Left ventricular volume vs. time

So this is our left ventricular pressure curve, and I've divided it into four sections. And actually, I chunked in this extra bit here. This is actually kind of going into the second heartbeat. And the reason I did that, remember, is because I wanted to make sure that you can see the entire last chunk of the heart cycle, this blue bit, instead of having to try and remember adding this part in. So just to keep it easy on the eyes, I just went into the next heartbeat to make you see very easily that this is all one part of the cycle in a sense. Now, instead of looking at pressure, what I want to do is actually look at volume. And so what I'm going to do is I'm actually going to draw out the same axis. So we're going to have time using seconds over here. And I'm going to follow the heart, specifically the left ventricle, in the same way I was following it before, in four sets. This is, let's say, 1.2 seconds. This could be 1 second. This could be 0.75. This could be 0.5, and this could be 0.25, something like that. There we go. And on this side, I'm going to do volume, so volume in milliliters. And we're going to start with 0 down here. And we'll do 50 right there. Let's do 100 and 125. And these numbers, I'm actually just choosing because I think they're reasonable numbers. But, of course, we know that these numbers can change person to person. Now, to figure out what is happening over time, I'm actually going to label the four points as before, where the colors change on our graph-- A, B, C, D. And we know that going from A to B, this we called the isovolumetric contraction, meaning the volume in the heart stays the same while there's a contraction going on there. And on this side in green, we have isovolumetric relaxation, so the same idea that volume is not changing during these times. And because of that, I think that's an easy place to start our graph. So we're going to actually use A, B, C, and D for isovolumetric contraction and relaxation. Now, when we're talking about contraction, you know that at this point, the left ventricle is really full of blood. When it's about to contract, it's as loaded up as it's going to be. And so these are the two points A and B. And then for C and D, you basically have blood, what's residual in the heart, and that, let's say, is around 50. So these numbers, 125 and 50, I've chosen them because, again, they're reasonable numbers. But they could definitely change person to person. And I really just want you to get a sense for the overall pattern, what it looks like. So these two parts of our graph, I'm just sketching out like that. And in fact, I can even draw that last A, because it gets into the next heartbeat to be somewhere like that. That's resetting and restarting the next heartbeat. So the question is, what is the slope of the line here? Is it just a linear thing like that? Is it just a line where blood fills in, something like this? Or is it something a little bit different from that? And to answer this question, I think it really is helpful to revisit that old equation delta P equals Q times R, something like that, right? And in fact, I'm actually going to blow up two sections of the curve. I'm going to blow up one section like this, and I think you'll recognize which sections they are, just based on the color and the shape I'm drawing them in, and another section like this. So we've got two sections. And actually, maybe the slope is not quite like that. And it looks maybe like this. So there are two sections here. The way to apply this idea delta P equals Q times R, what I want you to do is think about this. Think about section one, which is right here, and section two separately. So this is section one and this is section two. And what's happening in terms of the aortic pressure during section one? Well, the aorta is, of course, coming in like this. And immediately the aortic valve opens, and then quickly the pressure rises, and it rises, and then finally catches up with the left ventricular pressure. And then at some point, let's say right here, it's going to do this and have that dicrotic notch we talked about. And on the bottom-- this is, of course, the aortic pressure, right? And on the bottom, we've got left atrial pressure to think about. So left atrial pressure is coming in like this, and it's rising quickly, and it's maxing out. Remember, it's very full, we said. And then it begins to fall, right? It begins to fall, and then it picks up again. So these are the kind of curves that you get for the left atrium and the aorta. Why did I draw this out? Why did I make it all big like that? Well, because if we're talking about delta P, all that means is the difference between the yellow line and the white line. That's all it is, delta P, difference in two pressures. So if I look at this, it's actually a nice difference, a good size difference. If I look up here, it's a medium-sized difference. And if I look over here, it's almost no difference. So delta P is starting big and getting small. So delta P is getting smaller and smaller with time. And over here, it's a similar situation. It starts out big, and then it gets medium, and then it goes eventually small. So it starts out big and then eventually get smaller. So, whenever you see delta P, change in pressure, and you see two pressure lines, that's kind of an immediate-- that's an easy one in a sense, right? You just have to look at the difference between the two lines. So how does that help us? Well, you can see that delta P equals Q times R. And what is Q exactly? Well, Q, remember, this is flow, blood flow, and the units on Q-- maybe you'll have an aha moment; I did when I first thought about this-- the blood flow is simply volume over time. And if you have volume over time, then that's nothing more than the slope of the line. The slope down here on this line is going to be volume over time. So if I can show differences in delta P-- and I guess here I have to state my assumption. My assumption is that resistance isn't changing much, so this is basically steady within the heart. There's not a huge changes in resistance from heartbeat to heartbeat within the heart. We don't assume that. So really, if you can see a change in delta P, then you'll see a change in flow. And that's exactly what happens. So initially, we said that there's a big delta P over here, a big delta P with aortic pressure. So that's looking at this point right here. And that means that there's going to be a big flow, that there's a lot of blood flowing, in this case, out of the heart. And if there's a lot of blood flowing out of the heart, then that means that this line, this slope of the line is going to be really steep and negative. And then eventually, you get a small flow. Eventually, the delta P becomes tinier, and the flow becomes less significant, so then you get a smaller flow. So you get basically something like that. So instead of that white line, the truth is that you get something that looks more like that yellow line. Now, what about the other side going from D to A? Well, going from D to A-- let me just switch colors here-- you have a similar situation. You've got a big delta P initially, a lot of blood flowing, this time into the left ventricle, so it kind of rises quickly. And then eventually, it gets smaller over time. So eventually, it's going to do this. And that's why on the other side, we have to change that white line as well. So this white line over here is going to change as well, and it's going to look more like that. So this is exactly what the volume time graph looks like. It has this interesting shape. And instead of just having you memorize the shape, I want you to understand where it comes from. So there you go.