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LORNA GIBSON: All right.

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So last time we were talking
about tissue engineering

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00:00:29,460 --> 00:00:30,664
scaffolds.

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00:00:30,664 --> 00:00:32,330
And what we're going
to talk about today

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00:00:32,330 --> 00:00:34,200
still has to do with tissue
engineering scaffolds,

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00:00:34,200 --> 00:00:36,680
but we're going to look at it
from a different perspective.

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00:00:36,680 --> 00:00:38,054
So last time we
were looking more

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00:00:38,054 --> 00:00:39,580
at sort of a
clinical perspective,

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00:00:39,580 --> 00:00:41,740
and looking at those
osteochondral scaffolds

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00:00:41,740 --> 00:00:44,740
for repairing small
defects in cartilage.

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00:00:44,740 --> 00:00:46,430
And today what we're
going to talk about

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00:00:46,430 --> 00:00:48,800
are how cells-- how
biological cells,

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00:00:48,800 --> 00:00:50,600
interact with the scaffolds.

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00:00:50,600 --> 00:00:52,660
And there's various
kinds of interactions.

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00:00:52,660 --> 00:00:54,620
So we're going to go
through a bunch of these.

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00:00:54,620 --> 00:00:56,310
So the first one I'm
going to talk about

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00:00:56,310 --> 00:00:58,830
is degradation of the scaffolds.

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00:00:58,830 --> 00:01:01,220
Then we'll talk about
the cell attachment.

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00:01:01,220 --> 00:01:06,750
Cell morphology-- so the shape
of the pores in the scaffold

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00:01:06,750 --> 00:01:10,300
can affect the way the
biological cells-- what

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00:01:10,300 --> 00:01:12,020
shape they have.

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00:01:12,020 --> 00:01:14,490
Biological cells could
also contract the scaffold

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00:01:14,490 --> 00:01:15,780
and apply mechanical forces.

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00:01:15,780 --> 00:01:18,030
So we're going to
talk about that.

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00:01:18,030 --> 00:01:20,360
The stiffness of the
scaffold and the pore size

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00:01:20,360 --> 00:01:22,736
can affect the speed
of cell migration.

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00:01:22,736 --> 00:01:24,110
And the stiffness
of the scaffold

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00:01:24,110 --> 00:01:27,790
can affect the differentiation
of cells, so from one cell type

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00:01:27,790 --> 00:01:28,565
to another.

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00:01:28,565 --> 00:01:30,190
So I thought today
I'd talk about that.

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00:01:30,190 --> 00:01:32,230
This probably won't
take the whole hour.

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00:01:32,230 --> 00:01:34,980
The next topic is on
energy absorption in foams.

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00:01:34,980 --> 00:01:38,100
And so we'll probably start that
towards the end of the lecture.

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00:01:38,100 --> 00:01:39,380
OK.

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00:01:39,380 --> 00:01:41,000
So the idea here is
that we're looking

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00:01:41,000 --> 00:01:43,070
at how scaffolds are
being used, really,

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00:01:43,070 --> 00:01:46,380
to provide a 3D
environment to characterize

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00:01:46,380 --> 00:01:47,530
the behavior of cells.

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00:01:47,530 --> 00:01:49,320
And in particular,
how the cells interact

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00:01:49,320 --> 00:01:50,960
with their environment.

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00:01:50,960 --> 00:01:52,490
So let's write that down.

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00:02:25,470 --> 00:02:28,460
So how the cell behavior is
affected by the substrate

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00:02:28,460 --> 00:02:28,970
it's on.

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00:02:51,540 --> 00:02:52,040
OK.

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00:02:52,040 --> 00:02:53,873
So the first thing we're
going to talk about

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00:02:53,873 --> 00:02:55,160
is scaffold degradation.

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00:02:55,160 --> 00:02:58,850
And if you think of the
native extracellular matrix,

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00:02:58,850 --> 00:03:03,040
the cells secrete enzymes
which resorb that matrix

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00:03:03,040 --> 00:03:04,722
and then they also
deposit new matrix.

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00:03:04,722 --> 00:03:06,180
So it was kind of
like what we were

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00:03:06,180 --> 00:03:07,346
talking about with the bone.

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00:03:07,346 --> 00:03:09,830
The bone is always being
resorbed and deposited.

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00:03:09,830 --> 00:03:12,270
And if there's a balance
between that those two,

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then the density of the
bone stays the same.

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And if one of the rates
gets out of whack,

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00:03:16,770 --> 00:03:19,200
then you get osteoporosis
and you lose bone mass.

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So the idea is that in just the
native extracellular matrix,

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the cells are producing enzymes
that degrade the scaffold.

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And those enzymes are also
going to degrade the tissue

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00:03:31,610 --> 00:03:33,640
engineering scaffolds as well.

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And you want to
be able to control

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the rate of degradation,
versus the rate

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at which the native
extracellular

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matrix gets deposited.

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Excuse me, sorry.

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00:03:44,880 --> 00:03:47,880
So you can kind of imagine
if the tissue engineering

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scaffold did not
resorb quickly enough,

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00:03:50,570 --> 00:03:52,020
you'd have scaffold there.

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And the cells would
be trying to put down

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their own extracellular
matrix, and there

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wouldn't be a place to put it.

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00:03:57,230 --> 00:04:00,274
And if it resorbs too
quickly, then the cells

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don't have something
to attach to.

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00:04:01,690 --> 00:04:04,500
So there has to be a balance
between the rate at which

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the enzymes are resorbing the
tissue engineering scaffold,

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versus the rate at which
the cells are depositing

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their own extracellular matrix.

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So in the native
extracellular matrix,

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the enzymes produced
by the cells

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00:04:32,670 --> 00:04:35,180
are resorbing the
extracellular matrix.

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And then the cells are
also synthesizing so they

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00:05:00,270 --> 00:05:02,526
synthesize ECM to replace it.

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00:05:11,410 --> 00:05:14,649
So the cells are also going to
degrade the tissue engineering

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00:05:14,649 --> 00:05:15,690
scaffold that you put in.

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00:05:23,690 --> 00:05:27,850
And the length of time that
the scaffold is insoluble,

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00:05:27,850 --> 00:05:30,940
or so that it remains
in the body as a solid,

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00:05:30,940 --> 00:05:32,370
is called the residence time.

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00:06:04,980 --> 00:06:09,180
And so then we require
the scaffold degradation

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00:06:09,180 --> 00:06:13,765
to occur over a time that
balances with the new ECM

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00:06:13,765 --> 00:06:14,265
synthesis.

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00:06:52,540 --> 00:06:55,570
And so the scaffold
residence time

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00:06:55,570 --> 00:06:57,430
must be about equal
to the time required

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00:06:57,430 --> 00:07:00,258
to make new native
extracellular matrix.

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00:07:38,460 --> 00:07:41,820
So the degradation rate
depends on the composition

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00:07:41,820 --> 00:07:44,974
of the scaffold, on how
much cross linking there is,

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00:07:44,974 --> 00:07:46,140
and on the relative density.

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Obviously, the more
scaffold there is,

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00:07:48,130 --> 00:07:50,375
the longer it's going
to take to degrade it.

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And with synthetic polymers you
can vary the molecular weight

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of the polymer.

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00:08:28,670 --> 00:08:30,460
And sometimes if
you have copolymers,

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one may degrade
faster than the other.

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00:08:32,610 --> 00:08:35,919
And you can control the balance
of how much of each copolymer

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00:08:35,919 --> 00:08:36,419
you have.

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00:09:07,360 --> 00:09:13,860
And for natural
proteins, like collagen,

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00:09:13,860 --> 00:09:16,920
you can control the
amount of cross linking.

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00:09:16,920 --> 00:09:19,700
So you can do the cross
linking by various techniques.

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00:09:19,700 --> 00:09:22,220
That's what's called
physical methods.

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00:09:22,220 --> 00:09:25,130
There's something called
dehydrothermal treatment, where

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00:09:25,130 --> 00:09:31,500
you heat the collagen up to
105 degrees C in a vacuum,

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00:09:31,500 --> 00:09:33,170
in a dry environment.

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And that eliminates water and
causes more cross linking.

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00:09:38,120 --> 00:09:40,740
There's a UV treatment,
ultraviolet light treatment,

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00:09:40,740 --> 00:09:41,510
you can use.

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00:09:41,510 --> 00:09:43,710
And there's also chemical
cross linkers you can use.

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00:11:29,900 --> 00:11:33,130
So there's different
chemical methods you can also

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00:11:33,130 --> 00:11:52,665
use to cross link the collagen.

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00:11:52,665 --> 00:11:53,164
OK.

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00:11:59,200 --> 00:12:03,220
So the next thing I wanted to
talk about was cell adhesion.

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00:12:03,220 --> 00:12:05,850
And let's just wait a minute
for people to catch up.

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00:12:15,670 --> 00:12:17,870
Are we just about there?

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00:12:17,870 --> 00:12:20,500
So this next slide shows
a sort of schematic

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00:12:20,500 --> 00:12:23,260
of how a cell would
adhere to a substrate.

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00:12:23,260 --> 00:12:26,730
So down at the bottom here,
all these little squiggly lines

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00:12:26,730 --> 00:12:29,065
are representing the
extracellular matrix

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00:12:29,065 --> 00:12:29,940
in the native tissue.

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00:12:29,940 --> 00:12:33,640
Or you can think of it as
a, say, a collagen scaffold.

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00:12:33,640 --> 00:12:35,500
But here we have the ECM.

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And this little blob
here is our cell.

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00:12:37,930 --> 00:12:40,470
This is the nucleus of the cell
here, the little green blob

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00:12:40,470 --> 00:12:41,550
in the middle.

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00:12:41,550 --> 00:12:45,210
And the cell is
attached to the ECM

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00:12:45,210 --> 00:12:47,920
through something called
focal adhesion points.

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00:12:47,920 --> 00:12:52,070
And this schematic here is a
blow up of that focal adhesion.

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00:12:52,070 --> 00:12:54,060
And at the focal
adhesion there's

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00:12:54,060 --> 00:12:55,810
proteins called integrins.

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00:12:55,810 --> 00:12:59,270
And integrins pass
across the cell membrane.

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00:12:59,270 --> 00:13:02,090
So the idea is the
integrins attach to ligands

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00:13:02,090 --> 00:13:03,950
on the extracellular matrix.

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00:13:03,950 --> 00:13:06,560
And then they also attached
to the sub membrane plaque

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00:13:06,560 --> 00:13:07,760
within the cell.

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00:13:07,760 --> 00:13:10,900
And then that plaque attaches
to the side of skeleton.

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00:13:10,900 --> 00:13:13,640
Things like actin
filaments within the cell.

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00:13:13,640 --> 00:13:15,800
So this is what
attaches the cell

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00:13:15,800 --> 00:13:18,390
as a whole to the
extracellular matrix,

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00:13:18,390 --> 00:13:22,610
is these focal
adhesion sites here.

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And different kinds of
cell behaviors-- obviously,

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things like cell
attachment, but also

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00:13:30,250 --> 00:13:32,690
things like cell
migration, are affected

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00:13:32,690 --> 00:13:34,458
by those focal adhesions there.

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00:13:40,320 --> 00:13:48,400
So we have that the cells attach
to the ECM at focal adhesions.

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00:13:55,100 --> 00:13:57,300
And sometimes you see those
referred to just as FA.

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00:14:03,671 --> 00:14:06,370
And at the adhesion point
the cell has integrins.

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00:14:12,650 --> 00:14:15,890
And the integrins are
transmembrane proteins,

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00:14:15,890 --> 00:14:17,220
so they go across the membrane.

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00:14:24,120 --> 00:14:28,790
And they bind to
like ends on the ECM.

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00:14:38,960 --> 00:14:40,770
And then the other
end of the integrin

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00:14:40,770 --> 00:14:43,980
is attached to the submembrane
plaque within the cell.

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00:15:10,370 --> 00:15:13,160
And then that connects
to the cytoskeleton.

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00:15:40,660 --> 00:15:44,520
And then different kinds
of cell behaviors-- so

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00:15:44,520 --> 00:15:48,040
for example, things
like adhesion,

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and proliferation,
and migration.

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00:15:57,040 --> 00:15:59,330
And that cell contraction,
we're going to talk more

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00:15:59,330 --> 00:16:00,460
about that in a minute.

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00:16:04,120 --> 00:16:07,442
They all depend in part on
this adhesion between the cells

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00:16:07,442 --> 00:16:08,650
and the extracellular matrix.

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00:17:07,550 --> 00:17:11,900
And the biological activity
depends on how many

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00:17:11,900 --> 00:17:13,150
binding sites there are.

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00:17:13,150 --> 00:17:15,000
So if you think of the
extracellular matrix,

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00:17:15,000 --> 00:17:16,930
it's got these
ligands and it depends

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00:17:16,930 --> 00:17:20,151
on the density of binding
sites, how much interaction

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00:17:20,151 --> 00:17:20,650
you can get.

