BENG 100: Frontiers of Biomedical Engineering

Lecture 13

 - Cardiovascular Physiology


Professor Saltzman discusses the biophysics of the circulatory system. He begins by describing the anatomy of different types of blood vessels, and states the relationship between pressure difference (ΔP) as the driving force for fluid flow (Q) in a tube (i.e., blood vessel) with some resistance R (ΔP = RQ). R can be calculated using if dimensions of the tube (L, r) and fluid viscosity (μ) are known: R = 8μL/πr4. Next, Professor Saltzman traces the blood flow through the circulatory system and explains how the body can regulate blood flow to specific regions of the body. Finally, he describes the heart and its function as the pressure generator in the system.

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Frontiers of Biomedical Engineering

BENG 100 - Lecture 13 - Cardiovascular Physiology

Chapter 1. Introduction [00:00:00]

Professor Mark Saltzman: This week we’re going to talk about cardiovascular physiology and the cardiovascular system, which includes the blood, the blood vessels, and the heart. We’re going to focus on several features. This is obviously a big topic, not only understanding the basic physiology of the cardiovascular system, but what can fail in the cardiovascular system in disease. Of course, cardiovascular disease is the number one or two cause of deaths in Western world. So, it’s serious and important topic for medicine. It’s also something that I realize you probably all know something about. We’re going to try to look at things in a slightly different way, look at them the way that an engineer, a biomedical engineer might look at the cardiovascular system, to try to understand the relationship. In particular, between pressure, blood pressure, which is the force that moves blood around through the circulatory system and flow; the actual movement of blood, which is what’s essential for distributing oxygen and nutrients and everything else that we move around in our circulatory system.

I’m going to talk briefly about the anatomy of the heart in the circulatory system. We’ll start by thinking about the whole level. I’m going to talk in some detail about how pressure differences generate flow, starting with a very simple example and building up to some of the complexity that we have within our cardiovascular systems. One of the most amazing things about the cardiovascular system is its ability to change the pattern of blood’s flow such that organs that need more blood can get more blood. It’s not just that there’s a static system where blood is flowing throughout the body and it flows at the same rate everywhere all the time. It increases in one region and decreases in another in response to physiological need.

We’ll talk about the sort of engineering principle that the cardiovascular system uses to accomplish that. Then next week we’ll talk about–we’ll talk in some detail this Thursday about how the heart generates the pressure that’s needed to move the blood and how you can create this flow with a relatively simple but durable machine, the heart. Next Tuesday we’ll talk about cardiac conduction electrophysiology, how the heart regulates it’s beating in order to generate orderly pattern of pressure generation. This is a cartoon of the cardiovascular system, not showing the blood except by the colors here, but showing the heart. In the center of this diagram is the heart and surrounding it is sort of a schematic diagram like you might see for plumbing in a house but certainly not in anatomical detail; this drawing isn’t of how blood flows from the heart to all the other regions of the body. Let’s just–now I know that you’ve seen diagrams like this before, you understand the basic connections between things, but let’s just go through them briefly.

Chapter 2. The Heart in the Circulatory System [00:03:46]

You have to start somewhere because this is a cyclic–it’s a closed system. You start at one point and you go around and you come back to the beginning again. If we start in the–in this side of the heart, this is the left side of the heart and there are two chambers in the left side of the heart: the atrium and the ventricle. You see that blood blows into the left side of the heart and it’s come from the lungs. The blood has come from the lungs and so it’s full of oxygen and in this diagram it’s indicated as red. If you follow the arrows here, the blood flows from the lungs into the left atrium, into the left ventricle, and out through a large vessel called the aorta.

Fairly simple; so far two chambers in the heart, blood flows through these two chambers, atrium first then ventricle, and out through the aorta. If I was able to measure flow at this point here in the aorta, I would measure the total rate of flow of blood out of the heart. You measure that in volume per minute, in liters per minutes let’s say. All of the blood flow is coming through this one vessel. If I could measure what the flow is through the aorta over a period of time, I would measure what’s called the ‘cardiac output’ or the rate of flow that the heart is producing in its function.

