BENG 100: Frontiers of Biomedical Engineering

Lecture 14

 - Cardiovascular Physiology (cont.)


Professor Saltzman describes the blood flow through the systemic and pulmonary circulatory system. More specifically, he describes, with the help of diagrams, the events that lead to blood flow in the body as a function of contraction/relaxation by specific chambers of the heart, and the effect of four valves which help direct flow. Important terms and concepts such as systole/diastole pressures, cardiac output (CO) as a function of heart rate (HR) and ejection volume (EV), and the action potential propagation that stimulates heart muscle contraction are discussed.

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Frontiers of Biomedical Engineering

BENG 100 - Lecture 14 - Cardiovascular Physiology (cont.)

Chapter 1. Review of Heart Anatomy and Physiology [00:00:00]

Professor Mark Saltzman: So, we’re going to continue the discussion of cardiovascular physiology today. In particular, pay attention to the heart and its role in creating the pressure that moves blood throughout the circulatory system. I’m going to take a step back and let’s review what we talked about at the end, and then we’ll get into the new material for today.

The heart is an element of the circulatory system. It’s a critical element, obviously and it–you can show it, as in this picture, in the center of the circulatory system where its role is to supply the pressure drop that moves blood through what’s called the systemic circulation, or the circulation to all of the tissues in the body, the circulation of oxygen rich blood to all the tissues in the body flowing from the aorta, through arteries, through arterioles, capillaries, collecting venules back to veins, back to the heart. The second circulatory system, the pulmonary circulatory system, which sends de-oxygenated, or oxygen-poor blood, through the lungs, through the pulmonary artery, arterioles, capillaries, veins, back through the pulmonary vein to the left side of the heart. One can think about the heart as two functioning units that are coupled in some way. We’re going to see that they’re coupled in almost every way. They’re coupled because the output from one side of the heart is the input to the other side. The output from the left side of the heart goes through this circuit and then back to the right side. The output from the right side goes through this circuit and then back to the left side, and so they’re coupled. They’re also coupled because it’s one organ, and so when this organ performs its function which is contraction, these things are happening simultaneously because it’s one individual organ that’s accomplishing it.

We talked briefly about the anatomy of the heart and I brought a model of the heart here, larger than actual size but with an–so it’s not like a real heart in that way. It’s also not like a real heart because you can open it up and take a look inside. I’m going to bring this to section if you want to look at it or you can come up and look at it after class. To illustrate some of the features that are shown in this cartoon, that there’s a difference in the muscular walls. That the left side of the heart has a thicker muscle than the right side of the heart and that there are vessels on the surface of the heart, so vessels that come off of the aorta, for example, the red vessels here that serve the myocardium or the surface of the heart and supply it with oxygen. That the right and left side of the heart is divided into two chambers. On the left side there’s the left ventricle, and the left atrium above it, right ventricle, right atrium above it.

If we look inside there are valves that guard the entrances between these compartments. There’s a valve in going from the right atrium to the right ventricle–I’m just going to put all the names up on the–there’s a valve in going from the right atrium to the right ventricle and that’s called the tricuspid valve. There’s a valve in going from the right ventricle into the pulmonary artery and that’s called the pulmonary valve. You can’t see it very well here but it’s up here. There’s a valve in going from the left atrium into the left ventricle and that’s call the mitral valve, and a valve in going from the left atrium into the aorta and that’s called the aortic valve. There’s four valves that are important and they guard the entrances. One of the key things we’re going to talk about today is the function of these valves in producing a flow.

Chapter 2. Valves and the Generation of Pressure [00:04:13]

You know that the heart functions, it creates pressure by beating, by contracting, it beats. How is pressure generated when that happens? You know that blood moves, blood flows because of a pressure drop. We talked last time about the relationship between a pressure drop and a flow. Whenever there’s a pressure drop if there is the possibility of flow, there’s some resistance to that flow, and a certain amount of flow is created which depends on the resistance. Resistance goes up; flow goes down for a fixed pressure drop. Resistance goes down; flow goes up for a fixed pressure drop. The pressure drop is what creates the flow.

You also know that pressure varies with volume. If I have a container that contains a liquid or a gas and I compress the container the pressure goes up inside. Why is that? Why does pressure go up as volume goes down? The most simple system to think about is an ideal gas. Ideal gas: PV = nRT; an ideal gas pressure times the volume = nRT. If temperature, the gas constant, and the number of molecules are constant, then when pressure goes up volume has to go down; volume goes down, pressure goes up. Why is that? What’s happening inside? Brian?

