So we're going to talk about the left ventricle.
I'm going to draw out the left ventricle here.
And I'm going to draw out the rest of the heart, as well,
but I'm just going to kind of leave dashes
here just to make sure that we kind of focus in
on just that one chamber, the left ventricle.
And this is, of course, next to the right ventricle.
And above both of them, you know you have the two atria.
Right?
These are the chambers of the heart that
are going to kind of hold onto the blood
until it's time to refill the ventricles.
This is our right atrium and our left atrium.
Now a question that came up to me, and might come up to you,
is why in the world does the left ventricle never have a rip
or tear?
I mean, if I look at my jeans or anything else,
you always get these kind of rips and tears over time.
And why is it that you don't get these tears
in the left ventricle?
I mean it would be disastrous, of course,
because the blood would start gushing out
of the left ventricle, but what prevents that from happening?
And also what are the stresses on the left ventricle?
What does it have to deal with exactly?
So to think about this, I actually
wanted to split it up into two categories.
You've got diastole, right?
And you've got systole.
And diastole, of course, is when you have refilling of the heart
and systole is during kind of the squeezing of the heart.
And when I say the heart, I should really be more specific.
I mean the squeezing of the left ventricle.
Because now I'm going to talk just
in the perspective of the left ventricle.
Now diastole, what is happening there?
Well, blood is really refilling that left ventricle
and so the volume of that chamber is going up, up, up.
And during systole, pressure is going up, up, up.
So these are the two major issues, right?
Now of course you have volume in systole
and, of course, you have some pressure in diastole.
That's not what I'm saying.
But what I am trying to get to is the idea
that the major issue in diastole is the fact
that you've got a full heart.
Especially by the end of diastole,
and you should have a full left ventricle,
the fullest it's going to be.
And in systole, the highest pressures
that the left ventricle is going to see.
So keeping this idea in mind, let's actually now go back
about 200 years to someone who thought
about a very similar situation around kind
of the stress of the wall, and what pressure and volume will
do to that.
So this guy, I'm going to draw up his picture, bring it up.
This guy is a French mathematician.
And his name was Laplace.
And we actually still honor him by kind
of talking about his formulas today.
And Laplace was a brilliant mathematician.
He actually gave a lot of thought to shapes.
And the shape that we're going to be kind of focusing on today
is the sphere, or a ball.
So you can just think of a ball like a baseball.
I'm drawing it kind of orange like a basketball, I suppose.
And this ball is essentially a hollow sphere, right?
And I'm going to draw on the side-- actually,
I'm going to write that sphere here-- I'm
going to draw on the side a left ventricle.
Or kind of my image of a left ventricle, right?
Something like that.
It actually starts looking quite similar to this sphere.
So the idea is that he, Laplace, thought about spheres,
but a lot of the ideas he put forward
actually apply beautifully to the left ventricle, as well.
So you've got something like this,
where you can see the obvious similarities.
Now Laplace thought about this in terms
of what would happen if you actually
cut away part of that sphere?
And let's say you could actually now kind of look down
at the cross section of it.
Something like that.
So he actually thought about it in those terms.
And, of course, I said that this is a hollow ball,
so you've got to fill it in.
You've got something like an inner circle I suppose.
Like that, right?
In fact, let me draw it on the side
here so you can make it really nice and easy to see.
I don't want you to have to try to figure out
what it is I'm drawing.
Something like that, right?
This is our cross section of the ball or the sphere.
And you could do the exact same thing with the left ventricle.
Now the first thing that Laplace thought about was volume.
He knew that volume is going to put some sort of stress
on the wall.
And volume, we know equals-- you can actually
write the formula out-- 4/3 pi r cubed.
So if you actually take away some of these numbers, 4/3
and pi, I mean these are just numbers.
Right?
You can get rid of those.
Then you could say, well, there's
a relationship or a proportion between volume and radius.
And you can actually write proportion as this symbol,
right?
That means proportional to.
And so you can take the cubed root of both sides.