Now, because it’s a closed system the rate of flow has to be the same anywhere in the cycle. If you imagined a simple tube that connects back to the–to itself. If I’m generating five liters per minute of flow here I have to have five liters per minute everywhere in the cycle. Otherwise what would happen? Well, otherwise the volume of the vessels would have to be expanding or contracting at some point if the flow rate is different there. It would have to be changing with time if the flow rates different and it doesn’t do that. It’s a steady state system where there’s a constant flow all throughout the cycle. We’re going to come back to this point but it’s important to remember.

Now, immediately after the blood comes out in the aorta there’s an opportunity for it to go somewhere else. There’s a branch point and that first branch point is from the aorta into this, what’s shown as a fairly large vessel, but they’re pretty small vessels actually. These are the coronary arteries, the arteries that actually bring blood to the surface of the heart in order to nourish it. You can imagine that the heart is using a lot of–it’s using a lot of energy. It’s generating work, that work is being transmitted into pressure and flow of the blood. It gets the energy to do that from nutrients, oxygen, glucose, and so it needs a lot of blood flow. It’s in the best possible position to get good blood flow because it’s getting it’s blood right off of the aorta where flow is a maximum.

We talked about stents last week that are used to treat disease in these blood vessels and we’ll talk more of that as we go through the next couple of weeks. What I want you to focus on now is just this phenomenon that the flow branches here. Some of the blood goes further down the aorta and some of it goes through the coronary arteries. Now, how much blood goes in which direction is going to be one of the main things we talk about in the rest of the lecture today, but first let’s just continue in our journey around. You’ll notice that this pattern repeats that there are points where the flow branches. For example, after the aorta, some of the flow goes up in ascending arteries. This goes up above the heart into the head, for example, and so the carotid arteries which carry blood flow up to your brain are descendants of this branch here. Those are important; blood to the brain is pretty important. Also, blood goes down through the abdominal aorta, so it splits in two directions down the abdominal aorta, That blood goes to your legs and all of your visceral organs that are below the heart. This pattern repeats itself. A pattern of flow, branch, branch, branch to ever smaller branches so that you can serve ever smaller regions of tissue.

Now, these vessels that carry oxygenated blood are called arteries and they have thick muscular walls. They’re generally large diameter, a centimeter or so, there’s a table in your book that gives you the diameters of different kinds of vessels. They don’t exchange materials with their outside environment. You can think of these as conduits whose function is to carry blood from the heart to a particular organ, but not to exchange nutrients, not to exchange oxygen, they’re just carrying the blood. Eventually, if we looked for example, at the branch of this artery that goes to the digestive tract, for example, to the organs of the gut where digestion takes place, you have continual branching of these arteries until they become very fine. Those smallest conducting pathways are called arterioles, small arteries or arterioles. Now they have the same basic anatomy as an artery. They have a muscular wall and we’ll talk about why that’s important in a minute and they don’t conduct any nutrients across their surface, they’re just smaller.

Eventually those arterioles branch into very fine vessels called capillaries. It’s in these capillary beds, which are illustrated here by these little meshes, where you have the smallest diameter vessels. They’re feeding very particular regions of tissue, not your whole intestine but only a very small region of the intestine. They have thin walls that lack muscle; they’re not muscular walls. It’s in these capillary beds that exchange of nutrients takes place. It’s in these capillary beds that exchange of oxygen, carbon dioxide, sugar, amino acids–that takes place in capillaries. Capillaries are not muscular but they’re able to transport nutrients and molecules.

What’s happened as we’ve gone from the aorta, a single vessel, down to a capillary bed and there are many, many capillary beds in your body. Well, if I could take a cross-section at any point–a cross-section of this–then the total flow rate into all the capillaries, the total flow rate through all the capillaries has to be the same as the flow rate through the aorta. By this process of branching where this total flow of 5L/min gets divided, and divided, and divided. By the time it gets to a capillary there’s a very small vessel carrying a very low flow rate, a very small fraction of this 5L/min, but there’s now millions of these of vessels all over your body. The blood is not flowing at a large flow rate through a big vessel, it’s flowing at a much smaller flow rate through many, many vessels but the total has to add up to the total that goes in.