Student: Normal activity can delay [inaudible].

Professor Mark Saltzman: Right, exactly. The molecules are closer together, they’re closer to the walls, the force of pressure is created by collisions of the molecules with the walls. This is a very simple description obviously, but you can imagine as the volume goes down and the pressure goes up, more molecules bouncing against the walls and creating pressure. Same thing happens in a liquid; only in a liquid the change is not so dramatic as in an ideal gas. In general, liquids are considered to be incompressible. You’re not pushing their molecules closer together so much because it’s a condensed fluid, but pressure still varies with volume in the same way. You can’t describe it by this equation anymore because this only applies for ideal gases, but the same thing is true that when volume goes down–the volume and the number of molecules is fixed–then the pressure goes up.

Another way of thinking about it that is far less scientific is–because everybody’s seen Star Wars, not the later imitation Star Wars but the first one where Luke Skywalker gets trapped with somebody. I forget even–in this room, in this garbage dump, and the walls start coming in. As the walls start coming in, he gets more and more urgent about getting out. His pressure is going up as the volume is going down and the pressure to get out gets higher and higher, it’s the same kind of thing here. Volume is decreasing, pressure goes up. When the heart beats or contracts it decreases the volume of these chambers. When the muscle contracts it decreases the volume of the chambers inside; the volume of the chambers goes down and there is blood inside and that blood gets squeezed as the pressure–as the volume goes down the pressure goes up. That’s how pressure is generated.

Why do you need valves? Why are valves important in the function of the heart? I already alluded to the fact that your heart cannot function properly without valves that are acting correctly. Why do you need a valve? Well, imagine that you had a simpler system than your heart. You had a balloon that was attached to a garden hose and the whole thing was filled with water. If I decrease the volume of the balloon, the pressure in the balloon goes up and water goes out the garden hose; if I decrease the volume. What if I expand it again? Well, then the pressure goes down inside the garden hose and all the water gets sucked back in. You can imagine if you had a water hose that–or a garden hose that was hooked up to a reservoir and a balloon on one end, and you inflated it, and deflated it, inflated it, and deflated it, you’d be pushing water out and pulling it in and it would go back and forth in this way. If you’re increasing and decreasing the volume by the same amount you’d be pushing out a volume of water and pulling it back in.

Now that’s a kind of a flow but it’s not the continuous one directional kind of flow that we have in our circulatory systems. That would be a–you could imagine a circulatory system that’s based on that, where you have a heart that pushes blood out and then sucks it back in, and then pushes it out and sucks it back in, but that’s not the way that the human heart functions. In order to get blood flowing in one direction you push the blood out, you close a gate, and then when you’re re-inflating the heart the blood can’t come back. The function of these valves is to prevent that reverse flow of blood back into the heart when it’s relaxing or increasing its volume. The basic function of the heart is to contract, decrease its volume, increase the pressure, blood goes out, valve closes preventing blood from coming back into the chamber that just ejected the blood. Then, that chamber relaxes and goes back to its original volume. That’s the basic function of the heart and we’re going to spend the rest of the time talking about the details of how that happens. It’s clear why valves are a necessary part of that cycle.

Pressure varies throughout the circulatory system. If pressure is indeed generated in the heart, as I’ve said, then you would expect the highest pressures to be in the regions that are closest to the heart. If I measured pressure in the aorta, and we talked about this last time, you would find that pressure varies with time. Because pressure is going up and down in the heart, that oscillation in pressure with heartbeat gets transmitted into the aorta as well and we’ll talk in a minute about why that happens.

If you looked over time an average pressure in the aorta would be somewhere between 120 and 80 mmHg, so let’s just call it 90 here. The pressure in the aorta is 90. If you think about the whole circuit, this blood has to flow from the aorta, through the systemic circulation and back into the right atrium. In the right atrium it’s at the end of its journey and that pressure there is approximately 0. The pressure drop that’s driving blood through the systemic circulatory system is ΔP of 90-0. The pressure that’s generated here gets used completely in driving the flow around. If I looked at intermediate positions I’d find that if I looked in the arterioles the pressure is about 35 mmHg, so the pressure dropped from here to here is 55 mmHg. The pressure drop from the arterioles to the venules is about 20 mmHg, and from the venules back to the right atrium is 15-0 or 15 mmHg.

