1 00:00:00,030 --> 00:00:02,470 The following content is provided under a Creative 2 00:00:02,470 --> 00:00:04,000 Commons license. 3 00:00:04,000 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high quality educational resources for free. 5 00:00:10,690 --> 00:00:13,300 To make a donation or view additional materials 6 00:00:13,300 --> 00:00:17,025 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,025 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:25,224 --> 00:00:26,874 LORNA GIBSON: So we're going to start 9 00:00:26,874 --> 00:00:28,540 talking about trabecular bone, and we're 10 00:00:28,540 --> 00:00:30,970 going to do a bone today and on Wednesday. 11 00:00:30,970 --> 00:00:34,120 And I'm hoping we can more or less finish it on Wednesday. 12 00:00:34,120 --> 00:00:36,000 So hello. 13 00:00:36,000 --> 00:00:37,137 Hold on a sec. 14 00:00:43,300 --> 00:00:45,960 So these are some images of trabecular bone, 15 00:00:45,960 --> 00:00:49,350 and you can see that it has a foam-like structure. 16 00:00:49,350 --> 00:00:52,560 And trabecular bone exists in certain places in the body. 17 00:00:52,560 --> 00:00:54,860 There's three main places that it exists. 18 00:00:54,860 --> 00:00:57,830 So it exists at the end of the long bones. 19 00:00:57,830 --> 00:01:00,830 And over here this is a femur. 20 00:01:00,830 --> 00:01:02,320 This is the very top of the femur, 21 00:01:02,320 --> 00:01:05,650 and you can see this is all trabecular bone in here. 22 00:01:05,650 --> 00:01:09,550 This is a tibia, and this is the top of your knee there. 23 00:01:09,550 --> 00:01:12,790 And you can see how the bone get more bulbous at the ends, 24 00:01:12,790 --> 00:01:14,770 and it's filled with a trabecular bone. 25 00:01:14,770 --> 00:01:15,820 This is a vertebrae. 26 00:01:15,820 --> 00:01:18,146 So vertebrae are actually mostly trabecular bone, 27 00:01:18,146 --> 00:01:19,520 and they have a really thin shell 28 00:01:19,520 --> 00:01:23,920 of what's called cortical bone, the dense bone, on top of it. 29 00:01:23,920 --> 00:01:27,530 So trabecular bone exists at the ends of the long bones, 30 00:01:27,530 --> 00:01:29,780 it exists in the core of the vertebrae, 31 00:01:29,780 --> 00:01:33,150 and it also exists in sort of shell or plate-like bones. 32 00:01:33,150 --> 00:01:35,140 So in your skull, for example, there's 33 00:01:35,140 --> 00:01:38,970 a layer of trabecular bone in between two layers 34 00:01:38,970 --> 00:01:41,010 of the compact dense bone. 35 00:01:41,010 --> 00:01:43,210 And in your pelvis, it's the same thing. 36 00:01:43,210 --> 00:01:45,199 So those of you who took 3032, you remember 37 00:01:45,199 --> 00:01:46,990 when I passed around the bird skulls, there 38 00:01:46,990 --> 00:01:49,273 was that very porous kind of trabecular bone. 39 00:01:52,360 --> 00:01:55,060 So trabecular bone is of interest medically 40 00:01:55,060 --> 00:01:57,520 in three main kind of medical situations. 41 00:01:57,520 --> 00:01:59,531 So the first one is osteoporosis. 42 00:01:59,531 --> 00:02:01,780 So I want to talk a little bit about osteoporosis now, 43 00:02:01,780 --> 00:02:05,020 and then we'll talk about it in more detail later on. 44 00:02:05,020 --> 00:02:06,670 I guess, we'll probably start today. 45 00:02:06,670 --> 00:02:10,729 Another medical issue is osteoarthritis, 46 00:02:10,729 --> 00:02:13,460 and the properties of the trabecular bone 47 00:02:13,460 --> 00:02:16,980 are important in arthritis, and the third issue 48 00:02:16,980 --> 00:02:18,370 is in joint replacements. 49 00:02:18,370 --> 00:02:21,000 And so we're going to talk a little bit about osteoporosis, 50 00:02:21,000 --> 00:02:23,670 osteoarthritis, and then joint replacements. 51 00:02:23,670 --> 00:02:25,170 And then I'll talk a little bit more 52 00:02:25,170 --> 00:02:28,310 about modeling bone like a foam and how it deforms 53 00:02:28,310 --> 00:02:30,290 and how it fails. 54 00:02:30,290 --> 00:02:34,020 And then we'll talk a little bit how we can model osteoporosis. 55 00:02:34,020 --> 00:02:37,605 So let me write down some of these things. 56 00:02:37,605 --> 00:02:39,450 I guess we'll start here. 57 00:02:47,830 --> 00:02:51,200 So trabecular bone has a foam-like structure, 58 00:02:51,200 --> 00:02:52,950 and what we're going to see is that we 59 00:02:52,950 --> 00:02:55,140 can use the models for foams to describe 60 00:02:55,140 --> 00:02:57,634 the mechanical behavior of the bone. 61 00:03:10,900 --> 00:03:13,104 It exists at the ends of the long bones. 62 00:03:13,104 --> 00:03:14,520 And at the ends of the long bones, 63 00:03:14,520 --> 00:03:16,760 the bones become more bulbous. 64 00:03:16,760 --> 00:03:20,190 And really what that's for is to increase the surface 65 00:03:20,190 --> 00:03:23,450 area so that there's cartilage between the ends of the two 66 00:03:23,450 --> 00:03:23,950 bones. 67 00:03:23,950 --> 00:03:25,430 So there would be a bone here and a bone there, 68 00:03:25,430 --> 00:03:26,971 and there's cartilage in between them 69 00:03:26,971 --> 00:03:29,150 that sort of lubricates that joint 70 00:03:29,150 --> 00:03:31,900 and makes low friction at the joint. 71 00:03:31,900 --> 00:03:35,760 And the bone gets larger to decrease the stresses 72 00:03:35,760 --> 00:03:36,506 on the cartilage. 73 00:03:36,506 --> 00:03:38,880 So if you have the same force and you have a larger area, 74 00:03:38,880 --> 00:03:40,500 you're going to have a smaller stress. 75 00:03:40,500 --> 00:03:43,320 So that's why the bone gets bulbous like that. 76 00:03:43,320 --> 00:03:45,780 And then by having the trabecular bone, because it's 77 00:03:45,780 --> 00:03:47,350 so porous and lightweight, you're 78 00:03:47,350 --> 00:03:49,140 not having a big, dense hunk of bone 79 00:03:49,140 --> 00:03:52,270 at the end of the long bones. 80 00:03:52,270 --> 00:03:56,367 So it exists at the ends of the long bones. 81 00:03:56,367 --> 00:03:58,950 And I'll just say the ends have a larger area than the shafts. 82 00:04:07,310 --> 00:04:10,872 And that's to distribute the loads on the cartilage 83 00:04:10,872 --> 00:04:12,580 or to reduce the stress on the cartilage. 84 00:04:21,300 --> 00:04:25,390 And then the trabecular bone reduces the weight. 85 00:04:33,680 --> 00:04:38,386 So it also exists in the core of the vertebrae, 86 00:04:38,386 --> 00:04:45,840 and in fact, it makes up most of the vertebrae 87 00:04:45,840 --> 00:04:49,460 and then in things like the skull and the pelvic bones 88 00:04:49,460 --> 00:04:51,469 in shell and plate-like bones. 89 00:05:14,060 --> 00:05:16,223 And so it's the core of a sandwich structure there. 90 00:05:27,350 --> 00:05:32,250 So it's of interest in osteoporosis, 91 00:05:32,250 --> 00:05:40,115 in osteoarthritis, and in joint replacements. 92 00:05:50,476 --> 00:05:57,780 So if we start by thinking about osteoporosis, 93 00:05:57,780 --> 00:05:59,430 you probably know that osteoporosis 94 00:05:59,430 --> 00:06:04,220 is a disease where the bone mass becomes reduced 95 00:06:04,220 --> 00:06:06,380 and there's a greater risk of fracture, 96 00:06:06,380 --> 00:06:09,070 so there's especially a greater risk of hip fractures 97 00:06:09,070 --> 00:06:10,774 and vertebral fractures. 98 00:06:10,774 --> 00:06:12,440 And it turns out in both of those sites, 99 00:06:12,440 --> 00:06:14,320 if you just look at these bones here, 100 00:06:14,320 --> 00:06:18,000 typically if you have a hip fracture, what happens is 101 00:06:18,000 --> 00:06:19,660 the neck of the femur breaks. 102 00:06:19,660 --> 00:06:21,000 So this is called the neck here. 103 00:06:21,000 --> 00:06:23,360 This is called the head, this spherical bit there. 104 00:06:23,360 --> 00:06:24,977 So the neck has a fracture, and you 105 00:06:24,977 --> 00:06:27,060 can see most of the bone there is trabecular bone, 106 00:06:27,060 --> 00:06:29,610 so it's really carrying most of the load and the same 107 00:06:29,610 --> 00:06:31,080 with the vertebrae. 108 00:06:31,080 --> 00:06:33,140 This sort of cylindrical part of the vertebrae 109 00:06:33,140 --> 00:06:35,090 here carries most of the load. 110 00:06:35,090 --> 00:06:37,410 It has a shell of really thin cortical bone, 111 00:06:37,410 --> 00:06:39,370 but it's mostly trabecular bone. 112 00:06:39,370 --> 00:06:42,064 And when the loads are vertical like this, 113 00:06:42,064 --> 00:06:43,730 that's really the trabecular bone that's 114 00:06:43,730 --> 00:06:45,210 carrying most of the load. 115 00:06:45,210 --> 00:06:48,240 And people get sometimes what are called wedge fractures 116 00:06:48,240 --> 00:06:50,970 where instead of having a sort of a cylinder with parallel 117 00:06:50,970 --> 00:06:54,000 faces like this, the trabecular bone fails, 118 00:06:54,000 --> 00:06:57,343 and the bone ends up like that so that there's-- yeah, I know. 119 00:06:57,343 --> 00:06:59,770 You make that wincing expression. 120 00:06:59,770 --> 00:07:00,492 It's like ouchy. 121 00:07:00,492 --> 00:07:02,894 And in fact, it's very ouchy for people who get that. 122 00:07:02,894 --> 00:07:04,810 And when you see little old ladies who are all 123 00:07:04,810 --> 00:07:06,210 hunched over, that's why. 124 00:07:06,210 --> 00:07:07,770 The bone has actually failed. 125 00:07:07,770 --> 00:07:10,840 It's actually been crushed into these wedge fractures, 126 00:07:10,840 --> 00:07:12,880 and there's no way they can straighten it out, 127 00:07:12,880 --> 00:07:14,560 and it's quite painful. 128 00:07:14,560 --> 00:07:17,359 So people who look at osteoporosis 129 00:07:17,359 --> 00:07:19,400 are quite interested in the mechanical properties 130 00:07:19,400 --> 00:07:22,340 of trabecular bone for this sort of reason. 