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# Arterial elastance (Ea) and preload

Video transcript

Let's talk about the
pressure-volume curve. And we're actually going
to use this to figure out how preload fits into the story. So let's do volume going that
way and pressure going up. And I'm going to use
our normal lines, our end-systolic pressure-volume
relationship, something like this. And I'll also use the
same color to show the end-diastolic
pressure-volume relationship. And I wanted to keep
an eye on this line because this is the one that's
going to be of interest to us right now. This is the end-diastolic
pressure-volume relationship. And I'm also going
to sketch over all of this the
arterial elastance. Remember, we talked
arterial elastance? That was E with a little
a, and the formula was pressure at
the end of systole divided by stroke volume. And I'm going to
quickly sketch out where those points would be. This would be our
end-systolic pressure. And our stroke volume
would be basically-- if we drop this dot,
something like this, right? So this would be our
stroke volume right here. So these two
numbers kind of help make our slope or
arterial elastance. And we can actually also
use these to help sketch out our pressure-volume loop. So it basically
would go down just like that and at some point
kind of pick up our curve. And we would pass over the
purple line, keep going. And right at the same mark
where the volume is, we go up, and we have contraction. So the heart is
contracting here, and it continues contracting. And then, finally, blood
gets ejected, knocked out, and that goes into the aorta. So that's our
pressure-volume loop. Now, I want to point out
to you a couple things. This one, in particular, this
is our end diastole point. And remember, when we
talk about end diastole, it should remind you of preload. In fact, I'm going to jot the
preload equation down here. Remember, preload we said is--
and this is from Mr. Laplace. This is wall stress at
the end of diastole. And I'm going actually
go ahead and write out the whole equation, just to
make sure that we're completely on the same page and that
we remember this equation. This is pressure times the
radius at the end of diastole divided by 2 times
the wall thickness at the end of diastole. So all this stuff is happening
at that point, the yellow arrow point. So here's the question-- what
would happen if we actually increased the pressure? In other words, at
the end of diastole. Or in other words,
increased the preload. So the pressure right now, if
I was to kind of figure it out, it'd be somewhere around there. That's the pressure at the
moment at the end of diastole. But let's say I increased it. I wanted to increase it to,
let's say, something like this. And I can kind sketch
out that that would be, let's say, right here. And immediately, you can
see what would happen. You'd have an
increase-- or it seems like you'd have an increase
in stroke volume, right? Because now you have
extra blood entering, so contraction would happen
only at this point right here. And I'm going to
start contraction. I'll finish off the
loop in a moment, but I want to actually jump
back to our elastance equation. I want to make sure we
follow the math on this one because it's going to
be helpful and make sure we don't get stuck in
any kind of mental traps. So you remember
that's the equation for elastance,
arterial elastance. And then we also said
previously that there's heart rate times
resistance, and that should all equal
each other, right? That's how we wrote it out. Now, I did not mention
changing the heart rate, and I didn't mention
changing resistance. I left all that the same. And if all of that's
the same, and now I'm increasing stroke
volume, I want you to take a guess as to what
would happen to pressure. Now, if it's going to
have to remain the same, the overall equation has
to be the same, then you know the only way to do that is
to also increase the pressure, right? There's no other way to do that. And that's the math. That's the beauty
of the numbers, and it helps us kind of
figure out what's going on. So if the pressure
is going to go up, then I can actually draw
that on my equation. I can say, well, my equation's
going to have maybe a point right here, where
the new pressure is. So this is my new pressure
at the end of systole. So let me go over that one
more time, why I knew that had to happen. I first said my stroke
volume was going up. And so if my stroke
volume goes up and I don't change the heart
rate or the resistance, then I know that the pressure
at the end of systole has to go up as well. So that's why it
mathematically makes sense. But I also want to make sure
it intuitively makes sense. In other words, if you put
more blood in the aorta, then it makes sense that the
pressure at the end of systole, which is the same as the
pressure in the aorta at that point, would be higher. So more blood in the aorta
it will create more pressure, and that makes sense, right? Because you have more molecules
kind of bouncing around, more blood molecules. And so, of course,
pressure would go up. So this is really
interesting because I know there's a
temptation to say, well, if you have an
increase like this-- and this is why I didn't
finish drawing it-- there's a temptation to kind
of say, well, then that just means that your
stroke volume is going to go up. And that's the end of the story. In fact, I see it drawn
like this quite a lot. And it's really confusing. And to put it bluntly,
it's actually wrong. It should not be
drawn like this. The truth is that the
stroke volume goes up, and it also increases the
end-systolic pressure. So the right way to draw
this is to say, OK, well, it goes up, up, up, up, up. And then, you have ejection,
something like that. And then, of course, it
goes down from that point. And it meets up like that. Now, you probably know
something right away, which is that if I'm
saying stroke volume is going up because of
all this, then isn't stroke volume going down
because you've lost a little bit a stroke volume on this side? And the answer is yes. Yes, you do have a little
bit less stroke volume because of this loss over here. But because you have so
much gain on this side, you actually make up for it. So overall, stroke
volume still goes up. So the old stroke volume,
which is right here, is still less than
the new stroke volume, which is right here. So that's something you should
definitely keep in mind. And you also have a
couple other changes, which is that you have an
increase in the afterload right here. So afterload is actually
going up as well. And so here I want to
show you that if you have a change that's driven
by just preload, if that's the main change, that the
loop entirely changes. But the slope of the line--
this purple line that we've been drawing-- actually
stays about the same. I'm just going to try to make
sure I draw it about the same, and it looks like that. So this is what the new line
would look like for preload. And now you can actually get
an appreciation for the fact that if you increase
preload, you're basically shifting
the line this way. And if you decrease
preload, I could show you the exact opposite, and
it would go the other way. So this is what increasing
and decreasing preload does to our line. It does not change
the slope of the line. So the elastance or the
slope stays the same, but where the line is
located on the volume axis actually shifts over.