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LORNA GIBSON: So
last time we were

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00:00:28,800 --> 00:00:31,710
talking about trabecular bone
and that it's this porous kind

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00:00:31,710 --> 00:00:33,390
of foam-like type of bone.

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00:00:33,390 --> 00:00:35,770
And we talked a little
bit about the modeling.

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00:00:35,770 --> 00:00:37,570
And I think I got
as far as starting

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00:00:37,570 --> 00:00:39,700
to talk about osteoporosis.

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00:00:39,700 --> 00:00:43,220
And I wanted to talk today about
how we can model osteoporosis

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00:00:43,220 --> 00:00:44,900
using those voronoi
honeycombs that we

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00:00:44,900 --> 00:00:47,490
talked about a while
ago when we were

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00:00:47,490 --> 00:00:49,500
talking about the structure.

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00:00:49,500 --> 00:00:53,920
So Bruno has a project on
trabecular bone for the class.

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00:00:53,920 --> 00:00:56,010
And he needed bone samples.

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00:00:56,010 --> 00:00:58,540
And so we talked about
different kind of bone samples

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00:00:58,540 --> 00:00:59,760
we could get.

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00:00:59,760 --> 00:01:02,440
And the thing is if you
get human bone-- well,

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00:01:02,440 --> 00:01:04,580
there's all sorts of
issues about just handling

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00:01:04,580 --> 00:01:07,360
human bone and permissions,
and it's complicated.

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00:01:07,360 --> 00:01:09,050
So that was too complicated.

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00:01:09,050 --> 00:01:10,526
We've used bovine bone before.

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00:01:10,526 --> 00:01:11,900
You just go to
the slaughterhouse

28
00:01:11,900 --> 00:01:13,420
and get bovine bone.

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00:01:13,420 --> 00:01:15,170
But one of the things
with trabecular bone

30
00:01:15,170 --> 00:01:19,567
is because it grows in response
to loads, the geometry of it

31
00:01:19,567 --> 00:01:21,150
can be different,
sort of architecture

32
00:01:21,150 --> 00:01:24,140
can vary from one spot
in the bone to another.

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00:01:24,140 --> 00:01:26,350
And I have a colleague
who started doing tests

34
00:01:26,350 --> 00:01:27,850
on whale bones,
just because it's

35
00:01:27,850 --> 00:01:30,730
a way of getting
nice, uniform bone.

36
00:01:30,730 --> 00:01:35,240
So I was on a Ph.D. Committee a
few years ago for a student who

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00:01:35,240 --> 00:01:36,840
was in the Woods Hole program.

38
00:01:36,840 --> 00:01:39,087
She was at MIT, but was
doing Woods Hole thing.

39
00:01:39,087 --> 00:01:41,670
And I don't know if you've heard
of the Atlantic right whales,

40
00:01:41,670 --> 00:01:43,003
the North Atlantic right whales.

41
00:01:43,003 --> 00:01:44,090
They're endangered.

42
00:01:44,090 --> 00:01:46,820
There's about 500 of
them left in the world.

43
00:01:46,820 --> 00:01:50,330
And they migrate between like
typically the Bay of Fundy

44
00:01:50,330 --> 00:01:52,180
and off the Florida coast.

45
00:01:52,180 --> 00:01:54,130
So they go up and
down the coast.

46
00:01:54,130 --> 00:01:57,710
And they sometimes
get hit by ships.

47
00:01:57,710 --> 00:02:00,460
And then bones break
and that kills them.

48
00:02:00,460 --> 00:02:04,535
And her study was on ship
impacts on right whales.

49
00:02:04,535 --> 00:02:06,410
And so I got to know
people at Woods Hole who

50
00:02:06,410 --> 00:02:07,640
worked on whales.

51
00:02:07,640 --> 00:02:10,370
So Bruno, I called up
my friend at Woods Hole.

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00:02:10,370 --> 00:02:12,330
And the Woods Hole guy
didn't have any bones.

53
00:02:12,330 --> 00:02:14,562
But he put me in
touch with somebody

54
00:02:14,562 --> 00:02:16,270
at the Mass Fish and
Wildlife Department.

55
00:02:16,270 --> 00:02:18,540
And he had a couple
of whale vertebrae

56
00:02:18,540 --> 00:02:20,060
that he was willing to give up.

57
00:02:20,060 --> 00:02:21,750
So I got one of them for you.

58
00:02:21,750 --> 00:02:23,090
So here it is.

59
00:02:23,090 --> 00:02:28,110
So I went out to the Mass
Fish and Wildlife yesterday.

60
00:02:28,110 --> 00:02:31,211
And they produced
this bone for me.

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00:02:31,211 --> 00:02:32,460
I could either pass it around.

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00:02:32,460 --> 00:02:35,210
It's not too heavy.

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00:02:35,210 --> 00:02:38,332
Or you could come up
and look afterwards.

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00:02:38,332 --> 00:02:39,290
Shall I pass it around?

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00:02:39,290 --> 00:02:41,100
Or do you want
came up afterwards?

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00:02:41,100 --> 00:02:42,940
Maybe come up-- pass it?

67
00:02:42,940 --> 00:02:44,060
OK.

68
00:02:44,060 --> 00:02:46,140
So one of the things
is our like vertebrae,

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00:02:46,140 --> 00:02:48,467
there's these things
that stick up like this.

70
00:02:48,467 --> 00:02:50,300
There's one that's
missing off of this bone.

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00:02:50,300 --> 00:02:52,008
There should have been
one down here too.

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00:02:52,008 --> 00:02:53,510
But this is sort
of what's called

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00:02:53,510 --> 00:02:54,860
the body of the vertebrae.

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00:02:54,860 --> 00:02:57,320
And in human vertebrae
it's about that big.

75
00:02:59,877 --> 00:03:01,710
But it's the same kind
of general structure.

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00:03:01,710 --> 00:03:04,310
There's these kind of
bony plates that come off.

77
00:03:04,310 --> 00:03:07,060
And the body is almost
all trabecular bone.

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00:03:07,060 --> 00:03:12,110
So you can see on this side,
this is a growth plate here.

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00:03:12,110 --> 00:03:13,770
But on this side,
there normally would

80
00:03:13,770 --> 00:03:16,529
have been a thin shell
of the cortical bone.

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00:03:16,529 --> 00:03:19,070
And when I pass it around, if
you look up at this point here,

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00:03:19,070 --> 00:03:20,790
you can see there's just
a little bit of that left.

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00:03:20,790 --> 00:03:22,260
But it's kind of
gotten worn out.

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00:03:22,260 --> 00:03:23,810
And the rest of
this, if you look,

85
00:03:23,810 --> 00:03:25,680
you can see it's
the trabecular bone.

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00:03:25,680 --> 00:03:28,060
And you can see
it's pretty uniform,

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00:03:28,060 --> 00:03:31,290
which is why I thought this
might be good for your tests.

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00:03:31,290 --> 00:03:34,000
So I thought you should get
in touch with Mike Tarkanian.

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00:03:34,000 --> 00:03:37,020
And I talked to him a
little bit about cutting it

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00:03:37,020 --> 00:03:38,306
with a water jet cutter.

91
00:03:38,306 --> 00:03:40,180
So I think we could use
the water jet cutter.

92
00:03:40,180 --> 00:03:41,264
And I think I emailed you.

93
00:03:41,264 --> 00:03:42,804
If you could cut it
in half, I'd like

94
00:03:42,804 --> 00:03:44,640
to have some pictures
of it cut in half.

95
00:03:44,640 --> 00:03:49,662
And he's got a diamond
corer, cylindrical corer.

96
00:03:49,662 --> 00:03:51,620
So you could make little
cylindrical specimens.

97
00:03:51,620 --> 00:03:53,580
And I know if you want to do
compression tests or beams.

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00:03:53,580 --> 00:03:55,110
AUDIENCE: Well, I was planning
to do compression tests.

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00:03:55,110 --> 00:03:56,818
LORNA GIBSON: Yeah,
so you could probably

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00:03:56,818 --> 00:04:01,430
use some kind of a bands or
something to cut them up.

101
00:04:01,430 --> 00:04:03,800
So, and this is where the
spinal column goes through

102
00:04:03,800 --> 00:04:05,600
in the whale.

103
00:04:05,600 --> 00:04:08,612
So there you have it.

104
00:04:08,612 --> 00:04:10,820
Anybody want to ask me
anything about the whale bone?

105
00:04:10,820 --> 00:04:12,495
OK, so let me pass that around.

106
00:04:12,495 --> 00:04:14,870
And I guess I have to tell
you a couple of other stories.

107
00:04:14,870 --> 00:04:16,950
So while I was there, they
have a brand new building.

108
00:04:16,950 --> 00:04:19,040
And it's all got solar
panels and geothermal heat.

109
00:04:19,040 --> 00:04:20,390
And it's all very groovy.

110
00:04:20,390 --> 00:04:23,275
And the guy who I was
talking to about the bone,

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00:04:23,275 --> 00:04:25,400
he wanted to give me a
little tour of the building.

112
00:04:25,400 --> 00:04:27,400
And he said, oh, you've
got to see your freezer.

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00:04:27,400 --> 00:04:28,200
OK, so the freezer.

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00:04:28,200 --> 00:04:29,550
So he opens the freezer door.

115
00:04:29,550 --> 00:04:31,050
The freezer's like a room.

116
00:04:31,050 --> 00:04:32,160
And there's like a bear.

117
00:04:32,160 --> 00:04:34,630
I'm serious, like a
bear on the floor,

118
00:04:34,630 --> 00:04:36,580
like a dead bear on the
floor of the freezer.

119
00:04:36,580 --> 00:04:38,990
And he said it was like a
two-year-old bear that had,

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00:04:38,990 --> 00:04:41,060
I guess, just come out of
hibernation a couple weeks ago.

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00:04:41,060 --> 00:04:43,040
I think it had gotten hit
by a car or something.

122
00:04:43,040 --> 00:04:44,623
And somebody must
have called them up.

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00:04:44,623 --> 00:04:45,410
And they have it.

124
00:04:45,410 --> 00:04:46,600
So they had this bear.

125
00:04:46,600 --> 00:04:48,060
They had like several deer.

126
00:04:48,060 --> 00:04:48,970
They had a coyote.

127
00:04:48,970 --> 00:04:51,664
They had like boxes full
of all kinds of animals.

128
00:04:51,664 --> 00:04:53,330
So anyway it was kind
interesting to see

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00:04:53,330 --> 00:04:55,160
all these animals there.

130
00:04:55,160 --> 00:04:56,880
And you know what he
said about the deer?

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00:04:56,880 --> 00:05:00,945
He said, normally deer in
Massachusetts don't starve.

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00:05:00,945 --> 00:05:02,820
Like if you live in the
suburbs, you actually

133
00:05:02,820 --> 00:05:05,270
have a problem with deer
eating your vegetable garden

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00:05:05,270 --> 00:05:07,030
because there's deer
all over the place.

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00:05:07,030 --> 00:05:08,850
But he said, this winter, you
know how much snow we've had

136
00:05:08,850 --> 00:05:09,480
and how cold it's been?

137
00:05:09,480 --> 00:05:11,560
He said, deer have been
starving this winter.

138
00:05:11,560 --> 00:05:12,630
And I think a couple
of the deer they'd had

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00:05:12,630 --> 00:05:13,960
had actually starved to death.

140
00:05:13,960 --> 00:05:15,001
And people had called up.

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00:05:15,001 --> 00:05:17,579
And they had come and kind
of collected the carcasses.

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00:05:17,579 --> 00:05:19,120
So anyway that was
my little trip out

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00:05:19,120 --> 00:05:23,410
to Mass Fish and
Wildlife yesterday.

144
00:05:23,410 --> 00:05:26,690
OK, so let's go back to
talking about the bone.

145
00:05:26,690 --> 00:05:29,490
And I think last time we kind
of left off more or less here.

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00:05:29,490 --> 00:05:33,740
So this was a slide of what
osteoporosis looks like.

147
00:05:33,740 --> 00:05:36,780
And you can see the bone
loss is a combination

148
00:05:36,780 --> 00:05:39,840
of thinning of the struts
and resorption of the struts.

149
00:05:39,840 --> 00:05:42,090
And we wanted to
try to model this,

150
00:05:42,090 --> 00:05:43,990
sort of an engineering sense.

151
00:05:43,990 --> 00:05:47,600
And the way we did that is we
used our voronoi honeycombs.

152
00:05:47,600 --> 00:05:50,110
So the bone has an
irregular structure.

153
00:05:50,110 --> 00:05:53,030
And we wanted to look and see
if we could model something that

154
00:05:53,030 --> 00:05:54,320
had an irregular structure.

155
00:05:54,320 --> 00:05:56,114
So we used the
voronoi honeycomb.

156
00:05:56,114 --> 00:05:57,530
And if you remember
when we talked

157
00:05:57,530 --> 00:05:59,980
about the structure
of cellular materials

158
00:05:59,980 --> 00:06:01,750
earlier on in the
course, we said

159
00:06:01,750 --> 00:06:05,510
that these are generated by
putting down random seed points

160
00:06:05,510 --> 00:06:08,050
and then drawing the
perpendicular bisectors.

161
00:06:08,050 --> 00:06:10,580
And if you have a constraint
that the seed points can't

162
00:06:10,580 --> 00:06:12,580
be closer than some
exclusion distance,

163
00:06:12,580 --> 00:06:16,330
then you get structure
where you have

164
00:06:16,330 --> 00:06:19,280
cells that are not all exactly
the same size, but roughly

165
00:06:19,280 --> 00:06:20,205
the same size.

166
00:06:20,205 --> 00:06:21,330
So that's what we did here.

167
00:06:21,330 --> 00:06:23,032
We got this structure here.

168
00:06:23,032 --> 00:06:24,740
And I had a graduate
student, Matt Silva,

169
00:06:24,740 --> 00:06:26,780
who did a lot of these studies.

170
00:06:26,780 --> 00:06:29,410
And then he used
this and analyzed it

171
00:06:29,410 --> 00:06:31,420
using finite element analysis.

172
00:06:31,420 --> 00:06:35,360
So the first thing he did was
he calculated the elastic moduli

173
00:06:35,360 --> 00:06:36,650
of the structure.