131 00:07:22,340 --> 00:07:24,470 The hip fractures are particularly 132 00:07:24,470 --> 00:07:28,071 serious because people become immobilized and then sometimes 133 00:07:28,071 --> 00:07:30,070 because they're immobilized, they get pneumonia, 134 00:07:30,070 --> 00:07:32,430 and in elderly people they sometimes die. 135 00:07:32,430 --> 00:07:36,820 So something like 40% of elderly patients who are over 65 136 00:07:36,820 --> 00:07:39,470 die within a year of having hip fracture. 137 00:07:39,470 --> 00:07:41,690 So it's not that the hip fracture kills them, 138 00:07:41,690 --> 00:07:44,980 it's that they become so immobile, and they can't move, 139 00:07:44,980 --> 00:07:47,930 and they can't walk around, and they end up getting pneumonia. 140 00:07:47,930 --> 00:07:49,780 So it's quite a serious thing. 141 00:07:49,780 --> 00:07:52,610 And there's something like 300,000 hip fractures a year 142 00:07:52,610 --> 00:07:55,790 in the US, and the cost of treating these hip fractures 143 00:07:55,790 --> 00:07:58,150 is something like $19 billion. 144 00:07:58,150 --> 00:08:00,290 So yeah, it's a huge problem. 145 00:08:00,290 --> 00:08:04,070 And as the population is aging, as baby boomers like 146 00:08:04,070 --> 00:08:07,880 me get older and older, there's going more people 147 00:08:07,880 --> 00:08:09,240 having hip fractures. 148 00:08:09,240 --> 00:08:13,510 So it's a huge deal, osteoporosis. 149 00:08:13,510 --> 00:08:24,050 So we'll say bone mass decreases with age, 150 00:08:24,050 --> 00:08:27,400 and osteoporosis is extreme bone loss. 151 00:08:35,247 --> 00:08:36,830 And a little later today I'll show you 152 00:08:36,830 --> 00:08:38,169 some pictures of what it looks like when 153 00:08:38,169 --> 00:08:39,210 people have osteoporosis. 154 00:08:44,950 --> 00:08:56,260 So the most common fractures are of the hip and the vertebrae, 155 00:08:56,260 --> 00:08:58,290 and at both sites, most of the load 156 00:08:58,290 --> 00:09:00,020 is carried by the trabecular bone. 157 00:09:18,750 --> 00:09:20,975 And the hip fractures you are the most serious. 158 00:09:26,980 --> 00:09:31,080 40% of elderly patients pass away within a year. 159 00:10:34,620 --> 00:10:38,420 So that's sort of a little introduction to osteoporosis. 160 00:10:38,420 --> 00:10:41,563 The next issue that people are interested in 161 00:10:41,563 --> 00:10:42,313 is osteoarthritis. 162 00:10:49,930 --> 00:10:52,310 And in osteoarthritis, there's a degradation 163 00:10:52,310 --> 00:10:56,210 of cartilage at the joints, and the stress on the cartilage 164 00:10:56,210 --> 00:10:58,260 is affected by the modulus of the bone that 165 00:10:58,260 --> 00:11:00,337 presses against the cartilage. 166 00:11:00,337 --> 00:11:02,420 You can kind of magic if you have a fiber compass, 167 00:11:02,420 --> 00:11:04,753 for instance, most of the stresses, if you're loading it 168 00:11:04,753 --> 00:11:07,030 along the fibers, is carried by the fibers 169 00:11:07,030 --> 00:11:08,170 because they're stiffer. 170 00:11:08,170 --> 00:11:10,970 So if you have like say trabecular bone that 171 00:11:10,970 --> 00:11:13,260 has varying density, the denser bits 172 00:11:13,260 --> 00:11:16,340 are going to have higher moduli, and it's 173 00:11:16,340 --> 00:11:19,020 there's going more stress associated with that. 174 00:11:19,020 --> 00:11:21,260 And so the modulus of the trabecular bone 175 00:11:21,260 --> 00:11:23,930 can affect how the loads are distributed in the cartilage, 176 00:11:23,930 --> 00:11:26,949 and that can affect the damage in the cartilage. 177 00:11:26,949 --> 00:11:28,490 And the shell, as I mentioned before, 178 00:11:28,490 --> 00:11:30,730 this sort of shell of cortical bone 179 00:11:30,730 --> 00:11:33,540 or the dense bone at the joints can be quite thin. 180 00:11:33,540 --> 00:11:35,420 It can be less than a millimeter. 181 00:11:35,420 --> 00:11:37,820 So I brought my little bones along with me again. 182 00:11:37,820 --> 00:11:41,050 So this is the head of a femur here, 183 00:11:41,050 --> 00:11:44,579 and this is a piece of a knee joint here from a tibia. 184 00:11:44,579 --> 00:11:46,120 And you can see just looking at these 185 00:11:46,120 --> 00:11:48,150 how thin the cortical shell is. 186 00:11:48,150 --> 00:11:51,147 So you can get an idea of how thin that is. 187 00:11:57,280 --> 00:12:02,650 So osteoarthritis involves a degradation 188 00:12:02,650 --> 00:12:04,130 of the cartilage at the joints. 189 00:12:21,780 --> 00:12:23,780 And the stress on the cartilage is 190 00:12:23,780 --> 00:12:33,630 affected by the moduli of the underlying bone, 191 00:12:33,630 --> 00:12:45,760 and the cortical shell, the totally dense bone, 192 00:12:45,760 --> 00:12:46,792 can be quite thin. 193 00:12:57,990 --> 00:13:00,474 So the mechanical properties of the trabecular bone 194 00:13:00,474 --> 00:13:02,640 can affect the stress distribution on the cartilage. 195 00:13:43,440 --> 00:13:46,570 And if osteoarthritis gets particularly bad, then 196 00:13:46,570 --> 00:13:48,810 sometimes people have joint replacements. 197 00:13:48,810 --> 00:13:51,190 So when it gets really bad, the cartilage 198 00:13:51,190 --> 00:13:54,260 is degraded completely, and the bone is rubbing on bone, 199 00:13:54,260 --> 00:13:55,760 and that's quite painful. 200 00:13:55,760 --> 00:13:58,490 And when it gets to that point, people generally 201 00:13:58,490 --> 00:14:00,800 have a joint replacement. 202 00:14:00,800 --> 00:14:02,760 And so the way the joint replacements are done 203 00:14:02,760 --> 00:14:06,490 is say somebody who is going to have a hip replacement, what 204 00:14:06,490 --> 00:14:09,490 they do is they chop off the top of the femur. 205 00:14:09,490 --> 00:14:12,580 So they would chop the femur off somewhere around here, 206 00:14:12,580 --> 00:14:14,950 and then they have a metal implant 207 00:14:14,950 --> 00:14:17,110 that has a spherical ball. 208 00:14:17,110 --> 00:14:18,770 That's like the head of the femur. 209 00:14:18,770 --> 00:14:21,250 And then it has a sort of stem and a shaft here 210 00:14:21,250 --> 00:14:24,140 that goes into the hollow part of the long part 211 00:14:24,140 --> 00:14:27,850 of the shaft of the femur. 212 00:14:27,850 --> 00:14:31,950 And so they use a number of different metals for this, 213 00:14:31,950 --> 00:14:33,710 titanium and stainless steel, and there's 214 00:14:33,710 --> 00:14:36,460 a cobalt-chromium alloy are also used. 215 00:14:36,460 --> 00:14:38,720 So you need metals that are biocompatible, 216 00:14:38,720 --> 00:14:40,261 aren't going to corrode, aren't going 217 00:14:40,261 --> 00:14:41,850 to have degradation products. 218 00:14:41,850 --> 00:14:44,930 And then the bone grows around that implant, 219 00:14:44,930 --> 00:14:48,240 and the bone grows in response to mechanical loads. 220 00:14:48,240 --> 00:14:50,750 So the density of the bone depends 221 00:14:50,750 --> 00:14:53,329 on the magnitude of the load, and the orientation 222 00:14:53,329 --> 00:14:55,870 of the trabeculae depends on the orientation of the principle 223 00:14:55,870 --> 00:14:57,800 stresses that are applied. 224 00:14:57,800 --> 00:14:59,300 So let me write that down. 225 00:15:38,360 --> 00:15:45,530 So they cut off the end of the bone, 226 00:15:45,530 --> 00:15:50,760 and they insert the implant into the hollow shaft 227 00:15:50,760 --> 00:15:52,090 of the remaining bone. 228 00:16:06,298 --> 00:16:18,930 And the metals they use are titanium, stainless steel, 229 00:16:18,930 --> 00:16:21,050 and a chromium-cobalt alloy. 230 00:16:28,250 --> 00:16:31,140 And then the bone grows into that implant. 231 00:16:36,970 --> 00:16:39,553 And the bone grows in response to mechanical loads. 232 00:16:52,974 --> 00:16:55,550 So the density of the bone depends 233 00:16:55,550 --> 00:17:07,940 on the magnitude of the stresses, 234 00:17:07,940 --> 00:17:13,829 and the orientation of the bone depends 235 00:17:13,829 --> 00:17:15,819 on the principle stresses. 236 00:17:56,430 --> 00:17:59,760 So one of the issues that comes up in joint replacements 237 00:17:59,760 --> 00:18:01,570 is that there's a mismatch in the moduli 238 00:18:01,570 --> 00:18:03,570 between the metal and the bone. 239 00:18:03,570 --> 00:18:06,220 So if you think the metal, like something like stainless steel, 240 00:18:06,220 --> 00:18:10,210 has a modulus of around 200, 210 gigapascals. 241 00:18:10,210 --> 00:18:11,890 And the cortical bone has a modulus 242 00:18:11,890 --> 00:18:15,330 of about 18 gigapascals, and the trabecular bone 243 00:18:15,330 --> 00:18:20,600 has a modulus between about 0.01 and 2 gigapascals, 244 00:18:20,600 --> 00:18:22,080 depending on its density. 245 00:18:22,080 --> 00:18:24,610 So you're taking the bone out, and you're replacing it 246 00:18:24,610 --> 00:18:26,710 with something that's much, much stiffer, and that 247 00:18:26,710 --> 00:18:30,850 changes the stress distribution around the remaining bone. 248 00:18:30,850 --> 00:18:33,040 And one of the things that can happen 249 00:18:33,040 --> 00:18:34,910 is you can get a loosening of the implant. 250 00:18:34,910 --> 00:18:37,070 So the bone can grow in initially, 251 00:18:37,070 --> 00:18:38,850 but over time, you get a different stress 252 00:18:38,850 --> 00:18:39,685 field in the bone. 253 00:18:39,685 --> 00:18:41,830 And if you have a different stress field, 254 00:18:41,830 --> 00:18:45,860 then the bone can resorb away from the implant and cause 255 00:18:45,860 --> 00:18:47,270 what's called loosening. 256 00:18:47,270 --> 00:18:49,600 So if the implant becomes loose, that's 257 00:18:49,600 --> 00:18:50,880 clearly not a good thing. 