Pressure drops throughout the circulatory system. If you look on the pulmonary side, you’ll find the same phenomenon, but in general, the pressures are lower. The pressure in the pulmonary artery is only about 15 mmHg, dropping to about 6 mmHg in the capillaries where oxygen exchange occurs, dropping back to 0 when you get to the left atrium. What does that tell you about the pulmonary circulation compared to the systemic circulation? The pressure drop across the systemic circulation is 90 mmHg, across the pulmonary circulation is 15 mmHg, what does that tell you about the pulmonary circulation in comparison to the systemic circulation? Justin?

Student: The flow isn’t as fast.

Professor Mark Saltzman: Flow is not as fast. Is that true? What do you think? What’s the flow through the aorta? It’s 5L/min and I think that was a good answer. The flow might be not as fast because there’s not as much of a pressure drop, but we know because this is an interconnected system, that the flow is actually 5L/min at every cross–every location in the circulatory system. It’s a continuous circuit, so the flow has to be the same everywhere. Justin’s answer was one possibility and it’s a good one, but that doesn’t work in this connected kind of a system. Then if the flow is the same what has to be different?

Student: [Inaudible]

Professor Mark Saltzman: I’m sorry, Naomi.

Student: It’s pulse generated, it’s not as fast and doesn’t have to go to the rest of the body.

Professor Mark Saltzman: It doesn’t have to go to the rest of the body, so it doesn’t have to generate as much pressure. You’re on the right track, so what does that tell you in terms of the numbers you were dealing with on your homework? Which system has a higher resistance? The systemic system has a higher resistance because it takes a higher pressure drop in order to create the same flow. The systemic circulation has a higher resistance than the pulmonary circulation–high resistance, high pressure circuit; low resistance, low pressure circuit.

There’s consequences of that. It sort of makes sense now that you’ve done your homework problem for this week that the resistance through the pulmonary system would be less because it–you don’t have so far too travel. The blood doesn’t have so far to travel so the length is much less, you don’t have to push the blood as far, it doesn’t have to go up to your head and down to your toes and so less overall resistance. Because it has less resistance you don’t need as much pressure drop. Because you don’t need as much pressure drop you don’t need as much muscle. I don’t need to generate as high a pressure, so the right side has less muscle mass than the left side. The reason for more muscle mass on the left is to create the higher pressure that’s needed to drive this high resistance circuit.

Chapter 3. The Cardiac Cycle [00:15:28]

This diagram shows you the events in what’s called the cardiac cycle. The cardiac cycle is this rhythmic movement that we call a heartbeat, and it goes through a very systematic cycle. It’s a cycle, so you could start and end it anywhere. We’re going to start in this region of the cycle that’s called late diastole, and diastole is the relaxation phase. Diastole is the relaxation phase; systole is the contraction phase. In late diastole that’s the moment right before the beat starts or the contraction starts. In late diastole, look at the situation here, there’s blood flowing back into the atria, coming from the circulation that’s driven by the pressure created by the last heartbeat. There’s some blood moving from the atrium into the ventricle. That’s true because this valve, the mitral valve is open; the mitral valve is open so blood is flowing back to the left atrium and back into the left ventricle. The heart is relaxed; it’s passively flowing into the heart.

At the beginning of contraction–another word for contraction is systole, diastole/systole–now the heart starts to contract, but one region of the heart starts to contract first. The contraction occurs in an orderly fashion, it starts in the atria and it moves to the ventricles, first the atrium contract. If you look at this they’re not very muscular, they have muscles but they’re not anything like the ventricle. You can think of it as a weaker muscle than the ventricle is. It contracts first and when it contracts the volume decreases. It increases the pressure inside the atrium, and more blood starts flowing from the atrium into the ventricle. What happens? This contraction decreases the volume, increases the pressure, increases the pressure drop between the atrium and the ventricle, and more blood gets–flows into the ventricle.