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00:17:20,650 --> 00:17:24,460
So things like how much
cell attachment you can get,

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00:17:24,460 --> 00:17:26,920
depends in part on just how
many of these binding sites

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00:17:26,920 --> 00:17:28,600
you've got for the
cells to attach to.

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00:17:53,430 --> 00:17:55,730
And that density of
the binding sites

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00:17:55,730 --> 00:17:58,230
or the density of the ligands
depends on the composition

185
00:17:58,230 --> 00:17:59,210
of the scaffold.

186
00:17:59,210 --> 00:18:02,060
But also on the surface area
per unit volume of the scaffold.

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00:18:27,930 --> 00:18:29,970
So if you think of first,
just the composition,

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00:18:29,970 --> 00:18:33,060
if you have native proteins,
like collagen, they

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00:18:33,060 --> 00:18:34,700
have binding sites themselves.

190
00:18:34,700 --> 00:18:36,390
They have native binding sites.

191
00:18:36,390 --> 00:18:38,900
But if you think of
synthetic polymers,

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00:18:38,900 --> 00:18:41,570
like the resorbable
sutured type of polymers

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00:18:41,570 --> 00:18:43,890
that we talked about, they
don't have binding sites

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00:18:43,890 --> 00:18:46,530
and you have to coat the
scaffold with some sort

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00:18:46,530 --> 00:18:48,040
of adhesive protein.

196
00:19:57,480 --> 00:20:00,960
And then the surface area per
unit volume of the scaffold

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00:20:00,960 --> 00:20:04,950
is related to the pore size
and the relative density.

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00:20:04,950 --> 00:20:12,100
Let's call the
specific surface area,

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00:20:12,100 --> 00:20:13,645
surface area per unit volume.

200
00:20:31,800 --> 00:20:35,410
And if you think of having
some scaffold that's

201
00:20:35,410 --> 00:20:39,150
like an open celled
foam, you can roughly

202
00:20:39,150 --> 00:20:42,430
calculate what the surface
area per unit volume is.

203
00:20:42,430 --> 00:20:44,860
So say each strut
was a cylinder,

204
00:20:44,860 --> 00:20:47,290
then the surface
area of each cylinder

205
00:20:47,290 --> 00:20:49,000
is going to be 2 pi rl.

206
00:20:49,000 --> 00:20:51,050
If each one has a
radius r and a length l.

207
00:20:51,050 --> 00:20:54,480
Say we had n of them, that
would be your surface area.

208
00:20:54,480 --> 00:20:58,240
And the volume of the whole
scaffold, or one cell,

209
00:20:58,240 --> 00:21:02,240
would go as l cubed, the
length of each strut cubed.

210
00:21:02,240 --> 00:21:05,200
So if we just forget about
all the constants here.

211
00:21:05,200 --> 00:21:06,430
Forget about n.

212
00:21:06,430 --> 00:21:11,790
This just goes as r
over l times 1 over l,

213
00:21:11,790 --> 00:21:17,270
and that goes as the relative
density to the 1/2 power

214
00:21:17,270 --> 00:21:20,310
times 1 over the pore size.

215
00:21:20,310 --> 00:21:23,610
So the specific surface area
depends on the relative density

216
00:21:23,610 --> 00:21:24,602
and on the pore size.

217
00:21:30,050 --> 00:21:33,645
And if you have a
tetrakaidecahedron cell,

218
00:21:33,645 --> 00:21:35,770
you can work out exactly
what that relationship is.

219
00:21:35,770 --> 00:21:36,790
It's sort of a model.

220
00:21:36,790 --> 00:21:38,910
And that gives you the
relationship there.

221
00:21:38,910 --> 00:21:40,670
And in this particular
case, I think

222
00:21:40,670 --> 00:21:43,200
the relative density was 0.5%.

223
00:21:43,200 --> 00:21:46,860
And so it's a constant
over the cell size.

224
00:21:46,860 --> 00:21:49,290
So one of the things
we did in my group

225
00:21:49,290 --> 00:21:52,090
was look at how cell
attachment varied

226
00:21:52,090 --> 00:21:54,230
with this specific surface area.

227
00:21:54,230 --> 00:21:57,170
So we seeded cells onto
scaffolds of different pore

228
00:21:57,170 --> 00:21:57,744
sizes.

229
00:21:57,744 --> 00:21:59,285
We kept the relative
density constant

230
00:21:59,285 --> 00:22:01,440
and we changed the pore sizes.

231
00:22:01,440 --> 00:22:04,040
Remember I said, when we make
these scaffolds by freeze

232
00:22:04,040 --> 00:22:05,800
drying we can control
the pore size,

233
00:22:05,800 --> 00:22:07,920
by controlling the
freezing temperature.

234
00:22:07,920 --> 00:22:11,060
And we see that it's just a
linear relationship between how

235
00:22:11,060 --> 00:22:13,620
many cells attach, or the
percentage of the cells

236
00:22:13,620 --> 00:22:17,430
that were seeded that attach,
and the specific surface area.

237
00:22:17,430 --> 00:22:19,710
In here we used MC 3T3 cells.

238
00:22:19,710 --> 00:22:22,270
It's sort of a standard
cell one that you can get.

239
00:22:22,270 --> 00:22:24,500
So Fergal O'Brien was
the post-doc in my group

240
00:22:24,500 --> 00:22:28,080
who did that.

241
00:22:28,080 --> 00:22:37,030
So I'll just say we
find cell attachment is

242
00:22:37,030 --> 00:22:39,300
proportional to the
specific surface area.

243
00:22:47,841 --> 00:22:48,340
OK.

244
00:22:48,340 --> 00:22:54,672
So that's the cell attachment.

245
00:22:54,672 --> 00:22:56,630
So you can see how the
scaffold design is going

246
00:22:56,630 --> 00:22:58,310
to affect how the cells attach.

247
00:22:58,310 --> 00:23:00,600
So there's some relationship
between them there.

248
00:23:00,600 --> 00:23:03,770
Another thing people have
looked at is cell morphology.

249
00:23:03,770 --> 00:23:06,630
And so if you change, the sort
of, orientation of the pores,

250
00:23:06,630 --> 00:23:09,630
how does that change the
orientation of the cells?

251
00:23:09,630 --> 00:23:11,380
So this was a study
done in another group.

252
00:23:11,380 --> 00:23:14,087
So here we have
randomly oriented fibers

253
00:23:14,087 --> 00:23:15,170
that make up the scaffold.

254
00:23:15,170 --> 00:23:17,430
And here they're not
perfectly oriented this way,

255
00:23:17,430 --> 00:23:18,554
but more or less.

256
00:23:18,554 --> 00:23:19,970
And then these are
cells that have

257
00:23:19,970 --> 00:23:22,630
been seeded onto them, so
that the green staining is

258
00:23:22,630 --> 00:23:23,650
the cells.

259
00:23:23,650 --> 00:23:25,880
And you can see if the
scaffold is random,

260
00:23:25,880 --> 00:23:29,040
the cells themselves line
up with that fiber structure

261
00:23:29,040 --> 00:23:30,600
and become more or less random.

262
00:23:30,600 --> 00:23:32,450
And if the scaffold
has fibers that

263
00:23:32,450 --> 00:23:34,380
are aligned, then
the cells, they also

264
00:23:34,380 --> 00:23:36,030
line up and be aligned.

265
00:23:36,030 --> 00:23:38,040
So the morphology
of the cells can

266
00:23:38,040 --> 00:23:41,040
be affected by the orientation
of the scaffold pores.

267
00:23:46,400 --> 00:23:48,390
Also the cell morphology
can be affected

268
00:23:48,390 --> 00:23:50,850
by the stiffness of the cells.

269
00:23:50,850 --> 00:23:52,880
Or the stiffness
of the substrate.

270
00:23:52,880 --> 00:23:55,110
So this is a substrate.

271
00:23:55,110 --> 00:24:00,140
Here this was a
PEG-fibrinogen hydrogel.

272
00:24:00,140 --> 00:24:03,340
And they varied the cross
linking of this hydrogel.

273
00:24:03,340 --> 00:24:05,400
So they got different
modularly for the hydrogel.

274
00:24:05,400 --> 00:24:08,730
So these numbers here, are
all the stiffness of the four

275
00:24:08,730 --> 00:24:10,630
different hydrogels.

276
00:24:10,630 --> 00:24:13,040
And you can see the
cell morphology changes

277
00:24:13,040 --> 00:24:19,130
from being a spread out thing
on the least stiff substrate,

278
00:24:19,130 --> 00:24:22,310
to being just a little
spherical or circular blob

279
00:24:22,310 --> 00:24:24,640
on the most stiff substrate.

280
00:24:24,640 --> 00:24:26,760
So the cells respond
to the substrate.

281
00:24:26,760 --> 00:24:29,420
And so how the cells
behave, depends

282
00:24:29,420 --> 00:24:30,695
in part on their environment.

283
00:24:35,060 --> 00:24:39,060
So I wanted to also talk
about womb contraction.

284
00:24:39,060 --> 00:24:43,060
And talk about how cells
contract scaffolds as well.

285
00:24:43,060 --> 00:24:45,900
So one of the things
people have found

286
00:24:45,900 --> 00:24:48,990
when they look at say, skin
and regeneration of skin--

287
00:24:48,990 --> 00:24:52,260
so say you had
somebody with a burn

288
00:24:52,260 --> 00:24:56,040
and the surgeons will
clean the burnt out.

289
00:24:56,040 --> 00:24:59,140
And then what will
happen as it heals,

290
00:24:59,140 --> 00:25:01,250
is scar tissue will form.

291
00:25:01,250 --> 00:25:04,240
And the scar tissue
forms in conjunction

292
00:25:04,240 --> 00:25:05,660
with the wound contracting.

293
00:25:05,660 --> 00:25:08,170
So cells will actually
migrate into the wound bed

294
00:25:08,170 --> 00:25:10,780
and they'll pull the
edges of the wound

295
00:25:10,780 --> 00:25:12,350
together to try to
close the wound.

296
00:25:12,350 --> 00:25:14,070
And they won't
close it completely,

297
00:25:14,070 --> 00:25:15,680
but they'll partially close it.

298
00:25:15,680 --> 00:25:17,520
And that's called
wound contraction.

299
00:25:17,520 --> 00:25:20,110
And that is thought to be
associated with the formation

300
00:25:20,110 --> 00:25:21,420
of scar tissue.

301
00:25:21,420 --> 00:25:24,310
So the cells can actually
apply mechanical loads.

302
00:25:24,310 --> 00:25:26,740
And they can contract the wound.

303
00:25:26,740 --> 00:25:29,190
And one of the things that
Professor Yannas found

304
00:25:29,190 --> 00:25:32,160
was that if you use one of his
collagen and gag scaffolds,

305
00:25:32,160 --> 00:25:34,010
you can inhibit that
wound contraction.

306
00:25:34,010 --> 00:25:36,510
And if you can prevent the wound
contraction from occurring,

307
00:25:36,510 --> 00:25:39,090
you also prevent the
formation of the scar tissue.

308
00:25:39,090 --> 00:25:41,080
And that allows
normal dermis to form.

309
00:25:41,080 --> 00:25:43,230
So you get normal skin.

310
00:25:43,230 --> 00:25:45,440
So this photograph
here is of somebody

311
00:25:45,440 --> 00:25:49,470
who had burns over
their entire torso.

312
00:25:49,470 --> 00:25:51,770
And they put this tissue
injury scaffold on this part

313
00:25:51,770 --> 00:25:54,000
at the bottom, but not
on that part at the top.

314
00:25:54,000 --> 00:25:59,630
And you can see these lines
here are contracture lines

315
00:25:59,630 --> 00:26:02,090
from the scar formation.

316
00:26:02,090 --> 00:26:06,380
And you can see this skin down
here is relatively normal.

317
00:26:06,380 --> 00:26:09,420
And in fact, when people look
at the histology of the skin

318
00:26:09,420 --> 00:26:11,430
the forms using
these scaffolds, they

319
00:26:11,430 --> 00:26:14,349
find that it is pretty much
the same as normal dermis.

320
00:26:14,349 --> 00:26:17,015
It doesn't have sweat glands and
it doesn't have hair follicles.

321
00:26:17,015 --> 00:26:19,980
So you can't sweat from that
skin and you don't grow hair.

322
00:26:19,980 --> 00:26:24,020
But apart from that, it's
more or less normal dermis.

323
00:26:24,020 --> 00:26:26,714
So this observation
that if you can inhibit

324
00:26:26,714 --> 00:26:28,880
the womb contraction, you
can prevent scar formation

325
00:26:28,880 --> 00:26:30,782
and you can get
normal dermis to form.

326
00:26:30,782 --> 00:26:32,240
That's led to some
interest in just

327
00:26:32,240 --> 00:26:36,970
seeing how is it that the cells
do this contract l process.

328
00:26:36,970 --> 00:26:40,417
I think hitting the thing
and my battery is dead.

329
00:26:40,417 --> 00:26:42,000
So one of the things
people have done,

330
00:26:42,000 --> 00:26:44,530
is they've just taken what's
called, free floating scaffold.