258 00:18:50,880 --> 00:18:52,400 It's a bad thing. 259 00:18:52,400 --> 00:18:54,515 And often orthopedic surgeons don't 260 00:18:54,515 --> 00:18:56,640 like to do these joint replacements in young people 261 00:18:56,640 --> 00:18:59,110 partly because they don't always loosen, 262 00:18:59,110 --> 00:19:00,690 but occasionally they do. 263 00:19:00,690 --> 00:19:03,300 And if they loosen they can go back and do a revision. 264 00:19:03,300 --> 00:19:05,076 But you can kind of imagine after they've 265 00:19:05,076 --> 00:19:06,450 chopped the head of the femur off 266 00:19:06,450 --> 00:19:08,340 and they put one implant in, it's 267 00:19:08,340 --> 00:19:11,117 not that easy to go back in and replace that with another one. 268 00:19:11,117 --> 00:19:12,700 You would need one with a longer stem, 269 00:19:12,700 --> 00:19:15,850 and the whole thing becomes a little bit more complicated. 270 00:19:15,850 --> 00:19:17,545 So this issue of stress shielding 271 00:19:17,545 --> 00:19:18,920 is what it's called when you have 272 00:19:18,920 --> 00:19:21,320 something much stiffer that's shielding 273 00:19:21,320 --> 00:19:23,502 the stresses in the bone. 274 00:19:23,502 --> 00:19:24,960 The issue of stress shielding means 275 00:19:24,960 --> 00:19:28,680 that they don't like to do the replacements on younger 276 00:19:28,680 --> 00:20:01,810 patients unless you can get stress shielding. 277 00:20:01,810 --> 00:20:10,050 And if we just compare-- if we look at the cobalt and chromium 278 00:20:10,050 --> 00:20:16,650 alloy, the modulus of that in gigapascals is about 210. 279 00:20:16,650 --> 00:20:19,770 If we look at the titanium alloys that are used, 280 00:20:19,770 --> 00:20:22,380 the modulus is about 110. 281 00:20:22,380 --> 00:20:24,100 If we look at the stainless steel-- 282 00:20:24,100 --> 00:20:32,400 it's 316 stainless steel-- it has a modulus of around 210. 283 00:20:32,400 --> 00:20:38,080 And then if we look at the bone, the cortical bone 284 00:20:38,080 --> 00:20:45,870 has a modulus of about 18, and the trabecular bone 285 00:20:45,870 --> 00:20:50,160 has a modulus 0.01 to 2 gigapascals 286 00:20:50,160 --> 00:20:51,480 depending on the density. 287 00:20:56,310 --> 00:20:59,840 So after the joint replacement happens, 288 00:20:59,840 --> 00:21:02,176 the remodeling of the bone is affected. 289 00:21:25,820 --> 00:21:30,450 So the idea is that the stiffer metal carries more of the load, 290 00:21:30,450 --> 00:21:32,953 and then the bone carries less load, and then it resorbs. 291 00:21:49,620 --> 00:21:53,240 And that can lead to this thing called loosening, 292 00:21:53,240 --> 00:21:54,545 which is not desirable. 293 00:22:09,371 --> 00:22:11,620 Now, this typically doesn't happen till about 15 years 294 00:22:11,620 --> 00:22:13,240 after you've had the implant, so it's not 295 00:22:13,240 --> 00:22:14,865 something that would happen right away, 296 00:22:14,865 --> 00:22:16,056 but it can happen later on. 297 00:22:36,930 --> 00:22:38,760 So these are all sort of medical reasons 298 00:22:38,760 --> 00:22:40,926 why people are interested in trabecular bone because 299 00:22:40,926 --> 00:22:46,380 of osteoporosis, osteoarthritis, and joint replacements. 300 00:22:46,380 --> 00:22:48,870 So I wanted to start by talking about the structure 301 00:22:48,870 --> 00:22:50,310 of trabecular bone. 302 00:22:56,430 --> 00:23:01,240 And then we'll talk about what the stress-strain curves look 303 00:23:01,240 --> 00:23:03,330 like in compression and tension, what 304 00:23:03,330 --> 00:23:05,490 are the mechanisms of deformation and failure, 305 00:23:05,490 --> 00:23:09,580 and how we can apply our models for foams to the trabecular 306 00:23:09,580 --> 00:23:11,690 bone. 307 00:23:11,690 --> 00:23:14,140 So the idea is that the structure of the bone 308 00:23:14,140 --> 00:23:17,400 resembles a foam, and here's some SCM 309 00:23:17,400 --> 00:23:20,150 images of trabecular bone. 310 00:23:20,150 --> 00:23:23,950 And you can see that the bone has a varying structure. 311 00:23:23,950 --> 00:23:25,910 If it's relatively low density, this 312 00:23:25,910 --> 00:23:28,609 is a bone that's almost like an open-cell foam 313 00:23:28,609 --> 00:23:30,150 if I didn't tell you that was a bone, 314 00:23:30,150 --> 00:23:33,370 you might actually think it was an open-cell foam. 315 00:23:33,370 --> 00:23:36,100 And here's a denser piece of bone, 316 00:23:36,100 --> 00:23:39,840 and you can see there's still interconnections between all 317 00:23:39,840 --> 00:23:41,470 the openings, so it's not exactly 318 00:23:41,470 --> 00:23:45,160 like a closed-cell foam, but it's much denser, 319 00:23:45,160 --> 00:23:47,190 and it's almost like there's perforated plates 320 00:23:47,190 --> 00:23:48,370 in the structure. 321 00:23:48,370 --> 00:23:51,734 And then as I said the bone can grow in response to loads. 322 00:23:51,734 --> 00:23:53,900 So if you have loads that are more or less vertical, 323 00:23:53,900 --> 00:23:55,970 the trabeculae tend to line up and be 324 00:23:55,970 --> 00:24:00,420 more or less vertical with some sort of horizontal bracing. 325 00:24:00,420 --> 00:24:02,880 So this is a piece of bone from a knee, 326 00:24:02,880 --> 00:24:06,020 the condyle is sort of towards the top of the knee. 327 00:24:06,020 --> 00:24:10,310 And you can see these are sort of plate-like pieces of bone. 328 00:24:10,310 --> 00:24:13,370 They're almost parallel, and not too surprisingly in your knee, 329 00:24:13,370 --> 00:24:15,416 the loads are typically vertical, 330 00:24:15,416 --> 00:24:16,790 and then there's a little bracing 331 00:24:16,790 --> 00:24:18,752 bits that go horizontally here. 332 00:24:18,752 --> 00:24:20,210 So you can get different structures 333 00:24:20,210 --> 00:24:23,710 depending on the loading on the bone, 334 00:24:23,710 --> 00:24:26,370 and the density of the bone corresponds 335 00:24:26,370 --> 00:24:28,520 to the magnitude of the load, and the orientation 336 00:24:28,520 --> 00:24:34,954 of the trabeculae corresponds to the orientation of the load. 337 00:24:34,954 --> 00:24:35,870 AUDIENCE: [INAUDIBLE]. 338 00:24:40,416 --> 00:24:42,380 LORNA GIBSON: Resorb. 339 00:24:42,380 --> 00:24:45,686 So when the bone density goes down, when you lose bone mass, 340 00:24:45,686 --> 00:24:46,727 that's called resorption. 341 00:24:50,340 --> 00:24:54,140 So the idea is that the trabecular bone 342 00:24:54,140 --> 00:24:55,253 resembles a foam. 343 00:24:59,690 --> 00:25:06,030 And in fact, the word trabecular comes from Latin, 344 00:25:06,030 --> 00:25:08,421 and in Latin, it means little beam. 345 00:25:13,210 --> 00:25:15,179 So the foams to form by bending. 346 00:25:15,179 --> 00:25:17,220 They act like little beams, and so the trabeculae 347 00:25:17,220 --> 00:25:21,140 are like little beams, even in Latin. 348 00:25:21,140 --> 00:25:23,556 There's a range of relative densities, 349 00:25:23,556 --> 00:25:25,180 and you can see in that image up there, 350 00:25:25,180 --> 00:25:26,664 you can see that there's a range. 351 00:25:30,300 --> 00:25:33,630 And they range typically between about a 5% in dense 352 00:25:33,630 --> 00:25:35,090 and 50% in dense. 353 00:25:39,320 --> 00:25:43,450 So something like 0.1 or 0.2 might be typical. 354 00:25:43,450 --> 00:25:48,920 And the low-density bone resembles an open-cell foam. 355 00:25:56,890 --> 00:25:59,270 And the higher density, it becomes more 356 00:25:59,270 --> 00:26:00,510 like perforated plates. 357 00:26:17,120 --> 00:26:19,680 And the structure can be highly anisotropic 358 00:26:19,680 --> 00:26:21,140 depending on the stress field. 359 00:26:46,050 --> 00:26:50,610 And then I've got another image here of the trabecular bone. 360 00:26:50,610 --> 00:26:52,930 These images are using what's called 361 00:26:52,930 --> 00:26:54,940 micro computed tomography. 362 00:26:54,940 --> 00:26:57,610 So you've probably heard of computed tomography. 363 00:26:57,610 --> 00:27:00,710 Say somebody has cancer, they get put in a CT machine, 364 00:27:00,710 --> 00:27:02,240 and they do a scan. 365 00:27:02,240 --> 00:27:04,620 The micro CT is more of a research tool. 366 00:27:04,620 --> 00:27:06,360 It's the same kind of technology, 367 00:27:06,360 --> 00:27:08,410 but it's got a much finer resolution, 368 00:27:08,410 --> 00:27:11,230 and typically, you put a small specimen into a machine 369 00:27:11,230 --> 00:27:11,740 to do this. 370 00:27:11,740 --> 00:27:14,920 So the specimen might be half an inch 371 00:27:14,920 --> 00:27:17,910 in diameter and an inch tall, something like that. 372 00:27:17,910 --> 00:27:20,860 So these are done by a colleague, Ralph Muller, who's 373 00:27:20,860 --> 00:27:24,110 in Zurich, and this is one of his bread and butter things 374 00:27:24,110 --> 00:27:27,280 that he has these images, and he looks at osteoporosis. 375 00:27:27,280 --> 00:27:30,310 And you can see here the difference in the structure 376 00:27:30,310 --> 00:27:31,680 for the different densities. 377 00:27:31,680 --> 00:27:36,680 So here's a 26% dense piece of bone in the femoral head. 378 00:27:36,680 --> 00:27:38,980 It looks pretty sturdy and substantial. 379 00:27:38,980 --> 00:27:43,210 Here's an 11% dense piece from the lumbar spine, 380 00:27:43,210 --> 00:27:45,450 and here's a 6% dense piece. 381 00:27:45,450 --> 00:27:50,970 And you can kind of see when you go from 26 to 11, 382 00:27:50,970 --> 00:27:53,180 the struts get a little bit thinner. 383 00:27:53,180 --> 00:27:56,954 And when you go from 11 to 6, the struts get very thin, 384 00:27:56,954 --> 00:27:58,370 and in fact, if they get too thin, 385 00:27:58,370 --> 00:28:01,050 the struts resorb altogether, and some of their struts 386 00:28:01,050 --> 00:28:02,560 can just disappear. 