Well, you know the rest of the story; the capillaries merge after they leave the tissue area. They merge into small veins; veins are collecting tubules for de-oxygenated blood. Now, this is blood that has transported all of its nutrients into the tissue that it serves so it doesn’t have a lot of oxygen anymore. It has a lot of waste products now, the waste products that are generated by these tissues during metabolism. It has a lot of carbon dioxide which is the end product of glucose metabolism, it has acids that are generated from metabolism, it has the end products of nitrogen metabolism, which is chiefly urea and ammonia, and that blood is indicated here as a blue line.

Now, we usually show these blue colored vessels, usually show them as red and blue, indicating lots of oxygen red, not very much oxygen blue. It’s not just oxygen that’s changed. The chemical composition has changed dramatically, there’s a lot more carbon dioxide, there’s a lot more urea, there’s a lot more of other things coming out of the–through the veins. These small veins called venules merge to form larger veins, eventually very large veins like the vena cava, which come back to the right side of the heart. The right side of the heart is anatomically very similar to the left side. There’s an atrium, there’s a ventricle, and blood flows out of the ventricle through the pulmonary artery to the lungs.

Now, notice that there’s something different here; that on this side of the circulatory system the part where the blood is going out to the rest of your body, the artery contains oxygenated blood. On this side, the pulmonary artery is an artery–it has the same features as a systemic artery like the aorta. It has a muscular wall, for example, and doesn’t transport nutrients, so it looks an artery but it carries de-oxygenated blood. It’s carrying it only one place, back to the lungs. It’s collected in the–collected on the other side of the lungs now with oxygen and returns to the point where we started.

It’s not just a closed system, it’s 2 closed systems. One that we’re going to call the system that’s fed by the left side of the heart where oxygenated blood goes out to the whole periphery of your body and is collected back by the right side of your heart, that’s one closed system. The second is the pulmonary vascular system which is–the force is generated by the right side of the heart, the flow is generated by the right side of the heart, flows only to the blood–to the lungs and oxygenated blood comes back to the left side, so it’s sort of like a figure 8; one loop, a second loop. What’s the–if the rate of flow is 5L/min through the aorta, what’s the flow rate in the pulmonary artery? They’re two independent systems, is that right? What’s the rate of flow in the pulmonary artery? It has to be 5L/min because they’re not independent. They’re really–I described them as two closed systems, really one closed system with a loop, so the flow has to be the same everywhere.

Chapter 3. Blood Flow and Pressure [00:15:43]

Let’s talk about blood flow in these vessels for a moment. Now you have this picture of the overall composition of the circulatory system, let’s think about a very simple problem that engineers have thought about for hundreds of years now. Turns out to have a lot of relevance in the cardiovascular system, but has relevance everywhere. It has relevance in terms of getting water to all the faucets in this building. You have to solve the same problem, and that is generating enough pressure to allow fluid to move through a length of tubing. We’ll think about a typical length of tubing and we’ll make it as simple as possible. It’s a vessel that has a constant diameter or radius and a known length. Fluid is going to flow in one end of this vessel and it’s going to flow out the other, and this is called internal flow through a tube.

Turns out to be one of the most well studied problems in all of engineering; I’m just going to tell you one aspect of this. Over a certain range of flow rates–so this isn’t true all the time but it’s going to be true most of the time in our circulatory system. If I try to generate a flow through this tube, and the flow again is going to be measured in something like volume per minute, so let’s say 1L/min, then the pressure that I need to produce the pressure drop, meaning, ‘What’s the pressure difference from one side of the tube to the other?’

I don’t care about absolute pressure I only care about a difference in pressure between one side and the other. That difference in pressure is proportional to the rate of flow and that’s what this equation says here. If I knew what the pressure drop was the flow is proportional to that and the constant of proportionality is this symbol R, the resistance to flow. We say that ΔP, the drop in pressure over the tubing is equal to R x flow rate, ΔP = R x Q. ΔP is a driving force, pressure difference is a driving force, it’s what causes the flow. The flow is what results from that, so ΔP = RQ.