Now the contraction moves to the ventricle. The ventricle starts to contract, and when it contracts the pressure starts going up inside. When the pressure goes up inside the mitral valve closes. That’s important because you don’t want blood to flow back into the atrium, and back into the pulmonary vein. The mitral valve closes and this contraction starts in a period called isovolumetric contraction. This isovolumetric contraction means that both of the entrances, both the entrance and the exit into the ventricle are closed. The mitral valve is closed, the aortic value is closed, contraction is proceeding, so the volume is trying to decrease but it can’t. ,The pressure goes up during contraction to the point where the aortic valve opens. This is pressurized blood which is ejected through the aorta, flow through the aorta, and then the aortic valve closes again when diastole is complete.

Just focus on what’s happening on the left side, the right side is doing the same thing but just at lower pressures. Systole begins, atria contracts, blood flows into the ventricle, ventricle contracts, both the doors are closed, the valves are closed, pressure gets higher. Then, eventually the aortic valve opens, and you get this event called ventricular ejection where a volume of blood bursts out of the ventricle into the aorta. The aortic valve closes again and the cycle repeats itself. This is a schematic diagram to show you sort of the sequence of events, contraction and valve activity that lead to the forward surge of blood. The amount of blood that is ejected from the left ventricle on each cycle is called the ejection volume. If you took the ejection volume and multiplied it by the heart rate you get the cardiac output.

The ejection volume or the volume of blood that’s ejected from the ventricle on each beat times the heart rate is equal to the cardiac output (EV * HR = CO). You know this is five–approximately at rest, 5L/min. If you assume that your cardiac output while you’re sitting there is 5L/min and you put your finger on your pulse and measure your heart rate, then you could calculate approximately how much blood is being ejected from the ventricle with each beat. Let’s think about that same kind of thing in more detail where we really track the pressures because it turns out that following the pressures and thinking about what’s happening in the chambers and the valves you can get a fairly complete picture of the physics of how cardiac ejection occurs.

This diagram is–it’s in the Power Points and–but it’s a little hard to see I think on the projection so I redrew it down here in color. What it shows is pressure from 0 to 120 as a function of time during the cardiac cycle. I didn’t write any time units on here but this is time progressing. This shows you two beats of the heart. The most prominent thing that you notice is the green line here which shows pressure in the ventricle. Which ventricle am I showing? How would you tell? I said they’re both roughly the same, but how would you tell if you this was the left or the right ventricle? The total pressure, and the pressure is high so this must be the left ventricle because it’s reaching about 90 mmHg, the pressure you need to drive the systemic circulation. This is indeed the left ventricle and it’s the left atrium. You could have also noticed this is the aorta I’m going to show you here, so if I’m showing the unit it must be the left side of the heart.

The first thing you notice is this big bump in pressure; this is the trace for the ventricle. If I had a pressure sensor in the ventricle and I was measuring how pressure changed as a function of time, I would measure what you see on this green line here. Pressure starts off fairly low and then goes up to 120 mmHg, and goes back down again, up to 120 mmHg, down again. This is the trace for the atrium on the bottom here. You’ll notice that the pressure in the atrium doesn’t go through these big excursions that the ventricle does. That’s because the atrium is not a powerful pump. It’s not a powerful muscle, and so it only generates a little bit of pressure when it contracts. The role of the atrium is to contract to basically fill up the ventricle so that when the ventricle goes through its massive contraction, it’s as full of blood as it can be.

The atrium gives a little beat in order to push whatever blood is in it into the ventricle. It doesn’t have to go very far so you don’t need so much pressure, and fill up the ventricle so that when the ventricle contracts you get as much ejection of blood as possible, the biggest volume ejected possible. If I looked at the difference in pressures between the atrium and the ventricle, at this point here, and this point here where I’m starting is late in diastole, remember what was happening late in diastole was that blood is flowing from the left atrium into the left ventricle and the mitral valve is open. That’s what you see here, the pressure is slightly higher in the atrium than it is in the ventricle. If I looked at the pressure drop at this point ΔP it’s higher in the atrium than it is in the ventricle and blood is naturally flowing that way. That only happens if the mitral valve is open and it is at this point; the mitral valve is open during diastole.

The atrium contracts, you see the little bump of pressure created by the atrium contraction, and then the ventricle contracts. This is the start of systole right here, where the contraction of the atrium starts is the beginning of the heartbeat. What happens? The atrium contracts, pressure stays higher in atrium than it is in the ventricle. So, blood is flowing from the atrium into the ventricle, and then all of a sudden the ventricle starts contracting. The ventricle has a bigger contraction, more muscle, so it’s going to generate more pressure. At some point very shortly after it starts to contract, the pressure in the ventricle becomes higher than the pressure in the atrium. When the pressure in the ventricle becomes higher than the pressure in the atrium, the valve between them, the mitral valve, closes. It closes strictly due to the fact–it closes for a number of reasons but one of the reasons it closes is because there’s more pressure here now then there is here and it slams the door shut. It’s a one way valve; when pressure becomes higher in the ventricle than the atrium, the valve closes.