387 00:28:02,560 --> 00:28:05,210 So when people get osteoporosis, what happens 388 00:28:05,210 --> 00:28:08,680 is they first lose bone mass by thinning the struts, 389 00:28:08,680 --> 00:28:12,270 but then at some point, the struts just resorb altogether. 390 00:28:12,270 --> 00:28:15,180 And if you think of the struts as a biological material, 391 00:28:15,180 --> 00:28:17,250 they have bone cells in them. 392 00:28:17,250 --> 00:28:20,760 So there's little osteoclasts and osteoblasts and osteocytes 393 00:28:20,760 --> 00:28:24,200 that live in the bone, the mineral thing, the bony thing. 394 00:28:24,200 --> 00:28:28,220 And those cells have dimensions of 10s of microns, so maybe 20, 395 00:28:28,220 --> 00:28:29,840 30 microns, something like that. 396 00:28:29,840 --> 00:28:31,780 So the struts can't get any thinner than that. 397 00:28:31,780 --> 00:28:34,154 If they get thinner than that, then the cells can't live, 398 00:28:34,154 --> 00:28:36,430 and the thing just disappears altogether. 399 00:28:36,430 --> 00:28:40,310 And you can think of from a mechanical point of view, 400 00:28:40,310 --> 00:28:43,160 if you lose density by thinning the struts, 401 00:28:43,160 --> 00:28:45,080 you can use our sort of foam equations. 402 00:28:45,080 --> 00:28:48,810 And say the density went from 0.2 to 0.1, 403 00:28:48,810 --> 00:28:51,160 you could make some estimate of how the modulus 404 00:28:51,160 --> 00:28:54,270 and how the strength would vary depending on our foam models. 405 00:28:54,270 --> 00:28:57,310 But if you lose density by resorbing the struts, 406 00:28:57,310 --> 00:28:59,490 the struts just disappear altogether, 407 00:28:59,490 --> 00:29:02,990 then it's as if you had a steel scaffold or a steel 408 00:29:02,990 --> 00:29:04,130 structure of a building. 409 00:29:04,130 --> 00:29:06,420 And now you're starting to remove columns and remove 410 00:29:06,420 --> 00:29:07,590 beams. 411 00:29:07,590 --> 00:29:08,280 Yes, I know. 412 00:29:08,280 --> 00:29:09,810 That's not good, not good. 413 00:29:09,810 --> 00:29:11,270 And so we'll talk a little bit more 414 00:29:11,270 --> 00:29:13,820 about that when we talk more about osteoporosis, 415 00:29:13,820 --> 00:29:15,700 and you can see the consequences of that. 416 00:29:15,700 --> 00:29:17,241 But this image here kind of gives you 417 00:29:17,241 --> 00:29:20,870 a little bit of a picture of what the bone structure looks 418 00:29:20,870 --> 00:29:23,280 like as it gets less dense. 419 00:29:23,280 --> 00:29:24,820 So I want to talk a little bit more 420 00:29:24,820 --> 00:29:27,410 about the bone growing in response to load. 421 00:29:27,410 --> 00:29:28,850 Let me rub off the board. 422 00:30:06,980 --> 00:30:09,720 So you're probably already a little bit familiar 423 00:30:09,720 --> 00:30:10,400 with this idea. 424 00:30:10,400 --> 00:30:13,670 So when astronauts go up into space, 425 00:30:13,670 --> 00:30:16,252 they often do exercises where they have a treadmill, 426 00:30:16,252 --> 00:30:18,710 and they've got springs, and they're pulling on the springs 427 00:30:18,710 --> 00:30:20,049 to try to exercise themselves. 428 00:30:20,049 --> 00:30:21,840 And the reason they do that is when they're 429 00:30:21,840 --> 00:30:25,450 in microgravity, if they were doing some kind of exercise, 430 00:30:25,450 --> 00:30:27,280 they would lose bone mass. 431 00:30:27,280 --> 00:30:30,900 And they will get back to Earth where we have Earth gravity, 432 00:30:30,900 --> 00:30:32,160 and they would have a problem. 433 00:30:32,160 --> 00:30:35,650 So you see it in astronauts, in microgravity. 434 00:30:35,650 --> 00:30:38,660 The other place you see this just in everyday life 435 00:30:38,660 --> 00:30:41,020 is in professional tennis players. 436 00:30:41,020 --> 00:30:44,100 People have done like x-rays of the bones 437 00:30:44,100 --> 00:30:46,320 of professional tennis players, and obviously, they 438 00:30:46,320 --> 00:30:49,420 have one arm that they hit the ball with their racquet. 439 00:30:49,420 --> 00:30:50,890 The bones in that arm actually get 440 00:30:50,890 --> 00:30:54,500 bigger because they're loading that bone over and over 441 00:30:54,500 --> 00:30:57,020 again pretty much every day when they're playing tennis, 442 00:30:57,020 --> 00:30:58,700 and they're not loading the other arm. 443 00:30:58,700 --> 00:31:01,350 So their two arms are not symmetrical because 444 00:31:01,350 --> 00:31:04,760 of this loading from hitting the racquet over and over. 445 00:31:04,760 --> 00:31:07,480 And the people in 3032 have already seen this, 446 00:31:07,480 --> 00:31:10,210 but I couldn't resist bringing up the Guinea fowl experiments 447 00:31:10,210 --> 00:31:11,580 again. 448 00:31:11,580 --> 00:31:14,270 So obviously, you can only do x-rays on human. 449 00:31:14,270 --> 00:31:16,590 You can't sacrifice the humans and look at their bones, 450 00:31:16,590 --> 00:31:18,050 but you can with Guinea fowl. 451 00:31:18,050 --> 00:31:20,600 And so people have done experiments 452 00:31:20,600 --> 00:31:23,470 where they run Guinea fowl on treadmills, 453 00:31:23,470 --> 00:31:25,700 and they have one set of Guinea fowl 454 00:31:25,700 --> 00:31:27,950 that they run on the treadmill that's horizontal. 455 00:31:27,950 --> 00:31:29,450 They have another set of Guinea fowl 456 00:31:29,450 --> 00:31:31,949 that they run on a treadmill that's inclined to 20 degrees, 457 00:31:31,949 --> 00:31:34,490 so one would think they might have more stress on their bones 458 00:31:34,490 --> 00:31:36,550 from that, and then they have a control group 459 00:31:36,550 --> 00:31:38,580 that they don't run on the treadmill at all. 460 00:31:38,580 --> 00:31:41,170 And then what they do is they have a forced 461 00:31:41,170 --> 00:31:44,360 plate on the treadmill so as the Guinea fowl is running, 462 00:31:44,360 --> 00:31:46,320 they measure the maximum force in they're 463 00:31:46,320 --> 00:31:47,820 taking high-speed video. 464 00:31:47,820 --> 00:31:49,850 And then they measure the angle of the knee 465 00:31:49,850 --> 00:31:52,490 at that point at which the force is maximum. 466 00:31:52,490 --> 00:31:53,940 And they can see there's a change 467 00:31:53,940 --> 00:31:57,160 in the angle of the knee when they put them on the inclined 468 00:31:57,160 --> 00:31:59,290 treadmill, not too surprisingly. 469 00:31:59,290 --> 00:32:01,870 And then these are juvenile Guinea fowl 470 00:32:01,870 --> 00:32:03,856 that haven't completely matured their bones. 471 00:32:03,856 --> 00:32:05,480 And then after about six weeks of this, 472 00:32:05,480 --> 00:32:09,070 they sacrifice the Guinea fowl, and they do scans on the bone, 473 00:32:09,070 --> 00:32:11,250 and they look at the orientation of the bone, 474 00:32:11,250 --> 00:32:14,560 and they measure what's called the orientation 475 00:32:14,560 --> 00:32:16,150 of the peak trabecular density, which 476 00:32:16,150 --> 00:32:19,600 is a way of characterizing the orientation of the bone. 477 00:32:19,600 --> 00:32:22,510 And they find that the angle of the knee when 478 00:32:22,510 --> 00:32:26,490 the Guinea fowl are running changes by about 14 degrees. 479 00:32:26,490 --> 00:32:28,130 And it turns out the angle of the bone, 480 00:32:28,130 --> 00:32:31,520 the orientation of the bone also changes by about 14 degrees. 481 00:32:31,520 --> 00:32:34,910 So the bone has remodeled to match that change 482 00:32:34,910 --> 00:32:37,710 in the forces that are applied as the Guinea fowl are running 483 00:32:37,710 --> 00:32:38,780 on a treadmill. 484 00:32:38,780 --> 00:32:40,410 So this is all a demonstration just 485 00:32:40,410 --> 00:32:43,410 to show that bone grows in response to load. 486 00:32:43,410 --> 00:32:47,230 So let me write down some of this stuff. 487 00:32:47,230 --> 00:32:51,840 So I will say astronauts-- did you 488 00:32:51,840 --> 00:32:55,600 see Michael Collins is going to come to the talk at MIT? 489 00:32:55,600 --> 00:32:58,840 When I was a kid in '60s, he was one of the Apollo astronauts. 490 00:32:58,840 --> 00:33:02,830 He was like one of the first NASA astronauts. 491 00:33:02,830 --> 00:33:11,232 Anyway astronauts, so in microgravity, 492 00:33:11,232 --> 00:33:13,065 they would lose bone if they don't exercise. 493 00:33:20,100 --> 00:33:41,330 And tennis players, the bones get larger in the arm 494 00:33:41,330 --> 00:33:43,982 that they hold the racket with. 495 00:33:43,982 --> 00:33:46,109 And then I'll just write a little bit 496 00:33:46,109 --> 00:33:47,900 of notes about the Guinea fowl experiments. 497 00:33:58,200 --> 00:34:09,934 So this was done by-- it's in a paper, Ponzer et al 2006. 498 00:34:09,934 --> 00:34:11,600 So they have one set of Guinea fowl that 499 00:34:11,600 --> 00:34:15,880 run on a level treadmill, they have 500 00:34:15,880 --> 00:34:22,900 another set that run on a inclined treadmill, 501 00:34:22,900 --> 00:34:25,590 and it's inclined at 20 degrees. 502 00:34:25,590 --> 00:34:27,322 And then they have a control group that 503 00:34:27,322 --> 00:34:28,530 doesn't run on the treadmill. 504 00:34:44,129 --> 00:34:52,400 And then they measure the angle at the knee at the moment 505 00:34:52,400 --> 00:34:54,238 of peak force on the treadmill. 506 00:35:06,450 --> 00:35:16,310 And after six weeks, they sacrificed the Guinea fowl, 507 00:35:16,310 --> 00:35:19,580 and they measured the orientation 508 00:35:19,580 --> 00:35:21,475 of the peak trabecular density. 509 00:35:38,600 --> 00:35:40,530 And they find that the knee flexion 510 00:35:40,530 --> 00:35:55,011 angle changed by 13.7 degrees. 