174
00:06:36,650 --> 00:06:38,220
So he applied loads.

175
00:06:38,220 --> 00:06:39,880
We calculated deformations.

176
00:06:39,880 --> 00:06:42,340
Figured out elastic moduli.

177
00:06:42,340 --> 00:06:46,590
And so this plot here
shows a comparison

178
00:06:46,590 --> 00:06:49,760
between the analytical
equations that we derived

179
00:06:49,760 --> 00:06:51,680
at the first part of
the course and what

180
00:06:51,680 --> 00:06:54,420
he calculated for these
voronoi honeycombs

181
00:06:54,420 --> 00:06:56,890
for the final element analysis.

182
00:06:56,890 --> 00:06:59,250
So here's Young's modulus
down here, for example.

183
00:06:59,250 --> 00:07:00,940
In the closed form,
the line, that's

184
00:07:00,940 --> 00:07:03,580
just the analytical
equation we had originally.

185
00:07:03,580 --> 00:07:06,880
And the little dashed line
is his finite element.

186
00:07:06,880 --> 00:07:08,960
Here's the Shear
modulus down here.

187
00:07:08,960 --> 00:07:11,712
And here's the
possum's ratio up here.

188
00:07:11,712 --> 00:07:13,670
So you can see, there's
a pretty good agreement

189
00:07:13,670 --> 00:07:15,950
between these two things here.

190
00:07:15,950 --> 00:07:19,720
So let me write some
of this on the board.

191
00:07:19,720 --> 00:07:21,600
And then I can keep
going after that.

192
00:07:39,010 --> 00:07:43,410
So for the 2D voronoi honeycomb,
we have the random seed points.

193
00:07:47,900 --> 00:07:49,685
And we used the
perpendicular bisectors.

194
00:07:57,500 --> 00:08:00,350
And we used a minimum separation
distance between the points.

195
00:08:14,330 --> 00:08:16,266
So we generated the structure.

196
00:08:16,266 --> 00:08:18,015
And then we did a
finite element analysis.

197
00:08:21,780 --> 00:08:23,600
And from that, we
calculated the modulus.

198
00:08:35,659 --> 00:08:38,600
And what we found was
the finite element

199
00:08:38,600 --> 00:08:42,200
analysis results were pretty
close to our closed form

200
00:08:42,200 --> 00:08:43,253
analytical model.

201
00:09:06,140 --> 00:09:07,730
And if we think
about the modulus,

202
00:09:07,730 --> 00:09:09,780
the modulus is the
average stiffness

203
00:09:09,780 --> 00:09:11,510
over the whole honeycomb.

204
00:09:11,510 --> 00:09:13,142
And when we look at
the strengths next,

205
00:09:13,142 --> 00:09:14,600
the strength is
going to be related

206
00:09:14,600 --> 00:09:18,020
to the weakest few struts.

207
00:09:18,020 --> 00:09:20,310
And we're going to find
that the strength doesn't

208
00:09:20,310 --> 00:09:21,440
work quite the same way.

209
00:10:17,300 --> 00:10:18,520
So first, we got the modulus.

210
00:10:18,520 --> 00:10:20,599
That's sort of the simplest
thing to calculate.

211
00:10:20,599 --> 00:10:22,390
And then after that,
we wanted to calculate

212
00:10:22,390 --> 00:10:25,370
the compressive strength.

213
00:10:25,370 --> 00:10:26,730
So we did a similar thing.

214
00:10:26,730 --> 00:10:30,050
We set up the voronoi honeycomb
in the finite element analysis.

215
00:10:30,050 --> 00:10:33,710
We had a few more elements
along the length of each strut.

216
00:10:33,710 --> 00:10:36,200
And then we modeled
the elastic buckling

217
00:10:36,200 --> 00:10:37,850
and the plastic
failure behavior.

218
00:10:37,850 --> 00:10:40,530
And we looked at honeycombs
that had different densities.

219
00:10:40,530 --> 00:10:42,770
And the lowest densities
failed by buckling.

220
00:10:42,770 --> 00:10:47,360
And the higher densities failed
by a sort of plastic yielding.

221
00:10:47,360 --> 00:10:50,300
And we assumed that the cell
walls were elastic, perfectly

222
00:10:50,300 --> 00:10:51,010
plastic.

223
00:10:51,010 --> 00:10:55,490
Remember we said if we have
a material where-- this

224
00:10:55,490 --> 00:10:58,720
is for the solids-- so say
this is the stress in the solid

225
00:10:58,720 --> 00:11:01,030
and that's the
strain in the solid.

226
00:11:01,030 --> 00:11:04,060
If it behaves like that, we
say that's elastic, perfectly

227
00:11:04,060 --> 00:11:04,560
plastic.

228
00:11:04,560 --> 00:11:08,240
So we modeled the walls as
elastic, perfectly plastic.

229
00:11:08,240 --> 00:11:10,260
And we made the ratio
of the solid modulus

230
00:11:10,260 --> 00:11:12,810
to the yield strength
similar to what it would be

231
00:11:12,810 --> 00:11:16,120
for bone, which is about 0.01.

232
00:11:16,120 --> 00:11:18,220
And for that particular
value, the transition

233
00:11:18,220 --> 00:11:21,710
between the elastic buckling
and the plastic yielding failure

234
00:11:21,710 --> 00:11:24,604
was at a relative
density of about 0.035.

235
00:11:24,604 --> 00:11:26,520
So then what we did was
we analyzed structures

236
00:11:26,520 --> 00:11:28,630
that were a little lower
than that were equal to that

237
00:11:28,630 --> 00:11:29,710
and then a little
higher than that.

238
00:11:29,710 --> 00:11:31,251
So we would try and
see what happened

239
00:11:31,251 --> 00:11:32,720
with these different
failure modes.

240
00:11:32,720 --> 00:11:38,080
And then we found that if we
look at the compressive stress

241
00:11:38,080 --> 00:11:44,200
strain curve, this model here
had a relative density of 15%.

242
00:11:44,200 --> 00:11:47,420
And the transition occurred at
a relative density about 3.5%.

243
00:11:47,420 --> 00:11:50,040
So this one here failed
by a plastic failure.

244
00:11:50,040 --> 00:11:52,290
You can see, if we
unload it, there's

245
00:11:52,290 --> 00:11:54,330
some plastic deformation.

246
00:11:54,330 --> 00:11:56,020
We get a little
strange softening here,

247
00:11:56,020 --> 00:11:58,710
which is kind of characteristic
of the plastic failure.

248
00:11:58,710 --> 00:12:01,180
When we look at the overall
deformation of the honeycomb,

249
00:12:01,180 --> 00:12:03,920
we saw local kind
of failure, like we

250
00:12:03,920 --> 00:12:05,449
do in aluminum honeycombs.

251
00:12:05,449 --> 00:12:06,990
So that was the kind
of stress strain

252
00:12:06,990 --> 00:12:11,300
curve for a relatively
dense honeycomb that

253
00:12:11,300 --> 00:12:12,600
failed by yielding.

254
00:12:12,600 --> 00:12:15,060
And then this is one for
a much lower density.

255
00:12:15,060 --> 00:12:18,670
This is now point 1.5%.

256
00:12:18,670 --> 00:12:20,440
And this one fails
by elastic buckling.

257
00:12:20,440 --> 00:12:22,070
And if we load it
up and unload it,

258
00:12:22,070 --> 00:12:26,160
we recover most of
the deformation.

259
00:12:26,160 --> 00:12:30,440
Barry, do you think you
could make that stop?

260
00:12:30,440 --> 00:12:32,136
Yeah.

261
00:12:32,136 --> 00:12:34,970
AUDIENCE: There's a
chance it could be--

262
00:12:34,970 --> 00:12:36,390
LORNA GIBSON: Below.

263
00:12:36,390 --> 00:12:37,850
Just because we're recording it.

264
00:12:37,850 --> 00:12:39,230
It just doesn't seem very good.

265
00:12:41,870 --> 00:12:45,110
OK, so what we did was we
made five different voronoi

266
00:12:45,110 --> 00:12:45,640
honeycomb.

267
00:12:45,640 --> 00:12:47,300
So we had five sets
of seed points.

268
00:12:47,300 --> 00:12:50,150
And we had five slightly
different geometries.

269
00:12:50,150 --> 00:12:52,690
And then we averaged
the results of those.

270
00:12:52,690 --> 00:12:55,880
So if we make that
calculation, this

271
00:12:55,880 --> 00:12:59,160
is the strength of the
voronoi honeycomb here divided

272
00:12:59,160 --> 00:13:03,260
by the strength of the periodic
regular hexagonal honeycomb.

273
00:13:03,260 --> 00:13:05,750
And this was plotted
against relative density.

274
00:13:05,750 --> 00:13:08,980
And you can see the strengths
for the voronoi structure are

275
00:13:08,980 --> 00:13:12,580
a little bit lower than for
the regular periodic hexagonal

276
00:13:12,580 --> 00:13:13,520
honeycomb.

277
00:13:13,520 --> 00:13:15,090
And they reach a minimum here.

278
00:13:15,090 --> 00:13:18,900
And the minimum's around
about 0.05 relative density.

279
00:13:18,900 --> 00:13:20,720
So this was the 1.5.

280
00:13:20,720 --> 00:13:22,280
That was a 3.5.

281
00:13:22,280 --> 00:13:25,210
That's 5% and 15%.

282
00:13:25,210 --> 00:13:30,967
AUDIENCE: Why is there like
a wide gap between 0.05 and--

283
00:13:30,967 --> 00:13:32,550
LORNA GIBSON: Well,
I think because we

284
00:13:32,550 --> 00:13:35,112
felt-- I think this one failed
by some combination of-- there

285
00:13:35,112 --> 00:13:37,320
was a limit to how many of
these we were going to do.

286
00:13:37,320 --> 00:13:39,140
And this is what we chose to do.

287
00:13:39,140 --> 00:13:40,640
We wanted one that
we knew was going

288
00:13:40,640 --> 00:13:41,840
to fail by plastic yielding.

289
00:13:41,840 --> 00:13:42,670
And that was this one.

290
00:13:42,670 --> 00:13:43,850
And we wanted one that
we knew it was going

291
00:13:43,850 --> 00:13:45,016
to fail by elastic buckling.

292
00:13:45,016 --> 00:13:46,800
And we wanted a
couple in between.

293
00:13:46,800 --> 00:13:48,830
So we didn't do--
I guess we were

294
00:13:48,830 --> 00:13:52,040
lazy is the real reason there's
not another point in the middle

295
00:13:52,040 --> 00:13:52,540
there.

296
00:13:52,540 --> 00:13:55,194
AUDIENCE: It just seems like
there might be a variable--

297
00:13:55,194 --> 00:13:57,860
LORNA GIBSON: You think it might
go [CAREENING NOISE] like that.

298
00:13:57,860 --> 00:13:59,960
Except there's a physical
reason why this happens.

299
00:13:59,960 --> 00:14:02,177
And I'm going to get
to that in a minute.

300
00:14:02,177 --> 00:14:03,760
So let me I'll finish
explaining this,

301
00:14:03,760 --> 00:14:07,080
and then I'll put the
notes on the board.

302
00:14:07,080 --> 00:14:09,409
So first of all,
the strength is less

303
00:14:09,409 --> 00:14:10,950
than the regular
hexagonal honeycomb.

304
00:14:10,950 --> 00:14:12,575
And then there's also
this minimum here

305
00:14:12,575 --> 00:14:15,580
around about 5% density.

306
00:14:15,580 --> 00:14:18,650
And I think the reason that
the strength is not the same

307
00:14:18,650 --> 00:14:21,700
as in the voronoi in
the periodic honeycomb

308
00:14:21,700 --> 00:14:25,140
is because if you look at
the distribution of strains--

309
00:14:25,140 --> 00:14:27,340
or you can think of the
distribution of stresses--

310
00:14:27,340 --> 00:14:31,340
so these were the normal strains
at the nodes in the honeycombs.

311
00:14:31,340 --> 00:14:34,464
And the distribution here is
for the voronoi honeycomb.

312
00:14:34,464 --> 00:14:35,880
So the voronoi
honeycomb, you have

313
00:14:35,880 --> 00:14:37,260
lots of members of
different lengths.

314
00:14:37,260 --> 00:14:38,690
There are different
orientations.

315
00:14:38,690 --> 00:14:41,880
And so there's some distribution
of stresses and strains

316
00:14:41,880 --> 00:14:43,090
in each member.

317
00:14:43,090 --> 00:14:44,950
And that gives you
the distribution.

318
00:14:44,950 --> 00:14:50,040
In the regular
hexagonal honeycomb,

319
00:14:50,040 --> 00:14:52,670
if you look at just
the nodes, there's

320
00:14:52,670 --> 00:14:55,500
really just the vertical member,
which has a certain strain.

321
00:14:55,500 --> 00:14:57,083
And all the vertical
members are going

322
00:14:57,083 --> 00:14:58,680
to have the same
strain at the nodes.

323
00:14:58,680 --> 00:15:02,010
And then the obliques members,
if you just look at the nodes,

324
00:15:02,010 --> 00:15:03,840
there's just going to
be a maximum tension

325
00:15:03,840 --> 00:15:07,110
and a maximum
compression at the nodes.

326
00:15:07,110 --> 00:15:08,910
Because there's a unit
cell and it repeats,

327
00:15:08,910 --> 00:15:10,625
all the oblique ones are
going to have the same maximum

328
00:15:10,625 --> 00:15:11,820
and the same minimum.

329
00:15:11,820 --> 00:15:14,650
So the dashed lines here are
for the regular hexagonal

330
00:15:14,650 --> 00:15:15,420
honeycomb.

331
00:15:15,420 --> 00:15:18,650
So the thing to observe
here is that the voronoi has

332
00:15:18,650 --> 00:15:21,250
some strains and
correspondingly some

333
00:15:21,250 --> 00:15:23,950
stresses that are
outside the range

334
00:15:23,950 --> 00:15:27,000
of the regular
periodic honeycomb.

335
00:15:27,000 --> 00:15:29,510
And so if there's parts of it
that are seeing higher strains

336
00:15:29,510 --> 00:15:32,370
and higher stresses, it's
going to fail at a lower load.

