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.