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Current time:0:00Total duration:13:33

I'm going to draw on
this axis pressure, and on the other axis,
I'm going put volume. And we're going to do a
little thought experiment. So I'll label it the way I
usually do with milliliters, but I'm going to leave off
all the numbers, just to make it a little bit easier
to see what's going on. So I'm not going to label
the axes with numbers. But you get the idea
that, of course, pressure is going to go up
this way and volumes going to go up that way. Now, let's say I go
over to the shelf. Let's say I've got a shelf
full of left ventricles, and I just grab the
first one that I see. And I pick it up, and it's
this little guy over here. And he's empty to
start out with, but I start putting
some blood in him. It's totally relaxed. This ventricle is not contracted
at all, which is important, of course. And I start filling
it up a blood. And as I do that, I
actually just keep track of how much blood I'm putting in
and what the pressure is inside of my left ventricle. And I notice that
the pressure is rising as I'm putting
more and more blood. In fact, as I really
start filling this up, let's say fill that up
completely with blood and try to squeeze in even
more, as I keep trying to stuff it with blood, I notice that
the pressure begins to rise and now kind of
rises really fast. So near the end, it starts
rising much more quickly. And this is my curve, and I
get to name it whatever I want. And so I'm going to call it the
end diastolic pressure volume relationship. Now, you might be thinking,
well, OK, pressure volume relationship, that
part makes sense. But why do I always have
to name it end diastolic? Why not just dropped
those two words, right? The reason I don't
drop those words is because it gives
you information. It tells you that it's
at the end of diastole that I'm doing this experiment. So, for example,
nobody can come by and tell me, well, was
there any contraction in this left ventricle of yours? I would say no it was
completely relaxed. And I can convey
that information just by using the word "end
diastolic," because it's understood that if I'm talking
about something at the end of diastole, the left ventricle
must have been relaxed. And, in fact, one
more thing I want to point out--
just because we're talking about
interesting points-- is that remember that if
this is pressure and volume, that the pressure
divided by volume, or the slope of this line, is
actually equal to elastance. So if I draw the line a
certain way, if I say, for example, what's
going on over here? Well, the slope is much
higher than it is over here. Another way of saying that is
that the elastance of my line is going up over time. So just keep in mind, that
the word "elastance" actually completely make sense
to use in this context. So now we have our
line, or a curve. And I guess one thing
we can think about is what would happen if I
actually, at this moment-- let's say right here,
this blue spot decided to let my heart contract. What would happen if the
left ventricle contracted? Well, of course, the
pressure would rise, and that's what happens
with contraction. But I guess the
question is, what were the conditions
at the moment? So if I say this is
end diastole, right? Because, of course, for
this situation-- let's call the situation A-- diastole
just ended at that point. What was the volume? And let's say the volume
is 125 milliliters, and let's say the pressure
is 10 millimeters of mercury. So those are the conditions
at the point where I just allowed the left
ventricle to contract. Now I can choose another point. I could say, well, what
about this point up here? What if I allowed contraction
to happen right there? Well, that just means I waited
a little bit longer, right? And let's call this situation
B. And now the volume is higher, and I'm just going to say
150, even though I guess maybe it looks like my drawing
is little skewed. But let's just assume
that 150 is that point. And the pressure is
just a smidge higher. I'm going to say it's 15
millimeters of mercury, a smidge higher, just
a little bit higher. So these are the
two points, A and B. So I could say, all
right, well, if I want to talk to someone about
this, I can say I have pressure and I have volume. And the pressure
for situation A-- let's go with A
first, of course. A had a pressure of 10
millimeters of mercury and a volume of 125. This is how I could convey
information about that spot. And if someone asks
me about situation B, I could say, well, situation B
had a slightly higher pressure and a slightly higher volume. And really what I'm
giving them is information about what the conditions
were at the time that contraction began. That's really what that
point represents-- conditions when the contraction began. Now you might thin, OK,
well, the story is done. What else is there to say? That was very interesting. But, actually,
there's another term that people use all the time
to describe the conditions when contraction begins. And the most common
thing is that people get confused when this
word is thrown around. The world is preload. And preload, I think
it's really important to define because
sometimes people say well preload is pressure
at the point the contraction began. And other people
say, no, no, no. Preload is volume when
contraction began. And I'm going to say that its
neither pressure nor volume, but it's something different. I'm going to define preload as
being equal to the wall stress. In fact, let me ask you go back
one step, half a step maybe. And I'll say not even
just wall stress, but I'm going to say
left ventricular wall stress when contraction began. But I'm not going to say
when contraction began, I'm going to use shorthand. I'm going to say
at end diastole. So at the point when diastole
ended, and in situation A and B those were two different
points, we just said, the point where
diastole ends, whatever the left ventricular wall stress
is at that moment is preload. So that's how I'm going
to define preload. And that's the way I think it's
most helpful to define preload. But, of course,