331
00:26:44,530 --> 00:26:46,321
They've just taken
little disks of scaffold

332
00:26:46,321 --> 00:26:50,160
and put it in a cell culture
medium in a Petri dish.

333
00:26:50,160 --> 00:26:52,690
And they find that if you
put, say fiberblast on it,

334
00:26:52,690 --> 00:26:55,096
the fiberblast will
contract that scaffold.

335
00:26:55,096 --> 00:26:56,470
And people have
measured how much

336
00:26:56,470 --> 00:26:58,490
the diameter of the
scaffold changes.

337
00:26:58,490 --> 00:27:00,490
And so they've kind of
measured this contraction

338
00:27:00,490 --> 00:27:03,030
just by-- it's almost
like measuring a strain.

339
00:27:03,030 --> 00:27:04,680
And what we wanted
to do is we wanted

340
00:27:04,680 --> 00:27:06,990
to try to measure the
forces that were involved.

341
00:27:06,990 --> 00:27:09,640
So we first developed something
called a cell force monitor,

342
00:27:09,640 --> 00:27:11,260
and I'll show you that.

343
00:27:11,260 --> 00:27:15,884
And then we tried to calculate
how much an individual cell

344
00:27:15,884 --> 00:27:17,300
could apply in
terms of the force.

345
00:27:19,960 --> 00:27:21,210
So we used this scaffold here.

346
00:27:21,210 --> 00:27:26,290
This is the same collagen GAG
scaffold I showed you before.

347
00:27:26,290 --> 00:27:27,840
And here's the
cell force monitor.

348
00:27:27,840 --> 00:27:30,690
So that's just a
schematic of holding

349
00:27:30,690 --> 00:27:34,170
a piece of the scaffold
between two clamps.

350
00:27:34,170 --> 00:27:37,017
So here it is in elevation view.

351
00:27:37,017 --> 00:27:38,850
And then I'll just build
the whole thing up,

352
00:27:38,850 --> 00:27:40,016
so you can see how it works.

353
00:27:40,016 --> 00:27:41,560
So it's on a base plate.

354
00:27:41,560 --> 00:27:45,030
It's attached to a horizontal
stage that's adjustable.

355
00:27:45,030 --> 00:27:47,612
Then there's a very
thin beam here.

356
00:27:47,612 --> 00:27:49,320
So this is another
adjustable stage here,

357
00:27:49,320 --> 00:27:51,190
and this very thin beam here.

358
00:27:51,190 --> 00:27:53,145
And that's attached to
one end of this clamp.

359
00:27:53,145 --> 00:27:54,320
And here's the matrix.

360
00:27:54,320 --> 00:27:57,480
And this is attached to this
other adjustable stage here.

361
00:27:57,480 --> 00:28:01,610
And then when we have
a proximity sensor-- so

362
00:28:01,610 --> 00:28:05,210
what's going to happen is,
this is fixed over here.

363
00:28:05,210 --> 00:28:06,830
The scaffold is
going to contract

364
00:28:06,830 --> 00:28:11,410
with the cells applying
these contract l forces.

365
00:28:11,410 --> 00:28:13,870
This beam here is going to
bend and the proximity sensor

366
00:28:13,870 --> 00:28:15,495
is going to tell us
how much it's bent.

367
00:28:15,495 --> 00:28:17,400
So we can measure
how much that's bent.

368
00:28:17,400 --> 00:28:19,460
If we know how much that's
bent, and we calibrate the beam,

369
00:28:19,460 --> 00:28:20,960
we can figure out the
force in the beam.

370
00:28:20,960 --> 00:28:21,460
OK.

371
00:28:21,460 --> 00:28:24,220
So we can figure out how much is
the total force that the cells

372
00:28:24,220 --> 00:28:26,020
are contracting with.

373
00:28:26,020 --> 00:28:28,070
And then this just is a
little silicone well with

374
00:28:28,070 --> 00:28:28,903
some culture medium.

375
00:28:28,903 --> 00:28:30,240
So that's the whole setup there.

376
00:28:30,240 --> 00:28:32,770
Toby Fryman was a student
who did that, who's

377
00:28:32,770 --> 00:28:34,360
married to Professor Van Vliet.

378
00:28:34,360 --> 00:28:38,110
And I have a very big soft
spot for both of them.

379
00:28:38,110 --> 00:28:39,720
So anyway, that's the set up.

380
00:28:39,720 --> 00:28:43,500
And the thing that Toby
measured was the force,

381
00:28:43,500 --> 00:28:46,600
by measuring how much
that beam deflected.

382
00:28:46,600 --> 00:28:48,830
And he measured the
force over time.

383
00:28:48,830 --> 00:28:52,900
And he found that if he put say,
a certain number of fiberblasts

384
00:28:52,900 --> 00:28:56,580
onto the scaffold, the force
would increase and then reach

385
00:28:56,580 --> 00:28:58,320
an asymptotic point.

386
00:28:58,320 --> 00:29:01,530
And you could describe these
curves by this equation here.

387
00:29:01,530 --> 00:29:03,160
Here's the asymptotic force.

388
00:29:03,160 --> 00:29:06,870
And it's a 1 minus exponential
of minus time over a time

389
00:29:06,870 --> 00:29:08,600
constant tao.

390
00:29:08,600 --> 00:29:11,260
And then this number here
is the number of fiberblast

391
00:29:11,260 --> 00:29:12,820
that were attached at 22 hours.

392
00:29:12,820 --> 00:29:14,900
So he ran these
tests for 22 hours.

393
00:29:14,900 --> 00:29:17,020
And when he was
finished, he could

394
00:29:17,020 --> 00:29:19,690
count the number of cells that
were attached in the scaffolds.

395
00:29:19,690 --> 00:29:22,650
So you would just wash off any
cells that weren't attached

396
00:29:22,650 --> 00:29:26,180
and you can do accounting
of how many cells are left.

397
00:29:26,180 --> 00:29:27,750
And one of the
things that he found

398
00:29:27,750 --> 00:29:31,220
was that if you plot that
asymptotic force-- if you plot

399
00:29:31,220 --> 00:29:35,470
through this force over here,
against the number of cells

400
00:29:35,470 --> 00:29:38,760
that were attached, you just
get a linear relationship.

401
00:29:38,760 --> 00:29:42,190
And the slope of that is
roughly the force per cell.

402
00:29:42,190 --> 00:29:45,100
And that's about
one nano neutron.

403
00:29:45,100 --> 00:29:47,930
Now this is a little deceptive
because not all the cells

404
00:29:47,930 --> 00:29:49,044
are contracting.

405
00:29:49,044 --> 00:29:51,210
And not all the cells are
lined up in one direction.

406
00:29:51,210 --> 00:29:53,085
So there are cells in
different orientations.

407
00:29:53,085 --> 00:29:54,700
But just as an
order of magnitude

408
00:29:54,700 --> 00:29:59,100
the cells are applying something
like one minute per cell.

409
00:29:59,100 --> 00:30:00,900
So that's the effect
of the cell number.

410
00:30:00,900 --> 00:30:02,350
Another thing he
did was he looked

411
00:30:02,350 --> 00:30:05,000
at what happens if you change
the stiffness of that beam if.

412
00:30:05,000 --> 00:30:08,090
You make that beam in the
device different stiffnesses,

413
00:30:08,090 --> 00:30:09,880
how do the cells react.

414
00:30:09,880 --> 00:30:14,810
And so the stiffness here are
the stiffness of the system.

415
00:30:14,810 --> 00:30:17,230
So there's 0.7 newtons
per meter up to ten,

416
00:30:17,230 --> 00:30:19,830
so it's a factor of a
little over ten difference.

417
00:30:19,830 --> 00:30:23,050
And you can see the
displacement per cell changes.

418
00:30:23,050 --> 00:30:29,350
The stiffer the system is the
less the cells can displace it.

419
00:30:29,350 --> 00:30:31,700
But if you then plot
the force per cell,

420
00:30:31,700 --> 00:30:34,260
you find that the force
per cell is about the same.

421
00:30:34,260 --> 00:30:36,320
So you develop about
the same force.

422
00:30:36,320 --> 00:30:38,970
So that suggests the cells
are capable of applying

423
00:30:38,970 --> 00:30:42,520
a certain amount of force,
and not any more force.

424
00:30:42,520 --> 00:30:44,000
No larger force.

425
00:30:44,000 --> 00:30:45,874
So he did that.

426
00:30:45,874 --> 00:30:48,290
Then we were interested in
what was the mechanism of this.

427
00:30:48,290 --> 00:30:50,200
How were the cells
applying this force?

428
00:30:50,200 --> 00:30:52,550
Because I was kind of
surprised to find out the cells

429
00:30:52,550 --> 00:30:54,247
even could apply forces.

430
00:30:54,247 --> 00:30:55,830
So we were interested
in understanding

431
00:30:55,830 --> 00:30:58,549
the mechanism of this.

432
00:30:58,549 --> 00:31:01,090
And one of the things we knew
that we didn't quite figure out

433
00:31:01,090 --> 00:31:02,850
how this all worked
together was,

434
00:31:02,850 --> 00:31:04,496
we knew that the
cells elongated.

435
00:31:04,496 --> 00:31:06,995
If you just take a substrate,
like even just a 2d substrate,

436
00:31:06,995 --> 00:31:10,160
and you put cells on it they'll
be rounded to start out with.

437
00:31:10,160 --> 00:31:12,490
And over time, over a few
hours, they'll spread.

438
00:31:12,490 --> 00:31:14,230
And that's pretty standard.

439
00:31:14,230 --> 00:31:15,940
Many types of
cells will do that.

440
00:31:15,940 --> 00:31:18,120
So we knew the cells were
starting off as rounded

441
00:31:18,120 --> 00:31:19,967
and they were spreading.

442
00:31:19,967 --> 00:31:22,300
So the cells are getting
longer, but our whole scaffolds

443
00:31:22,300 --> 00:31:23,060
getting shorter.

444
00:31:23,060 --> 00:31:25,640
And so it wasn't obvious how
was the cells going longer,

445
00:31:25,640 --> 00:31:27,570
but the scaffold's
getting shorter.

446
00:31:27,570 --> 00:31:29,810
And so the next thing
we thought we would do

447
00:31:29,810 --> 00:31:32,450
is just watch the cells
and see what they did.

448
00:31:32,450 --> 00:31:36,410
And so we measured the
aspect ratio of the cells

449
00:31:36,410 --> 00:31:37,980
at different time points.

450
00:31:37,980 --> 00:31:41,320
And we did this by
just impregnating

451
00:31:41,320 --> 00:31:43,280
the scaffold in the
cells at different time

452
00:31:43,280 --> 00:31:46,200
points with a resin,
and then using a stain,

453
00:31:46,200 --> 00:31:49,202
and then using digital
image analysis.

454
00:31:49,202 --> 00:31:51,410
So what we found was that
the fiber of the fiberglass

455
00:31:51,410 --> 00:31:53,050
morphology looked like this.

456
00:31:53,050 --> 00:31:55,430
So the long thready
things of the scaffold,

457
00:31:55,430 --> 00:31:58,600
and these little blobs here are
the fiberblast of the cells.

458
00:31:58,600 --> 00:32:01,110
So here at time 0 you
can see-- like I said,

459
00:32:01,110 --> 00:32:03,700
the cells are pretty rounded
they're not very spread out.

460
00:32:03,700 --> 00:32:05,610
Here at eight hours
you can see-- here's

461
00:32:05,610 --> 00:32:07,190
a cell that's gotten longer.

462
00:32:07,190 --> 00:32:08,040
Here's another one.

463
00:32:08,040 --> 00:32:10,400
This guy here is still
rounded, it's not doing much.

464
00:32:10,400 --> 00:32:14,300
22 hours, again, some of the
cells are quite elongated.

465
00:32:14,300 --> 00:32:16,290
Some of them are still
not that elongated.

466
00:32:16,290 --> 00:32:18,405
So they don't all become active.

467
00:32:18,405 --> 00:32:19,780
But one of the
things we noticed,

468
00:32:19,780 --> 00:32:22,680
if you look at this image
here, you can see these cells

469
00:32:22,680 --> 00:32:24,666
are attached at one end,
and at the other end.

470
00:32:24,666 --> 00:32:26,290
But they're not
attached in the middle.

471
00:32:26,290 --> 00:32:29,480
There's sort of a gap between
the cell and the strut.

472
00:32:29,480 --> 00:32:31,020
And this is another
example here.

473
00:32:31,020 --> 00:32:34,740
Here's a cell here, and this
is the collagen GAG strut

474
00:32:34,740 --> 00:32:36,204
that it's attached to.

475
00:32:36,204 --> 00:32:38,120
And you can see it's
attached to the two ends,

476
00:32:38,120 --> 00:32:39,430
but not in the middle.

477
00:32:39,430 --> 00:32:42,420
And this starts
to explain how it

478
00:32:42,420 --> 00:32:45,630
is that the cells are elongating
but the scaffolds getting

479
00:32:45,630 --> 00:32:46,460
shorter.