At this point here, where the lines cross, this is the mitral valve closing. What’s happening at the other–at the exit? Well the aorta is this–the pressure in the aorta is this orange line here. The pressure in the aorta is high. Why is the pressure in the aorta high? Because it was filled up with blood from the last heartbeat, it was–this blood was ejected into the aorta at high pressure, that pressure stays there from the last heartbeat. Now, why does it do that? Because the aortic valve is closed; during diastole the aortic valve is closed. That means that the pressure that was generated stays high in the aorta, even as the ventricle is relaxing. The blood can’t get sucked back from the aorta into the ventricle because at this point the aortic valve is closed. When the mitral valve closes, the aortic valve is already closed, that means the ventricle is sealed off. That’s what I showed you in the diagram here right after atrial systole. Both valves are closed and the ventricle is contracting. Because both valves are closed and the ventricle is contracting we have the Luke Skywalker situation, where pressure starts to rise dramatically inside the closed chamber.

Eventually that pressure is going to rise enough that the pressure in the ventricle crosses over the pressure in the aorta. At this point what happens? The aortic valve opens and blood can be ejected from the ventricle into the aorta. Now, that’s the only path for the blood to go because the mitral valve is still closed. The mitral valve is still closed because the pressure in the ventricle is still much higher than it is in the atrium. What this diagram shows you is a couple of different things. It shows you pressure in each of the chambers, think about the chamber, the atrium, the ventricle, the aorta. Depending on where one pressure sits with respect to the other, if the pressure in the ventricle is higher than the pressure in the aorta, then the aortic valve is open. If it’s the other way the aortic valve is closed, and the same thing with the ventricle and the atrium.

The aortic valve opens here, contraction continues. This is the active phase of ejection, which is shown in the diagram here, mitral valve closed, aortic valve open, pressure high here, pressure lower here. So, blood is ejected from the heart, the muscle eventually starts to relax, contraction is complete, the ventricle starts relaxing. When the ventricular pressure passes through this point and drops below the aortic pressure, then the aortic valve closes. When the ventricular pressure–the ventricle continues to relax, eventually it falls even below the pressure in the atrium, and the mitral valve opens and the ventricle begins refilling for the next contraction. Does this make sense?

This diagram–If you understand this diagram then you understand the biophysics of pressure generation and flow generation by the heart. It’s a little bit hard to grasp all at once, but if you walk through it in the way that I showed you then I think you’ll begin to understand it. Another way to understand it is to look at this diagram. I’ve shown it a little bit more clearly here, the mitral valve closing, aortic valve opening, aortic valve closing, mitral valve reopening. If you can follow the pressures and keep this diagram in mind, why those valves open at the times they do makes sense. The fact that they open in the sequence they do allow the heart to undergo a cyclic contraction and relaxation which results in a net forward flow of blood.

This shows just where the active contraction of systole and diastole fall on this curve. Systole begins when the atrium begins to contract, atrium contracts, ventricle contracts, systole ends here, and the ventricle starts to relax at that point and that’s diastole. Early diastole, the ventricle is still relaxing, late diastole everything is fully relaxed and prepared for the next heartbeat. What’s the time of this whole sequence? Well, how fast–what’s a heart rate? 60 to 70 beats per minute; so this whole sequence here takes about a second. Athletes, it’s well known, training can decrease your heart rate. What does that tell you? Do athletes need less blood flow? No, they need about the same blood flow but they have a higher ejection volume. Their heart is operating very efficiently; ejecting more volume per beat and so they need less beats to supply the cardiac output.

There are other changes that occur during training as well, that’s not the only thing, but that’s one thing that certainly occurs. As you become more cardiovascular–as your cardiovascular fitness increases you can–what happens when you start to exercise? Two things happen when you start to exercise. One is your heart rate goes up, the second is your heart starts beating with more force, so both the heart rate and the ejection volume go up in order to create more cardiac output. A conditioned athlete will be able to do both of those very efficiently. They can create a higher cardiac output with less work from the heart. That’s why with conditioning and training, you can start to be more–your performance will be enhanced even though your heart rate might not go up as someone who is out of condition.