preload has a lot to do with pressure and volume. It's not like it's got nothing
to do with those terms at all. Let me make a
little bit of space, and build out my
argument, and see If I can try to
convince you that what I'm saying make sense. So to understand
this, you've got to remember what wall stress is. Remember Laplace
had this law, and he said wall stress is
equal to P, pressure, times the radius divided by
2 times the wall thickness. w is wall thickness, right? And remember, Laplace was not
working with left ventricles like we are. He was working with spheres. So he was working with something
that looked a little bit more like this. He was saying, OK, well,
if you have a sphere, this is your sphere. I'm going to try to
draw it as best I can. Then if you actually take a look
at the inside of that sphere-- let's say you take that
sphere, and now I'm going to just chop
away half of it. Let's say you just
cut away the top half, just look at the mid
section of that sphere. He said what you would
notice is on the inside-- I'm going to draw it
with a white line. On the inside, you've
got a doughnut. You've got something like this. And then you could actually look
at it, and you would see this. You would see that if
you look down at it, this doughnut begins to
look a little bit like this. So Laplace said if you
have a situation where you have some sort of a
sphere, and you can actually open up and look at
it, well, then you can actually start making
some interesting observations. You could say, well,
from this point to this point-- let's call
this the radius of the inside. I'm going to call it radius IN. And then from this point to
this point, right here to here, we are going to call that w,
or wall thickness, we said. And then if you combine those,
you get the total radius. So he said R-total equals
radius of the inside plus wall thickness, something like that. And remember now--
and then, of course, after mention of pressure,
you might be thinking, oh, where does pressure
fit into all this? Pressure is just kind of what's
forcing out on the walls. That is pressure. But now, remember,
there's a relationship, an interesting relationship,
between volume and radius of the inside. So there's volume
equals 4/3 pi r cubed. And in this case, when we say
r, I mean radius on the inside. So I should say r inside. I wrote lowercase r, but let
me just make it really easy but just writing the uppercase
R. So that's the relationship. So If you want to move things
around, you can actually say, OK, well, then
radius on the inside is simply the cube
root of-- and then you flip around all of
the equation, right? You say, OK, 3 over 4 pi,
and this is v for volume. And now if you have
the volume information, you can figure out the
radius of the inside. So we can actually do that. We can say what is the
radius on the inside? Well, if these are the volumes--
I actually calculated this beforehand so I wouldn't have
to sit here and take the cube root of stuff, while you
wait patiently for me-- you can actually
calculate this stuff and say, OK, if I
have 125 milliliters, then the radius on the
inside ends up being what? It ends up being
about 3.1 centimeters. And remember, you might
think, well, how in the world do you get from
milliliters to centimeters? Remember that 1 milliliter--
and I'll just write it here. 1 milliliter equals
1 cubic centimeter. Actually, that's nice
because then when you to take the cube root, you
get centimeters left behind. So that's the situation
A. In situation B, if I plug in 150
into this equation, then I get that my radius on the
inside becomes 3.3 centimeters. And then I could also
do the next variable. I could do wall thickness. And for this I just assume--
and this is a fair assumption-- that my left ventricle
is really not going to change a whole lot
from heartbeat to heartbeat, and that, in general, given
my size and my weight, I'm going to have a wall
thickness of let's say about 1 centimeter just to
make the math kind of easy. And so then the
final variable we need is the total
radius, which is simply the radius on the inside
plus the wall thickness. So this is just adding
those two numbers together. So I just add those very
easily and say, OK, well, the total radius is
just 4.1 centimeters. This will be 4.3 centimeters. And then finally, we can
calculate preload now. You can just take
all these numbers and say Mr. Laplace
asked me for pressure. I got it right there. Mr. Laplace asked me
for my total radius, and I got it right there. And Mr. Laplace asked me
for my wall thickness, and I got it right there. So all of the
things that we need to calculate wall stress at the
end of diastole-- of course, that's really important;
we have those number at the end of
diastole-- we have them. And so we can actually calculate
preload, which is so cool, which actually makes
it, just instead of a word we throw
down, it's actually something you can quantify. So let's go through it,
and let's calculate it. Let's do situation A first. In situation A, I'm just
going to write A now again. We have 10 times 4.1. So that's 41 divided
by 2 times 1. So that ends up
being-- I'm just going to give you a round number. This is about 21
millimeters of mercury. So preload, another
interesting thing about it, it's measured in pressure units. And in situation B, we got
15 times 4.3 again divided by 2 times 1. So that math works
out to 32, right? 32. Again, I'm rounding off, so
32 millimeters of mercury. And so you can actually see
that going from situation A to situation B-- and actually
let me just draw on my doughnut here what the wall stress is. Remember, wall
stress is actually the force over area pulling
the heart muscle apart. And that makes sense, right? In the beginning
of contraction when the heart is about to contract,
how much stress is there on the wall? That is your preload. And, of course, it takes
into account things like pressure and
volume, of course. And you can now say
to someone, yeah, we went from a preload of
21 millimeters of mercury right here to a preload of
32 millimeters of mercury right here. And that's actually a very
rarely done calculation, but I think a very valuable one.