480
00:32:46,460 --> 00:32:49,090
It's that the cells are
just attached at two ends.

481
00:32:49,090 --> 00:32:51,070
And the cells are
moving along a strut

482
00:32:51,070 --> 00:32:52,860
and they're attached
to the two ends.

483
00:32:52,860 --> 00:32:55,300
And if you think of
the cells attached

484
00:32:55,300 --> 00:32:57,320
through those focal
adhesion points,

485
00:32:57,320 --> 00:33:00,500
they're applying
tension to the cell.

486
00:33:00,500 --> 00:33:03,540
And the actin filaments in
the cell are in tension.

487
00:33:03,540 --> 00:33:05,450
Obviously, filaments
can't be in compression.

488
00:33:05,450 --> 00:33:06,960
They're only going
to be in tension.

489
00:33:06,960 --> 00:33:09,990
And what happens is that puts
the stress into compression.

490
00:33:09,990 --> 00:33:12,050
And if the struts in
compression, at some point

491
00:33:12,050 --> 00:33:13,200
it's going to buckle.

492
00:33:13,200 --> 00:33:15,680
And you can see this
strut here has basically

493
00:33:15,680 --> 00:33:17,710
buckled under that cell.

494
00:33:17,710 --> 00:33:19,830
And so if the cells
are getting longer,

495
00:33:19,830 --> 00:33:22,860
and they're buckling
the struts, then that's

496
00:33:22,860 --> 00:33:25,021
going to shorten the struts
and the whole scaffold

497
00:33:25,021 --> 00:33:26,020
is going to get shorter.

498
00:33:28,630 --> 00:33:32,500
And so then Toby plotted the
aspect ratio of the cell,

499
00:33:32,500 --> 00:33:35,690
so that is a measure of their
elongation against the time.

500
00:33:35,690 --> 00:33:37,580
And again, he found
one of these curves

501
00:33:37,580 --> 00:33:40,310
with the same kind
of form as the curve

502
00:33:40,310 --> 00:33:42,220
for the forced development.

503
00:33:42,220 --> 00:33:44,210
And he found the
time constant here

504
00:33:44,210 --> 00:33:47,550
for the change in the aspect
ratio was about five hours.

505
00:33:47,550 --> 00:33:50,640
And for the development of the
force it was about 5.7 hours.

506
00:33:50,640 --> 00:33:54,350
So the time constant for
the elongation of the cells,

507
00:33:54,350 --> 00:33:56,200
more or less matches
up with a time

508
00:33:56,200 --> 00:33:59,560
constant for
developing the force.

509
00:33:59,560 --> 00:34:01,560
So that's what that says.

510
00:34:01,560 --> 00:34:04,280
And that suggests there's a
link between the elongation

511
00:34:04,280 --> 00:34:07,170
of the cell population and
the macroscopic contraction

512
00:34:07,170 --> 00:34:08,760
of the population.

513
00:34:08,760 --> 00:34:11,250
So then we wanted to
take it one step further.

514
00:34:11,250 --> 00:34:13,849
And we wanted to look at what
the cells were doing live.

515
00:34:13,849 --> 00:34:15,239
Like as they were doing it.

516
00:34:15,239 --> 00:34:18,429
So Toby devised this little
schematic thing here.

517
00:34:18,429 --> 00:34:20,179
So he had just an
optical microscope.

518
00:34:20,179 --> 00:34:26,449
He had a microscope slide with
a fairly thick well in it,

519
00:34:26,449 --> 00:34:29,040
so that we could put
culture medium in the well.

520
00:34:29,040 --> 00:34:31,800
We put a cell seeded
matrix in here.

521
00:34:31,800 --> 00:34:34,290
And he had a heated stage here.

522
00:34:34,290 --> 00:34:37,067
And then he took little videos
of what the cells were doing.

523
00:34:37,067 --> 00:34:39,400
And this required some patience
because as you could see

524
00:34:39,400 --> 00:34:40,510
not all the cells did anything.

525
00:34:40,510 --> 00:34:42,179
Some of them just sat
there and did nothing.

526
00:34:42,179 --> 00:34:43,960
So he would set this up for
a day, and watch a cell,

527
00:34:43,960 --> 00:34:45,050
and it would do nothing.

528
00:34:45,050 --> 00:34:46,883
And then he would have
to find another cell.

529
00:34:46,883 --> 00:34:48,810
But he did find
some cells that were

530
00:34:48,810 --> 00:34:50,230
responsible for the contraction.

531
00:34:50,230 --> 00:34:52,560
And that was it
was kind of neat.

532
00:34:52,560 --> 00:34:53,769
So here's the scaffold again.

533
00:34:53,769 --> 00:34:55,601
All these little bits
here are the scaffold.

534
00:34:55,601 --> 00:34:57,090
This is a strut of the scaffold.

535
00:34:57,090 --> 00:35:00,710
And this is a fiberblast
parked on the scaffold.

536
00:35:00,710 --> 00:35:03,340
And this has a
little video here.

537
00:35:03,340 --> 00:35:06,780
And you can see what's
happening is the strut here

538
00:35:06,780 --> 00:35:08,300
is starting to buckle.

539
00:35:08,300 --> 00:35:10,877
And you can see
these two sides here,

540
00:35:10,877 --> 00:35:12,710
those two things are
coming closer together.

541
00:35:12,710 --> 00:35:14,860
So they originally
were this piece here,

542
00:35:14,860 --> 00:35:15,750
and that piece there.

543
00:35:15,750 --> 00:35:18,357
And now they're at
that point there.

544
00:35:18,357 --> 00:35:20,190
And then if I let it
go a little bit longer,

545
00:35:20,190 --> 00:35:23,290
it continues to do that process.

546
00:35:23,290 --> 00:35:27,860
And then the final thing--
this kind of smushed up mess

547
00:35:27,860 --> 00:35:31,740
here is these two things having
me brought completely together.

548
00:35:31,740 --> 00:35:35,470
And this strut here is
some strut down over here.

549
00:35:35,470 --> 00:35:39,110
So you can see how the cells
are elongating and causing

550
00:35:39,110 --> 00:35:41,580
contraction of the scaffold.

551
00:35:41,580 --> 00:35:45,240
Here's a series of stills taken
from another video that he did.

552
00:35:45,240 --> 00:35:47,840
So this sort of square
thing is the scaffold.

553
00:35:47,840 --> 00:35:49,100
So b is the scaffold.

554
00:35:49,100 --> 00:35:52,510
And a, this little blob
here, is the fiberblast.

555
00:35:52,510 --> 00:35:54,904
And you can see, even from
this image to this one,

556
00:35:54,904 --> 00:35:57,070
you can see that the
fiberblast has spread a little.

557
00:35:57,070 --> 00:35:59,730
Do you see how it's kind of
oozed out along the scaffold

558
00:35:59,730 --> 00:36:00,930
there.

559
00:36:00,930 --> 00:36:03,186
And eventually it
attaches over here.

560
00:36:03,186 --> 00:36:04,560
And you can see
that it's buckled

561
00:36:04,560 --> 00:36:06,322
this strut underneath it.

562
00:36:06,322 --> 00:36:08,030
And here it's a little
bit more deformed.

563
00:36:08,030 --> 00:36:10,420
It then grabs on
down here somewhere

564
00:36:10,420 --> 00:36:11,560
and deforms it even more.

565
00:36:11,560 --> 00:36:13,920
So you can see
that's more deformed.

566
00:36:13,920 --> 00:36:18,920
And then Toby put alcohol
on the whole thing,

567
00:36:18,920 --> 00:36:20,829
which kills the cells
and the cell let's go.

568
00:36:20,829 --> 00:36:22,995
And you can see you recover
some of the deformation.

569
00:36:22,995 --> 00:36:26,920
You don't recover all of it,
but you recover some of it.

570
00:36:26,920 --> 00:36:28,685
This was another example.

571
00:36:28,685 --> 00:36:30,060
And this was kind
of interesting.

572
00:36:30,060 --> 00:36:32,780
Here there was a
scaffold junction

573
00:36:32,780 --> 00:36:35,310
where there were three
struts that came together,

574
00:36:35,310 --> 00:36:36,870
a little bit like a strut.

575
00:36:36,870 --> 00:36:38,890
And there was a little
cell right there.

576
00:36:38,890 --> 00:36:40,570
And you can see
the cell elongates.

577
00:36:40,570 --> 00:36:42,920
You see how this
elongated and its grabbing

578
00:36:42,920 --> 00:36:44,670
on up here somewhere.

579
00:36:44,670 --> 00:36:47,680
But the amount of
force the cell was

580
00:36:47,680 --> 00:36:52,930
kind of pulling with must
have been less than the--

581
00:36:52,930 --> 00:36:54,610
or rather must been
more than the force

582
00:36:54,610 --> 00:36:55,720
of the focal adhesion.

583
00:36:55,720 --> 00:36:57,178
Because what happens
was eventually

584
00:36:57,178 --> 00:36:58,860
the focal adhesion let go.

585
00:36:58,860 --> 00:37:01,630
And the cell kind of bounces
back and ends up over here.

586
00:37:01,630 --> 00:37:03,130
So the cell was
kind of snapped back

587
00:37:03,130 --> 00:37:05,430
on to the other focal
adhesion over here.

588
00:37:05,430 --> 00:37:07,080
And here it's rounded again.

589
00:37:07,080 --> 00:37:08,770
And here it elongates again.

590
00:37:08,770 --> 00:37:10,860
And then this focal
adhesion lets go

591
00:37:10,860 --> 00:37:14,260
and now it's moved
back over to there.

592
00:37:14,260 --> 00:37:16,900
So these struts
here are so stiff.

593
00:37:16,900 --> 00:37:18,770
They're much stiffer,
I think, partly

594
00:37:18,770 --> 00:37:19,978
because they're triangulated.

595
00:37:19,978 --> 00:37:22,820
And it looks like they're just
shorter and a lot thicker.

596
00:37:22,820 --> 00:37:25,340
The cell isn't being
able to deform those.

597
00:37:25,340 --> 00:37:29,510
But it's elongating and then
focal adhesion was letting go.

598
00:37:29,510 --> 00:37:32,720
So this is a little schematic
of what we thinks going on.

599
00:37:32,720 --> 00:37:35,490
So the cell starts out--
it's some elongation here.

600
00:37:35,490 --> 00:37:36,810
It's attached at that point.

601
00:37:36,810 --> 00:37:38,460
It's attached at
that point there.

602
00:37:38,460 --> 00:37:40,930
And the cell is getting longer.

603
00:37:40,930 --> 00:37:43,270
And if you think about it as
the cell's getting longer--

604
00:37:43,270 --> 00:37:46,260
if you think about the
Euler Buckling formula,

605
00:37:46,260 --> 00:37:48,200
the buckling load goes
as 1 over l squared.

606
00:37:48,200 --> 00:37:50,780
So the longer the
length of this piece

607
00:37:50,780 --> 00:37:54,940
of the strut of the scaffold
underneath the cell is,

608
00:37:54,940 --> 00:37:58,367
the smaller the load it takes
to actually cause it to buckle.

609
00:37:58,367 --> 00:37:59,950
So at some point it
buckles like this.

610
00:37:59,950 --> 00:38:02,060
And this is just a
little force diagram.

611
00:38:02,060 --> 00:38:03,930
So the actin fibers
are in tension

612
00:38:03,930 --> 00:38:05,870
and the matrix strut
is in compression.

613
00:38:05,870 --> 00:38:07,980
Sometimes we saw some bending.

614
00:38:07,980 --> 00:38:11,040
So you could see if a cell was
spanning between two struts,

615
00:38:11,040 --> 00:38:13,390
you could get the cell
bending the struts as well.

616
00:38:13,390 --> 00:38:15,860
That was another possibility.

617
00:38:15,860 --> 00:38:18,310
And so we think that
the cell elongation

618
00:38:18,310 --> 00:38:20,070
was related to the contraction.

619
00:38:20,070 --> 00:38:23,650
The time constants for the two
things were almost the same.

620
00:38:23,650 --> 00:38:27,450
And as the cell elongates
there's a gap between the cell

621
00:38:27,450 --> 00:38:30,060
and the matrix on
the central portion.

622
00:38:30,060 --> 00:38:33,740
And then the cell is adhered at
the periphery of the adhesion

623
00:38:33,740 --> 00:38:34,700
points.

624
00:38:34,700 --> 00:38:36,860
And then the tensile
forces in these act.

625
00:38:36,860 --> 00:38:39,430
And filaments inside the
cell induce compression

626
00:38:39,430 --> 00:38:42,690
in the strut, and
that causes buckling.

627
00:38:42,690 --> 00:38:44,240
And then Toby graduated.

628
00:38:44,240 --> 00:38:46,310
And then I got another
student, Brendan.

629
00:38:46,310 --> 00:38:49,620
And Brendan saw what
Toby did and he wanted

630
00:38:49,620 --> 00:38:51,540
to do a little more with that.