511 00:35:55,011 --> 00:36:08,640 And if you compared the inclined versus the level treadmill, 512 00:36:08,640 --> 00:36:11,170 and they found the orientation of the peak trabecular 513 00:36:11,170 --> 00:36:28,690 density, which they called OPDD, also changed by 13.6 degrees. 514 00:36:28,690 --> 00:36:31,000 So the idea is that the orientation of the trabeculae 515 00:36:31,000 --> 00:36:33,870 changed to match the orientation of the loading. 516 00:37:12,990 --> 00:37:14,420 Then I have a little video here. 517 00:37:18,390 --> 00:37:19,490 Do you like video? 518 00:37:19,490 --> 00:37:22,170 So I have a colleague who's at Harvard who studies animal 519 00:37:22,170 --> 00:37:25,160 locomotion, and they didn't do this set of experiments, 520 00:37:25,160 --> 00:37:27,250 but they do do experiments on Guinea fowl running 521 00:37:27,250 --> 00:37:30,250 on treadmills, and thought you might find this amusing. 522 00:37:30,250 --> 00:37:34,220 So let me see if I can make this work. 523 00:37:34,220 --> 00:37:36,830 [VIDEO PLAYBACK] 524 00:37:36,830 --> 00:37:39,340 -Sometimes you walk into a lab and you just 525 00:37:39,340 --> 00:37:46,026 think this is what science is all about. 526 00:37:46,026 --> 00:37:47,900 -I just put the Guinea fowl on the treadmill, 527 00:37:47,900 --> 00:37:50,090 and this is something that we commonly do. 528 00:37:57,360 --> 00:37:59,480 -Welcome to the Concord Field Station, 529 00:37:59,480 --> 00:38:04,650 a defunct Nike missile base turned scientific menagerie. 530 00:38:04,650 --> 00:38:07,630 It's owned by Harvard, and biologist Andy Biewener 531 00:38:07,630 --> 00:38:08,800 is the director here. 532 00:38:08,800 --> 00:38:10,070 So think of it as-- 533 00:38:10,070 --> 00:38:13,270 -A research lab facility for doing comparative biomechanics 534 00:38:13,270 --> 00:38:16,350 and physiology of largely animal movement. 535 00:38:16,350 --> 00:38:19,920 -And the birds are just the tip of the iceberg. 536 00:38:19,920 --> 00:38:22,751 -So do you want to see the baby goat and the emu? 537 00:38:22,751 --> 00:38:23,250 -Obviously. 538 00:38:23,250 --> 00:38:23,749 -OK. 539 00:38:38,660 --> 00:38:42,330 We keep it because it's sort of like a mascot. 540 00:38:42,330 --> 00:38:44,780 There used to be a lizard colony. 541 00:38:44,780 --> 00:38:46,876 You can hear the African greys. 542 00:38:46,876 --> 00:38:50,400 Then the jerboas are housed in this room here. 543 00:38:50,400 --> 00:38:53,580 This is where we originally did our pigeon flight studies. 544 00:38:53,580 --> 00:38:56,815 So usually the ones with claws and sharp teeth 545 00:38:56,815 --> 00:38:59,190 and aggressive behaviors, you want to watch out for them. 546 00:38:59,190 --> 00:39:00,440 -As you might expect. 547 00:39:00,440 --> 00:39:02,780 But did you know that Guinea fowl-- 548 00:39:02,780 --> 00:39:04,357 -They're really lovely to work with. 549 00:39:04,357 --> 00:39:04,856 -Sometimes. 550 00:39:07,590 --> 00:39:08,410 Or that-- 551 00:39:08,410 --> 00:39:10,210 -Rats are not very good on treadmills. 552 00:39:10,210 --> 00:39:10,830 -Yes. 553 00:39:10,830 --> 00:39:12,690 That's what a rat treadmill looks like. 554 00:39:12,690 --> 00:39:13,330 And this? 555 00:39:13,330 --> 00:39:15,200 -And this was historically a treadmill 556 00:39:15,200 --> 00:39:18,260 of note, the treadmill that they first taught kangaroos 557 00:39:18,260 --> 00:39:20,819 on and showed that kangaroos stored energy in their tendons 558 00:39:20,819 --> 00:39:23,360 enough that they don't actually increase their metabolic rate 559 00:39:23,360 --> 00:39:25,580 when they hop at faster speeds. 560 00:39:25,580 --> 00:39:27,490 -These are the kind of discoveries made here 561 00:39:27,490 --> 00:39:31,150 with the use of high-speed video and x-ray machines 562 00:39:31,150 --> 00:39:34,400 and semi cooperative animals. 563 00:39:34,400 --> 00:39:37,230 But beyond the basic biology, Biewener 564 00:39:37,230 --> 00:39:39,310 says engineers are using this research 565 00:39:39,310 --> 00:39:41,340 to build better robots, and it can 566 00:39:41,340 --> 00:39:43,470 help improve medical treatment for people 567 00:39:43,470 --> 00:39:45,250 with movement disorders. 568 00:39:45,250 --> 00:39:48,160 Today the big excitement at the lab is happening here. 569 00:39:48,160 --> 00:39:51,810 Ivo Ros is studying how heart rate changes when cockatiels 570 00:39:51,810 --> 00:39:53,020 fly at different speeds. 571 00:39:53,020 --> 00:39:56,450 So this is a way to look at how much energy it takes to fly, 572 00:39:56,450 --> 00:39:58,640 and that cord is measuring heart rate. 573 00:39:58,640 --> 00:40:02,228 But instead of the birds flying faster, the wind changes speed. 574 00:40:02,228 --> 00:40:03,478 -I'm going to turn it on then. 575 00:40:10,460 --> 00:40:14,430 -It's hard to fly fast, and it's hard to fly slow, Ros says. 576 00:40:14,430 --> 00:40:16,800 So the expectation is that the heart rate should 577 00:40:16,800 --> 00:40:20,090 be shaped like a U. But so far Ros is 578 00:40:20,090 --> 00:40:22,240 finding that it's a flat line. 579 00:40:22,240 --> 00:40:25,520 It's like the bird goes into a stress reaction 580 00:40:25,520 --> 00:40:27,090 when it takes off. 581 00:40:27,090 --> 00:40:28,920 Is that just because of the wind tunnel? 582 00:40:28,920 --> 00:40:30,045 What Ros wants to know is-- 583 00:40:30,045 --> 00:40:32,670 - --whether or not they need to be stressed to fly in the first 584 00:40:32,670 --> 00:40:33,220 place. 585 00:40:33,220 --> 00:40:35,810 -That's something that Ros is looking into, 586 00:40:35,810 --> 00:40:38,150 but today is mostly about training. 587 00:40:38,150 --> 00:40:38,770 -Keep going. 588 00:40:38,770 --> 00:40:39,530 Come on. 589 00:40:39,530 --> 00:40:40,940 -Imagine you're a cockatiel. 590 00:40:40,940 --> 00:40:43,590 A wind tunnel is kind of a strange experience. 591 00:40:43,590 --> 00:40:45,720 -A bird in a wind tunnel has to confront the fact 592 00:40:45,720 --> 00:40:48,150 that the world is not moving past, which 593 00:40:48,150 --> 00:40:50,290 defies its normal sensory cues. 594 00:40:50,290 --> 00:40:52,781 -Which pretty well sums up the Concord Field Station 595 00:40:52,781 --> 00:40:53,280 generally. 596 00:41:03,110 --> 00:41:04,940 For Science Friday, I'm Flora Lichtman. 597 00:41:04,940 --> 00:41:05,080 [END PLAYBACK] 598 00:41:05,080 --> 00:41:07,030 And if read The New York Times, Flora Lichtman 599 00:41:07,030 --> 00:41:10,920 used to work for NPR and would make these Science Friday 600 00:41:10,920 --> 00:41:12,530 videos for them. 601 00:41:12,530 --> 00:41:15,870 But now she has a gig doing things for The New York Times, 602 00:41:15,870 --> 00:41:17,900 and she does science videos still. 603 00:41:17,900 --> 00:41:19,776 I don't know if you quite call them videos, 604 00:41:19,776 --> 00:41:22,150 but what they do is they have these little paper puppets, 605 00:41:22,150 --> 00:41:24,930 and the paper puppets are animated and re-enact 606 00:41:24,930 --> 00:41:27,250 different episodes in science. 607 00:41:27,250 --> 00:41:31,200 And it's kind of amazing how they do these little science 608 00:41:31,200 --> 00:41:32,030 videos. 609 00:41:32,030 --> 00:41:33,710 So if you Google Flora Lichtman, you'll 610 00:41:33,710 --> 00:41:37,107 see more Science Videos with all sorts of things. 611 00:41:37,107 --> 00:41:38,690 I guess the other interesting anecdote 612 00:41:38,690 --> 00:41:40,790 is I went to the Concord Field Station once. 613 00:41:40,790 --> 00:41:44,090 And I had done a study on quills and animals 614 00:41:44,090 --> 00:41:47,937 that have quills because the quills have a foamy structure 615 00:41:47,937 --> 00:41:48,520 in the middle. 616 00:41:48,520 --> 00:41:49,620 So they're carrot, and they have sort 617 00:41:49,620 --> 00:41:50,930 of like carrot-like structures. 618 00:41:50,930 --> 00:41:52,680 And they have an outer shell that's dense, 619 00:41:52,680 --> 00:41:54,730 and then they have a foamy thing in the middle. 620 00:41:54,730 --> 00:41:56,950 Anyway I did this paper on quills 621 00:41:56,950 --> 00:41:58,550 and how they work mechanically. 622 00:41:58,550 --> 00:42:00,709 And Technology reviewed a little article about it, 623 00:42:00,709 --> 00:42:02,750 and they said they wanted to take a picture of me 624 00:42:02,750 --> 00:42:03,769 with a hedgehog. 625 00:42:03,769 --> 00:42:05,560 The hedgehogs are little European-- they're 626 00:42:05,560 --> 00:42:08,320 like little small, cute things. 627 00:42:08,320 --> 00:42:10,360 And I said, well, if you can find a hedgehog, 628 00:42:10,360 --> 00:42:12,300 I'm happy to have my photograph taken. 629 00:42:12,300 --> 00:42:14,540 And they had a hedgehog at the Concord Field Station. 630 00:42:14,540 --> 00:42:17,070 So we went out there, and we had these big leather gloves 631 00:42:17,070 --> 00:42:18,030 and took a picture. 632 00:42:18,030 --> 00:42:20,280 And I don't if it was Andy or I don't know who it was, 633 00:42:20,280 --> 00:42:21,760 but I said one of the people there, 634 00:42:21,760 --> 00:42:23,093 what did you do with a hedgehog? 635 00:42:23,093 --> 00:42:26,570 And he said, well, we tried to do the treadmill study. 636 00:42:26,570 --> 00:42:28,020 But hedgehogs are like porcupines. 637 00:42:28,020 --> 00:42:30,269 When they get scared, they curl up into a little ball. 638 00:42:30,269 --> 00:42:32,172 And so they said they would put the hedgehog 639 00:42:32,172 --> 00:42:34,380 down under the treadmill, and they would start it up, 640 00:42:34,380 --> 00:42:35,970 and it would make a noise, and it would get scared it. 641 00:42:35,970 --> 00:42:38,345 And it would just go into a little ball and kind of slide 642 00:42:38,345 --> 00:42:41,040 along to the end, and then it would kind of get flopped off. 643 00:42:41,040 --> 00:42:43,609 So that was the end of the hedgehog experiments. 