337
00:15:32,370 --> 00:15:34,162
So I think it's
this distribution

338
00:15:34,162 --> 00:15:35,870
because you've got
this random structure,

339
00:15:35,870 --> 00:15:39,190
and you've got different lengths
and different orientations

340
00:15:39,190 --> 00:15:40,340
of the members.

341
00:15:40,340 --> 00:15:44,950
So that's one reason why
these strengths are less

342
00:15:44,950 --> 00:15:47,490
than the periodic structure.

343
00:15:47,490 --> 00:15:51,016
I think there's a
minimum here, because-- I

344
00:15:51,016 --> 00:15:52,390
think before the
test I mentioned

345
00:15:52,390 --> 00:15:55,300
there's some interaction between
elastic buckling and plastic

346
00:15:55,300 --> 00:15:56,190
yielding.

347
00:15:56,190 --> 00:15:58,310
And when you get
that interaction,

348
00:15:58,310 --> 00:16:00,320
that also reduces the strength.

349
00:16:00,320 --> 00:16:03,220
And so there's a
minimum near where

350
00:16:03,220 --> 00:16:05,690
the crossover is between
the elastic buckling

351
00:16:05,690 --> 00:16:07,670
and the plastic yielding.

352
00:16:07,670 --> 00:16:10,070
So let me write some notes
of the compressive strength.

353
00:16:14,370 --> 00:16:32,680
So we'll say the cell wall--
so the cell wall elastic,

354
00:16:32,680 --> 00:16:35,380
perfectly plastic.

355
00:16:35,380 --> 00:16:39,100
And the yield strength relative
to the modulus for the solid

356
00:16:39,100 --> 00:16:44,290
was 0.1, which is pretty
much what it is for bone.

357
00:16:44,290 --> 00:16:52,210
And we assumed that the possum's
ratio of the solid was 0.3.

358
00:16:52,210 --> 00:16:59,830
And for this value
of sigma Ys over Es,

359
00:16:59,830 --> 00:17:10,430
the transition between elastic
buckling and plastic yielding

360
00:17:10,430 --> 00:17:13,060
is at about 3.5%
relative density.

361
00:17:28,200 --> 00:17:29,890
So then we made
models with densities

362
00:17:29,890 --> 00:17:31,730
that were a little bit less
than that and a little bit more

363
00:17:31,730 --> 00:17:32,348
than that.

364
00:19:04,944 --> 00:19:06,860
And then the strengths
we got from the voronoi

365
00:19:06,860 --> 00:19:10,221
were between about
0.6 and 0.8 times

366
00:19:10,221 --> 00:19:11,470
what we got from the periodic.

367
00:19:29,190 --> 00:19:31,430
So then what we looked at
were these maximum strains

368
00:19:31,430 --> 00:19:32,870
of the nodes.

369
00:19:32,870 --> 00:19:36,230
And we found that because
the voronoi honeycomb

370
00:19:36,230 --> 00:19:38,780
had a much broader distribution
of those strains, that

371
00:19:38,780 --> 00:19:39,960
led to the lower strengths.

372
00:21:22,957 --> 00:21:24,540
And then we found
the minimum strength

373
00:21:24,540 --> 00:21:25,900
was at a density of about 5%.

374
00:21:47,170 --> 00:21:50,640
And if you think just
about a pin ended column,

375
00:21:50,640 --> 00:21:54,000
and you make a plot
of the strength--

376
00:21:54,000 --> 00:21:56,400
so I'm just going
to say the strength

377
00:21:56,400 --> 00:22:00,420
of that columm-- against
l/r, the slenderness ratio.

378
00:22:00,420 --> 00:22:02,336
So say it's a cylinder,
l would be the length.

379
00:22:02,336 --> 00:22:04,540
r would be the radius.

380
00:22:04,540 --> 00:22:07,014
If you just had
Euler buckling, you

381
00:22:07,014 --> 00:22:08,430
get a curve that
looked like that.

382
00:22:08,430 --> 00:22:15,410
The Euler buckling load is pi
squared EI over l. squared.

383
00:22:15,410 --> 00:22:17,630
So I goes as r to the 4th.

384
00:22:17,630 --> 00:22:20,131
And if we get the
stress, then it's

385
00:22:20,131 --> 00:22:22,255
going to be that divided
by the area of the column.

386
00:22:22,255 --> 00:22:27,400
So it's pi squared
E. Moment of inertia

387
00:22:27,400 --> 00:22:31,180
is pi r to the 4th
over 4 l squared.

388
00:22:31,180 --> 00:22:32,620
And the area is pi r squared.

389
00:22:38,870 --> 00:22:42,970
So it goes is as r over l
squared, or 1 over l over r

390
00:22:42,970 --> 00:22:43,830
squared.

391
00:22:43,830 --> 00:22:45,330
So this would be
the Euler buckling.

392
00:22:45,330 --> 00:22:46,455
So that's elastic buckling.

393
00:22:51,900 --> 00:22:53,900
But at some point, the
column is going to yield.

394
00:22:53,900 --> 00:22:56,310
If I make it really,
really short, then it's

395
00:22:56,310 --> 00:22:58,340
going to yield
before it buckles.

396
00:22:58,340 --> 00:23:01,860
And at some point, this would
be the real stress here.

397
00:23:01,860 --> 00:23:04,605
And this would be failure
by the plastic yielding.

398
00:23:09,570 --> 00:23:12,240
And in practice, there's not
like a sharp corner here.

399
00:23:12,240 --> 00:23:15,489
You know, if you made columns
of progressively longer length,

400
00:23:15,489 --> 00:23:17,780
and you tested them, the
little short ones would yield.

401
00:23:17,780 --> 00:23:19,470
So they'd be along here.

402
00:23:19,470 --> 00:23:22,700
But they don't kind of yield
and the next one buckles.

403
00:23:22,700 --> 00:23:24,370
In fact, you get
something like that.

404
00:23:24,370 --> 00:23:27,070
So that when you're near
that transition, when you're

405
00:23:27,070 --> 00:23:29,665
near this point here,
the actual failure stress

406
00:23:29,665 --> 00:23:32,010
is a little bit less than that.

407
00:23:32,010 --> 00:23:34,482
And I think that's partly
what's going on over there.

408
00:23:34,482 --> 00:23:35,190
It's the minimum.

409
00:23:40,900 --> 00:23:43,420
OK, so those two
studies, we just

410
00:23:43,420 --> 00:23:47,870
looked at the modeling and
the strength of honeycombs.

411
00:23:47,870 --> 00:23:51,520
And we were kind of looking at
how does the random structure

412
00:23:51,520 --> 00:23:53,124
change the properties.

413
00:23:53,124 --> 00:23:54,540
So the randomness
of the structure

414
00:23:54,540 --> 00:23:56,750
didn't really change
the modulus much at all.

415
00:23:56,750 --> 00:23:59,274
But it did affect the strength.

416
00:23:59,274 --> 00:24:00,690
And then the next
thing we did was

417
00:24:00,690 --> 00:24:03,430
we looked at putting
defects into the bone.

418
00:24:03,430 --> 00:24:06,230
So we knew that the
bone, partly the density

419
00:24:06,230 --> 00:24:08,540
is reduced by
thinning of the struts

420
00:24:08,540 --> 00:24:11,610
and partly by resorption
when there's a lot of density

421
00:24:11,610 --> 00:24:13,065
loss, a lot of bone loss.

422
00:24:13,065 --> 00:24:15,440
So we wanted to look at putting
defects where we actually

423
00:24:15,440 --> 00:24:17,040
removed some of the struts.

424
00:24:17,040 --> 00:24:21,810
So we did another series
of voronoi models.

425
00:24:27,800 --> 00:24:30,000
So we did another
series of tests

426
00:24:30,000 --> 00:24:34,410
where we looked at it if we have
a certain density that we start

427
00:24:34,410 --> 00:24:37,760
with and then we look at
losing the same bone mass

428
00:24:37,760 --> 00:24:40,150
or relative density
in our honeycomb,

429
00:24:40,150 --> 00:24:43,550
and we look at what happens if
we thin the struts versus if we

430
00:24:43,550 --> 00:24:45,010
remove struts.

431
00:24:45,010 --> 00:24:46,870
So these plots here show that.

432
00:24:46,870 --> 00:24:48,660
And Matt Silva also did this.

433
00:24:48,660 --> 00:24:52,060
So this is the residual modulus
plotted against the reduction

434
00:24:52,060 --> 00:24:53,570
in relative density.

435
00:24:53,570 --> 00:24:55,550
So residual modulus
is the modulus

436
00:24:55,550 --> 00:24:57,780
after we've reduced the
density by some amount

437
00:24:57,780 --> 00:25:00,540
relative to the initial modulus.

438
00:25:00,540 --> 00:25:03,220
And if we have an intact
honeycomb where we just

439
00:25:03,220 --> 00:25:05,930
thin the struts, we don't
remove any of the struts,

440
00:25:05,930 --> 00:25:09,670
if we have an intact honeycomb,
as you reduce the density,

441
00:25:09,670 --> 00:25:11,822
the modulus just
goes down like that.

442
00:25:11,822 --> 00:25:14,280
So that's really just the same
as those analytical formulas

443
00:25:14,280 --> 00:25:15,500
that we had.

444
00:25:15,500 --> 00:25:16,900
But if you start
removing struts,

445
00:25:16,900 --> 00:25:20,000
not too surprisingly,
the modulus

446
00:25:20,000 --> 00:25:22,410
goes down substantially more.

447
00:25:22,410 --> 00:25:26,630
And at this value here, I
think it was 30% or 35% density

448
00:25:26,630 --> 00:25:29,220
reduction, you reach what's
called the percolation

449
00:25:29,220 --> 00:25:29,910
threshold.

450
00:25:29,910 --> 00:25:31,430
At the percolation
threshold, you

451
00:25:31,430 --> 00:25:33,710
have two separate
pieces of material.

452
00:25:33,710 --> 00:25:35,620
So obviously the
mechanical properties

453
00:25:35,620 --> 00:25:38,119
are going to go down to zero
when you reach that percolation

454
00:25:38,119 --> 00:25:38,639
threshold.

455
00:25:38,639 --> 00:25:40,930
And then this plot over here
is the same sort of thing,

456
00:25:40,930 --> 00:25:42,010
but now for strength.

457
00:25:42,010 --> 00:25:43,840
So it's the strength
of the bone,

458
00:25:43,840 --> 00:25:46,570
or the strength
of the honeycomb,

459
00:25:46,570 --> 00:25:48,380
after you've either
thinned or resorbed

460
00:25:48,380 --> 00:25:50,850
the wall, divided
by the strength

461
00:25:50,850 --> 00:25:52,080
of the intact honeycomb.

462
00:25:52,080 --> 00:25:54,820
And again, you're
reducing the density here.

463
00:25:54,820 --> 00:25:57,200
And this is for the intact
model where you're just

464
00:25:57,200 --> 00:25:58,850
thinning the struts.

465
00:25:58,850 --> 00:26:01,690
And this is for the models where
you're removing the struts.

466
00:26:01,690 --> 00:26:04,140
So you can see that
if you think of-- this

467
00:26:04,140 --> 00:26:06,701
is kind of a simple model,
but if you think of the bone,

468
00:26:06,701 --> 00:26:08,200
if you first thin
the struts, you're

469
00:26:08,200 --> 00:26:09,640
going to lose a little
bit of strength.

470
00:26:09,640 --> 00:26:11,400
But then if you start
removing the struts,

471
00:26:11,400 --> 00:26:13,024
you're going to lose
a lot of strength.

472
00:26:13,024 --> 00:26:15,630
So that's really where
people run into-- there's

473
00:26:15,630 --> 00:26:18,230
much higher risk of fracture
once you get to the point

474
00:26:18,230 --> 00:26:22,017
where you might be
resorbing struts.

475
00:26:27,280 --> 00:26:33,090
OK, so let me see,
what's next thing?

476
00:26:33,090 --> 00:26:34,930
OK, let me just
finish the slides,

477
00:26:34,930 --> 00:26:36,290
and then I'll put the notes up.

478
00:26:36,290 --> 00:26:37,706
So this is the
same sort of thing,

479
00:26:37,706 --> 00:26:40,450
just plotting the strength and
the modulus on the same plot.

480
00:26:40,450 --> 00:26:42,790
So you can see the shape of
the curves is very similar.

481
00:26:42,790 --> 00:26:45,700
The modulus is a little bit more
sensitive than the strength.

482
00:26:45,700 --> 00:26:47,900
And here we are
thinning, and here we

483
00:26:47,900 --> 00:26:51,850
are removing the struts.

484
00:26:51,850 --> 00:26:54,930
And then the next step was
that we made a model that

485
00:26:54,930 --> 00:26:56,074
was more similar to bones.

486
00:26:56,074 --> 00:26:57,740
So let me write down
the notes for this.

487
00:26:57,740 --> 00:27:00,031
And then we'll do that one
that's more similar to bone.

488
00:28:47,405 --> 00:28:48,655
Thought it didn't makes sense.

489
00:30:39,650 --> 00:30:42,269
OK, so then we were
interested in trying

490
00:30:42,269 --> 00:30:44,060
to model something that
was a little closer

491
00:30:44,060 --> 00:30:45,266
to the structure of bone.

492
00:30:58,760 --> 00:31:00,840
And so we set up
this model here.

493
00:31:00,840 --> 00:31:02,950
So we started with
just a square voronoi.

494
00:31:02,950 --> 00:31:06,660
So you just force the points
into a square, voronoi,

495
00:31:06,660 --> 00:31:09,322
or a square pattern, you
get a square voronoi.

496
00:31:09,322 --> 00:31:11,030
And then what we did
is we just perturbed

497
00:31:11,030 --> 00:31:12,350
the points a little bit.

498
00:31:12,350 --> 00:31:15,440
And we got this
perturbed voronoi array.

499
00:31:15,440 --> 00:31:18,740
And so we made this model here.

500
00:31:18,740 --> 00:31:21,600
And we took a piece
of vertebral bone.

501
00:31:21,600 --> 00:31:24,280
And we measured the
angle of orientation

502
00:31:24,280 --> 00:31:25,690
of a lot of the struts.