Does that kind of equation look familiar to anybody from their high school physics? Have you ever seen an equation like that? ΔP = RQ–driving force is equal to some constant times a flow. Ever seen ΔV = RI? Anybody know where that equation comes from?

Student: [inaudible]

Professor Mark Saltzman: Circuits–it’s the flow through an electrical circuit. What’s the potential for flow through an electrical circuit? It’s a driving force, it’s a voltage driving force, you hook up a battery to a length of wire, for example. What flows is electrons current, and how much flows through wire–how much flows through a circuit in response to a voltage change depends on a property of the wire, its resistance. Thicker wires, more cross-section has less resistance, you can flow more current through it, thinner wires less. It takes more–for a given driving force, for a given voltage less current flows. If you haven’t seen that before don’t worry about it. If you have seen it then hopefully this will be useful in thinking about this. Which is the same thing, that the pressure drop produces as flow and how much you produce for a given pressure drop depends on a property called the resistance.

Now the resistance is a property of the geometry of the vessel. If I have a very–a vessel with a very large diameter for a given pressure drop I can create a large flow. For a vessel with a small diameter, for that same pressure drop I get less flow. Imagine your–whatever your favorite beverage is, think about a milkshake because those are difficult to draw through straws. If you’re going to drink a milkshake in your favorite flavor, do you hope you get a narrow straw or a big, thick straw? You would not pick the narrow straw if you really like the milkshake because you can only generate a certain pressure drop with your mouth. If you generate that pressure drop you’re not going to get much milkshake, you’re not going to get much flow. If I have a bigger tube, same pressure drop, bigger flow, more milkshake.

Here the resistance, it turns out, we can for very simple vessels like this, the resistance can be related to the geometry of the vessel. That is, if I told you what shape this vessel was how–what it’s diameter was and how long it is you can calculate what the resistance is from this formula here, R = 8µL/πr4. Now you know what all these things are, you know what π is, that’s 3.14–π is familiar; r is the radius; L is the length. What’s µµ is a property of the fluid and it’s the viscosity. Milkshakes have high viscosity, water has a low viscosity. So, if you’re going to drink water you’re not so worried about how big your straw is. You would accept a small straw not just because milkshakes are more delicious, but because you don’t need to generate as much of a pressure drop to move water as you do to move a milkshake, because milkshakes have a higher viscosity. The viscosity of the blood is in general a constant, it’s a constant that is about 3 centipoise. You can read in the book about units of viscosity and how they’re defined. It tells you something about the force that you need in order to cause the fluid to flow.

We’re going to be dealing with fluids in here that are basically constant in their viscosity. Blood is about three times as viscous as water. Why is blood more viscous than water, why is it harder to flow? It’s largely water, it’s mostly water, that’s the major component, why isn’t the viscosity of blood the same as the viscosity of water?

Student: [Inaudible]

Professor Mark Saltzman: It has molecules in it and so that makes a difference. It also has something else, 50% of the volume of blood is cells. A concentrated solution of cells, like red blood cells, is not as easy to flow as water is, so that’s why water is more viscous. If you wanted to then think about how much flow there is through this vessel, and I told you what the dimensions were, and I told you that blood was flowing, you could calculate r and then you would know everything about flow through this vessel. You would know if I have a pressure drop of so many units, this is the flow that would result. Justin?

Student: [Inaudible]

Professor Mark Saltzman: The interior surface of the tube could make a difference. Now it turns out for low flows, surprisingly, the surface of the tube doesn’t make a difference if the flow rate is a below a certain level. You’re thinking about, ‘What if the surface of the tube is rough?’ Then, fluid that’s flowing past that surface is going to experience more friction than if it was flowing past a very smooth surface. At low flow rates the friction that occurs when a liquid meets a solid is so high that fluid at the surface doesn’t really move at all. For low rates, fluid that’s right at the surface doesn’t move at all, and so roughness doesn’t matter when you have no flow there. As the flow rate increases then roughness becomes more important.