644 00:42:43,609 --> 00:42:45,650 But they did have wallabies there the day I went. 645 00:42:45,650 --> 00:42:47,390 So they have all sorts of animals 646 00:42:47,390 --> 00:42:50,610 that they put on to treadmills, birds that they fly, 647 00:42:50,610 --> 00:42:53,090 so it's kind of interesting to go there. 648 00:42:53,090 --> 00:42:55,370 But the main idea here is that there 649 00:42:55,370 --> 00:42:57,480 was this set of experiments with Guinea fowl that 650 00:42:57,480 --> 00:43:00,970 showed just how precisely the orientation of the bone 651 00:43:00,970 --> 00:43:02,810 matches the orientation of the loads. 652 00:43:02,810 --> 00:43:05,310 AUDIENCE: Was there a difference between the control groups? 653 00:43:05,310 --> 00:43:07,120 LORNA GIBSON: Ah, so I have slides. 654 00:43:07,120 --> 00:43:07,950 I have slides. 655 00:43:07,950 --> 00:43:09,220 Hang on a sec. 656 00:43:09,220 --> 00:43:11,990 I got distracted by my video. 657 00:43:11,990 --> 00:43:14,730 Sorry. 658 00:43:14,730 --> 00:43:18,220 So here's the sort of schematic of Guinea fowl on treadmill. 659 00:43:18,220 --> 00:43:22,540 And where's the little doo-da here? 660 00:43:22,540 --> 00:43:24,490 So on the level, the knee flexion angle 661 00:43:24,490 --> 00:43:28,480 was whatever this is, 76.3, and here was the 62.6, 662 00:43:28,480 --> 00:43:30,790 so the difference is 13.7. 663 00:43:30,790 --> 00:43:34,200 And then this kind of table here summarizes these results. 664 00:43:34,200 --> 00:43:38,970 So this is the maximum trabecular density, 665 00:43:38,970 --> 00:43:40,280 and this is the angle. 666 00:43:40,280 --> 00:43:43,007 And here we have the incline. 667 00:43:43,007 --> 00:43:44,590 Let's see, the control was the yellow, 668 00:43:44,590 --> 00:43:47,000 and the level was the blue, and they've 669 00:43:47,000 --> 00:43:51,020 got the values for that peak trabecular density orientation. 670 00:43:51,020 --> 00:43:52,650 So they've got that for the level. 671 00:43:52,650 --> 00:43:54,510 And then they looked at the difference 672 00:43:54,510 --> 00:43:58,340 between the incline and the level in the knee angle. 673 00:43:58,340 --> 00:44:00,809 That's what this thing here is. 674 00:44:00,809 --> 00:44:02,600 And then between the level and the control, 675 00:44:02,600 --> 00:44:04,860 there wasn't really any difference in the knee 676 00:44:04,860 --> 00:44:10,040 angle because the control ones, they were just walking around. 677 00:44:10,040 --> 00:44:15,460 So that's the sort of slide that has the actual data on it. 678 00:44:15,460 --> 00:44:16,190 All right. 679 00:44:16,190 --> 00:44:18,360 And then I showed you the video. 680 00:44:18,360 --> 00:44:18,860 All right. 681 00:44:18,860 --> 00:44:21,287 So we need to do a couple more things before we 682 00:44:21,287 --> 00:44:22,120 get to the modeling. 683 00:44:26,050 --> 00:44:27,200 Let me get a drink. 684 00:44:34,200 --> 00:44:37,020 So if we want to use the models for foams 685 00:44:37,020 --> 00:44:38,920 to try to describe the trabecular bone, 686 00:44:38,920 --> 00:44:41,420 we need to know something about the properties of the solid. 687 00:44:41,420 --> 00:44:44,550 Remember we used the properties of the solid in the models. 688 00:44:44,550 --> 00:44:47,360 So we want to get the properties of the solid in the trabeculae, 689 00:44:47,360 --> 00:44:49,530 and there's a couple of ways you can do this. 690 00:44:49,530 --> 00:44:53,480 To get the moduli, you can use an ultrasonic wave propagation 691 00:44:53,480 --> 00:44:56,165 method, and you can measure a modulus that way. 692 00:44:56,165 --> 00:44:57,540 And if they do that, they measure 693 00:44:57,540 --> 00:45:00,680 a modulus between about 15 and 18 gigapascals. 694 00:45:00,680 --> 00:45:03,610 Another way to do it is to take a piece of bone, 695 00:45:03,610 --> 00:45:07,690 do a compression test on it, measure the modulus. 696 00:45:07,690 --> 00:45:10,670 Before you do the test, you put it in the micro CT machine, 697 00:45:10,670 --> 00:45:13,060 and you get a picture of the structure, 698 00:45:13,060 --> 00:45:14,650 and then you use that as the input 699 00:45:14,650 --> 00:45:16,390 to a finite element analysis. 700 00:45:16,390 --> 00:45:17,830 So the finite element analysis is 701 00:45:17,830 --> 00:45:22,080 a computer numerical analysis to do mechanical calculations. 702 00:45:22,080 --> 00:45:26,260 And if you know what the modulus of the structure is, 703 00:45:26,260 --> 00:45:28,640 you can back out what the modulus of the solid 704 00:45:28,640 --> 00:45:31,020 must have been from the fine element thing. 705 00:45:31,020 --> 00:45:33,210 And those sorts of experiments also 706 00:45:33,210 --> 00:45:35,400 showed that the modulus was around 18. 707 00:45:35,400 --> 00:45:37,940 And it turns out that moduli is about the same as cortical 708 00:45:37,940 --> 00:45:41,820 bone, and the properties of the solid trabeculae 709 00:45:41,820 --> 00:45:44,860 are very similar to the solid cortical bone. 710 00:45:44,860 --> 00:45:46,260 So let me scoot over here. 711 00:46:51,560 --> 00:47:00,800 So if you use an ultrasonic wave propagation, 712 00:47:00,800 --> 00:47:04,200 people have measured a modulus for the solid in trabecular 713 00:47:04,200 --> 00:47:14,650 bone of 18 gigapascals, or you can do a finite element 714 00:47:14,650 --> 00:47:22,420 calculation based on micro CT data for the structure. 715 00:47:35,540 --> 00:47:38,140 And then you measure the overall modulus for the trabecular 716 00:47:38,140 --> 00:47:48,380 bone, and then you back out the modulus of the solid. 717 00:47:52,150 --> 00:47:54,660 And people who've done that have gotten values 718 00:47:54,660 --> 00:48:01,700 of around 18 gigapascals too, and that's very similar to what 719 00:48:01,700 --> 00:48:02,900 the cortical bone is. 720 00:48:10,780 --> 00:48:14,650 And so we're going to use the following properties 721 00:48:14,650 --> 00:48:17,380 for the solid in the trabecular bone. 722 00:48:17,380 --> 00:48:19,690 We're going to say the density is 1,800 723 00:48:19,690 --> 00:48:21,770 kilograms per cubic meter. 724 00:48:21,770 --> 00:48:26,930 The Young's modulus is 18 gigapascals. 725 00:48:26,930 --> 00:48:30,960 The yield strength has different values 726 00:48:30,960 --> 00:48:32,780 in tension and compression. 727 00:48:32,780 --> 00:48:35,680 It's about 182 megapascals in compression. 728 00:48:39,670 --> 00:48:45,310 And it's about 115 megapascals in tension. 729 00:48:53,109 --> 00:48:54,525 So those are the solid properties. 730 00:49:48,280 --> 00:49:50,440 So then if we look at the compressive stress-strain 731 00:49:50,440 --> 00:49:54,760 curves, they have the shape shown on the screen there. 732 00:49:54,760 --> 00:49:57,090 And you can see how similar the stress-strain curves 733 00:49:57,090 --> 00:49:58,420 are for those for a foam. 734 00:49:58,420 --> 00:50:00,400 So there's the same three regimes 735 00:50:00,400 --> 00:50:01,930 that we see for the foam. 736 00:50:01,930 --> 00:50:04,060 There is a linear elastic regime over here, 737 00:50:04,060 --> 00:50:06,120 there's a stress plateau here, and there's 738 00:50:06,120 --> 00:50:08,310 some densification regime here. 739 00:50:08,310 --> 00:50:11,000 These are three curves for three different relative densities. 740 00:50:11,000 --> 00:50:14,280 As the relative density goes up, the stiffness goes up, 741 00:50:14,280 --> 00:50:17,380 the plateau stress goes up, and the densification strain 742 00:50:17,380 --> 00:50:17,880 goes down. 743 00:50:17,880 --> 00:50:22,410 So is the same as the foams that we've looked at before. 744 00:50:22,410 --> 00:50:27,570 And if we look at the mechanisms of deformation and failure, 745 00:50:27,570 --> 00:50:29,570 people have looked at this. 746 00:50:29,570 --> 00:50:31,650 These are on a whale vertebrae. 747 00:50:31,650 --> 00:50:35,440 So these are tests that are done in a micron CT machine, 748 00:50:35,440 --> 00:50:37,590 again, by Ralph Muller's group. 749 00:50:37,590 --> 00:50:39,600 And here the specimen is unloaded, 750 00:50:39,600 --> 00:50:41,190 and here's the same specimen loaded. 751 00:50:41,190 --> 00:50:43,580 So you can see this platen has come down a little bit. 752 00:50:43,580 --> 00:50:45,800 And if you look at this column here, 753 00:50:45,800 --> 00:50:48,780 this trabecular here, you can see it's bent out 754 00:50:48,780 --> 00:50:50,240 and bowed out more. 755 00:50:50,240 --> 00:50:51,810 And people have found that usually 756 00:50:51,810 --> 00:50:54,060 the linear elastic behavior is controlled 757 00:50:54,060 --> 00:50:57,410 by bending of that trabeculae, and the plateau 758 00:50:57,410 --> 00:51:00,570 stress is usually controlled by some sort of buckling. 759 00:51:00,570 --> 00:51:01,880 But it's not elastic buckling. 760 00:51:01,880 --> 00:51:02,670 You don't recover it. 761 00:51:02,670 --> 00:51:04,670 If you take a piece of bone and you compress it, 762 00:51:04,670 --> 00:51:07,200 it's going to have a permanent deformation. 763 00:51:07,200 --> 00:51:10,010 So it's inelastic buckling. 764 00:51:10,010 --> 00:51:12,310 And I think we have some more pictures. 765 00:51:12,310 --> 00:51:14,120 This is another example from whale bone 766 00:51:14,120 --> 00:51:17,510 from Ralph Muller's group. 767 00:51:17,510 --> 00:51:19,670 So here's the bone unloaded. 768 00:51:19,670 --> 00:51:22,390 Here it's loaded to 4% strain, here it's to 8%. 