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Current time:0:00Total duration:10:26

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.