Two things about it in our vascular systems, the flow rates are generally low enough that you don’t have worry about that. Our vessels are all really very similar in terms of their microscopic geometry, and that all of the blood vessels are covered with a monolayer of cells called endothelial cells that basically form a blanket over the entire surface of the inside of the circulatory system. There’s very little frictional resistance to flow. That’s a really good point. Other questions?

Okay, so this equation sort of makes sense, right? If you go on to study Biomedical Engineering you’ll learn exactly where this equation comes from and you’d be able to derive it yourself. For now, just accept it and it is true for almost all the vessels in our body, under all the circumstances of human physiology. It tells us that resistance varies with viscosity, length, and radius and it varies in kind of the way that you would expect. As viscosity of the fluid goes up resistance goes up, as the length of the tube goes up, resistance goes up; harder to pull through a long straw than through a short straw. As the radius goes up resistance goes down, because the radius is in the denominator here, so as radius goes up the resistance goes down.

Remarkably, the resistance goes with the fourth power of the radius. What does that mean? That means a 2-fold increase in radius leads to a 16-fold reduction. A 16-fold reduction in resistance; so resistance is, of all the parameters, resistance is most sensitive to radius. Caitlin, did you have a question?

Student: [Inaudible]

Professor Mark Saltzman: Yeah. So what’s the unit here? Well let’s think of it. What unit would you measure pressure in? What’s a unit of pressure? Pascals (Pa) is one; Newtons per millimeters squared (N/m2), so its force per area is pressure. What’s a more commonly–those are great units–sorry? Pounds per square inch is another unit, PSI. What’s the pressure in the room here? 1 Atmosphere (atm); atmosphere is another pressure, so relative to atmospheric pressure and if you have a–any others? Millimeters of mercury (mmHg); it turns out that all of those are proper units for pressure and you could convert between one or the other as long as you knew what the conversion factor was between the–we usually atmospheres to describe Atmospheric Pressure. Physiologists usually use millimeters of mercury to describe pressure in the circulatory system. So, 1 atm is 760 mmHg.

What are the blood pressures that are relevant in your circulatory system? How many millimeters of mercury do you think? Anybody know what their blood pressure is? 120/80 what? They don’t tell you that–120 mmHg over 80 mmHg. We’re going to talk about where those numbers–where those pressures actually exist in a few minutes but that’s the range of pressures in your circulatory system from 0 mmHg up to 120 mmHg; roughly and we’ll see you go outside that range sometimes.

Now these are pressures that are inside our circulatory system so they must be–but they’re only a fraction of 1 atm, how can that be? An atm is 760 mmHg, that’s the pressure in this room. If your blood pressure is 120/80 what does that mean? Well, pressure is–we only care about differences in pressure. It’s relative pressure that matters not the absolute pressure. When you say your blood pressure is 120/80 that means 120 mmHg above Atmospheric; 80 mmHg above Atmospheric. Otherwise our blood vessels would collapse because we’re surrounded by air that’s 760 mmHg, that to inflate those vessels you have to be at pressures above that. Since all we care about are pressure differences then the pressure that you measure when you measure blood pressure is pressure above Atmospheric. Does that make sense? ΔP is in mmHg, Q is in L/min, so R is in units of mmHg/(L/min). It’s in units of–if we just write this out mmHg= R, and this is L/min, then R must be in units of mmHg/(L/min).

This resistance changes, it changes with geometry, the most sensitive thing that changes is the radius. Imagine if you had a vessel that could change its radius, that could become smaller or could become larger. Then, that would be a vessel that could regulate its resistance. If that vessel was faced with a pressure drop, let’s say a pressure drop of 10 mmHg from beginning to end of this vessel here, and it could change its radius then it could change the amount of blood flow through it. If it decreased its radius, the rate of blood flow would go down even though the pressure drop stays the same. If it expanded its radius, the rate of low would go up even though the pressure drop remains the same. Does that make sense?

I mentioned before that arteries, arterioles, small arteries, all arteries have muscular walls. They have a special kind of muscle called smooth muscle which is arranged circumferentially, sort of wrapped around the vessel, and that muscle can contract to constrict the vessel or relax to dilate the vessel. One feature of arteries that makes them important in physiology is that they can change their diameter. When they change their diameter they change their resistance, and they change the flow that goes through them at a fixed pressure drop.