631
00:38:51,540 --> 00:38:54,041
Brandon was also involved
that osteochondral project

632
00:38:54,041 --> 00:38:55,290
that I talked about last time.

633
00:38:55,290 --> 00:38:57,940
And Brendan this other thing
as well for his project.

634
00:38:57,940 --> 00:39:01,390
So he wanted to measure the
force of an individual cell.

635
00:39:01,390 --> 00:39:03,460
So when we had that
cell force monitor,

636
00:39:03,460 --> 00:39:06,540
that was the total force of
all the cells in that one

637
00:39:06,540 --> 00:39:07,720
direction.

638
00:39:07,720 --> 00:39:09,670
But Brendan wanted to
know if he could measure

639
00:39:09,670 --> 00:39:11,600
the force of a single cell.

640
00:39:11,600 --> 00:39:14,480
And now that we knew that the
contractal process was related

641
00:39:14,480 --> 00:39:16,590
to buckling, We thought,
well, we could just

642
00:39:16,590 --> 00:39:18,570
use Euler's formula.

643
00:39:18,570 --> 00:39:20,830
If we knew what the
modulus of the solid

644
00:39:20,830 --> 00:39:24,690
was, and we knew what the
dimensions of the struts were.

645
00:39:24,690 --> 00:39:27,220
So that would allow us to
calculate the contractile force

646
00:39:27,220 --> 00:39:30,271
of a single fiberblast.

647
00:39:30,271 --> 00:39:32,020
So I think I've shown
you this thing here.

648
00:39:32,020 --> 00:39:34,061
So Brendan was the one
who did these experiments.

649
00:39:34,061 --> 00:39:37,840
He cut a single strut
out of the scaffold.

650
00:39:37,840 --> 00:39:41,090
And the single strut is
about 100 microns long.

651
00:39:41,090 --> 00:39:42,750
He used a microscope to do this.

652
00:39:42,750 --> 00:39:45,510
He then glued it
onto a glass slide

653
00:39:45,510 --> 00:39:48,640
and he used the atomic
force microscope probe

654
00:39:48,640 --> 00:39:51,140
to bend the strut like
a cantilever beam.

655
00:39:51,140 --> 00:39:54,010
And he measured this
displacement here.

656
00:39:54,010 --> 00:39:56,940
And from that he could back out
what the modulus of the solid

657
00:39:56,940 --> 00:39:57,890
was.

658
00:39:57,890 --> 00:39:59,920
He did these tests
in the dry state.

659
00:39:59,920 --> 00:40:02,340
But we could extrapolate
to the wet state

660
00:40:02,340 --> 00:40:04,760
from looking at the behavior
of the whole scaffold.

661
00:40:04,760 --> 00:40:10,190
So he had a modulus for
the wet scaffold solid.

662
00:40:10,190 --> 00:40:13,760
And then this is our formula
for Euler buckling here.

663
00:40:13,760 --> 00:40:17,240
So that's just the
standard formula.

664
00:40:17,240 --> 00:40:20,590
I had a student from
civil engineering, who

665
00:40:20,590 --> 00:40:24,067
looked at hydrostatic loading
of a tetrakaidecahedral cell

666
00:40:24,067 --> 00:40:25,150
and he looked at buckling.

667
00:40:25,150 --> 00:40:27,310
If you had a
tetrakaidecahedral cell and you

668
00:40:27,310 --> 00:40:29,397
load it in all three directions.

669
00:40:29,397 --> 00:40:30,480
He looked at the buckling.

670
00:40:30,480 --> 00:40:33,110
And he had calculated that
the n constraint factor--

671
00:40:33,110 --> 00:40:36,060
the n squared was point 0.34.

672
00:40:36,060 --> 00:40:39,010
So we have some idea of what
that n squared value should be.

673
00:40:39,010 --> 00:40:41,750
Although it's somewhat
of an estimate.

674
00:40:41,750 --> 00:40:44,000
I had a UROP student
who took Toby's images

675
00:40:44,000 --> 00:40:46,420
and measured the
dimensions of the struts.

676
00:40:46,420 --> 00:40:50,422
So he measured the diameter and
the thickness of the struts.

677
00:40:50,422 --> 00:40:52,130
And from that, we just
plugged everything

678
00:40:52,130 --> 00:40:53,480
into the Euler formula.

679
00:40:53,480 --> 00:40:56,070
And we found that the
average single cell

680
00:40:56,070 --> 00:40:59,220
force is somewhere between
about 11 and 41 nano neutron.

681
00:40:59,220 --> 00:41:01,169
It was something like
26 nano neutrons.

682
00:41:01,169 --> 00:41:03,460
So it would make sense that
it's more than the one nano

683
00:41:03,460 --> 00:41:06,040
neutron per cell because not
all of those cells were active

684
00:41:06,040 --> 00:41:08,850
and they weren't all going
in the same direction.

685
00:41:08,850 --> 00:41:11,950
So Brendan Harley and Matt Wong
did that part of the project.

686
00:41:16,070 --> 00:41:16,570
OK.

687
00:41:16,570 --> 00:41:17,710
So that's the contraction.

688
00:41:17,710 --> 00:41:19,220
Are we good with contraction?

689
00:41:19,220 --> 00:41:21,386
So it's kind of interesting
that cells will contract

690
00:41:21,386 --> 00:41:23,490
and we can measure some forces.

691
00:41:23,490 --> 00:41:26,015
So the next type of
interaction between the cells

692
00:41:26,015 --> 00:41:27,890
and the scaffolds that
I wanted to talk about

693
00:41:27,890 --> 00:41:29,890
is cell migration.

694
00:41:29,890 --> 00:41:32,427
And these are some studies
from the literature.

695
00:41:32,427 --> 00:41:33,760
These are two different studies.

696
00:41:33,760 --> 00:41:36,870
But the top one here, they've
measured migration rate

697
00:41:36,870 --> 00:41:38,730
as a function of
the cross linking

698
00:41:38,730 --> 00:41:40,790
treatment of a scaffold.

699
00:41:40,790 --> 00:41:44,327
And the decreasing
stiffness goes this way.

700
00:41:44,327 --> 00:41:46,660
And so they're seeing that
the speed of migration-- this

701
00:41:46,660 --> 00:41:48,810
is in millimeters per day.

702
00:41:48,810 --> 00:41:50,110
Cells don't move too quickly.

703
00:41:50,110 --> 00:41:52,330
They go millimeters per day.

704
00:41:52,330 --> 00:41:55,370
But you can see that the
migration speed, the speed

705
00:41:55,370 --> 00:41:57,340
at which the cells
can move, depends

706
00:41:57,340 --> 00:42:01,050
on the stiffness of the scaffold
that they're attached to.

707
00:42:01,050 --> 00:42:03,790
And in this study on the
bottom here, what they did was

708
00:42:03,790 --> 00:42:07,440
they had just a
flat 2d substrate.

709
00:42:07,440 --> 00:42:09,550
Just a flat polymer.

710
00:42:09,550 --> 00:42:12,420
And what they did was they cross
linked one part of the polymer

711
00:42:12,420 --> 00:42:14,660
more than the other
part of polymer.

712
00:42:14,660 --> 00:42:17,600
So over here, this was
the less cross linked.

713
00:42:17,600 --> 00:42:19,040
That was the soft part.

714
00:42:19,040 --> 00:42:20,790
And this was the more
highly cross linked.

715
00:42:20,790 --> 00:42:22,460
This was the stiffer part.

716
00:42:22,460 --> 00:42:25,110
And they found that if they
put a cell on the soft part

717
00:42:25,110 --> 00:42:27,730
it would migrate
onto the stiff part.

718
00:42:27,730 --> 00:42:30,230
But if they put a cell
on the stiff part,

719
00:42:30,230 --> 00:42:32,702
it would start going this
way towards the soft part.

720
00:42:32,702 --> 00:42:34,160
But when it got to
the interface it

721
00:42:34,160 --> 00:42:36,290
would just spread out
along the interface.

722
00:42:36,290 --> 00:42:38,790
And it wouldn't go
into the soft part.

723
00:42:38,790 --> 00:42:40,540
So the cells were
somehow sensing

724
00:42:40,540 --> 00:42:42,152
the stiffness of the substrate.

725
00:42:42,152 --> 00:42:44,610
And for some reason, I don't
know what, but for some reason

726
00:42:44,610 --> 00:42:46,450
these particular
cells seem to prefer

727
00:42:46,450 --> 00:42:48,559
being on the stiff substrate.

728
00:42:48,559 --> 00:42:50,350
So this is just really
showing that there's

729
00:42:50,350 --> 00:42:53,440
some interaction between the
substrate stiffness and the way

730
00:42:53,440 --> 00:42:56,440
the cells are behaving
and migrating.

731
00:42:56,440 --> 00:43:01,030
And then Brendan also
wanted to study this.

732
00:43:01,030 --> 00:43:04,172
And he got some of the
collagen GAG scaffold.

733
00:43:04,172 --> 00:43:05,380
He made some of the scaffold.

734
00:43:05,380 --> 00:43:08,000
And he stained that with a
stain that made it turn red.

735
00:43:08,000 --> 00:43:12,660
So these lines here are all
red struts in the scaffold.

736
00:43:12,660 --> 00:43:15,440
And then he put fiberblasts
on to the scaffold

737
00:43:15,440 --> 00:43:16,530
and stained them green.

738
00:43:16,530 --> 00:43:20,430
So all these little blobs here
that are green are the cells.

739
00:43:20,430 --> 00:43:22,290
And then he used
confocal microscopy.

740
00:43:22,290 --> 00:43:24,170
And the confocal
microscopy allowed

741
00:43:24,170 --> 00:43:27,560
him to look at a certain
volume of the scaffold.

742
00:43:27,560 --> 00:43:29,210
And he had some
software that would

743
00:43:29,210 --> 00:43:31,460
track the centroid
of each cell as it

744
00:43:31,460 --> 00:43:33,230
moved through the scaffold.

745
00:43:33,230 --> 00:43:36,950
And so he had a thing
he called spot tracking.

746
00:43:36,950 --> 00:43:40,310
So each of these little spheres
here corresponds to a cell.

747
00:43:40,310 --> 00:43:43,115
And the white box is
the volume of material

748
00:43:43,115 --> 00:43:45,150
that you could see
in the scaffold.

749
00:43:45,150 --> 00:43:48,470
And this color scale here
really corresponds to time.

750
00:43:48,470 --> 00:43:50,180
So I've forgotten which round.

751
00:43:50,180 --> 00:43:52,730
I think blue is the
original time 0,

752
00:43:52,730 --> 00:43:55,360
and then red is
maybe five seconds,

753
00:43:55,360 --> 00:43:56,520
and yellow was 10 seconds.

754
00:43:56,520 --> 00:43:59,360
The different colors
correspond to different times.

755
00:43:59,360 --> 00:44:01,910
So he could track
the path of each cell

756
00:44:01,910 --> 00:44:05,090
and also what the position
was at different time points.

757
00:44:05,090 --> 00:44:08,145
So he knew what the position
was at different time points.

758
00:44:08,145 --> 00:44:09,520
And obviously from
that, he could

759
00:44:09,520 --> 00:44:12,200
get the speed of the scaffold.

760
00:44:12,200 --> 00:44:14,730
And he did these
experiments on scaffolds

761
00:44:14,730 --> 00:44:18,170
of different stiffnesses, as
well as, different pore size.

762
00:44:18,170 --> 00:44:21,110
And here you can
see the cell speed.

763
00:44:21,110 --> 00:44:23,680
He's measuring it in
microns per hour now.

764
00:44:23,680 --> 00:44:25,760
The cell speed
increases at first

765
00:44:25,760 --> 00:44:28,780
and then decreases with
the strut stiffness.

766
00:44:28,780 --> 00:44:31,140
So we don't know
exactly why this is.

767
00:44:31,140 --> 00:44:34,950
But there is an effect between
the stiffness of the scaffold

768
00:44:34,950 --> 00:44:36,727
and the migration speed.

769
00:44:36,727 --> 00:44:38,310
And another thing
he did was he looked

770
00:44:38,310 --> 00:44:42,070
at how the cell speed
varies with the pore size.

771
00:44:42,070 --> 00:44:46,560
And as the pore size gets
smaller, the speed goes up.

772
00:44:46,560 --> 00:44:48,310
And we're not entirely
sure why that is.

773
00:44:48,310 --> 00:44:50,560
But I think that might be
related to this binding site

774
00:44:50,560 --> 00:44:53,095
thing too.

775
00:44:53,095 --> 00:44:56,730
As the pore size goes down,
the number of binding sites

776
00:44:56,730 --> 00:44:57,860
is going to go up.

777
00:44:57,860 --> 00:45:00,160
And if you think of
the cells migrating

778
00:45:00,160 --> 00:45:02,940
by having these adhesion sites,
and the adhesion sites are just

779
00:45:02,940 --> 00:45:05,700
at the ends of the cells, and
the cells kind of putting out

780
00:45:05,700 --> 00:45:10,330
a little extension, and then
looking for somewhere else

781
00:45:10,330 --> 00:45:10,996
it can bind.

