the volume per heartbeat and if you know how many beats there are per minute, then you can actually figure out the volume per minute, right.

Because the beats would just cancel each other out. And it just turns out, it happens to be, that I’m about 70 kilos. That’s me. I’m 70 kilos. And for a 70 kilogram person, the stroke volume is about 70 milliliters. So for a 70 kilo person, you can expect about 70 milliliters per beat. And as I write this, let’s say my heart rate is about 70 beats per minute. I feel pretty calm, and so it’s not too fast. So the beats cancel as we said, and I’m left with 70 milliliters times 70 per minute.

So that’s about 4,900 milliliters per minute. Or if I was to simplify, that’s a 5, let’s say about. So the flow is about 5 liters per minute. So I figured out the blood flow, and that was simply because I happen to know my weight, and my weight tells me the stroke volume. And I know that there’s a change in pressure. We’ve got to figure that out soon. And lastly, this last thing over here is resistance. And know I’ve said it before. I just want to point out to you again,.

The resistance is going to be proportional to 1 over R to the fourth. And so just remember that this is an important issue. R is radius. And that’s the radius of the vessel. So let’s figure out this equation. Let’s figure out the variables in this equation and how it’s going to help us solve the question I asked you what is the total body resistance OK. So if I have to figure out total body resistance let me clear out the board I’ve got, let’s say, the heart. I like to do the heart in red.

And it’s pumping blood at my aorta. So blood is going out of the aorta. And then it’s going and branching here. And then it’s going to branch some more. And then it’s going to branch some more. And you can see where this is going. It’s going to keep branching. And eventually every branch kind of collects on the venous side. All the blood is kind of filtering back in slowly into venules and veins. And finally into a vena cava. And I should really draw this going like that.

The blood is going to go back into the vena cava. So that’s my system. And I got to figure out what the total body resistance is here. So if I have a system drawn out for myself, and I happen to know that here I said 95. And here I said the pressure was 5. Then delta P equals 95 minus 5, which is 90. And I know that there are 5 liters of blood flowing through per minute. And that was my Q. So I could say 90 equals 5 liters per minute.

Actually let me take a step back from that. Instead of 90, let me write the units. 90 millimeters of mercury equals 5 liters per minute. That was my flow. That’s my Q. And I’ve got delta P here. And my resistance is the unknown. So I’ll just leave that as R. So let’s just solve for R. So I’ll move my flow to the other side. So R equals I’ll put it here 90 divided by 5, which is 18. And the units are a little funky, but I’ll just write them out anyway.

Millimeters of mercury times minutes divided by meters. So this is the answer to my question what is the total body resistance Well, we know what the pressures are at the beginning and end of our system. And we know that the flow has to be around 5 liters per minute, because that’s based on my weight and my heart rate. Therefore, the resistance must be 18 millimeters of mercury times minutes over liters. Whatever that set of units means to you. It’s kind of an abstract thing. But basically, I want to demonstrate to you.

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