Why is that important? Well, let’s say you get up and you start running; lecture’s over, you’re excited to tell your friends about it, so you get up and you run out of class, and you went from resting to running. Now, all of a sudden your muscles need more blood because they’re going to start generating work. The blood–the arteries that feed your muscles are going to contract–are going to relax. The diameter will get bigger, the pressure available is the same, they’ll get more flow. That flow has to come from somewhere so simultaneously other vessels are constricting. What would those vessels be? Well, probably the vessels that go to non-essential functions when you’re starting to run. Not your brain, you want to keep blood flow to your brain so you don’t run into the wall, but you might have less flow going to your digestive organs. You’d stop digestion for some period or slow it down; provide less blood flow for that purpose. Does that make sense?

Well if we look at how pressure varies through the circulatory system, your blood pressure is generated by the heart. Blood pressure ranges between 120/80 mmHg. We’re going to see this in a few minutes but those numbers represent the maximum pressure and the minimum pressure during a heartbeat. The maximum pressure occurs when the heart is actively contracting or beating. We’ll talk about that more in a few minutes and we’ll talk about that in great detail on Thursday. Then it drops when the heart is relaxing. Blood pressure is generated in a cyclic fashion because of beating of the heart, contract, relax, contract, relax, 120, 80, 120, 80, 120, 80. That pressure of 120/80 gets transmitted to the aorta. The pressure in the aorta is roughly the same as it is in the heart.

Now why is that? Why isn’t there a pressure drop through the aorta? Well there is a pressure drop through the aorta but it’s very small. The reason it’s small is that the aorta is big; has a large diameter and so it’s resistance is low. In order to generate 5L/min of flow you don’t need much pressure. In order to–even this whopping flow that goes through the aorta, because of the large size of the aorta, you don’t need much pressure drop to generate that flow. If I measured pressure drop over the aorta, from the beginning to the end of the aorta, I’d find that pressure doesn’t really change very much and that’s what’s shown in this diagram here. As I move from the beginning of the aorta to the end there must be some drop in pressure. Has to be, otherwise blood wouldn’t flow at all but there’s not very much of a drop.

Similarly, the large arteries would still have large diameters, have low resistances. Doesn’t take much pressure to move a flow rate through those large arteries, so over the large arteries there’s not much pressure drop either. This would be the branches, like the main branch that goes to your arm, the branch that goes to the carotids that goes up to your brain, the branch that goes down to your leg called the femoral artery. Still large arteries, large diameter, not much pressure drop needed to generate a large flow.

As we move to more branches, smaller and smaller vessels, it turns out at some point, and the point at which this occurs is the arterioles, the diameter has gotten small enough that the resistance becomes significant compared to the flow rate. Now, there’s so many branches that occurred before this that these individual vessels aren’t getting 5L/min, they’re only getting some small fraction of that. There might be 1,000 of these arterioles, let’s say, and so they’re all getting 1/1,000th of the maximum flow. How could that pressure drop be more? How come they need a big pressure drop, which is what’s illustrated here. It takes a substantial drop in pressure in order to move this lower flow rate through these smaller vessels. How could that be?

Well remember that the resistance changed with r4. That means that as the radius goes down it’s not a linear relationship between the radius going down and the resistance going up, it’s a 4th-power relationship. As it gets small resistance starts to become very, very high. When you divide a flow between vessels that’s kind of a linear process, it goes two ways, it goes four ways, it goes eight–but this r4 starts to dominate when you get down to a certain radius. It turns out that that’s at the level of the arterioles. Most of the pressure drop on this side of your–on this left side of the cardiovascular system, most of the pressure drop occurs at the level of the r4. There’s a significant pressure drop through the arteries and then not much pressure drop at all through the veins. The veins are low pressure vessels, generally large in diameter, and not much resistance to flow.