769 00:51:22,390 --> 00:51:25,250 And you can start seeing right in this area here 770 00:51:25,250 --> 00:51:29,310 if you compare with up there, it's starting to form. 771 00:51:29,310 --> 00:51:31,700 And if you go up here to 12% strain, 772 00:51:31,700 --> 00:51:33,440 you see that strut right there. 773 00:51:33,440 --> 00:51:35,900 That was this guy up here, and you can see 774 00:51:35,900 --> 00:51:37,210 that it's buckled right over. 775 00:51:37,210 --> 00:51:39,740 So people have made measurements like this in observations, 776 00:51:39,740 --> 00:51:41,550 and you can actually see the buckling. 777 00:51:41,550 --> 00:51:44,810 And people have also done finite element modeling. 778 00:51:44,810 --> 00:51:48,170 They can take a micro CT scan and input that 779 00:51:48,170 --> 00:51:49,412 to the fine element model. 780 00:51:49,412 --> 00:51:50,870 And then if they do the compression 781 00:51:50,870 --> 00:51:52,720 and they input the properties of the solid, 782 00:51:52,720 --> 00:51:55,590 they can see that they get a buckling kind of failure. 783 00:51:55,590 --> 00:52:01,150 If you have trabeculae that are very aligned-- we have more. 784 00:52:01,150 --> 00:52:02,590 Here's one more in the buckling. 785 00:52:02,590 --> 00:52:04,660 So this is one of Ralph's little movies. 786 00:52:04,660 --> 00:52:07,040 So when it unloads, it looks like it recovers, 787 00:52:07,040 --> 00:52:09,880 but this is all just an animation. 788 00:52:09,880 --> 00:52:12,270 He takes several stills and puts them together, 789 00:52:12,270 --> 00:52:13,627 and it doesn't actually recover. 790 00:52:13,627 --> 00:52:14,960 It's just the way that it shows. 791 00:52:14,960 --> 00:52:17,490 But again, these are two different specimens 792 00:52:17,490 --> 00:52:19,050 of different densities. 793 00:52:19,050 --> 00:52:23,390 You can see how the struts deform. 794 00:52:23,390 --> 00:52:24,772 They bend and then they buckle. 795 00:52:27,451 --> 00:52:29,784 Let me stop there, and I'll put some stuff on the board. 796 00:52:35,000 --> 00:52:40,430 So we'll say the compressive stress-strain curve 797 00:52:40,430 --> 00:52:43,570 has the characteristic shape of cellular solids. 798 00:53:06,240 --> 00:53:09,060 And the mechanisms of deformation and failure, 799 00:53:09,060 --> 00:53:15,310 usually there is bending followed by, usually, 800 00:53:15,310 --> 00:53:16,825 inelastic or plastic buckling. 801 00:54:00,770 --> 00:54:03,860 And sometimes if the trabeculae are 802 00:54:03,860 --> 00:54:05,930 aligned like that knee that I showed you, 803 00:54:05,930 --> 00:54:08,346 or if the trabecular are aligned or if they're very dense, 804 00:54:08,346 --> 00:54:11,760 then the actual deformation is important. 805 00:54:11,760 --> 00:54:13,850 And I'll just say people have found this 806 00:54:13,850 --> 00:54:23,230 by making observations using micro computer tomography 807 00:54:23,230 --> 00:54:27,788 or by finite element calculations. 808 00:55:09,410 --> 00:55:11,540 And this is a stress-strain curve and tension 809 00:55:11,540 --> 00:55:14,760 here, a tension you get failure at small strains, then 810 00:55:14,760 --> 00:55:16,447 you get micro cracks in the bone. 811 00:55:35,880 --> 00:55:39,320 And these next plots just show some data for the bone. 812 00:55:39,320 --> 00:55:43,930 So we're plotting the Young's modulus here. 813 00:55:43,930 --> 00:55:46,030 So this is a relative Young's modulus, 814 00:55:46,030 --> 00:55:48,400 the modulus of the bone divided by the solid cell wall 815 00:55:48,400 --> 00:55:49,430 material. 816 00:55:49,430 --> 00:55:50,960 Here's the relative density. 817 00:55:50,960 --> 00:55:54,130 Here's data for lots of different specimens of bone. 818 00:55:54,130 --> 00:55:56,250 So some of this data is for human bones, 819 00:55:56,250 --> 00:55:59,190 some is for bovine bone. 820 00:55:59,190 --> 00:56:01,860 Sometimes the data is taken where 821 00:56:01,860 --> 00:56:03,657 the orientation of the trabeculae 822 00:56:03,657 --> 00:56:05,740 doesn't line up with the direction of the loading. 823 00:56:05,740 --> 00:56:08,073 So you might have trabeculae that are oriented this way, 824 00:56:08,073 --> 00:56:09,370 but you're loading it this way. 825 00:56:09,370 --> 00:56:13,310 There's sometimes different strain rates. 826 00:56:13,310 --> 00:56:13,830 Let's see. 827 00:56:13,830 --> 00:56:17,280 There's different groups, and so there's a huge scatter 828 00:56:17,280 --> 00:56:19,500 in the range of the data. 829 00:56:19,500 --> 00:56:21,370 But you can see if you look at it broadly 830 00:56:21,370 --> 00:56:23,780 and you look at that whole cluster of data, 831 00:56:23,780 --> 00:56:28,040 the data lie close to a line of a slope of 2. 832 00:56:28,040 --> 00:56:30,000 And if you think of the open-celled foam model 833 00:56:30,000 --> 00:56:31,460 and you had bending of the cell walls, 834 00:56:31,460 --> 00:56:32,935 you'd expect that the modulus would vary 835 00:56:32,935 --> 00:56:34,260 [? to the ?] density squared. 836 00:56:34,260 --> 00:56:37,107 So that's kind of the limit of how we do the modeling. 837 00:56:37,107 --> 00:56:39,690 We're really just interested in seeing how the properties vary 838 00:56:39,690 --> 00:56:40,947 with density. 839 00:56:40,947 --> 00:56:42,530 If you had a particular piece of bone, 840 00:56:42,530 --> 00:56:44,904 I don't think you could use the models to exactly predict 841 00:56:44,904 --> 00:56:46,900 what the modulus of that bone would be. 842 00:56:46,900 --> 00:56:48,995 And here's the compressive strength here. 843 00:56:48,995 --> 00:56:50,870 So this is the relative compressive strength. 844 00:56:50,870 --> 00:56:52,980 Here we've normalized it with the yield 845 00:56:52,980 --> 00:56:57,480 stress of the solid bone, and here's the relative density. 846 00:56:57,480 --> 00:57:00,340 And you can see, again, this line is of slope 2, 847 00:57:00,340 --> 00:57:03,890 so that kind of speaks to the buckling-type failure mode. 848 00:57:03,890 --> 00:57:05,970 And I think I have another one here. 849 00:57:05,970 --> 00:57:07,680 This is the tensile strength. 850 00:57:07,680 --> 00:57:09,200 So if you pull the bone in tension, 851 00:57:09,200 --> 00:57:10,699 you wouldn't expect to get buckling, 852 00:57:10,699 --> 00:57:13,120 you'd expect to get plastic yielding. 853 00:57:13,120 --> 00:57:16,030 And if you got yielding and you use the open-cell foam model, 854 00:57:16,030 --> 00:57:19,980 you'd expect a slope of 3/2, so this line has a slope of 3/2. 855 00:57:19,980 --> 00:57:22,480 And this line is sort of towards the upper bound 856 00:57:22,480 --> 00:57:23,450 of that set of data. 857 00:57:23,450 --> 00:57:26,650 You can imagine a line that went through it a little bit lower 858 00:57:26,650 --> 00:57:28,080 but the same slope. 859 00:57:28,080 --> 00:57:30,360 And so these open-celled foam models, 860 00:57:30,360 --> 00:57:32,140 they don't predict the properties 861 00:57:32,140 --> 00:57:34,130 of a particular piece of bone because the bone 862 00:57:34,130 --> 00:57:36,900 can have some anisotropy to it. 863 00:57:36,900 --> 00:57:39,950 The orientation of these things may not be perfectly lined up 864 00:57:39,950 --> 00:57:41,520 with the loading. 865 00:57:41,520 --> 00:57:44,100 But overall the models give you a sense 866 00:57:44,100 --> 00:57:49,450 of how the bone is deforming and failing. 867 00:57:49,450 --> 00:57:51,330 So let me write some of this down. 868 00:58:02,455 --> 00:58:04,920 So that's data for the modulus, the compressive strength, 869 00:58:04,920 --> 00:58:06,840 and the tensile strength. 870 00:58:06,840 --> 00:58:10,350 And those have been on those plots. 871 00:58:10,350 --> 00:58:16,310 Those values are normalized by data for cortical bone. 872 00:58:27,229 --> 00:58:28,520 I thought somebody was talking. 873 00:58:28,520 --> 00:58:29,770 It's just the chair squeaking. 874 00:58:37,520 --> 00:58:40,580 And as I said the spread in the data is large, 875 00:58:40,580 --> 00:58:50,120 and that's due to anisotropy in the bone and misalignment 876 00:58:50,120 --> 00:58:52,640 between the bone orientation and the loading direction. 877 00:59:07,430 --> 00:59:10,950 So when people first started doing tests on trabecular bone, 878 00:59:10,950 --> 00:59:13,710 they typically were orthopedics labs. 879 00:59:13,710 --> 00:59:16,970 And the orthopedics labs tended to initially cut the bone 880 00:59:16,970 --> 00:59:19,840 specimens on anatomical axes. 881 00:59:19,840 --> 00:59:22,180 So they would do you know the superior-inferior, 882 00:59:22,180 --> 00:59:25,190 or the medial-lateral, or the posterior-anterior. 883 00:59:25,190 --> 00:59:28,469 But the bone orientation didn't line up with those directions. 884 00:59:28,469 --> 00:59:30,010 So the bone might have been this way, 885 00:59:30,010 --> 00:59:31,440 but they were loading it this way, 886 00:59:31,440 --> 00:59:34,856 and so that gave this misalignment. 887 00:59:34,856 --> 00:59:36,230 And there could be some variation 888 00:59:36,230 --> 00:59:37,470 in the solid properties too. 889 00:59:40,550 --> 00:59:43,070 So you could imagine some solid might have more micro cracks 890 00:59:43,070 --> 00:59:45,470 than another. 891 00:59:45,470 --> 00:59:49,195 So if you took say human bone of different ages, 892 00:59:49,195 --> 00:59:50,820 you might expect the older bone to have 893 00:59:50,820 --> 00:59:51,960 more micro cracks in it. 894 00:59:56,830 --> 01:00:01,725 So these plots put a lot of data together, 895 01:00:01,725 --> 01:00:05,800 and then the lines are based on models for open-cell foams. 896 01:00:14,690 --> 01:00:16,660 So the relative modulus goes roughly 897 01:00:16,660 --> 01:00:21,565 as a relative density squared, and the cell walls are bending. 