503
00:31:25,690 --> 00:31:30,060
And we matched our voronoi
model to that distribution

504
00:31:30,060 --> 00:31:31,330
in the bone.

505
00:31:31,330 --> 00:31:33,260
So our model looked
something like this.

506
00:31:33,260 --> 00:31:35,400
So you can kind of
see how it's more

507
00:31:35,400 --> 00:31:38,280
or less vertical and
horizontal, but not exactly.

508
00:31:38,280 --> 00:31:42,205
And here's a sort of comparison
with a slice of vertebral bone.

509
00:31:42,205 --> 00:31:44,080
And again, because the
loads are more or less

510
00:31:44,080 --> 00:31:46,430
vertical in the
bone, the trabeculae

511
00:31:46,430 --> 00:31:47,470
tend to orient that way.

512
00:31:47,470 --> 00:31:49,557
And then have some
horizontal struts.

513
00:31:49,557 --> 00:31:51,140
So here you can see
on the left, we've

514
00:31:51,140 --> 00:31:54,761
got a voronoi model that's
more or less representative

515
00:31:54,761 --> 00:31:55,260
of the bone.

516
00:31:55,260 --> 00:31:57,330
And we've removed
some of the struts.

517
00:31:57,330 --> 00:31:59,371
So we're going to the same
thing with this model.

518
00:31:59,371 --> 00:32:00,270
We thin the struts.

519
00:32:00,270 --> 00:32:01,660
And we remove the struts.

520
00:32:01,660 --> 00:32:03,970
And we try to see what
the residual strength is.

521
00:32:03,970 --> 00:32:06,570
And you can see there's for
of at least a 2d model this

522
00:32:06,570 --> 00:32:11,950
isn't a bad representation of
the vertebral trabecular bone.

523
00:32:11,950 --> 00:32:14,220
And this was the
stress strain curve

524
00:32:14,220 --> 00:32:17,780
for both the specimen of
the vertebral bone that

525
00:32:17,780 --> 00:32:21,490
was tested and then the
honeycomb model that we

526
00:32:21,490 --> 00:32:23,430
made to kind of match it.

527
00:32:23,430 --> 00:32:25,410
So a similar kind of behavior.

528
00:32:25,410 --> 00:32:29,010
This is how our model failed,
this sort of a local band

529
00:32:29,010 --> 00:32:31,050
of struts that fail.

530
00:32:31,050 --> 00:32:33,500
Let's call it local
deformation band.

531
00:32:33,500 --> 00:32:36,540
And then what we
did was we thought

532
00:32:36,540 --> 00:32:37,870
about changing the density.

533
00:32:37,870 --> 00:32:40,180
And what we did was we
removed either horizontal

534
00:32:40,180 --> 00:32:43,930
or vertical struts, or we
thinned either the vertical

535
00:32:43,930 --> 00:32:45,470
or the horizontal struts.

536
00:32:45,470 --> 00:32:47,890
So these are the same kinds
of plots as I showed before.

537
00:32:47,890 --> 00:32:49,430
This is the residual modulus.

538
00:32:49,430 --> 00:32:51,330
This is the residual strength.

539
00:32:51,330 --> 00:32:53,210
This is the density reduction.

540
00:32:53,210 --> 00:32:55,570
And here we're
reducing the density

541
00:32:55,570 --> 00:32:57,620
by making struts thinner.

542
00:32:57,620 --> 00:32:58,740
So it's still intact.

543
00:32:58,740 --> 00:32:59,990
We haven't removed any struts.

544
00:32:59,990 --> 00:33:02,480
But each of the
struts gets thinner.

545
00:33:02,480 --> 00:33:09,052
And this top line is for
thinning the longitudinal

546
00:33:09,052 --> 00:33:10,010
or the vertical struts.

547
00:33:10,010 --> 00:33:13,560
And this was for thinning
the transverse or horizontal

548
00:33:13,560 --> 00:33:14,290
struts.

549
00:33:14,290 --> 00:33:16,160
And then this is for
removing struts here.

550
00:33:16,160 --> 00:33:18,100
So we're removing
a bigger number.

551
00:33:18,100 --> 00:33:20,950
So the more we remove, the
more the density changes.

552
00:33:20,950 --> 00:33:23,560
And then this plot here
is for the strength.

553
00:33:23,560 --> 00:33:25,020
So again, this is thinning.

554
00:33:25,020 --> 00:33:26,650
So we're moving
either the horizontal

555
00:33:26,650 --> 00:33:28,185
or the vertical
ones-- I'm sorry,

556
00:33:28,185 --> 00:33:30,560
thinning either the horizontal
ones or the vertical ones.

557
00:33:30,560 --> 00:33:32,800
And then this is
for removing struts.

558
00:33:32,800 --> 00:33:37,205
And again removing more to
reduce the density more.

559
00:33:37,205 --> 00:33:38,580
So you can kind
of see we're kind

560
00:33:38,580 --> 00:33:42,840
of working our way to
more complex models here.

561
00:33:42,840 --> 00:33:44,836
So this one here was
looking at the bone.

562
00:33:44,836 --> 00:33:46,210
Let me write some
notes for this.

563
00:33:46,210 --> 00:33:47,950
And then we did a
3D voronoi model.

564
00:33:47,950 --> 00:33:50,860
So I'll do that one next.

565
00:33:50,860 --> 00:33:53,690
Oop, over here.

566
00:33:53,690 --> 00:33:56,480
So I'll just say the
model was adapted

567
00:33:56,480 --> 00:33:59,210
to reflect the trabecular bones
study in the vertebrae more.

568
00:34:56,760 --> 00:35:02,130
So we perturb a square
with array of seed points

569
00:35:02,130 --> 00:35:04,180
to get a structure that
was more like the bone.

570
00:35:34,860 --> 00:35:40,030
And then we looked at the
reduction in the thickness

571
00:35:40,030 --> 00:35:43,691
and the number of strides in
the longitudinal and transverse

572
00:35:43,691 --> 00:35:44,190
directions.

573
00:36:38,700 --> 00:36:43,220
OK, and then the next model
we did was the 3D version.

574
00:36:43,220 --> 00:36:44,790
So we made a same kind of thing.

575
00:36:44,790 --> 00:36:49,140
But with the 3D model, we had
fewer cells in that model,

576
00:36:49,140 --> 00:36:50,880
because once it
goes to 3D, you've

577
00:36:50,880 --> 00:36:54,136
got more struts in each cell.

578
00:36:54,136 --> 00:36:55,260
But this was the same idea.

579
00:36:55,260 --> 00:36:59,106
We uniformly thinned the struts,
or we removed the struts.

580
00:36:59,106 --> 00:37:00,980
And again, you can see
removing the struts is

581
00:37:00,980 --> 00:37:02,134
a much bigger effect.

582
00:37:02,134 --> 00:37:03,800
And also the other
thing to look at here

583
00:37:03,800 --> 00:37:07,130
is for 3D the percolation
threshold is 50%.

584
00:37:07,130 --> 00:37:09,144
So it kind of makes
sense that if it's in 3D,

585
00:37:09,144 --> 00:37:10,810
and you've got struts
in all directions,

586
00:37:10,810 --> 00:37:13,196
you're going to have
to remove more of them.

587
00:37:13,196 --> 00:37:14,820
You're going to reduce
the density more

588
00:37:14,820 --> 00:37:18,370
to break it into two separate
pieces at the percolation

589
00:37:18,370 --> 00:37:19,280
threshold.

590
00:37:19,280 --> 00:37:23,140
So that was the 3D model there.

591
00:37:23,140 --> 00:37:26,210
And then this is just
a comparison of the 3D

592
00:37:26,210 --> 00:37:27,710
with the 2D for the modulus.

593
00:37:27,710 --> 00:37:29,740
We just did the modulus
for the 3D structure

594
00:37:29,740 --> 00:37:33,050
because it sort of gets
computationally more involved.

595
00:37:33,050 --> 00:37:36,300
So the 3D, these two
lines here corresponded

596
00:37:36,300 --> 00:37:39,500
to removing the struts and
the change in the modulus.

597
00:37:39,500 --> 00:37:43,740
And the little triangles were
the 3D voronoi calculation

598
00:37:43,740 --> 00:37:44,830
that we did.

599
00:37:44,830 --> 00:37:48,770
The little crosses here were
the same sort of calculation

600
00:37:48,770 --> 00:37:51,310
done for tetratridecahedron.

601
00:37:51,310 --> 00:37:54,380
One of my former
students had loaded that.

602
00:37:54,380 --> 00:37:58,710
And then at the bottom
here are the lines

603
00:37:58,710 --> 00:38:02,260
for the 2D structures, for
either a regular hexagonal cell

604
00:38:02,260 --> 00:38:03,714
or for a 2D voronoi cell.

605
00:38:03,714 --> 00:38:05,630
And you can see, there's
not a huge difference

606
00:38:05,630 --> 00:38:07,770
whether or not you take
a regular structure

607
00:38:07,770 --> 00:38:09,910
or a voronoi random structure.

608
00:38:09,910 --> 00:38:12,620
But there's a fairly
significant difference

609
00:38:12,620 --> 00:38:13,790
between the 2D and the 3D.

610
00:38:13,790 --> 00:38:17,310
So the 3D, just you have
to remove more material

611
00:38:17,310 --> 00:38:20,886
before you get the same
reduction in modulus.

612
00:38:20,886 --> 00:38:22,920
So let me write
some notes for that.

613
00:38:36,860 --> 00:38:38,370
So it's the same
kind of analysis,

614
00:38:38,370 --> 00:38:39,860
but just with a 3D model.

615
00:39:57,010 --> 00:39:59,070
So do you see the idea
with these models?

616
00:39:59,070 --> 00:40:01,850
It was an attempt
to look at a way

617
00:40:01,850 --> 00:40:07,220
that you could computationally
estimate how much modulus loss

618
00:40:07,220 --> 00:40:10,610
or strength loss you get by
either thinning the struts

619
00:40:10,610 --> 00:40:12,000
or removing the struts.

620
00:40:12,000 --> 00:40:16,350
So I gave you a way to
model the osteoperotic bone.

621
00:40:19,090 --> 00:40:19,718
Yes.

622
00:40:19,718 --> 00:40:22,651
AUDIENCE: Can you clarify
the percolation threshold?

623
00:40:22,651 --> 00:40:24,400
LORNA GIBSON: So the
percolation threshold

624
00:40:24,400 --> 00:40:27,480
is say you have some network
and you start removing things.

625
00:40:27,480 --> 00:40:31,030
If your remove enough, you have
two separate pieces of things.

626
00:40:31,030 --> 00:40:35,320
If you remove enough struts,
you have two separate pieces.

627
00:40:35,320 --> 00:40:38,090
That's called the
percolation threshold.

628
00:40:38,090 --> 00:40:40,627
So I think it's-- you want
to know why it's called that?

629
00:40:40,627 --> 00:40:42,460
So I think that originated
because it wasn't

630
00:40:42,460 --> 00:40:43,900
used in this kind of context.

631
00:40:43,900 --> 00:40:46,400
I think instead it
was used in a context

632
00:40:46,400 --> 00:40:51,080
where imagine you have 2D plate.

633
00:40:51,080 --> 00:40:54,080
So you put 2D holes in
it, little circular holes.

634
00:40:54,080 --> 00:40:57,797
And they we're looking at flow
of a fluid through the plate.

635
00:40:57,797 --> 00:40:59,630
So you can imagine, if
you put enough holes,

636
00:40:59,630 --> 00:41:01,339
eventually they line
up or they-- line up

637
00:41:01,339 --> 00:41:03,421
is not the right term--
but there's enough of them

638
00:41:03,421 --> 00:41:04,390
that they connect.

639
00:41:04,390 --> 00:41:05,764
And you end up
with two separate.

640
00:41:05,764 --> 00:41:07,864
You have a path
through for the fluid.

641
00:41:07,864 --> 00:41:09,530
That's called the
percolation threshold.

642
00:41:09,530 --> 00:41:12,740
But in mechanics it's sort
of two separate pieces.

643
00:41:12,740 --> 00:41:14,490
OK, does that makes sense?

644
00:41:14,490 --> 00:41:16,290
So you know, at the
percolation threshold,

645
00:41:16,290 --> 00:41:19,360
the stiffness is zero because
you have two separate things

646
00:41:19,360 --> 00:41:22,408
and the strength is 0.

647
00:41:22,408 --> 00:41:26,910
AUDIENCE: So the two doesn't
have to be like separated by--

648
00:41:26,910 --> 00:41:29,890
LORNA GIBSON: It
could be-- yeah, yeah,

649
00:41:29,890 --> 00:41:32,454
it doesn't have to
be a straight line.

650
00:41:32,454 --> 00:41:33,870
AUDIENCE: Does it
make a threshold

651
00:41:33,870 --> 00:41:36,610
between whether everything
is interconnected?

652
00:41:36,610 --> 00:41:37,640
LORNA GIBSON: Yes.

653
00:41:37,640 --> 00:41:39,960
Or there's some path
that separates them.

654
00:41:39,960 --> 00:41:42,410
Yeah, that's what it is.

655
00:41:42,410 --> 00:41:44,860
OK, so that's the end of
the bit on osteoporosis.

656
00:41:44,860 --> 00:41:48,430
I had a couple more things I
wanted to talk about on bone.

657
00:41:48,430 --> 00:41:52,490
So the next part is on the idea
of using metal foams as a bone

658
00:41:52,490 --> 00:41:54,280
substitute materials.

659
00:41:54,280 --> 00:41:58,490
So when they make hip implants--
so they're typically metals.

660
00:41:58,490 --> 00:42:00,920
They're titanium or
stainless steel or something.

661
00:42:00,920 --> 00:42:04,570
Often what they do is they
coat the outside with some sort

662
00:42:04,570 --> 00:42:06,010
of porous coating.

663
00:42:06,010 --> 00:42:07,560
And the idea is
the porous coating

664
00:42:07,560 --> 00:42:09,260
allows the bone to grow in.

665
00:42:09,260 --> 00:42:12,300
So you can kind of imagine,
like especially on the stem

666
00:42:12,300 --> 00:42:15,860
and around the head of a
femur, you'd like the bone

667
00:42:15,860 --> 00:42:17,840
to grow into that to attach.