782
00:45:10,996 --> 00:45:12,370
The more binding
sites there are,

783
00:45:12,370 --> 00:45:14,100
the faster it's going
to find a binding site.

784
00:45:14,100 --> 00:45:16,070
And the faster, I think,
it's going to move on.

785
00:45:16,070 --> 00:45:19,910
So I think that the cell speed
depends on pore size, at least

786
00:45:19,910 --> 00:45:23,290
in part because of the
increase in the binding sites

787
00:45:23,290 --> 00:45:26,470
with smaller pore sizes.

788
00:45:26,470 --> 00:45:29,350
So pore size and the migration.

789
00:45:29,350 --> 00:45:31,300
And then the last thing
I wanted to talk about

790
00:45:31,300 --> 00:45:33,470
was cell differentiation.

791
00:45:33,470 --> 00:45:35,870
And this is a study
study by Engler.

792
00:45:35,870 --> 00:45:39,470
And one of the things he found
was he put mesenchymal stem

793
00:45:39,470 --> 00:45:41,880
cells on 2d substrates.

794
00:45:41,880 --> 00:45:44,370
Just flat 2d substrates
of different stiffnesses.

795
00:45:44,370 --> 00:45:48,200
And again, he could control
the stiffness by cross linking.

796
00:45:48,200 --> 00:45:51,000
And what he's showing
up here in the first bit

797
00:45:51,000 --> 00:45:55,330
is that he's looking at
the stiffness of tissues

798
00:45:55,330 --> 00:45:56,450
of different kinds.

799
00:45:56,450 --> 00:45:59,270
So here's brain type tissue.

800
00:45:59,270 --> 00:46:00,790
Something like one kilo pascal.

801
00:46:00,790 --> 00:46:04,110
Muscle might be something
like 10 kilo pascal.

802
00:46:04,110 --> 00:46:06,030
And collagenous
bone-- this is sort

803
00:46:06,030 --> 00:46:08,790
of the osteoid that is
the precursor of bone, not

804
00:46:08,790 --> 00:46:09,820
the bone itself.

805
00:46:09,820 --> 00:46:13,540
Is about 100 kilo pascals.

806
00:46:13,540 --> 00:46:16,210
And what he did was he
put these mesenchymal

807
00:46:16,210 --> 00:46:20,150
stem cells-- so here's his
cell onto his substrate.

808
00:46:20,150 --> 00:46:22,830
And he varied the
stiffness of the substrate.

809
00:46:22,830 --> 00:46:25,010
And then he looked at
the shape of the cells.

810
00:46:25,010 --> 00:46:28,400
So here's the least
stiff substrate,

811
00:46:28,400 --> 00:46:30,930
so between point 1
and 1 kilo pascals.

812
00:46:30,930 --> 00:46:34,090
And here's 4 hours,
24 hours, 96 hours.

813
00:46:34,090 --> 00:46:39,280
And these cells
formed long processes

814
00:46:39,280 --> 00:46:41,510
extending beyond the cell body.

815
00:46:41,510 --> 00:46:43,490
And they looked kind
of like neurons.

816
00:46:43,490 --> 00:46:45,660
So they he called
those neuron like.

817
00:46:45,660 --> 00:46:49,270
Then there's an intermediate
stiffness of substrate here.

818
00:46:49,270 --> 00:46:53,330
And these cells became
even more elongated.

819
00:46:53,330 --> 00:46:57,180
And became something like a
muscle cell, myoblast like.

820
00:46:57,180 --> 00:47:01,115
And then cells that were
put onto a substrate that

821
00:47:01,115 --> 00:47:04,270
was between about 25
and 40 kilo pascals,

822
00:47:04,270 --> 00:47:07,430
they developed a shape that was
something like an osteoblast,

823
00:47:07,430 --> 00:47:09,460
like a bone cell.

824
00:47:09,460 --> 00:47:11,600
So one of the things
he was looking at here,

825
00:47:11,600 --> 00:47:13,820
was how the stiffness
of the substrate

826
00:47:13,820 --> 00:47:16,310
affected how a stem
cell might differentiate

827
00:47:16,310 --> 00:47:18,250
into different cell types.

828
00:47:18,250 --> 00:47:23,680
And another thing that he did
was he looked at different cell

829
00:47:23,680 --> 00:47:24,790
markers.

830
00:47:24,790 --> 00:47:28,490
And he found that the
cells were expressing

831
00:47:28,490 --> 00:47:33,670
markers that were corresponding
to the types of tissue.

832
00:47:33,670 --> 00:47:35,840
So I couldn't tell you the
names of all these things

833
00:47:35,840 --> 00:47:36,590
and what they are.

834
00:47:36,590 --> 00:47:39,840
But I think the red
here is expressing

835
00:47:39,840 --> 00:47:41,220
more of a particular marker.

836
00:47:41,220 --> 00:47:44,470
And I think these wounds
were related to nerve tissue.

837
00:47:44,470 --> 00:47:46,860
These wounds here, were
related more to muscle tissue.

838
00:47:46,860 --> 00:47:49,357
And these wounds here were
related more to bone tissue.

839
00:47:49,357 --> 00:47:51,190
So the things the cells
were expressing also

840
00:47:51,190 --> 00:47:54,380
seemed to correspond to the
different types of tissue

841
00:47:54,380 --> 00:47:58,680
that they were corresponding to.

842
00:47:58,680 --> 00:48:01,500
So I'm just going to
end this part by going

843
00:48:01,500 --> 00:48:02,890
through a little summary here.

844
00:48:02,890 --> 00:48:04,390
So what I've tried
to show you today

845
00:48:04,390 --> 00:48:07,530
is different types
of cell behavior

846
00:48:07,530 --> 00:48:09,400
that are affected
by the scaffold.

847
00:48:09,400 --> 00:48:11,600
And they're affected by
things like the number

848
00:48:11,600 --> 00:48:13,670
of binding sites,
by the pore size,

849
00:48:13,670 --> 00:48:15,640
by the stiffness
of the scaffold.

850
00:48:15,640 --> 00:48:17,410
So we started with
a cell attachment.

851
00:48:17,410 --> 00:48:19,900
We saw that the cell
attachment increases linearly

852
00:48:19,900 --> 00:48:21,655
with a specific surface area.

853
00:48:21,655 --> 00:48:24,260
We saw that the cell morphology
depends on the orientation

854
00:48:24,260 --> 00:48:24,880
of the pores.

855
00:48:24,880 --> 00:48:26,296
And that kind of
makes sense, they

856
00:48:26,296 --> 00:48:27,830
got to line up with the pores.

857
00:48:27,830 --> 00:48:29,679
We talked about the
contraction behaviors.

858
00:48:29,679 --> 00:48:31,970
So the cells bind at the
periphery, the cells elongate,

859
00:48:31,970 --> 00:48:33,490
and that causes this buckling.

860
00:48:33,490 --> 00:48:35,390
And you can calculate
the buckling forces.

861
00:48:35,390 --> 00:48:39,870
It's around 10 to
40 nano neutrons.

862
00:48:39,870 --> 00:48:41,890
We looked at the
cell migration speed.

863
00:48:41,890 --> 00:48:45,170
That increases with the
stiffness of 1D fibers.

864
00:48:45,170 --> 00:48:49,360
And we looked at cell migration
in the collagen gag scaffolds.

865
00:48:49,360 --> 00:48:51,802
So that depends on the
stiffness of the pore size.

866
00:48:51,802 --> 00:48:53,260
And then there was
this final study

867
00:48:53,260 --> 00:48:55,350
on the cell differentiation.

868
00:48:55,350 --> 00:48:57,400
So I wasn't going to
write any notes on this

869
00:48:57,400 --> 00:48:59,710
because the slides I think
pretty much explain it.

870
00:48:59,710 --> 00:49:01,251
So I was just going
to put the slides

871
00:49:01,251 --> 00:49:03,970
on the website at the end
after today's lecture.

872
00:49:03,970 --> 00:49:06,060
So are we good with how
cells and the scaffolds

873
00:49:06,060 --> 00:49:08,892
of the environments interact?

874
00:49:08,892 --> 00:49:10,350
Because I think
it's not so obvious

875
00:49:10,350 --> 00:49:14,230
that this actual mechanical
environment makes a difference.

876
00:49:14,230 --> 00:49:18,756
People think of the chemical,
the biochemical environment.

877
00:49:18,756 --> 00:49:20,130
That obviously
affects the cells.

878
00:49:20,130 --> 00:49:22,690
But people don't think
at first that something

879
00:49:22,690 --> 00:49:27,990
like the sort of structure
of the pores, the pore size,

880
00:49:27,990 --> 00:49:31,062
or the orientation of the pores,
or the mechanical properties

881
00:49:31,062 --> 00:49:32,770
are going to affect
how the cells behave.

882
00:49:32,770 --> 00:49:34,530
But in fact, they do.

883
00:49:34,530 --> 00:49:35,110
So that's it.

884
00:49:35,110 --> 00:49:37,070
And this is all various
people who worked

885
00:49:37,070 --> 00:49:38,580
with me on these projects.

886
00:49:38,580 --> 00:49:40,060
So it was a lot of fun.

887
00:49:40,060 --> 00:49:42,060
OK.

888
00:49:42,060 --> 00:49:46,310
So hang on a sec here.

889
00:49:46,310 --> 00:49:47,272
What's this all about?

890
00:49:47,272 --> 00:49:48,480
I'm going to get rid of that.

891
00:49:48,480 --> 00:49:49,560
Go away.

892
00:49:49,560 --> 00:49:50,160
Here we go.

893
00:49:50,160 --> 00:49:50,660
OK.

894
00:49:50,660 --> 00:49:54,640
So are we good with
cells and substrates?

895
00:49:54,640 --> 00:49:55,310
Yeah?

896
00:49:55,310 --> 00:49:57,460
OK.

897
00:49:57,460 --> 00:49:59,585
So let's just take
a little moment

898
00:49:59,585 --> 00:50:00,710
and I'll rub the board off.

899
00:50:00,710 --> 00:50:02,168
And then we can
start the next bit.

900
00:50:43,616 --> 00:50:44,116
OK.

901
00:51:10,040 --> 00:51:10,540
OK.

902
00:51:10,540 --> 00:51:14,560
So that's the end of the
medical material stuff.

903
00:51:14,560 --> 00:51:16,989
So we talked about the bone.

904
00:51:16,989 --> 00:51:19,030
We talked about the tissue
engineering scaffolds.

905
00:51:19,030 --> 00:51:21,840
And then we talked about the
cell scaffold interactions.

906
00:51:21,840 --> 00:51:25,200
So now we're going to go back
to more engineering topics.

907
00:51:25,200 --> 00:51:27,310
And the next thing I
wanted to talk about

908
00:51:27,310 --> 00:51:29,550
was energy absorption in foams.

909
00:51:29,550 --> 00:51:31,980
So foams are very widely
used for energy absorption

910
00:51:31,980 --> 00:51:34,030
applications, things
like bicycle helmets,

911
00:51:34,030 --> 00:51:35,400
different kinds of helmets.

912
00:51:35,400 --> 00:51:38,300
You buy a new computer, it
comes in foam packaging.

913
00:51:38,300 --> 00:51:40,430
And the reason foams
are used so much

914
00:51:40,430 --> 00:51:43,660
is they're extremely good at
absorbing energy from impact.

915
00:51:43,660 --> 00:51:45,410
And in fact, they're
better than the solid

916
00:51:45,410 --> 00:51:46,960
that they're made from.

917
00:51:46,960 --> 00:51:51,670
So let's just look at this
curve here for a minute.

918
00:51:51,670 --> 00:51:55,480
So here's a stress strain curve
in compression for the foam.

919
00:51:55,480 --> 00:51:57,500
And the material
that it's made from

920
00:51:57,500 --> 00:52:00,070
would have the stiffness
something like this.

921
00:52:00,070 --> 00:52:02,450
It would be much, much
stiffer than the foam.

922
00:52:02,450 --> 00:52:05,950
And if you think about how
much energy you can absorb,

923
00:52:05,950 --> 00:52:08,020
the energy you can
absorb is just the area

924
00:52:08,020 --> 00:52:09,390
under the stress/strain curve.

925
00:52:09,390 --> 00:52:12,280
That's the energy you can absorb
in a given volume of foam.

926
00:52:12,280 --> 00:52:16,490
And so when you're thinking
about these energy absorption

927
00:52:16,490 --> 00:52:18,380
problems, it's not
just that you need

928
00:52:18,380 --> 00:52:19,640
to absorb a certain energy.

929
00:52:19,640 --> 00:52:22,110
You need to absorb it without
exceeding a certain peak

930
00:52:22,110 --> 00:52:22,906
stress.

931
00:52:22,906 --> 00:52:25,280
So whatever it is you're trying
to protect, at some point

932
00:52:25,280 --> 00:52:26,839
it's going to break.