You could just say, OK, what's the cubed root of this side?
And the cubed root of this side?
And you could say, well, that means
that radius-- because that cancels-- radius
is proportional to the cubed root of v, or volume.
And on our two pictures, let me just write it on this picture,
actually, just to be clear.
This would be our radius.
So this is our radius.
Now a second point, I'm just going to first label
our picture, and then you'll see how it all kind of comes
together, is pressure.
And pressure is a little simpler to imagine.
We know that that's just a force divided by an area.
And here I can draw little blue arrows
to signify the pressure on the walls of this left ventricle.
This is our pressure.
I say left ventricle or sphere.
Kind of interchangeably, I guess, right?
At the moment.
And third is the wall itself.
Right?
The wall thickness.
How thick is the wall?
And that's obviously going to affect
how much stress the wall feels.
So wall thickness would be kind of this quantity.
And I'll write w for wall thickness.
Now putting it all together, Laplace came up with this.
He said, well, the stress of the wall,
we'll call it wall stress, is equal to some
of these other factors.
He said, it's equal to pressure-- let
me write that first-- pressure times the radius divided by 2
times the wall thickness.
2 times w.
So that was the relationship.
And if you think about it, you get some interesting kind
of ideas from this.
You say, well, OK, radius, what is that?
Well, radius is like a length, right?
You're going to measure that out,
like centimeters or millimeters.
And wall thickness is also a length.
Right?
So you've got very similar.
You've got millimeters or centimeters.
And we just got through saying pressure is just
force divided by an area.
So what units are wall stress?
Well, length cancels length.
So all you're left with is force over area.
So really, wall stress-- and this
is pretty cool-- is in units of pressure.
So it's kind of a pressure, isn't it?
But that might make you feel kind of puzzled.
Because you think, well, wait a second.
What is wall stress exactly?
You might have thought that wall stress was
the stress on a wall.
Maybe it was something like this.
But actually, it's not, right?
Because that would then just be the p,
the pressure that we had in the first place.
So then what is wall stress?
What would it look like?
Well, wall stress you can imagine as this.
The stress is the-- we said it's a pressure.
Think of the pressure, the pulling pressure.
That's kind of how I think of it.
Pulling pressure.
Literally, the pressure that's pulling apart the wall.
So, in our first question, when I opened up the video,
I said, what is keeping our wall from just
having rips and tears?
And the wall stress is literally the force--
or I shouldn't say force-- the force divided
by area, the pressure that's going
to cause those rips and tears.
So you can see that, in a way, we
should have some rips and tears in our left ventricular wall.
But we don't.
Why don't we?
So these, in that little white box,
I'm going to draw for you what's inside there.
And you know it's going to be little heart cells.
Right?
So little heart cells are lining this wall.
And you've got thousands of them, of course, right?
Thousands of little heart cells going every which way.
And you've got them crossing and going
over and under each other.
Something like this.
So what happens is that you literally
have thousands of heart cells and they're
attached to each other.
And these little attachments are--
I'm going to draw on white-- called desmosomes.
So desmosomes are one of the reasons why
your heart doesn't just rip apart.
You've got these tiny little desmosomes and their job
is to keep everything kind of tidy and tucked.
They want to keep the heart cells attached.
And that means if they're going to be attached that they're not
getting ripped apart.
So these white little arrows are literally counteracting
those purple pulling pressure arrows.
So this is how you can think about wall stress
and why it is that our heart doesn't just rip apart.
Lastly, I want to point out that the pressure is actually
going to be in our equation, but we don't really
have volume in our equation, we have radius.
And the relationship is a cubed root, right?
So if you have a cubed root here, but pressure is direct,
then that means that between the two of them,
volume versus pressure, pressure has a bigger influence
on wall stress than volume does.
So that's one interesting point.
Another interesting point is that wall thickness, which
is right here, makes perfect sense.
Because if you have more and more of these heart cells,
that means you have more and more desmosomes that
are going to counteract the effects of pressure and radius
in this equation.