668
00:42:17,840 --> 00:42:20,217
And having a porous
coating helps.

669
00:42:20,217 --> 00:42:22,300
And there's a couple of
ways they do it currently.

670
00:42:22,300 --> 00:42:24,320
They use porous sintered beads.

671
00:42:24,320 --> 00:42:26,590
So they put little beads
of metal on the outside.

672
00:42:26,590 --> 00:42:29,000
And the idea is that the bone
grows into the little gaps

673
00:42:29,000 --> 00:42:30,020
between the beads.

674
00:42:30,020 --> 00:42:32,570
Or sometimes if they
have-- not so much for hip

675
00:42:32,570 --> 00:42:36,510
implants but sometimes when
people have say car accidents

676
00:42:36,510 --> 00:42:39,040
and their face get
sort of smashed up,

677
00:42:39,040 --> 00:42:41,590
and they have to have, say,
a plate put in their face,

678
00:42:41,590 --> 00:42:43,290
and they need like
a flatter plate,

679
00:42:43,290 --> 00:42:44,472
they use like a wire mesh.

680
00:42:44,472 --> 00:42:46,930
And they have sort of a wire
mesh that goes on the outside.

681
00:42:46,930 --> 00:42:47,930
And it's the same thing.

682
00:42:47,930 --> 00:42:51,050
It's the idea to try to get the
bone to grow into that plate.

683
00:42:51,050 --> 00:42:53,600
So some people are
thinking instead

684
00:42:53,600 --> 00:42:55,430
of using the porous
sintered beads,

685
00:42:55,430 --> 00:42:58,590
or instead of using one
of these wire mesh plates,

686
00:42:58,590 --> 00:43:00,010
that you could use metal foams.

687
00:43:00,010 --> 00:43:01,385
And so there's
been some interest

688
00:43:01,385 --> 00:43:04,889
in using metal foams in
coatings of implants.

689
00:43:04,889 --> 00:43:06,680
And longer term, there's
been some interest

690
00:43:06,680 --> 00:43:09,770
in trying to make sort
of a vertebral body that

691
00:43:09,770 --> 00:43:12,460
would involve using a metal
foam from the vertebral body.

692
00:43:12,460 --> 00:43:14,126
So you know that whale
bone that we just

693
00:43:14,126 --> 00:43:16,770
passed around, that vetebral
body, that cylindrical part,

694
00:43:16,770 --> 00:43:18,870
it's almost all trabecular bone.

695
00:43:18,870 --> 00:43:21,500
So there's some
interest in trying

696
00:43:21,500 --> 00:43:27,080
to use metal foams
for spinal surgeries.

697
00:43:27,080 --> 00:43:28,750
Maybe not to replace
the whole body.

698
00:43:28,750 --> 00:43:31,050
But to use in part
of the surgery.

699
00:43:31,050 --> 00:43:32,510
So I have a little
slide here which

700
00:43:32,510 --> 00:43:35,310
shows a bunch of metal
foams that people

701
00:43:35,310 --> 00:43:40,610
have made with the idea in
mind that perhaps some of this

702
00:43:40,610 --> 00:43:44,350
could be used in
orthopedic surgery.

703
00:43:44,350 --> 00:43:47,000
So these are some different
kinds of metal foams.

704
00:43:47,000 --> 00:43:50,750
And these ones are made
from titanium or tantalum.

705
00:43:50,750 --> 00:43:53,810
So typically, the metals that
they use in orthopedic implants

706
00:43:53,810 --> 00:43:56,630
are the cobalt chromium alloys.

707
00:43:56,630 --> 00:44:00,070
Titanium, they sometimes use
tantalum or stainless steel.

708
00:44:00,070 --> 00:44:02,540
And they use those because
they're biocompatible.

709
00:44:02,540 --> 00:44:04,890
And they're very
corrosion resistant.

710
00:44:04,890 --> 00:44:06,980
So these ones here
are mostly titanium.

711
00:44:06,980 --> 00:44:08,900
And this is one
that's a tantalum.

712
00:44:08,900 --> 00:44:10,750
So let me just go over
how they make them.

713
00:44:10,750 --> 00:44:12,430
And then I've got another
slide that goes over it

714
00:44:12,430 --> 00:44:13,160
in more detail.

715
00:44:13,160 --> 00:44:15,060
And I'll write a few notes down.

716
00:44:15,060 --> 00:44:18,500
So this guy on the
top left up here,

717
00:44:18,500 --> 00:44:22,160
that's made by taking an
open cell polyurethane foam,

718
00:44:22,160 --> 00:44:24,540
like a seating foam,
like a cushion.

719
00:44:24,540 --> 00:44:29,290
And then what they do
is they heat that up

720
00:44:29,290 --> 00:44:31,410
in an inert atmosphere,
so that they

721
00:44:31,410 --> 00:44:33,330
are left just with the carbon.

722
00:44:33,330 --> 00:44:35,380
So it's a sort of
vitreous carbon.

723
00:44:35,380 --> 00:44:37,910
And then what they do
is they coat that carbon

724
00:44:37,910 --> 00:44:41,010
by a CVD process with tantalum.

725
00:44:41,010 --> 00:44:43,620
And so they end up
with a tantalum foam

726
00:44:43,620 --> 00:44:49,020
with a very thin layer
of carbon at the core.

727
00:44:49,020 --> 00:44:50,840
The carbon makes up
something like 1%

728
00:44:50,840 --> 00:44:54,850
of the final composition
and the tantalum is the 99%.

729
00:44:54,850 --> 00:44:57,890
So that's sort of a
replica process there.

730
00:44:57,890 --> 00:45:00,330
This one here is made by
another replica process.

731
00:45:00,330 --> 00:45:02,700
They take an open cell
polyurethane foam.

732
00:45:02,700 --> 00:45:04,390
They infiltrate
it with a slurry,

733
00:45:04,390 --> 00:45:07,105
which has the titanium
hydride particles in it.

734
00:45:07,105 --> 00:45:09,230
Remember when we talk about
processing of the foams

735
00:45:09,230 --> 00:45:12,320
at the beginning, I said, if you
heat up the titanium hydride,

736
00:45:12,320 --> 00:45:14,200
eventually the hydrogen
would be driven off,

737
00:45:14,200 --> 00:45:16,190
and you'd be left
with the titanium.

738
00:45:16,190 --> 00:45:18,430
So they do that, and
then they sinter it,

739
00:45:18,430 --> 00:45:20,830
and they get a titanium foam.

740
00:45:20,830 --> 00:45:23,316
This one is made by a
fugitive phase process.

741
00:45:23,316 --> 00:45:24,690
So the idea with
a fugitive phase

742
00:45:24,690 --> 00:45:26,810
is you burn off some phase.

743
00:45:26,810 --> 00:45:29,869
So you could mix powders,
consolidate the powders,

744
00:45:29,869 --> 00:45:31,410
then you burn off
one of the powders.

745
00:45:31,410 --> 00:45:33,620
And you're left
with the other one.

746
00:45:33,620 --> 00:45:35,380
And then you need to
sinter that together

747
00:45:35,380 --> 00:45:39,730
to make it have some reasonable
mechanical properties.

748
00:45:39,730 --> 00:45:43,880
This one here is made by
using a foaming agent.

749
00:45:43,880 --> 00:45:46,116
This one's made by
expansion of argon gas.

750
00:45:46,116 --> 00:45:47,990
I think when we talked
about the metal foams,

751
00:45:47,990 --> 00:45:50,060
we talked about the
idea of packing, say,

752
00:45:50,060 --> 00:45:52,230
titanium powder in a can.

753
00:45:52,230 --> 00:45:54,010
And then you evaporate the can.

754
00:45:54,010 --> 00:45:57,690
And you then pressurize
the can with argon gas.

755
00:45:57,690 --> 00:45:59,060
And then you heat treat it.

756
00:45:59,060 --> 00:46:00,210
So you heat it up.

757
00:46:00,210 --> 00:46:02,280
And as you heat it up,
the argon gas expands.

758
00:46:02,280 --> 00:46:06,480
And you're left with the pores.

759
00:46:06,480 --> 00:46:09,390
This one's made by a
freeze casting process.

760
00:46:09,390 --> 00:46:10,060
I have a slide.

761
00:46:10,060 --> 00:46:11,830
And I'll talk about
that in a minute.

762
00:46:11,830 --> 00:46:14,510
This one's made by a
selective laser sensory.

763
00:46:14,510 --> 00:46:16,960
So it's like a 3D printing.

764
00:46:16,960 --> 00:46:19,440
But instead of printing
in ink, this time

765
00:46:19,440 --> 00:46:21,090
you have a bed of a powder.

766
00:46:21,090 --> 00:46:24,240
And you've got a laser
that selectively sinters.

767
00:46:24,240 --> 00:46:25,900
So you turn the
laser on and off.

768
00:46:25,900 --> 00:46:28,040
And where it's on, it's
going to bind the material.

769
00:46:28,040 --> 00:46:30,030
When it's off, it's not
going to bind the material.

770
00:46:30,030 --> 00:46:30,810
And then you raise the thing.

771
00:46:30,810 --> 00:46:31,990
You make a little
bit more powder.

772
00:46:31,990 --> 00:46:33,250
You do it all over again.

773
00:46:33,250 --> 00:46:35,070
And you can get
different patterns.

774
00:46:35,070 --> 00:46:38,960
And then this is made
by a sort of process

775
00:46:38,960 --> 00:46:41,390
in which they take powders and
press them and ignite them.

776
00:46:41,390 --> 00:46:44,730
But I think that's not
very commonly used.

777
00:46:44,730 --> 00:46:47,960
So this is some more details
about how they might do it.

778
00:46:47,960 --> 00:46:51,070
So this is the fugitive
phase process here.

779
00:46:51,070 --> 00:46:53,790
You could take a titanium
and a filler powder,

780
00:46:53,790 --> 00:46:54,610
pack them together.

781
00:46:54,610 --> 00:46:56,530
You know, you'd mix them
up, pack them together.

782
00:46:56,530 --> 00:46:58,321
You would raise it to
a certain temperature

783
00:46:58,321 --> 00:46:59,370
to decompose the filler.

784
00:46:59,370 --> 00:47:01,220
So typically the
filler decomposes

785
00:47:01,220 --> 00:47:03,970
at a lower temperature than
what you sinter the powder,

786
00:47:03,970 --> 00:47:05,910
the metal powder that's left.

787
00:47:05,910 --> 00:47:07,590
So you decompose the filler.

788
00:47:07,590 --> 00:47:08,399
You drive that off.

789
00:47:08,399 --> 00:47:09,940
And then you sinter
the metal powder.

790
00:47:09,940 --> 00:47:13,470
And you're left with
porous titanium.

791
00:47:13,470 --> 00:47:15,450
This one's the expansion
of the foaming agent.

792
00:47:15,450 --> 00:47:17,150
So you take your
titanium powder.

793
00:47:17,150 --> 00:47:19,420
You might have a binder
and then a foaming agent.

794
00:47:19,420 --> 00:47:20,870
Mix those all together.

795
00:47:20,870 --> 00:47:23,430
They heat them up until
typically the binder

796
00:47:23,430 --> 00:47:24,250
becomes a liquid.

797
00:47:24,250 --> 00:47:27,710
And the foam foams
up the liquid binder.

798
00:47:27,710 --> 00:47:29,184
Then they drive off the binder.

799
00:47:29,184 --> 00:47:31,600
And then they sinter at a
higher temperature the titanium.

800
00:47:31,600 --> 00:47:36,140
So you you've got a
porous titanium left.

801
00:47:36,140 --> 00:47:40,350
This is the freeze casting
or the freeze drying process.

802
00:47:40,350 --> 00:47:44,220
So here they would take titanium
powder and put it in agar.

803
00:47:44,220 --> 00:47:45,320
And the agar's in water.

804
00:47:45,320 --> 00:47:48,830
So the agar is like
a jelly, like a gel.

805
00:47:48,830 --> 00:47:50,270
But it's mostly water.

806
00:47:50,270 --> 00:47:53,380
And then if you freeze it, what
happens is the water freezes.

807
00:47:53,380 --> 00:47:55,510
And it drives off
the titanium agar

808
00:47:55,510 --> 00:47:58,710
into the interstitial zones
between the frozen ice

809
00:47:58,710 --> 00:47:59,532
crystals.

810
00:47:59,532 --> 00:48:01,490
So these little dots here
are the ice crystals.

811
00:48:01,490 --> 00:48:03,870
The ice crystals are
growing as it gets colder.

812
00:48:03,870 --> 00:48:05,900
And as the ice crystals
get bigger and bigger,

813
00:48:05,900 --> 00:48:08,160
you're left with the
titanium and the agar

814
00:48:08,160 --> 00:48:10,390
in between those ice crystals.

815
00:48:10,390 --> 00:48:12,527
And then if you
sublimate the ice off,

816
00:48:12,527 --> 00:48:13,860
you're left with a porous thing.

817
00:48:13,860 --> 00:48:15,940
And you can sinter the
titanium if you want

818
00:48:15,940 --> 00:48:18,410
to make it a little more dense.

819
00:48:18,410 --> 00:48:20,890
And this is a rapid
prototyping thing here.

820
00:48:20,890 --> 00:48:23,690
So you spread the powder.

821
00:48:23,690 --> 00:48:25,360
You could either
print a binder or you

822
00:48:25,360 --> 00:48:30,520
could use a laser to sort
of almost weld the particles

823
00:48:30,520 --> 00:48:31,870
together.

824
00:48:31,870 --> 00:48:34,220
Then you would drop the
piston, put more powder down,

825
00:48:34,220 --> 00:48:37,260
have the binder go again
until you made your product.

826
00:48:37,260 --> 00:48:39,900
And then you would get rid
of all the unbound material.

827
00:48:39,900 --> 00:48:41,461
And you'd have
your final product.

828
00:48:41,461 --> 00:48:42,960
OK, so these are
some of the methods

829
00:48:42,960 --> 00:48:44,459
they can use for
making metal foams.

830
00:48:47,590 --> 00:48:49,500
I don't know, should
I write notes?

831
00:48:49,500 --> 00:48:51,970
Or are you good if I just
put the notes on the website?