933
00:52:26,839 --> 00:52:28,130
This is what you want to avoid.

934
00:52:28,130 --> 00:52:29,570
You want to avoid it breaking.

935
00:52:29,570 --> 00:52:31,659
So you don't want to
have a stress bigger

936
00:52:31,659 --> 00:52:33,200
than the stress
that's going to break

937
00:52:33,200 --> 00:52:36,540
whatever it is, your computer,
or your head, or whatever.

938
00:52:36,540 --> 00:52:39,370
So say you have a
given peak stress

939
00:52:39,370 --> 00:52:41,010
that you can tolerate here.

940
00:52:41,010 --> 00:52:43,450
And we've normalized things
by the solid modules.

941
00:52:43,450 --> 00:52:45,730
But just say that's
a peak stress here.

942
00:52:45,730 --> 00:52:47,910
The foam is going to absorb
this amount of energy

943
00:52:47,910 --> 00:52:50,470
up here, this whole
little shaded region.

944
00:52:50,470 --> 00:52:53,280
And the solid is going to absorb
that little, teeny weeny bit

945
00:52:53,280 --> 00:52:54,160
in there.

946
00:52:54,160 --> 00:52:56,790
So what you want to do
is absorb the energy

947
00:52:56,790 --> 00:52:58,970
without exceeding a
certain peak stress.

948
00:52:58,970 --> 00:53:01,990
And the foam is always going
to be better than the solid

949
00:53:01,990 --> 00:53:03,890
that it's made from.

950
00:53:03,890 --> 00:53:06,140
There's a couple other things
that make the foams good

951
00:53:06,140 --> 00:53:09,020
because they're more or less
isotropic, maybe not perfectly.

952
00:53:09,020 --> 00:53:11,562
But roughly, they have the same
properties in all directions.

953
00:53:11,562 --> 00:53:13,728
Sometimes you don't know
what direction the impact's

954
00:53:13,728 --> 00:53:14,530
going to come from.

955
00:53:14,530 --> 00:53:16,196
And so if you've got
the same properties

956
00:53:16,196 --> 00:53:19,460
in all directions or roughly
the same, that's a good thing.

957
00:53:19,460 --> 00:53:23,030
You also want the protective
thing to be light.

958
00:53:23,030 --> 00:53:25,990
If you're paying for shipping
for your computer or whatever,

959
00:53:25,990 --> 00:53:27,730
the fact that the
packaging is light

960
00:53:27,730 --> 00:53:29,732
makes the shipping easier.

961
00:53:29,732 --> 00:53:31,190
If you have a helmet
for your head,

962
00:53:31,190 --> 00:53:32,690
you don't want some
big heavy thing.

963
00:53:32,690 --> 00:53:34,100
You want something fairly light.

964
00:53:34,100 --> 00:53:35,070
And foams are cheap.

965
00:53:35,070 --> 00:53:39,040
So the fact that they're roughly
isotropic, they're light,

966
00:53:39,040 --> 00:53:42,080
they're cheap, this
all helps as well.

967
00:53:42,080 --> 00:53:44,670
But from a mechanical
point of view,

968
00:53:44,670 --> 00:53:47,130
foams are very good
at absorbing energy.

969
00:53:47,130 --> 00:53:49,870
And so what we're going
to do in the next--

970
00:53:49,870 --> 00:53:52,530
the rest of this lecture
and on Wednesday-- we're

971
00:53:52,530 --> 00:53:55,700
going to see how we can
convert these stress/strain

972
00:53:55,700 --> 00:53:59,010
curves into what are called
energy absorption diagrams.

973
00:53:59,010 --> 00:54:01,446
We're going to look at some
energy absorption diagrams

974
00:54:01,446 --> 00:54:03,570
that we just measure from
the stress/strain curves.

975
00:54:03,570 --> 00:54:05,530
And we're going to look at
how we can predict the energy

976
00:54:05,530 --> 00:54:07,027
absorption diagrams as well.

977
00:54:09,760 --> 00:54:12,560
OK.

978
00:54:12,560 --> 00:54:17,950
So the main idea here is
that the impact protection

979
00:54:17,950 --> 00:54:19,960
has to absorb the
energy from the impact

980
00:54:19,960 --> 00:54:22,056
but without exceeding
a certain peak stress.

981
00:55:12,300 --> 00:55:14,630
So the direction of loading
may not be predictable.

982
00:55:24,350 --> 00:55:26,570
And foams are good because
they're roughly Isotropic.

983
00:55:33,234 --> 00:55:35,150
And they would have the
same energy absorption

984
00:55:35,150 --> 00:55:36,502
capacity from any direction.

985
00:55:45,040 --> 00:55:46,689
And foams are also
light and cheap.

986
00:56:07,110 --> 00:56:13,840
We can say for a given peak
stress the foam is always

987
00:56:13,840 --> 00:56:16,750
going to absorb more energy
than the solid it's made from.

988
00:56:41,380 --> 00:56:42,920
So other things
that make foams good

989
00:56:42,920 --> 00:56:45,567
are that they have a capacity
to undergo large deformations.

990
00:56:59,790 --> 00:57:02,300
And they do that at
roughly constant stress.

991
00:57:08,580 --> 00:57:10,540
So that if you look
at the stress strain

992
00:57:10,540 --> 00:57:17,780
curve for the foam,
you're going to be

993
00:57:17,780 --> 00:57:21,220
able to absorb all
this energy under here.

994
00:57:21,220 --> 00:57:23,250
And these strains that
the foam might go to

995
00:57:23,250 --> 00:57:28,210
might be 0.08 to 0.09, so
huge strains on an engineering

996
00:57:28,210 --> 00:57:30,930
scale.

997
00:57:30,930 --> 00:57:34,240
And then this is your
energy-- would absorb

998
00:57:34,240 --> 00:57:39,160
is that area under the
stress/strain curve.

999
00:57:39,160 --> 00:57:41,716
So I wanted to say something
about strain rates too.

1000
00:57:45,340 --> 00:57:47,260
So typically we're
going to be talking

1001
00:57:47,260 --> 00:57:48,580
about problems of impact.

1002
00:57:48,580 --> 00:57:51,080
And in impact, the strain
rates are typically

1003
00:57:51,080 --> 00:57:55,090
on the order of 10 to 100 per
second, something like that.

1004
00:57:55,090 --> 00:57:57,410
We're not going to talk
about things like blast.

1005
00:57:57,410 --> 00:57:59,229
If you have a blast
loading, then you

1006
00:57:59,229 --> 00:58:01,020
have to take inertial
effects into account.

1007
00:58:01,020 --> 00:58:02,910
And blasts involves
strain rates,

1008
00:58:02,910 --> 00:58:06,890
which are 1,000 to 10,000 per
second, much, much higher.

1009
00:58:06,890 --> 00:58:08,810
So we're going to talk
about strain rates that

1010
00:58:08,810 --> 00:58:13,530
are about 10 to 100 per second,
maybe a bit more than that.

1011
00:58:13,530 --> 00:58:16,099
And for instance,
you can roughly

1012
00:58:16,099 --> 00:58:18,140
estimate what one of these
impact rates would be.

1013
00:58:18,140 --> 00:58:20,960
So you had something
that you dropped

1014
00:58:20,960 --> 00:58:22,210
from a height of 1 meter.

1015
00:58:28,110 --> 00:58:32,260
Then the velocity on
impact is just if you just

1016
00:58:32,260 --> 00:58:34,430
equate the potential energy
with a kinetic energy.

1017
00:58:34,430 --> 00:58:36,730
The velocity and impact is
just the square root of 2gh.

1018
00:58:36,730 --> 00:58:39,920
So g's the gravity acceleration.

1019
00:58:39,920 --> 00:58:41,850
And h is the height.

1020
00:58:41,850 --> 00:58:45,030
So that's the square root
of 2 plus 9.81 meters

1021
00:58:45,030 --> 00:58:48,050
per second times 1 meter.

1022
00:58:48,050 --> 00:58:53,490
And that comes out to
4.4 meters per second.

1023
00:58:53,490 --> 00:58:55,400
And say you had some
foam packaging that

1024
00:58:55,400 --> 00:58:57,422
was 100 millimeters thick.

1025
00:59:02,570 --> 00:59:05,935
Then you could say roughly
that the strain rate would

1026
00:59:05,935 --> 00:59:13,160
be approximately equal to that
velocity over the thickness, so

1027
00:59:13,160 --> 00:59:19,500
4.4 per second over 0.1 meters.

1028
00:59:19,500 --> 00:59:22,350
That' would be 44 per second.

1029
00:59:22,350 --> 00:59:23,869
So it's somewhere in that range.

1030
00:59:23,869 --> 00:59:26,160
Obviously, the thickness
could be a little bit smaller,

1031
00:59:26,160 --> 00:59:27,140
it could be bigger.

1032
00:59:27,140 --> 00:59:29,050
But it's in that ballpark.

1033
00:59:29,050 --> 00:59:31,950
And if you do tests on
servo controlled instrons

1034
00:59:31,950 --> 00:59:33,392
or you do a drop
hammer test, you

1035
00:59:33,392 --> 00:59:34,975
can get strain rates
in that ballpark.

1036
00:59:59,220 --> 00:59:59,840
OK.

1037
00:59:59,840 --> 01:00:02,726
So we're talking about
impact and not blast.

1038
01:00:39,660 --> 01:00:41,670
OK.

1039
01:00:41,670 --> 01:00:45,060
So most of the energy
that's absorbed

1040
01:00:45,060 --> 01:00:47,700
is really absorbed in
that stress plateau.

1041
01:00:47,700 --> 01:00:52,464
So if you think of the
stress/strain curve,

1042
01:00:52,464 --> 01:00:54,380
most of the area under
the stress/strain curve

1043
01:00:54,380 --> 01:00:58,150
comes from the area from
underneath the stress plateau.

1044
01:00:58,150 --> 01:01:00,219
So the mechanisms of
absorbing the energy

1045
01:01:00,219 --> 01:01:02,760
are going to be mechanisms that
are associated with a plateau

1046
01:01:02,760 --> 01:01:03,530
stress.

1047
01:01:03,530 --> 01:01:06,000
So for elastomeric
foams, we've got

1048
01:01:06,000 --> 01:01:07,500
elastic buckling of the cells.

1049
01:01:17,610 --> 01:01:21,530
And one of the advantages
or disadvantages-- depending

1050
01:01:21,530 --> 01:01:24,600
on what you want-- of this
is that the deformation

1051
01:01:24,600 --> 01:01:26,450
is recoverable and you
got to have rebounds.

1052
01:01:26,450 --> 01:01:29,380
So if you have an object and you
drop it onto elastomeric foam,

1053
01:01:29,380 --> 01:01:31,270
it's going to bounce
around like that.

1054
01:01:36,380 --> 01:01:41,913
So the elastic deformation
is going to be recovered,

1055
01:01:41,913 --> 01:01:43,246
and you're going to get rebound.

1056
01:02:02,730 --> 01:02:05,880
If you have a foam that
has a plastic yield point

1057
01:02:05,880 --> 01:02:08,200
or is brittle, then
the deformation

1058
01:02:08,200 --> 01:02:11,177
is going to be largely from
dissipating plastic work

1059
01:02:11,177 --> 01:02:12,010
or work of fracture.

1060
01:02:31,060 --> 01:02:34,100
And in that case,
there's no rebound.

1061
01:02:34,100 --> 01:02:36,340
But once you've loaded it,
you've crushed the thing,

1062
01:02:36,340 --> 01:02:40,070
and you've permanently deformed
it, and you can't use it again.

1063
01:02:40,070 --> 01:02:42,870
So sometimes if you ride
your bicycle like I do,

1064
01:02:42,870 --> 01:02:45,880
if you have a helmet, you
should wear your bicycle helmet.

1065
01:02:45,880 --> 01:02:48,460
If you have a problem,
if you have an accident,

1066
01:02:48,460 --> 01:02:50,192
and your helmet get
smooshed, that's it.

1067
01:02:50,192 --> 01:02:51,650
You have to throw
your helmet away.

1068
01:02:51,650 --> 01:02:52,608
You can't use it again.

1069
01:02:52,608 --> 01:02:53,695
And this is why.

1070
01:02:53,695 --> 01:02:55,175
[INAUDIBLE], even
if it doesn't get

1071
01:02:55,175 --> 01:02:57,300
smooshed, if you hit your
head at all, [INAUDIBLE].

1072
01:02:57,300 --> 01:02:58,690
Exactly.

1073
01:02:58,690 --> 01:03:00,150
[INAUDIBLE]

1074
01:03:00,150 --> 01:03:00,650
Yeah.

1075
01:03:00,650 --> 01:03:01,670
You need a new helmet.

1076
01:03:01,670 --> 01:03:03,280
Yeah.

1077
01:03:03,280 --> 01:03:04,070
Go ahead.

1078
01:03:04,070 --> 01:03:07,741
Talk about helmets because I'm
on a helmet conversion thing.

1079
01:03:07,741 --> 01:03:08,240
Yes.