Now why–if you were going to design a system like this, is there any advantage to having the largest pressure drop occur over the arterioles, or the largest relative resistance occurring over the arterioles? Well, there’s a huge advantage because wherever the pressure drop occurs, that’s the place where you have the best opportunity to adjust the flow because small changes in radius are going to lead to large changes in relative resistance. It’s at the arterioles, or the very smallest arteries that are supplying blood to our tissues, where we have the most control over flow rate. That makes sense because sometimes you’re not making big movements in blood flow, like saying, ‘I want very little blood flow to my gut and a lot of blood flow to my muscle’–that’s a big change. You’re making smaller changes within a tissue; like, ‘I want more blood to go to the region of my brain that’s involved in talking and less to the region in my brain that’s involved in reading.’ When you’re talking versus reading you want to regulate where the blood flows on a more smaller scale, on the scale of a tissue, and its arterioleswhich are branching within tissues that have the capacity to do that.

You could do something like this, let’s say this is a very imaginary situation, but I drew it just for illustrative purposes. Let’s say that this was an artery that was feeding some tissue and so there was a blood flow that’s coming in here and it splits five different ways. So, here are five different regions of the tissue that are served by these arterioles. Now, I could draw this–one of the nice things if you do know this analogy between this equation describing pressure drop flow relationships and this equation describing voltage current relationships, is that you could draw a diagram for pressure flow relationships. It looks just like a circuit diagram because the equations are the same.

That’s what I’ve done here is taken this anatomical picture, cartoon, and converted it into an equivalent circuit where I’m not thinking about flow of electrons now or current, I’m thinking about flow of fluid. I’m drawing a resistance not as an electrical resistance but as a flow resistance; as this kind of a resistance. Let’s say that the blood is flowing in at a rate of 100 mm/min and that the resistance here is one unit, and the resistance here on each of these smaller segments is smaller–or higher. These are smaller–it branches into smaller vessels so they have a higher resistance, and it’s five units here and one unit here and the units are these. Well, if all the resistances are the same then the–of the blood that flows in here it’s going to flow equally through each one of these tubes, and so basically this 100 mm/min of flow gets split five ways.

You could do this calculation yourself; the pressure drop here is just 1 mmHg and if you did this calculation it should work out okay, the total resistance of this circuit with 1 mmHg gives you 100 mm/min of flow. What if one of these vessels changes its diameter? Let’s say it’s this one and let’s say that it shrinks its diameter so this resistance goes up. Goes up here from five units to 100 units, so I made a big change in that, goes up by a factor of 20 so that would be about a factor of two difference in radius, because of the 4th-power. If this one goes up to 100 now there’s more resistance through this particular vessel here and the same resistance through these three, so what happens? Less flow goes through this vessel and the same flow goes through the others, so that the total flow now is 89 mm/min.

Now why did the total–you could understand sort of because that’s pretty obvious right why, when I decreased the radius and increased the resistance of this vessel, why less flow went through it than through its partners, that kind of makes sense. You’ve got a smaller vessel so now I’ve got four large vessels and one smaller one, and if I feed them with the same pressure drop more of the flow is going to go through the big vessels because there’s least resistance there. Fluid takes the path of least resistance, some goes through but not as much, that makes sense.

Why does the overall flow through the whole circuit change? Why does the overall flow through this whole thing change? Well, because if any one of the vessels in here increases its resistance it increases the overall resistance of the aggregate of vessels. If the pressure that I have available is constant, and it is, the pressure I have available is constant in this example, it’s 1 mmHg, then when the whole thing increases its resistance that means the flow rate through the whole circuit has to go down as well.

There’s two things that are really illustrated here. One is that you could regulate in pathways that are competing with each other for flow then the relative resistance between equal members determines how much flow goes to each vessel; that’s one thing that’s illustrated. The other is that the whole–the flow through this whole piece of the circulatory system, this whole part of the network, depends on the resistance of every single vessel within it. One vessel changing its resistance changes the whole thing.