832
00:48:51,970 --> 00:48:55,970
I'll put the notes
on the website.

833
00:48:55,970 --> 00:49:01,070
And then this is a stress strain
curve for a titanium foam.

834
00:49:01,070 --> 00:49:03,270
So it looks like all
these other kinds of foams

835
00:49:03,270 --> 00:49:05,830
and bone and wood and everything
else that we've looked at.

836
00:49:05,830 --> 00:49:08,940
And this is some data
for titanium foams

837
00:49:08,940 --> 00:49:10,650
that are made by
different processes.

838
00:49:10,650 --> 00:49:13,745
And we've just taken different
data from the literature

839
00:49:13,745 --> 00:49:15,150
and put it together.

840
00:49:15,150 --> 00:49:16,490
So this is the modulus here.

841
00:49:16,490 --> 00:49:18,360
This is a slope of 2.

842
00:49:18,360 --> 00:49:20,720
You can see some of the data
is sort of near that slope,

843
00:49:20,720 --> 00:49:22,410
but below it.

844
00:49:22,410 --> 00:49:25,490
And there is obviously a
large spread in the data too.

845
00:49:25,490 --> 00:49:27,890
But if you go back and
look at the different types

846
00:49:27,890 --> 00:49:29,640
of structures,
then not all these

847
00:49:29,640 --> 00:49:31,940
have this kind of typical
foam-like structures.

848
00:49:31,940 --> 00:49:34,740
The structures aren't all
quite like a foam either.

849
00:49:34,740 --> 00:49:35,348
Yeah?

850
00:49:35,348 --> 00:49:39,590
AUDIENCE: So is there
any objective in this

851
00:49:39,590 --> 00:49:44,340
to make the foam similar in
structure to the bone that

852
00:49:44,340 --> 00:49:45,366
will be growing into it?

853
00:49:45,366 --> 00:49:48,192
Or does it just need
to be scaffolding?

854
00:49:48,192 --> 00:49:49,900
LORNA GIBSON: I think
for this, they just

855
00:49:49,900 --> 00:49:51,060
want to make a porous thing.

856
00:49:51,060 --> 00:49:52,559
And they're thinking
about coatings.

857
00:49:52,559 --> 00:49:54,030
So the coatings
aren't necessarily

858
00:49:54,030 --> 00:49:56,022
similar to the bone.

859
00:49:56,022 --> 00:49:57,480
When we finish the
section on bone,

860
00:49:57,480 --> 00:49:59,160
we're going to start
talking, I think,

861
00:49:59,160 --> 00:50:00,520
about tissue engineering.

862
00:50:00,520 --> 00:50:02,350
And when we talk about
tissue engineering,

863
00:50:02,350 --> 00:50:05,100
people have made
scaffolds to try

864
00:50:05,100 --> 00:50:10,410
to make them the same shape
as the anatomical part

865
00:50:10,410 --> 00:50:12,440
that they're trying to mimic.

866
00:50:12,440 --> 00:50:14,950
And then they make a
cellular kind of core.

867
00:50:14,950 --> 00:50:18,536
So they have made some more
of an attempt to do that.

868
00:50:18,536 --> 00:50:19,910
I could give you
a sneak preview.

869
00:50:19,910 --> 00:50:21,520
Would you like a preview?

870
00:50:21,520 --> 00:50:28,330
So these are some scaffolds
that are generated from a making

871
00:50:28,330 --> 00:50:29,430
different kinds of tissue.

872
00:50:29,430 --> 00:50:31,370
These aren't all from bone.

873
00:50:31,370 --> 00:50:34,170
But this one here, for example,
is for regenerating bone.

874
00:50:34,170 --> 00:50:37,940
And they've printed it
in this exact geometry,

875
00:50:37,940 --> 00:50:41,400
because that's going to
replace some anatomical piece.

876
00:50:41,400 --> 00:50:43,990
And they want it
in that geometry.

877
00:50:43,990 --> 00:50:45,199
So I'll talk more about that.

878
00:50:45,199 --> 00:50:47,239
But so for the scaffolds,
they sometimes do that.

879
00:50:47,239 --> 00:50:49,060
But not so much for
these bone coatings.

880
00:50:52,911 --> 00:50:53,410
Let's see.

881
00:50:53,410 --> 00:50:54,070
Se we did that.

882
00:50:54,070 --> 00:50:55,844
We did that.

883
00:50:55,844 --> 00:50:56,760
So these are the data.

884
00:50:56,760 --> 00:51:00,070
And then over here, there's
the compressive strength.

885
00:51:00,070 --> 00:51:02,670
And again, you know, this is
our line with a slope of 3/2.

886
00:51:02,670 --> 00:51:04,670
Again, there's a lot of
scatter, because there's

887
00:51:04,670 --> 00:51:07,039
a lot of variation in the
structure of these things.

888
00:51:07,039 --> 00:51:08,080
But it's in the ballpark.

889
00:51:11,157 --> 00:51:12,490
So are we good with metal foams?

890
00:51:12,490 --> 00:51:14,800
And there's just like a page
and a half of little notes.

891
00:51:14,800 --> 00:51:16,383
Should I just put
that on the website?

892
00:51:16,383 --> 00:51:17,190
You're good?

893
00:51:17,190 --> 00:51:18,240
OK.

894
00:51:18,240 --> 00:51:21,030
OK, so the last topic I
wanted to talk about on bone

895
00:51:21,030 --> 00:51:24,510
has to do with how people
look at the structure of bone

896
00:51:24,510 --> 00:51:28,310
in evolution and in
evolutionary studies.

897
00:51:28,310 --> 00:51:30,950
So the idea here
is, in particular

898
00:51:30,950 --> 00:51:34,480
in looking at sort of
pre-human species, sort

899
00:51:34,480 --> 00:51:38,240
of hominid species, people
are interested in when

900
00:51:38,240 --> 00:51:41,520
primates went from being
quadruplets to bipeds.

901
00:51:41,520 --> 00:51:44,560
So obviously, bipedalism,
walking on two legs,

902
00:51:44,560 --> 00:51:46,850
is characteristic of us.

903
00:51:46,850 --> 00:51:48,410
And people would
like to know if they

904
00:51:48,410 --> 00:51:52,940
find some fossil-- you can't
just tell from the fossil

905
00:51:52,940 --> 00:51:55,400
directly is it a
biped or a quadraped.

906
00:51:55,400 --> 00:51:57,320
You can't see the
species moving because it

907
00:51:57,320 --> 00:51:58,640
doesn't exist anymore.

908
00:51:58,640 --> 00:52:01,330
So you'd like to have some
way of making some estimate of

909
00:52:01,330 --> 00:52:03,860
whether or not it was
a biped or a quadruped.

910
00:52:06,700 --> 00:52:08,460
Let me get my notes
together here.

911
00:52:11,600 --> 00:52:15,010
So I wanted to kind of look at
the big picture a little bit

912
00:52:15,010 --> 00:52:18,320
and look at the evolution
of different species.

913
00:52:18,320 --> 00:52:22,120
And this is a phylogenetic
sort of chart.

914
00:52:22,120 --> 00:52:25,220
And this is kind of-- have
you heard of the tree of life?

915
00:52:25,220 --> 00:52:26,470
This is like the tree of life.

916
00:52:26,470 --> 00:52:29,230
So this piece of it is--
metazoa is for animals.

917
00:52:29,230 --> 00:52:31,860
So not plants, animals.

918
00:52:31,860 --> 00:52:35,830
And this goes back
about 1.2 billion years.

919
00:52:35,830 --> 00:52:37,490
So these are millions
of years ago.

920
00:52:37,490 --> 00:52:39,800
And then these are different
sort of eras and ages

921
00:52:39,800 --> 00:52:42,060
that are defined.

922
00:52:42,060 --> 00:52:46,500
And when we have a branch here,
this is a common ancestor.

923
00:52:46,500 --> 00:52:48,760
And then this is a
branch in one direction,

924
00:52:48,760 --> 00:52:50,950
and that's a branch
in another direction.

925
00:52:50,950 --> 00:52:52,850
So these points
here, like 1 and 2

926
00:52:52,850 --> 00:52:54,764
and so on, the
implication there is

927
00:52:54,764 --> 00:52:56,680
that there was a common
ancestor to everything

928
00:52:56,680 --> 00:52:58,480
that traces back to there.

929
00:52:58,480 --> 00:53:02,330
So this point here, 1,
is 1.2 billion years ago.

930
00:53:02,330 --> 00:53:05,620
So this was sort of very
early kind of species.

931
00:53:05,620 --> 00:53:09,240
And the very first things were,
well, multicellular things.

932
00:53:09,240 --> 00:53:11,670
I mean, there were little
amoeba type things.

933
00:53:11,670 --> 00:53:14,470
But the more sort of
sophisticated animals

934
00:53:14,470 --> 00:53:15,840
were sponges.

935
00:53:15,840 --> 00:53:18,080
And there's three kind of
classes of the sponges.

936
00:53:18,080 --> 00:53:19,760
There's calcarea.

937
00:53:19,760 --> 00:53:22,250
And they're called calcarea
because they're mineralized.

938
00:53:22,250 --> 00:53:25,020
And they're mineralized
with a calcium carbonate.

939
00:53:25,020 --> 00:53:27,390
And then there's
another branch of them

940
00:53:27,390 --> 00:53:29,600
called-- I don't know if
I'm going to say this right,

941
00:53:29,600 --> 00:53:31,870
but hexactinellida.

942
00:53:31,870 --> 00:53:33,805
And those have glass.

943
00:53:33,805 --> 00:53:36,290
Those are called glass
sponges because they have

944
00:53:36,290 --> 00:53:38,710
SiO2 is the mineral in those.

945
00:53:38,710 --> 00:53:41,180
And then there's these
guys here the demospongiae.

946
00:53:41,180 --> 00:53:43,460
I think some of those have
calcium carbonate and some

947
00:53:43,460 --> 00:53:44,670
of them don't.

948
00:53:44,670 --> 00:53:46,640
Oh, no, some of
them have silica.

949
00:53:46,640 --> 00:53:48,740
And some of them don't.

950
00:53:48,740 --> 00:53:52,750
So these things here are sort
of very early multicellular

951
00:53:52,750 --> 00:53:53,810
structures.

952
00:53:53,810 --> 00:53:55,870
And the mineral in
them is either calcium

953
00:53:55,870 --> 00:53:57,881
carbonate or silica.

954
00:53:57,881 --> 00:53:59,380
And then if we move
up, I've sort of

955
00:53:59,380 --> 00:54:00,463
highlighted a few of them.

956
00:54:00,463 --> 00:54:02,120
The cnideria-- I
know there's a C,

957
00:54:02,120 --> 00:54:04,260
but that's actually--
when I say s-nideria,

958
00:54:04,260 --> 00:54:05,740
my biologist
friends laugh at me.

959
00:54:05,740 --> 00:54:07,750
And they say no, no,
no, it's nideria.

960
00:54:07,750 --> 00:54:11,040
The cnideria are the
corals and the jellyfish.

961
00:54:11,040 --> 00:54:15,280
And corals are also mineralized
with calcium carbonate.

962
00:54:15,280 --> 00:54:17,940
And you can see they
branched off something

963
00:54:17,940 --> 00:54:20,260
like a billion years ago.

964
00:54:20,260 --> 00:54:21,250
Then we get up here.

965
00:54:21,250 --> 00:54:22,370
These are the mollusks.

966
00:54:22,370 --> 00:54:24,210
So the mollusks are
things like bivalves,

967
00:54:24,210 --> 00:54:27,480
like if you like to eat
claims, things like that.

968
00:54:27,480 --> 00:54:31,110
So bivalves, snails, and
things like octopi, octopus.

969
00:54:31,110 --> 00:54:33,500
So those are all molluscs.

970
00:54:33,500 --> 00:54:35,970
And molluscs, when
they're mineralized,

971
00:54:35,970 --> 00:54:38,430
also are calcium carbonate.

972
00:54:38,430 --> 00:54:42,261
So those are the calcium
carbonate kind of shell.

973
00:54:42,261 --> 00:54:44,010
So we haven't got up
to anything bony yet.

974
00:54:44,010 --> 00:54:47,120
Bone is collagen plus
a calcium phosphate.

975
00:54:47,120 --> 00:54:49,960
So we haven't gotten to anything
that's a calcium phosphate yet.

976
00:54:49,960 --> 00:54:54,030
Then another large
class is arthropoda.

977
00:54:54,030 --> 00:54:56,480
That's insects and
spiders and crustaceans.

978
00:54:56,480 --> 00:54:59,030
Those all have a
chiton skeleton.

979
00:54:59,030 --> 00:55:02,290
So if you think of like the
exoskeleton of an insect

980
00:55:02,290 --> 00:55:05,180
or a spider, those are chiton.

981
00:55:05,180 --> 00:55:07,570
And crustaceans, things
like lobsters, those

982
00:55:07,570 --> 00:55:09,580
also have a chiton shell.

983
00:55:09,580 --> 00:55:11,540
And in crustaceans, it
might be mineralized.

984
00:55:11,540 --> 00:55:14,300
But again, the mineral
is a calcium carbonate.

985
00:55:14,300 --> 00:55:17,070
So all the way up here,
most of these things,

986
00:55:17,070 --> 00:55:22,570
if there is any mineral,
it's calcium carbonate.

987
00:55:22,570 --> 00:55:24,800
And if we get up finally
to the vertebraes,

988
00:55:24,800 --> 00:55:29,780
the vertebraes have the calcium
phosphate and have a bone,

989
00:55:29,780 --> 00:55:31,389
like what we think
of as real bone.

990
00:55:31,389 --> 00:55:33,180
So the vertebrates
obviously involve things

991
00:55:33,180 --> 00:55:35,614
like mammals, birds,
snakes, and fish.

992
00:55:35,614 --> 00:55:37,530
So this is kind of the
big picture going back.

993
00:55:37,530 --> 00:55:39,238
And sort of one of
the interesting things

994
00:55:39,238 --> 00:55:41,320
is that bone doesn't
come along until you

995
00:55:41,320 --> 00:55:44,220
get somewhere over here.

996
00:55:44,220 --> 00:55:46,122
And I have one more
little, nice slide here.