1080
01:03:08,240 --> 01:03:09,720
You've got to wear your helmet.

1081
01:03:09,720 --> 01:03:11,770
And you should change
it every now and then.

1082
01:03:11,770 --> 01:03:15,050
Anything else you'd like to add
about bicycle helmet safety?

1083
01:03:15,050 --> 01:03:15,950
No, absolutely.

1084
01:03:15,950 --> 01:03:16,680
You've got to wear your helmet.

1085
01:03:16,680 --> 01:03:18,929
So I know several people who
would have had their head

1086
01:03:18,929 --> 01:03:21,270
smooshed had they not
been wearing their helmet.

1087
01:03:21,270 --> 01:03:24,031
So you have to wear your helmet.

1088
01:03:24,031 --> 01:03:24,530
Let's see.

1089
01:03:24,530 --> 01:03:27,290
OK.

1090
01:03:27,290 --> 01:03:30,230
If you think about natural
cellular materials, things

1091
01:03:30,230 --> 01:03:37,150
like wood, they
often have cell walls

1092
01:03:37,150 --> 01:03:38,330
that are fiber compensates.

1093
01:03:38,330 --> 01:03:41,980
And you can dissipate energy by
mechanisms related to the fiber

1094
01:03:41,980 --> 01:03:45,210
nature, so by things like
fiber pull out fracture.

1095
01:04:17,594 --> 01:04:21,660
And then you can also have
open cell foams with fluids.

1096
01:04:21,660 --> 01:04:23,506
You can have fluid
within the cells.

1097
01:04:28,870 --> 01:04:34,670
And if the cells are open
cells, the fluid effect

1098
01:04:34,670 --> 01:04:36,170
is really only going
to be important

1099
01:04:36,170 --> 01:04:39,690
if the cells are extremely small
or the fluid is particularly

1100
01:04:39,690 --> 01:04:42,280
viscous, or the strain
rates are very high.

1101
01:05:09,750 --> 01:05:11,880
So in most cases,
the fluid effects

1102
01:05:11,880 --> 01:05:14,260
aren't important
in open cell foams.

1103
01:05:14,260 --> 01:05:16,520
But, for example, you could
try to make an open cell

1104
01:05:16,520 --> 01:05:19,570
foam that had more energy
absorption by putting

1105
01:05:19,570 --> 01:05:20,410
a fluid into it.

1106
01:05:20,410 --> 01:05:22,600
So you could put
glycerin into the fluid,

1107
01:05:22,600 --> 01:05:25,262
and that would increase how
much energy it would absorb.

1108
01:05:25,262 --> 01:05:26,720
Or, you can put
this honey into it.

1109
01:05:26,720 --> 01:05:30,250
That would make it
more energy absorption.

1110
01:05:30,250 --> 01:05:38,040
And enclosed cell foams,
you may have an effect

1111
01:05:38,040 --> 01:05:39,847
of the gas within the cells.

1112
01:05:39,847 --> 01:05:41,680
But it's really only
going to be significant

1113
01:05:41,680 --> 01:05:43,220
if you have
elastimeric foams where

1114
01:05:43,220 --> 01:05:44,860
the cell faces don't rupture.

1115
01:05:44,860 --> 01:05:46,380
The cell faces
rupture, then the gas

1116
01:05:46,380 --> 01:05:48,310
is just going to
flow out of them,

1117
01:05:48,310 --> 01:05:50,200
and that's not going to do much.

1118
01:07:08,640 --> 01:07:11,140
So the next step is I
want to go from having

1119
01:07:11,140 --> 01:07:13,240
the stress/strain curve
that we've become very

1120
01:07:13,240 --> 01:07:16,110
familiar with,
and make something

1121
01:07:16,110 --> 01:07:19,930
with that that is a little
easier to see graphically

1122
01:07:19,930 --> 01:07:21,842
that shows how much
energy we can absorb.

1123
01:07:21,842 --> 01:07:24,050
Remember, what I said what
we're really interested in

1124
01:07:24,050 --> 01:07:25,675
is absorbing a certain
amount of energy

1125
01:07:25,675 --> 01:07:28,760
without exceeding a
certain peak stress.

1126
01:07:28,760 --> 01:07:31,550
So what I'm going to
do is plot another plot

1127
01:07:31,550 --> 01:07:33,280
that's based on that.

1128
01:07:33,280 --> 01:07:35,940
It's going to be
the energy absorbed.

1129
01:07:35,940 --> 01:07:38,840
So w is going to be energy
absorbed per unit volume.

1130
01:07:49,080 --> 01:07:52,235
And I'm going to plot that
against the peak stress.

1131
01:08:04,220 --> 01:08:05,360
OK.

1132
01:08:05,360 --> 01:08:08,290
So we're going to look at
three different regimes here.

1133
01:08:08,290 --> 01:08:10,050
We're going to look
at what happens

1134
01:08:10,050 --> 01:08:13,930
in the linear elastic part, what
happens in the stress plateau,

1135
01:08:13,930 --> 01:08:16,779
and then what happens in
the densification part.

1136
01:08:16,779 --> 01:08:21,740
So let's think about the
elastic regime first.

1137
01:08:21,740 --> 01:08:25,720
And if I moved up-- say
I moved up to some point

1138
01:08:25,720 --> 01:08:29,319
right there where the little x
is on the stress/strain curve.

1139
01:08:29,319 --> 01:08:31,050
Then the amount of
energy I absorbed

1140
01:08:31,050 --> 01:08:35,580
would just be equal to
this little bit here.

1141
01:08:35,580 --> 01:08:38,920
And if I moved up, and then the
peak stress would be this peak

1142
01:08:38,920 --> 01:08:39,840
stress there.

1143
01:08:39,840 --> 01:08:43,880
We'll call that sigma p1 and w1.

1144
01:08:43,880 --> 01:08:48,970
And if I moved up over
here, I'd be at w2.

1145
01:08:48,970 --> 01:08:51,250
And that would be
sigma p2, right?

1146
01:08:51,250 --> 01:08:54,170
And if I know the modulus, I
know what that relationship is.

1147
01:08:54,170 --> 01:08:56,057
And I get a relationship.

1148
01:08:56,057 --> 01:08:58,640
And these are going to be-- I'm
going to do this on log scales

1149
01:08:58,640 --> 01:08:59,140
here.

1150
01:08:59,140 --> 01:09:03,140
There's going to be log,
and that's going to be log.

1151
01:09:03,140 --> 01:09:07,510
I'm going to get in that
linear elastic regime.

1152
01:09:07,510 --> 01:09:15,260
The energy is going to go as
the peak stress squared over 2

1153
01:09:15,260 --> 01:09:17,720
times the modulus of the foam.

1154
01:09:17,720 --> 01:09:22,920
Remember, energy is a
half stress times strain.

1155
01:09:22,920 --> 01:09:26,550
And I can say strain
is sigma p over e.

1156
01:09:26,550 --> 01:09:30,000
So it's 1/2 sigma
p squared over e.

1157
01:09:30,000 --> 01:09:31,790
So on my log1 plot
here, this is just

1158
01:09:31,790 --> 01:09:35,260
going to be a straight
line like that.

1159
01:09:35,260 --> 01:09:37,430
And then I'm going to
get to this value here.

1160
01:09:37,430 --> 01:09:42,492
I'm going to get to my
collapse stress here.

1161
01:09:42,492 --> 01:09:44,609
So let's call that single star.

1162
01:09:44,609 --> 01:09:49,270
And at that point, the
more I go along here,

1163
01:09:49,270 --> 01:09:51,620
every point I go
along, like that,

1164
01:09:51,620 --> 01:09:53,859
I'm going to absorb
more and more energy.

1165
01:09:53,859 --> 01:09:56,590
But the stress isn't
going to go up at all.

1166
01:09:56,590 --> 01:10:01,009
So then this thing here is going
to go like that because I'm

1167
01:10:01,009 --> 01:10:02,300
absorbing more and more energy.

1168
01:10:02,300 --> 01:10:04,740
But the stress just
stays the same.

1169
01:10:04,740 --> 01:10:08,930
So this is good news if
we want to absorb energy.

1170
01:10:08,930 --> 01:10:11,690
And then once I get to
the densification point,

1171
01:10:11,690 --> 01:10:14,010
then it's going to do
the opposite thing.

1172
01:10:14,010 --> 01:10:17,220
As I go along here,
at each increment

1173
01:10:17,220 --> 01:10:19,180
I'm not absorbing
that much more energy.

1174
01:10:19,180 --> 01:10:21,130
But the stress is going up.

1175
01:10:21,130 --> 01:10:25,730
So at some point it turns
and starts to look like that.

1176
01:10:25,730 --> 01:10:28,930
So this part here corresponds
to linear elasticity.

1177
01:10:31,470 --> 01:10:37,560
This bit here corresponds
to the stress plateau.

1178
01:10:37,560 --> 01:10:44,770
And this bit here
corresponds to densification.

1179
01:10:48,150 --> 01:10:51,410
And the point where
I would like to be

1180
01:10:51,410 --> 01:10:53,120
is right here,
because here I'm going

1181
01:10:53,120 --> 01:10:55,470
to absorb the most
energy possible

1182
01:10:55,470 --> 01:10:57,710
through the peak stress.

1183
01:10:57,710 --> 01:11:01,480
So you can think of that as
sort of an optimal point.

1184
01:11:01,480 --> 01:11:08,736
And I'm going to refer
to that as a shoulder

1185
01:11:08,736 --> 01:11:10,360
because it's the
shoulder between where

1186
01:11:10,360 --> 01:11:11,955
the curve bends over again.

1187
01:11:15,750 --> 01:11:21,460
So I've only got a
couple minutes left.

1188
01:11:21,460 --> 01:11:23,800
But let me just
show you one thing

1189
01:11:23,800 --> 01:11:26,960
and then we'll talk about
this more next time.

1190
01:11:26,960 --> 01:11:30,250
So I've just done this
for one relative density.

1191
01:11:30,250 --> 01:11:32,740
But if you look
at the screen, you

1192
01:11:32,740 --> 01:11:35,810
can imagine I would have
stress/strain curves for lots

1193
01:11:35,810 --> 01:11:37,165
of different relative densities.

1194
01:11:37,165 --> 01:11:39,290
And let's say these are
all at the same temperature

1195
01:11:39,290 --> 01:11:41,220
and all at the same strain rate.

1196
01:11:41,220 --> 01:11:43,860
And I could draw a curve
that looks like that

1197
01:11:43,860 --> 01:11:45,940
for each stress/strain curve.

1198
01:11:45,940 --> 01:11:48,200
And if I did that, I'd
get a family of them.

1199
01:11:48,200 --> 01:11:50,770
So this is our
energy absorbed here.

1200
01:11:50,770 --> 01:11:53,480
I've normalized it by
dividing by the solid modulus.

1201
01:11:53,480 --> 01:11:55,360
This is our peak stress here.

1202
01:11:55,360 --> 01:11:57,902
And I've normalized that by
dividing by a solid modulus.

1203
01:11:57,902 --> 01:12:00,110
And I've got a sort of family
of these things, right?

1204
01:12:00,110 --> 01:12:01,318
They all have the same shape.

1205
01:12:01,318 --> 01:12:03,810
But they shift depending
on the relative density.

1206
01:12:03,810 --> 01:12:06,600
And then the thing
that makes life good is

1207
01:12:06,600 --> 01:12:10,370
that these shoulder points
you can connect with a line.

1208
01:12:10,370 --> 01:12:12,360
And you can mark off
the relative density

1209
01:12:12,360 --> 01:12:14,600
for those shoulder
points on each line.

1210
01:12:14,600 --> 01:12:16,990
And then the last
step you can do

1211
01:12:16,990 --> 01:12:19,045
is you can just
plot these lines.

1212
01:12:19,045 --> 01:12:21,170
And you can repeat this
for different strain rates.

1213
01:12:21,170 --> 01:12:24,850
So this would be a family
of these guys here.

1214
01:12:24,850 --> 01:12:27,272
There's a family of those lines
at different strain rates.

1215
01:12:27,272 --> 01:12:29,480
And then you would join up
the points that correspond

1216
01:12:29,480 --> 01:12:30,610
to each relative density.

1217
01:12:30,610 --> 01:12:32,110
So you can make a
drawing that looks

1218
01:12:32,110 --> 01:12:37,040
like this that summarizes the
most energy you can absorb

1219
01:12:37,040 --> 01:12:39,004
for a certain peak
stress for foams

1220
01:12:39,004 --> 01:12:41,420
of different relative densities
tested at different strain

1221
01:12:41,420 --> 01:12:42,011
rates.

1222
01:12:42,011 --> 01:12:44,510
You could do it for different
temperatures if you wanted to.

1223
01:12:44,510 --> 01:12:46,180
So next time, we'll
talk about that.

1224
01:12:46,180 --> 01:12:48,280
But I'm going to
stop there for today.

1225
01:12:48,280 --> 01:12:48,780
OK?

1226
01:12:48,780 --> 01:12:50,520
Are we good?