Arterial elastance (Ea) and afterload

Let's go ahead and use our pressure volume loop. I'm going to sketch out how afterload would make things change on this. So let's just quickly sketch this out. I'm going to put pressure over here. And I'm going to start out with just two lines. First, and this is probably the one I want you to keep an eye on, this is the end systolic pressure volume relationship. And then I'm going to also put on there the end diastolic pressure volume relationship, something like that. And so these are kind of the first two lines that we know are going to be helpful in sketching out our pressure volume loop. Then we have this other line, right? We have this EA line. This is Arterial Elastance. And there's a good formula here that is very, very helpful. It's the pressure at the end of systole over stroke volume. Remember, any elastance is kind of thinking along the lines of a pressure over a volume. And this red dot represents the pressure at the end of systole. And this other red dot here is going to kind of show you where it crosses the x-axis, the volume. And that's helpful because then we can kind of quickly figure out what the stroke volume would be. This would be our stroke volume here. So we have it sketched out. And I can actually take this and now draw in the PV loop, which would be something like this kind of chugging along. And you might be tempted to make it cross right there at the point where the purple line is, but remember, we have to go a little bit further because that's not where the volume is going to be. The volume is actually going to be a little bit further along. So to be true to that, I'm just going to draw it a little bit further. But I wanted to draw the first line just to show you how you might have thought it looked. But that is not where it crosses. And then, of course, you have contraction, and you have ejection of blood into the aorta. So this is our pressure volume loop, right? This is what it looks like. And at the top of this loop, we have ejection. This is where blood, I said, is coming out of the left ventricle and going into the aorta. And if I actually just kind of trace around this part of it-- this is ejection-- you would probably remember that this is where something important is taking place. And specifically, I'm talking about afterload. Remember, we actually defined afterload. According to this part of the pressure volume loop, we said-- and this is going back to Laplace. We said that afterload is basically wall stress happening during ejection. So during the entire ejection phase, the wall stress is what our afterload is. And we actually simplified this to-- or not simplified, but kind of wrote this out, I should say, to Laplace's law, which is pressure times radius of the left ventricle during ejection divided by 2 times the wall thickness during ejection. So this is the formula for afterload. And we have to remember that it's occurring during the entire ejection, during the entire part I traced out. But for simplicity, because a lot of times we don't actually sit there and calculate all the different points, we oftentimes look to this value, this pressure at the end of systole. Because, of course, this is definitely one of the points during ejection. You could say the final moment of ejection would be that point right there , where the pressure is end systolic. And so we often use that value to kind of be a marker for what afterload is doing. And remember, we know that pressure and afterload are very closely related. You can see it in the formula right there. So we do use the end systolic pressure as a marker. And I guess now the question I want to pose is what would happen if we actually increased that number? What if we increased the pressure at the end of systole? What would happen? So on the graph it would basically look maybe something like this, where now your value is higher. This is our new pressure. This is the new pressure at the end of systole. I'll put p prime. And if that's the new pressure at the end of systole, then we have to think through what else would change? I guess that's the question. And you know, of course, the first thing to think about is the fact that this is going to drop down, this line. And if our pressure has gone up, then you know our stroke volume has gone down. So our stroke volume is going to be a little bit more contracted or smaller. And you remember now we have a formula. I may actually just jot down the formula for us, just make a little bit of space. Maybe I'll just actually leave it. That way, you can see everything. But I'll put the formula over here. We have our formula, which says that elastance, or arterial elastance, equals pressure at end systole divided by stroke volume. And all that equals heart rate times resistance, right? And in this case, I'm saying that I'm going to increase this number, and I'm going to decrease this number. So what I've done is basically changed the slope. So I know that the elastance is going to change. And if I've done that, the only way to really accomplish that would be to either increase the heart rate or increase the resistance. Already I'm getting some interesting information about how this might have happened. I can ask, hey, did that person's heart rate go up? Or are their blood vessels more constricted? Because one of those two things must have happened to cause this increase in afterload that I'm drawing for you. And either way, to draw it out, it would be kind of the same. You'd basically say, OK, well, if this is my new end systolic pressure, I know that I need to draw it so that the point where it crosses the volume axis is the same. And actually, I can make it kind of extend on the other side, too. I can say something like that. And this is what would happen. So one of the things I want to point out is there is a difference between EA and afterload. So let's talk about that difference. When I talk about afterload, I really want you to keep remembering or keep in mind the fact that we're talking about the entire line, so this entire area or this entire part of the curve, which I'll redraw here, which would look something like this, right? That entire thing is the afterload. And we kind of simplified that. I keep reminding us that we keep simplifying that down to just pressure at end systole. But really, afterload is more than just that one point. But we use that as kind of a marker for how afterload is doing at every other point. And we can see pretty clearly that, of course, the afterload has gone up at every point including the very last point, which is end systolic. And the new curve, of course, if I was just to draw it in, would look like this. Let me just keep a blue line so it stays steady. The new line would look like this and would actually come up like this and do this. That would be my new line. So the pressure volume loop does change. And you can see that if afterload is pressure end systole, if that's what we're using as our marker-- I guess maybe I should put it in quotes just to make sure we don't actually think that that's afterload because we know that the definition of afterload is much more than just that-- then EA is going to include part of that. It's the end systolic pressure. But it's also includes stroke volume. So one of them is the pressure over volume and the other is just the pressure. And if we're thinking about that, remember that many things are going to affect, then, this end systolic pressure, many things, including things like contractility will affect this. And preload will affect this. So many things are going to affect afterload. But not too many things are going to affect our EA. So remember, if you're having a change in EA, the things that are going to change EA would be like heart rate and resistance. So truly when you're breaking this down, just try to keep this in mind that the formula you want to always remember is this guy. And this will always get you to the right answer, that if you are thinking afterload, you're really talking about everything that could affect afterload including preload and contractility, because all those things can affect which direction this goes, because they are going to change stroke volume. Whereas if you're going to talk about the elastance, then really the only things that are going to change the overall elastance, this whole thing, are going to be things like heart rate or resistance. So it's actually pretty simple when you look at the formula. But I know a lot of times people confuse the word "elastance," arterial elastance, with afterload, and they think it could be the same thing. And it's true that they're very related, but they're not exactly the same thing. So as a final point, in this case, we increased the arterial elastance by either changing the heart rate-- increasing it-- or increasing the resistance . But we could have also decreased the heart rate resistance, and we would have seen a smaller arterial elastance.