997
00:55:46,122 --> 00:55:47,580
So when I talked
about the sponges,

998
00:55:47,580 --> 00:55:51,710
they were these guys here
with the glass sponges.

999
00:55:51,710 --> 00:55:54,770
Joanna Aizenberg at Harvard did
a nice study on glass sponges.

1000
00:55:54,770 --> 00:55:56,500
And she looked at this one here.

1001
00:55:56,500 --> 00:55:58,080
It's called the
Venus flower basket

1002
00:55:58,080 --> 00:56:00,690
is kind of the common name.

1003
00:56:00,690 --> 00:56:02,470
And it has this
hierarchical structure.

1004
00:56:02,470 --> 00:56:04,560
And it's remarkably
stiff and tough.

1005
00:56:04,560 --> 00:56:07,180
And what she did
in her paper was

1006
00:56:07,180 --> 00:56:09,030
look at optical and
mechanical properties.

1007
00:56:09,030 --> 00:56:11,809
But they looked at the structure
at different length scales.

1008
00:56:11,809 --> 00:56:14,350
So there's kind of a cellular
structure at this length scale.

1009
00:56:14,350 --> 00:56:17,220
It's kind of a tube.

1010
00:56:17,220 --> 00:56:20,570
This was just a picture I took
in a natural history museum.

1011
00:56:20,570 --> 00:56:22,690
But if you look at
higher magnification,

1012
00:56:22,690 --> 00:56:27,350
each little strut is
made up of sort of fibers

1013
00:56:27,350 --> 00:56:30,580
and has a hierarchical
structure itself.

1014
00:56:30,580 --> 00:56:33,150
So that's just one
of the sponges.

1015
00:56:33,150 --> 00:56:36,930
And here's a similar
chart for the vertebrates.

1016
00:56:36,930 --> 00:56:40,150
So this point here is where
the other chart kind of

1017
00:56:40,150 --> 00:56:41,480
branched off.

1018
00:56:41,480 --> 00:56:43,760
And if we start with the
earliest things again,

1019
00:56:43,760 --> 00:56:46,170
the earliest ones with
the most common ancestor

1020
00:56:46,170 --> 00:56:50,180
back here is something
called cyclostomata.

1021
00:56:50,180 --> 00:56:52,730
And those are things
like jawless fish,

1022
00:56:52,730 --> 00:56:55,095
so things like
lamprey and hagfish.

1023
00:56:55,095 --> 00:56:56,870
Do you know what a hagfish is?

1024
00:56:56,870 --> 00:56:58,320
It's this kind of eely thing.

1025
00:56:58,320 --> 00:57:00,190
And I have the
video for you if you

1026
00:57:00,190 --> 00:57:01,990
don't know what a hagfish is.

1027
00:57:01,990 --> 00:57:04,510
So let me get out of
here because it's just

1028
00:57:04,510 --> 00:57:06,650
an amazing thing, the hagfish.

1029
00:57:06,650 --> 00:57:11,416
OK, so let's see,
I got my sound on.

1030
00:57:11,416 --> 00:57:12,110
[VIDEO PLAYBACK]

1031
00:57:12,110 --> 00:57:14,150
REPORTER: Here, at the
University of Guelph,

1032
00:57:14,150 --> 00:57:17,850
about an hour outside
Toronto, materials scientist

1033
00:57:17,850 --> 00:57:22,170
Atsuko Negishi and
biologist Julia Herr

1034
00:57:22,170 --> 00:57:25,930
think that these lovely
creatures, called hagfish,

1035
00:57:25,930 --> 00:57:30,760
may revolutionize how we
make strong materials.

1036
00:57:30,760 --> 00:57:32,780
ATSUKO NEGISHI: These
are specific hagfish.

1037
00:57:32,780 --> 00:57:36,569
They're well known for their
unique defense mechanism.

1038
00:57:36,569 --> 00:57:38,860
REPORTER: So if I wanted to
see this, what would we do?

1039
00:57:38,860 --> 00:57:40,467
Like could we poke
at it with a stick?

1040
00:57:40,467 --> 00:57:43,050
JULIA HERR: I think the best way
to do it is to reach in there

1041
00:57:43,050 --> 00:57:46,850
and grab one.

1042
00:57:46,850 --> 00:57:50,400
REPORTER: Oh, my gosh,
look at that disgusting--

1043
00:57:50,400 --> 00:57:56,536
oh, no, I've been slimed.

1044
00:57:56,536 --> 00:57:59,490
I feel like an outtake
from Ghostbusters.

1045
00:57:59,490 --> 00:58:02,030
Look at the quantities
of this stuff.

1046
00:58:02,030 --> 00:58:03,320
[END PLAYBACK]

1047
00:58:03,320 --> 00:58:04,720
LORNA GIBSON: He used to do
this for The New York Times.

1048
00:58:04,720 --> 00:58:06,414
And I think he's got
his own going on,

1049
00:58:06,414 --> 00:58:08,080
but he used to make
these little videos.

1050
00:58:08,080 --> 00:58:11,490
And he had a show on PBS a year
or two ago all about materials.

1051
00:58:11,490 --> 00:58:13,420
And there were like
four different episodes.

1052
00:58:13,420 --> 00:58:15,040
And he talked about
different kinds of materials.

1053
00:58:15,040 --> 00:58:16,289
And he went to different labs.

1054
00:58:16,289 --> 00:58:17,917
But he's quite a character.

1055
00:58:17,917 --> 00:58:20,000
But anyway the hagfish
have this defense mechanism

1056
00:58:20,000 --> 00:58:21,374
where they make the slime.

1057
00:58:21,374 --> 00:58:23,540
And I don't know if you
know Professor McKinley over

1058
00:58:23,540 --> 00:58:26,180
in mechanical
engineering here at MIT,

1059
00:58:26,180 --> 00:58:28,510
but he collaborates with
those people of Guelph.

1060
00:58:28,510 --> 00:58:31,350
And he studies what he
calls non-Newtonian fluids.

1061
00:58:31,350 --> 00:58:33,840
Well, a lot of people
call non-Newtonian fluids.

1062
00:58:33,840 --> 00:58:35,720
A Newtonian fluid is
a thing like water,

1063
00:58:35,720 --> 00:58:39,540
where the viscosity is a
constant no matter what sort

1064
00:58:39,540 --> 00:58:41,110
of strain rate you shear it at.

1065
00:58:41,110 --> 00:58:44,870
And a non-Newtonian fluid
does not have that property.

1066
00:58:44,870 --> 00:58:46,170
The viscosity changes.

1067
00:58:46,170 --> 00:58:48,990
And some of them have a
strength, like in the hagfish

1068
00:58:48,990 --> 00:58:50,200
one has a strength.

1069
00:58:50,200 --> 00:58:54,084
So Gareth's studies things like
this kind of hagfish slime.

1070
00:58:54,084 --> 00:58:55,500
I don't know if
he still has them.

1071
00:58:55,500 --> 00:58:57,310
He used to have hagfish
in his lab over him

1072
00:58:57,310 --> 00:59:01,100
building, whatever it is, 1
or 3 or something over there.

1073
00:59:01,100 --> 00:59:02,750
OK, so that's what
the hagfish are,

1074
00:59:02,750 --> 00:59:04,930
just because that's amusing.

1075
00:59:04,930 --> 00:59:07,630
And they don't have bone.

1076
00:59:07,630 --> 00:59:11,350
So they and the jawless
fish don't have bone,

1077
00:59:11,350 --> 00:59:13,440
even though they're
called vertebrates.

1078
00:59:13,440 --> 00:59:16,520
Then the next sort
of most recent thing

1079
00:59:16,520 --> 00:59:18,350
is the chondrocytes.

1080
00:59:18,350 --> 00:59:21,480
Those are the cartilaginous
fish, so things like shark.

1081
00:59:21,480 --> 00:59:23,610
So sharks don't
actually have bones.

1082
00:59:23,610 --> 00:59:24,470
They have cartilage.

1083
00:59:24,470 --> 00:59:26,303
And they have a little
bit of mineralization

1084
00:59:26,303 --> 00:59:29,390
in the cartilage, but they
don't actually have bone.

1085
00:59:29,390 --> 00:59:31,330
And the first thing
that actually has a bone

1086
00:59:31,330 --> 00:59:34,090
is the ray finned fish,
which are these guys here.

1087
00:59:34,090 --> 00:59:37,740
And that occurred about
450 million years ago.

1088
00:59:37,740 --> 00:59:40,307
And then everything in the
vertebrate since then is bony.

1089
00:59:40,307 --> 00:59:42,890
So there's coelacanth-- I don't
know if you've ever see those.

1090
00:59:42,890 --> 00:59:45,348
Every now and then they find
one of these things in Florida

1091
00:59:45,348 --> 00:59:46,560
or something-- lung fish.

1092
00:59:46,560 --> 00:59:48,976
There's these guys here, which
are the frogs and the toads

1093
00:59:48,976 --> 00:59:50,360
and the salamanders.

1094
00:59:50,360 --> 00:59:52,010
So it's finally
getting to be spring

1095
00:59:52,010 --> 00:59:53,680
after the winter from hell.

1096
00:59:53,680 --> 00:59:55,520
And the salamanders
are going to come out

1097
00:59:55,520 --> 00:59:57,100
into the vernal pools and mate.

1098
00:59:57,100 --> 00:59:57,830
And it's cute.

1099
00:59:57,830 --> 01:00:00,830
So anyway, they come
out this time of year.

1100
01:00:00,830 --> 01:00:02,830
And then there's
the amniota, things

1101
01:00:02,830 --> 01:00:04,947
that have eggs of
one sort or another.

1102
01:00:04,947 --> 01:00:07,280
So that includes us, the
mammals, the birds, the snakes,

1103
01:00:07,280 --> 01:00:08,740
and the turtles.

1104
01:00:08,740 --> 01:00:12,290
And so those would have
branched off about there.

1105
01:00:12,290 --> 01:00:14,210
So the last thing I
wanted to point out here

1106
01:00:14,210 --> 01:00:16,700
is that there's this
huge kind of diversity

1107
01:00:16,700 --> 01:00:19,690
of animals that have
evolved over millions

1108
01:00:19,690 --> 01:00:21,160
and millions of years.

1109
01:00:21,160 --> 01:00:23,340
And that the first ones
that were mineralized

1110
01:00:23,340 --> 01:00:27,150
used the calcium carbonate and
that the bony type materials

1111
01:00:27,150 --> 01:00:30,230
didn't really evolve or
didn't appear until about 450

1112
01:00:30,230 --> 01:00:31,996
million years ago.

1113
01:00:31,996 --> 01:00:33,620
And then these are
the vertebrates that

1114
01:00:33,620 --> 01:00:35,085
have these kind of bony things.

1115
01:00:37,760 --> 01:00:41,310
So as I've said many
times now, the bone

1116
01:00:41,310 --> 01:00:43,140
grows in response to loads.

1117
01:00:43,140 --> 01:00:45,690
And the bone structure
reflects the mechanical loads

1118
01:00:45,690 --> 01:00:46,760
and the function.

1119
01:00:46,760 --> 01:00:50,280
And evolutionary studies have
looked at both cortical bone

1120
01:00:50,280 --> 01:00:51,980
and trabecular bone
architecture to try

1121
01:00:51,980 --> 01:00:55,710
to say something about the
locomotion of the animal

1122
01:00:55,710 --> 01:00:56,869
or of the species.

1123
01:00:56,869 --> 01:00:58,660
So there's ones that
look at cortical bone.

1124
01:00:58,660 --> 01:01:02,310
But I'm just going to talk about
one that deals with trabecular

1125
01:01:02,310 --> 01:01:03,630
bone.

1126
01:01:03,630 --> 01:01:06,950
So this study was done
by a group of peoples,

1127
01:01:06,950 --> 01:01:08,630
the first author was Rook.

1128
01:01:08,630 --> 01:01:10,740
And what they studied
was the ileum.

1129
01:01:10,740 --> 01:01:13,130
So this is a pelvis.

1130
01:01:13,130 --> 01:01:16,480
And there's the ileum is one
of the bones in the pelvis.

1131
01:01:16,480 --> 01:01:20,000
And they found fossils
of a hominid species that

1132
01:01:20,000 --> 01:01:25,095
was about 8 million years old,
called Oreopithecus bambolii.

1133
01:01:25,095 --> 01:01:27,360
And bambolii refers
to the place in Italy

1134
01:01:27,360 --> 01:01:30,090
where these fossils were found.

1135
01:01:30,090 --> 01:01:33,290
And so they found two--
or at least somebody

1136
01:01:33,290 --> 01:01:36,240
found two pieces of an ilium.

1137
01:01:36,240 --> 01:01:38,160
And they took x-rays.

1138
01:01:38,160 --> 01:01:39,750
And they made a
digital reconstruction

1139
01:01:39,750 --> 01:01:41,800
so that they would get
one ilium-- it turned out

1140
01:01:41,800 --> 01:01:44,299
that the two pieces were two
different parts-- so they could

1141
01:01:44,299 --> 01:01:46,310
make a whole one out
of the two pieces.

1142
01:01:46,310 --> 01:01:48,040
And then they looked at the
structure of the trabecular

1143
01:01:48,040 --> 01:01:48,540
bone.

1144
01:01:48,540 --> 01:01:50,690
And they compared that
structure to the structure

1145
01:01:50,690 --> 01:01:53,107
of the trabecular bone in
humans and other primates.

1146
01:01:53,107 --> 01:01:55,440
And they wanted to see is it
more like the humans, which

1147
01:01:55,440 --> 01:01:56,856
are obviously
biped, or is it more

1148
01:01:56,856 --> 01:01:59,540
like some of the primates,
which are quadrupeds.

1149
01:01:59,540 --> 01:02:06,100
So this just shows for a
human and a non-human primate

1150
01:02:06,100 --> 01:02:08,570
what the structure
of the ilium is.

1151
01:02:08,570 --> 01:02:11,260
And these little black
boxes with the letters

1152
01:02:11,260 --> 01:02:13,410
are what are called
anatomical landmarks.

1153
01:02:13,410 --> 01:02:15,990
So they're sort of
comparable spots on the bone

1154
01:02:15,990 --> 01:02:17,310
of different species.