That’s a feature of our circulatory system. If I want more blood to go to the brain there’s two ways to get more blood to the brain. Well, there’s more than two ways, but two ways as long as the pressure–blood pressure stays the same. One way is to dilate the vessels of the brain to create less resistance there. The other way is to constrict the vessels somewhere else to create more resistance there. Either one of those is going to get me more flow to the brain. Because it’s a closed system, everything is interconnected and a change in flow in one place can influence flows throughout the whole system. Does this make sense?

Chapter 4. Blood Flow Within the Closed Circulatory System [00:45:03]

I want to go back to this picture, now, and talk about what we’ve learned in terms of flows. Now you can think about this in a little bit different way, that if there’s flows going through here and here, how much goes each direction, depends on the relative resistance between this vessel and this vessel. It does depend on the relative size between this vessel and this vessel, but it depends on the relative resistance of the whole network after it as well. It depends on the whole resistance–even if you have a big tube here, if it’s feeding lots of very constricted tubes down here, the overall resistance that the fluid experiences at this branch point is going to be high in this direction. The whole–the resistance of the whole circuit matters. Think about that.

Let’s now think about what’s driving this flow. That is, what’s generating the pressure and you know that what’s generating the pressure is the heart. That’s the only place where pressure gets generated within this closed system. The pressure that’s generated by the heart, which is experienced by the aorta, is what drives flow throughout all of these vessels. The only opportunity that individual vessels out here have to adjust how much flow goes to them is by changing their diameters, which they do. The only way to change the overall rate of flow is to change the overall pressure drop which can only be done by the heart.

How does the heart work? Well let me just start this and then we’ll talk about this in much more detail next time. This is a picture of the heart. It sits–about the size of your fist, basically in the center of your chest, but shifted a little bit to the left hand side. You can find out where yours are by just putting a finger there and feeling where you can feel the heartbeat, it’s fairly easy to define. The apex of the heart, the tip of it sits downward like that and the major vessels are near the center line; so the tip is down here, the major vessels are near the center line. The heart has muscular walls. The walls of the heart are called the myocardium, muscle heart. ‘Myo’ is muscle, ‘cardium’ is heart and there’s muscular walls so it’s a big muscle basically.

There are blood vessels on the surface and so this is the aorta coming up here. Where this arrow is here is the aorta, this is the aortic arch, and then goes down to the abdomen and up to the brain. These are those coronary vessels that I mentioned earlier. The first branches off of the aorta are to these coronary arteries which branch over the surface of the heart, so now you can see this branching pattern more clearly in one particular tissue. Here’s a coronary artery the blood flows through, here’s a branch, one goes more to the left, one goes more down the center line, branches again, branches again, and by continuously branching you define smaller arteries which serve smaller regions of tissue. These blood vessels provide nutrients to the muscle in the muscular walls of the heart.

There are inflows and outflows, you know this is the aorta up here; this is the vena cava which is bringing blood back down here. The heart has a right side and a left side. If I divided it into the right side and the left side I could put a dotted line here, where the left ventricle and left atrium are on this side of the line and the right ventricle and the right atrium are on the other side of the line. What we’ll see when we talk about this more next time, is that the left side of the heart is more muscular and slightly larger than the right side of the heart, even though they’re generating the same flow rate. The left side of the heart is larger.

If we reduce this down to a simpler picture, this is where I’m going to start next time and take out the anatomy and replace it with this cartoon, you can see that there’s a difference between the thickness of the muscular walls. The muscular walls on the left side of the heart are slightly thicker than the muscular walls on the right side of the heart. You don’t see them in this diagram, but if you looked at a real heart you would see that that’s true. The right and left side of the heart are divided into two chambers, atrium, ventricle, atrium, ventricle: left ventricle, right ventricle, right atrium, left atrium.

The inflows and the outflows are guarded by valves and there are four valves that are important here. There’s a valve which is shown by this sort of floppy structure here between the left atrium and the left ventricle. There’s another valve between the left ventricle and the aorta. Same thing on the other side, there’s a valve between the right atrium and the right ventricle, and between the right ventricle and the pulmonary artery. What we’re going to talk about next time is how these valves function in order to convert the work that’s done by the heart in generating pressure into a directional flow. That’s what we’ll start with next time.

[end of transcript]

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