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# Arterial elastance (Ea) and afterload

## Video udskrift

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.