1155
01:02:17,310 --> 01:02:18,810
And what they were
doing was looking

1156
01:02:18,810 --> 01:02:22,924
at the trabecular architecture
at these different spots.

1157
01:02:22,924 --> 01:02:24,340
So you can kind
of see how they're

1158
01:02:24,340 --> 01:02:28,430
more or less analogous in
the two different species.

1159
01:02:28,430 --> 01:02:31,460
And this is the digitally
reconstructed ilium

1160
01:02:31,460 --> 01:02:35,000
that they put together
from their fossil species.

1161
01:02:35,000 --> 01:02:37,230
And again, these
little letters refer

1162
01:02:37,230 --> 01:02:39,420
to these anatomical landmarks.

1163
01:02:39,420 --> 01:02:43,110
And then what they
did was they compared

1164
01:02:43,110 --> 01:02:48,140
the Oreopithicus, the fossil,
with the human and then three

1165
01:02:48,140 --> 01:02:49,380
non-human primates.

1166
01:02:49,380 --> 01:02:52,080
So these four images
are all from the fossil.

1167
01:02:52,080 --> 01:02:53,270
These are the human.

1168
01:02:53,270 --> 01:02:56,280
These are champi,
siamang and baboon.

1169
01:02:56,280 --> 01:03:00,760
And this square here
corresponds to that one there.

1170
01:03:00,760 --> 01:03:02,780
This is B, corresponds
to that one.

1171
01:03:02,780 --> 01:03:05,840
And C and D are those two there.

1172
01:03:05,840 --> 01:03:10,070
So they had two
fossils, they made

1173
01:03:10,070 --> 01:03:11,430
the digital reconstruction.

1174
01:03:11,430 --> 01:03:13,170
They looked at certain areas.

1175
01:03:13,170 --> 01:03:15,630
And then they looked at
the same or analogous areas

1176
01:03:15,630 --> 01:03:16,840
in these other species.

1177
01:03:16,840 --> 01:03:19,470
And they tried to look for
similarities and differences

1178
01:03:19,470 --> 01:03:21,140
in the bone structure.

1179
01:03:21,140 --> 01:03:26,160
So let's look at this first
box A. You can see there's

1180
01:03:26,160 --> 01:03:27,470
a very white bit here.

1181
01:03:27,470 --> 01:03:29,450
And the white corresponds
to more dense.

1182
01:03:29,450 --> 01:03:32,430
So there's a white bit that's
more dense in their fossil.

1183
01:03:32,430 --> 01:03:36,260
And in the human bone, you
see is a similar sort of band

1184
01:03:36,260 --> 01:03:37,220
right there.

1185
01:03:37,220 --> 01:03:39,220
And if you look at the
other non-human primates,

1186
01:03:39,220 --> 01:03:40,710
that band is missing.

1187
01:03:40,710 --> 01:03:43,080
So that says to them,
OK, this feature,

1188
01:03:43,080 --> 01:03:47,040
this one feature at least, is
more similar to the-- sorry,

1189
01:03:47,040 --> 01:03:49,410
in the fossil here is
more similar to the human

1190
01:03:49,410 --> 01:03:51,400
than it is to the
non-human primates.

1191
01:03:51,400 --> 01:03:53,070
And then they had
three other landmarks

1192
01:03:53,070 --> 01:03:54,680
that they looked at like that.

1193
01:03:54,680 --> 01:03:57,030
So this one here again is
a sort of dense regions.

1194
01:03:57,030 --> 01:03:58,979
So you can see that
white dense region.

1195
01:03:58,979 --> 01:03:59,770
There's some there.

1196
01:03:59,770 --> 01:04:00,640
There's some here.

1197
01:04:00,640 --> 01:04:02,795
So those are the
fossil and the human.

1198
01:04:02,795 --> 01:04:04,920
But there's a teeny bit
here and a teeny bit there.

1199
01:04:04,920 --> 01:04:07,180
But it's not as pronounced
in the non-human primates.

1200
01:04:07,180 --> 01:04:07,680
Yes.

1201
01:04:10,880 --> 01:04:13,832
AUDIENCE: From I
get at least so far,

1202
01:04:13,832 --> 01:04:18,560
the portions of the bone that
are dense versus not dense

1203
01:04:18,560 --> 01:04:22,050
seem less relevant
to the direction

1204
01:04:22,050 --> 01:04:24,920
of loading than the
orientation of the foamy parts

1205
01:04:24,920 --> 01:04:26,707
of the trabecular bone.

1206
01:04:26,707 --> 01:04:28,790
LORNA GIBSON: So the density
reflects more or less

1207
01:04:28,790 --> 01:04:30,570
the magnitude of the stresses.

1208
01:04:30,570 --> 01:04:33,690
So if the stresses are higher,
it's going to be denser.

1209
01:04:33,690 --> 01:04:37,030
And the orientation of the
bone, like whether or not

1210
01:04:37,030 --> 01:04:38,790
which way the
struts are oriented,

1211
01:04:38,790 --> 01:04:43,500
that reflects the sort of ratio
of the principal stresses.

1212
01:04:43,500 --> 01:04:46,250
So if the principal stresses
go in a certain direction,

1213
01:04:46,250 --> 01:04:48,500
the bone's going to tend to
line up in that direction.

1214
01:04:48,500 --> 01:04:51,310
That's what that Guinea fowl
study was kind of about.

1215
01:04:51,310 --> 01:04:51,810
OK?

1216
01:04:51,810 --> 01:04:52,620
Are we good?

1217
01:04:52,620 --> 01:04:53,780
OK.

1218
01:04:53,780 --> 01:04:55,897
And then these
other two, so in B--

1219
01:04:55,897 --> 01:04:57,480
and you can't really
see it from here,

1220
01:04:57,480 --> 01:05:00,281
but they looked at the sort of
architecture of the trabecular

1221
01:05:00,281 --> 01:05:00,780
bone.

1222
01:05:00,780 --> 01:05:03,300
And they said that it was
more similar in the fossil

1223
01:05:03,300 --> 01:05:06,900
in the human than it was in
these other three primates.

1224
01:05:06,900 --> 01:05:10,121
And this region here, this looks
very similar to that bit there

1225
01:05:10,121 --> 01:05:10,620
to me.

1226
01:05:10,620 --> 01:05:13,837
But I think there was some
other feature about this region

1227
01:05:13,837 --> 01:05:14,920
that they were looking at.

1228
01:05:14,920 --> 01:05:17,340
And again, it was more
similar to the human

1229
01:05:17,340 --> 01:05:19,410
than it was to the
non-human primates.

1230
01:05:19,410 --> 01:05:21,450
So by just looking at
the pattern of the bone

1231
01:05:21,450 --> 01:05:23,283
and the density of the
bone and comparing it

1232
01:05:23,283 --> 01:05:25,727
to these other species, they
said that the-- and you know

1233
01:05:25,727 --> 01:05:27,680
the hip, because we're
standing like this,

1234
01:05:27,680 --> 01:05:29,971
you would kind of expect to
see differences in the hip.

1235
01:05:29,971 --> 01:05:33,830
That's why they wanted
to look at the ilium.

1236
01:05:33,830 --> 01:05:36,970
So the conclusion they made
was that these observations

1237
01:05:36,970 --> 01:05:39,450
suggested that the
species was bipedal,

1238
01:05:39,450 --> 01:05:44,880
or at least spent some of
its time as a bipedal animal.

1239
01:05:44,880 --> 01:05:46,150
And I think that might be it.

1240
01:05:46,150 --> 01:05:48,770
Do I have more I have
one little summary here.

1241
01:05:48,770 --> 01:05:51,090
So just to summarize what
we've done on bone this week.

1242
01:05:51,090 --> 01:05:52,840
We talked about the
structure of the bone.

1243
01:05:52,840 --> 01:05:55,730
We talked about mechanical
properties in the foam models.

1244
01:05:55,730 --> 01:05:57,920
We talked about osteoporosis
in the voronoi models,

1245
01:05:57,920 --> 01:06:00,260
how you can try to
represent the loss of bone

1246
01:06:00,260 --> 01:06:02,430
and the loss of bone
strength using those models.

1247
01:06:02,430 --> 01:06:04,180
We talked just a little
bit about the idea

1248
01:06:04,180 --> 01:06:06,350
of using metal foams
as bone substitutes

1249
01:06:06,350 --> 01:06:08,390
or coatings as
implants, and then

1250
01:06:08,390 --> 01:06:10,780
this little bit on
trabecular architecture

1251
01:06:10,780 --> 01:06:14,220
and evolutionary studies.

1252
01:06:14,220 --> 01:06:15,720
I have some notes,
but I think we've

1253
01:06:15,720 --> 01:06:17,011
got just a couple minutes left.

1254
01:06:17,011 --> 01:06:19,490
So maybe I'll just scan those
and put them on the website?

1255
01:06:19,490 --> 01:06:21,480
Are we good with that?

1256
01:06:21,480 --> 01:06:24,010
AUDIENCE: I have a question
about what we just looked

1257
01:06:24,010 --> 01:06:25,440
at about the different species.

1258
01:06:25,440 --> 01:06:29,485
We always consider on
the density changes.

1259
01:06:29,485 --> 01:06:32,282
Can there always be
changes in the solids?

1260
01:06:35,750 --> 01:06:37,750
LORNA GIBSON: So it
changes a little bit

1261
01:06:37,750 --> 01:06:38,970
from one species to another.

1262
01:06:38,970 --> 01:06:42,190
So the question is, does the
solid properties of the bone,

1263
01:06:42,190 --> 01:06:44,780
the solid bone itself change?

1264
01:06:44,780 --> 01:06:47,030
So if you look at cortical
bone in different species,

1265
01:06:47,030 --> 01:06:50,130
it changes a little bit, but
like 10%, not a huge amount.

1266
01:06:50,130 --> 01:06:52,365
So the two most common
things people have compared

1267
01:06:52,365 --> 01:06:54,460
are bovine bone and human bone.

1268
01:06:54,460 --> 01:06:57,220
And there is a slight
difference between them.

1269
01:06:57,220 --> 01:06:59,960
But it's not a huge difference.

1270
01:06:59,960 --> 01:07:02,760
One of the other things people
have looked at in osteoporosis

1271
01:07:02,760 --> 01:07:04,630
that I didn't really
talk about was

1272
01:07:04,630 --> 01:07:07,020
there's another
whole set of things

1273
01:07:07,020 --> 01:07:09,670
that can go on that reflect
what you're talking about.

1274
01:07:09,670 --> 01:07:12,060
So they talk about
bone quality as well.

1275
01:07:12,060 --> 01:07:14,000
And when they talk
about bone quality,

1276
01:07:14,000 --> 01:07:16,860
they're talking about are there
micro cracks in the solid.

1277
01:07:16,860 --> 01:07:18,900
So you might imagine
as you get older,

1278
01:07:18,900 --> 01:07:20,549
it's not just that
you lose the struts

1279
01:07:20,549 --> 01:07:22,590
or that the struts get
thinner, but the solid bit

1280
01:07:22,590 --> 01:07:24,510
itself has more cracks in it.

1281
01:07:24,510 --> 01:07:27,060
So you can imagine if
the solid bone itself had

1282
01:07:27,060 --> 01:07:30,360
little micro cracks, then
it too would be weaker.

1283
01:07:30,360 --> 01:07:33,080
And then you think
what I put up was bad.

1284
01:07:33,080 --> 01:07:36,180
It gets even worse if
you put that in as well.

1285
01:07:36,180 --> 01:07:39,160
So, yes, people do look
at bone quality, which

1286
01:07:39,160 --> 01:07:41,950
is sort of looking at with age.

1287
01:07:41,950 --> 01:07:45,590
And typically it's
fairly elderly people

1288
01:07:45,590 --> 01:07:47,290
that the bone
quality is an issue.

1289
01:07:47,290 --> 01:07:49,581
I guess there are certain
diseases where it's an issue.

1290
01:07:49,581 --> 01:07:53,170
But in osteoporosis, it's
sort of elderly people.

1291
01:07:53,170 --> 01:07:54,610
Any thing else?

1292
01:07:54,610 --> 01:07:56,719
Should I stop there for today?

1293
01:07:56,719 --> 01:07:58,510
So there were hardly
any equations in this.

1294
01:07:58,510 --> 01:07:59,250
Did you know that?

1295
01:07:59,250 --> 01:08:01,500
So we got to the part where
there's lots of equations.

1296
01:08:01,500 --> 01:08:04,467
So next week I'm going to
talk about tissue engineering.

1297
01:08:04,467 --> 01:08:06,050
I think I'm going
to talk a little bit

1298
01:08:06,050 --> 01:08:09,130
about different kinds of
scaffolds, how they make

1299
01:08:09,130 --> 01:08:11,690
scaffolds, how the
scaffolds fit sort

1300
01:08:11,690 --> 01:08:14,830
of into an anatomical
things, what is that supposed

1301
01:08:14,830 --> 01:08:18,640
to represent, how they use
them clinically a little bit.

1302
01:08:18,640 --> 01:08:22,514
And we had a research project
on osteochondrol scaffold,

1303
01:08:22,514 --> 01:08:26,220
so scaffolds for replacing
bone and cartilage.

1304
01:08:26,220 --> 01:08:27,830
And I'm going to
talk a little bit

1305
01:08:27,830 --> 01:08:30,740
about that as sort of a case
study in tissue engineering

1306
01:08:30,740 --> 01:08:31,760
scaffolds.

1307
01:08:31,760 --> 01:08:34,240
And I have some stuff
on cell mechanics

1308
01:08:34,240 --> 01:08:36,520
and how biological cells
interact with scaffold.

1309
01:08:36,520 --> 01:08:38,478
I don't if we're going
to get to that next week

1310
01:08:38,478 --> 01:08:40,560
or not, but somewhere
close to that.

1311
01:08:40,560 --> 01:08:43,460
So the next bit is on tissue
engineering scaffolds,

1312
01:08:43,460 --> 01:08:48,120
osteochondrol scaffolds,
cell mechanics.

1313
01:08:48,120 --> 01:08:50,840
And there's not that many
equations in that part either.

1314
01:08:50,840 --> 01:08:53,000
So OK.