This is just another picture of the cardiac cycle where now I’ve sort of combined everything together. You can see this pressure curve here, the pressure curve for the aorta, for the ventricle, for the atrium, and you can visually correlate that with what’s happening in each event. Late diastole, all the muscles are relaxed and blood is passively flowing back into the left atrium and through the mitral valve which is open to the left ventricle. When contraction begins, first in the atrium, blood is pumped into the ventricle. The role of atrial contraction is roughly to fill up the ventricle as much as possible. When the ventricle starts to contract, pressure in the ventricle rises above pressure in the atrium, causing the mitral valve to close. The aortic valve is already closed, so now you have a closed chamber here.

This contraction is an isovolumetric contraction, fixed volume of blood trying to increase–the heart is working to try to decrease the volume, it can’t, so the pressure goes up. When the pressure goes up above what it is in the aorta, the aortic valve opens, blood is ejected, the muscle starts to relax, and the aortic valve closes. Now this is key; if your aortic valve didn’t close what would happen here? You’d pull in that blood that you just ejected into the aorta, you’d pull it back into the ventricle. A little bit does come back because the valve doesn’t close immediately; a little bit does come back but not very much.

When physicians are listening to your heart one of the things they’re listening for is sounds that aren’t normally present in a functioning heart. Those sounds often have to do with valves that are not functioning properly. If during late systole, right after systole is over, if they hear a ‘whoosh’ of blood when they shouldn’t, that might be because your aortic valve isn’t functioning properly and blood is whooshing back into the ventricle when it shouldn’t be. Same thing with the mitral valve, if they hear a noise at this point in the cardiac cycle, that might be a flow of blood back from the ventricle into the atrium when it shouldn’t be happening, that might be because your mitral valve is not functioning properly. That’s what physicians are listening for when they listen to your chest during a physical exam. Wilma?

Student: What causes the pressure in the left atrium to rise a little bit after the mitral valve closes?

Professor Mark Saltzman: Here? So, what causes this little blip of pressure here after the mitral valve closes do you think? Well, it probably happens just because you’re getting this massive contraction in the ventricle that’s right underneath it. There’s some change in volume here as well even though the atrial contraction is almost complete. Tou’re also getting sort of a bystander effect from this very large contraction down here and so that is–follows very closely the pressure rise in the ventricle and is just a byproduct of that. Other questions?

Chapter 4. The Cardiac Conduction System and Conclusion [00:36:58]

What I want to talk about–so that’s the end of the material that’s covered on your mid-term exam which is next Thursday. What I want to talk about next week is–on Tuesday–is the cardiac conduction system. I think you can see now that for this orderly sequence of events to occur it has to be regulated in some way. The proper function of your heart requires all these things to occur in a very specific sequence. The atrium has to contract before the ventricle and in order for this logical progression of pressures, proper functioning of the valves, etc.

Well, it’s the cardiac conduction system or this specialized system that moves electrical impulses through the heart that is responsible for coordinating the function of the heart on the heartbeat. The cardiac conduction system is an electrical system where impulses are carried through the substance of the heart. Now, heart tissue is muscular tissue, it’s also electrically active tissue. Each of the cells are capable of undergoing an action potential just like action potentials in nerves. The action potential in a muscle cell is not strictly informational like it is in the nervous system. An action potential was the way that an electrical signal got propagated from one end of the nerve to the other.

In muscle cells electrical signals get propagated from one muscle cell to another, but another thing happens. This electrical signal also activates the contraction mechanism inside cells. As they’re passing the electrical signal they’re also getting the message to contract. Electrical activity in muscle cells is linked to contraction and so as this electrical activity passes over the heart in an orderly fashion, because of the cardiac conduction system, as it passes in an orderly fashion over the surface of the heart, as you’ll see next time, I’m showing it this way, this is the way the electrical signal passes from right atrium down through left ventricle. As it passes in that orderly way the muscles are activated to contract in an orderly way as well, I’d like you to review for next time what we talked about in terms of action potentials that are in Chapter 6 because we’re going to talk about those in the context of a heart for next time. Questions? I’ll see you this afternoon.

[end of transcript]

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