898 01:00:24,250 --> 01:00:29,450 And the compressive strength goes roughly 899 01:00:29,450 --> 01:00:36,590 as the modulus squared, and that's 900 01:00:36,590 --> 01:00:39,880 related to this plastic buckling. 901 01:00:39,880 --> 01:00:45,470 And then the tensile stress or tensile strength 902 01:00:45,470 --> 01:00:48,620 depends on the formation of plastic hinges, 903 01:00:48,620 --> 01:00:51,600 and it goes roughly as the density to the 3/2 power. 904 01:01:00,840 --> 01:01:08,310 And one observation that people have made 905 01:01:08,310 --> 01:01:13,690 is that in compression, if the modulus and the strength both 906 01:01:13,690 --> 01:01:16,040 go as a density squared, then the ratio 907 01:01:16,040 --> 01:01:19,180 of the strength to the modulus is just a constant, and that, 908 01:01:19,180 --> 01:01:22,260 in fact, is just the strain at failure, 909 01:01:22,260 --> 01:01:24,950 or the strain for that say, the plateau. 910 01:01:32,310 --> 01:01:35,190 And that's a strain of about 0.7%, 911 01:01:35,190 --> 01:01:37,370 and that's pretty consistent in trabecular bone. 912 01:01:41,476 --> 01:01:42,155 Let's see. 913 01:01:56,260 --> 01:01:58,815 And we said sometimes the bone was relatively aligned. 914 01:01:58,815 --> 01:02:00,560 So here's that picture of the femoral 915 01:02:00,560 --> 01:02:04,770 condyle again in the knee, and you can see the bones lined up. 916 01:02:04,770 --> 01:02:06,900 If you have bone that's lined up like that 917 01:02:06,900 --> 01:02:09,660 and you load it along the direction of alignment, 918 01:02:09,660 --> 01:02:13,460 then you can get axial deformation in the trabeculae. 919 01:02:13,460 --> 01:02:15,940 And then you would expect the moduli would go linearly 920 01:02:15,940 --> 01:02:17,800 with the density. 921 01:02:17,800 --> 01:02:20,980 And here's some data for the Young's modulus 922 01:02:20,980 --> 01:02:24,430 and the compressive strength of bone that was fairly aligned. 923 01:02:24,430 --> 01:02:26,160 So this was selected to be aligned. 924 01:02:26,160 --> 01:02:27,950 So here's the modulus here. 925 01:02:27,950 --> 01:02:33,630 And the square data points are the longitudinal direction, 926 01:02:33,630 --> 01:02:37,160 and the little diamond, these little stars, are transverse. 927 01:02:37,160 --> 01:02:40,800 So here's a line of slope 1, and again, they don't all 928 01:02:40,800 --> 01:02:43,810 lie perfectly on that line, but roughly the slope is about 1 929 01:02:43,810 --> 01:02:44,400 there. 930 01:02:44,400 --> 01:02:47,520 And then similarly here, this is the compressive strength. 931 01:02:47,520 --> 01:02:51,140 Now the little squares are the longitudinal data, 932 01:02:51,140 --> 01:02:53,420 and they're not exactly on a slope of 1, 933 01:02:53,420 --> 01:02:55,170 but they're more or less on a slope of 1. 934 01:02:58,480 --> 01:03:00,140 So I'll just say in some regions, 935 01:03:00,140 --> 01:03:01,193 the bone may be aligned. 936 01:03:12,000 --> 01:03:14,040 And then axial deformation is important. 937 01:03:18,660 --> 01:03:22,700 And then you would expect the modulus to go linearly 938 01:03:22,700 --> 01:03:26,110 with the density and the strength 939 01:03:26,110 --> 01:03:29,120 to go linearly with the density in the longitudinal direction. 940 01:03:43,640 --> 01:03:46,190 Then finally I wanted to finish up the bit on the modeling 941 01:03:46,190 --> 01:03:48,160 by making one of these plots a little bit 942 01:03:48,160 --> 01:03:49,890 like we did for wood. 943 01:03:49,890 --> 01:03:52,470 So here's the Young's modulus of bone plotted 944 01:03:52,470 --> 01:03:53,920 against the density. 945 01:03:53,920 --> 01:03:55,600 The trabecular bone is down here. 946 01:03:55,600 --> 01:03:57,710 It's sort the lowest density. 947 01:03:57,710 --> 01:04:00,040 And then this is the collagen that's 948 01:04:00,040 --> 01:04:01,850 in the solid part of the bone, and this 949 01:04:01,850 --> 01:04:04,200 is hydroxyapatite, the mineral. 950 01:04:04,200 --> 01:04:07,640 So the modulus of hydroxyapatite is around 120 gigapascals, 951 01:04:07,640 --> 01:04:10,800 and the modulus of collagen is somewhere around 5. 952 01:04:10,800 --> 01:04:13,560 And if you make composites of collagen and hydroxyapatite, 953 01:04:13,560 --> 01:04:17,380 their moduli are going to be in this envelope here, 954 01:04:17,380 --> 01:04:19,910 and compact bone, the modulus fits in around here. 955 01:04:19,910 --> 01:04:22,694 Remember I said it was around 18 gigapascals. 956 01:04:22,694 --> 01:04:24,110 So then if you take a compact bone 957 01:04:24,110 --> 01:04:25,920 and you turn it into trabecular bone, 958 01:04:25,920 --> 01:04:30,020 you'd expect the modulus would go down along a slope of 2. 959 01:04:30,020 --> 01:04:32,840 So here's our little slope of 2, and more or less that's 960 01:04:32,840 --> 01:04:35,330 what you see with the trabecular bone. 961 01:04:35,330 --> 01:04:37,260 So the idea is that the models give you 962 01:04:37,260 --> 01:04:40,241 kind of a general idea of how the bone is behaving, 963 01:04:40,241 --> 01:04:41,740 but it's not really meant to predict 964 01:04:41,740 --> 01:04:42,980 a particular piece of bone. 965 01:04:42,980 --> 01:04:44,438 Because a particular piece is going 966 01:04:44,438 --> 01:04:46,470 to have a particular geometry. 967 01:04:46,470 --> 01:04:49,830 Typically they're not equi ax and isotropic. 968 01:04:49,830 --> 01:04:50,600 All right. 969 01:04:50,600 --> 01:04:53,400 So are we good with the general overview? 970 01:04:53,400 --> 01:04:55,440 Are we good with how fewer equations there 971 01:04:55,440 --> 01:04:57,790 are now that we got past the first part of the course? 972 01:05:02,760 --> 01:05:05,552 So I'm going to talk a bit more about osteoporosis, 973 01:05:05,552 --> 01:05:07,260 and I'm going to talk about some modeling 974 01:05:07,260 --> 01:05:11,707 that my group did to look at the consequences of osteoporosis. 975 01:05:11,707 --> 01:05:13,790 And then later on we're going to talk a little bit 976 01:05:13,790 --> 01:05:17,030 about using metal foams as a possible replacement material 977 01:05:17,030 --> 01:05:18,970 for a trabecular bone as well. 978 01:05:18,970 --> 01:05:20,860 And I have a little bit of a talk 979 01:05:20,860 --> 01:05:25,280 on using trabecular bone in evolutionary studies 980 01:05:25,280 --> 01:05:29,144 to see whether or not a species was bipedal or quadrupedal. 981 01:05:29,144 --> 01:05:31,310 So I think I talked about this a little bit in 3032, 982 01:05:31,310 --> 01:05:35,800 but I have more slides and more stuff I'm going to talk about. 983 01:05:35,800 --> 01:05:37,555 So let me get myself organized. 984 01:06:18,880 --> 01:06:21,420 So osteoporosis comes from the Latin, 985 01:06:21,420 --> 01:06:23,450 and it actually means porous bones. 986 01:06:23,450 --> 01:06:26,910 So osteo means bone, and not too surprisingly 987 01:06:26,910 --> 01:06:31,700 porosis means porous. 988 01:06:31,700 --> 01:06:34,180 So this next slide gives you some idea what 989 01:06:34,180 --> 01:06:36,510 osteoporotic bone looks like. 990 01:06:36,510 --> 01:06:39,770 So the top slide is normal bone in a 55-year-old woman. 991 01:06:39,770 --> 01:06:42,590 These are sections from the lumbar spine. 992 01:06:42,590 --> 01:06:45,130 And that bone up here is 17% dense, 993 01:06:45,130 --> 01:06:47,520 so the relative density is point 0.17. 994 01:06:47,520 --> 01:06:51,550 And this is a section from the same area 995 01:06:51,550 --> 01:06:55,770 of bone in an 86-year-old woman, and it's 7% dense. 996 01:06:55,770 --> 01:06:58,180 So you can see there's a huge difference in the density, 997 01:06:58,180 --> 01:06:59,721 and you can start to see what happens 998 01:06:59,721 --> 01:07:01,930 when you lose bone mass. 999 01:07:01,930 --> 01:07:06,282 So if you look at this bone up here, it's all well connected. 1000 01:07:06,282 --> 01:07:07,740 Each little trabeculae is connected 1001 01:07:07,740 --> 01:07:09,470 to its neighboring friends. 1002 01:07:09,470 --> 01:07:11,790 And you can see down here, I mean, you look at this 1003 01:07:11,790 --> 01:07:13,670 and you kind of go ouch just looking at it. 1004 01:07:13,670 --> 01:07:16,970 Because this piece of bone here is just kind of dangling off, 1005 01:07:16,970 --> 01:07:18,680 not connected to anything. 1006 01:07:18,680 --> 01:07:20,840 And you can see the struts have gotten thinner, 1007 01:07:20,840 --> 01:07:23,290 so they've lost bone mass by thinning. 1008 01:07:23,290 --> 01:07:25,980 And then as I said when the thickness gets 1009 01:07:25,980 --> 01:07:29,710 less than they are roughly equal to the size of the cells, 1010 01:07:29,710 --> 01:07:31,190 then the cells can't live anymore, 1011 01:07:31,190 --> 01:07:34,720 and the bone strut just disappears altogether. 1012 01:07:34,720 --> 01:07:37,330 So it's not too surprising that if you lose this much bone 1013 01:07:37,330 --> 01:07:40,980 mass, there's mechanical consequences, 1014 01:07:40,980 --> 01:07:43,110 and there's a greater risk of fracture. 1015 01:07:43,110 --> 01:07:47,880 And as I said the two most common types of fractures 1016 01:07:47,880 --> 01:07:50,000 are hip fractures and vertebral fractures. 1017 01:07:53,890 --> 01:07:56,240 So let's see here. 1018 01:07:56,240 --> 01:08:00,735 So as people age, everybody loses bone mass. 1019 01:08:07,000 --> 01:08:09,580 And happily for you and not so happily for me, 1020 01:08:09,580 --> 01:08:12,200 the bone mass peaks at about 25 years old. 1021 01:08:12,200 --> 01:08:14,440 So you're probably either not at the peak 1022 01:08:14,440 --> 01:08:16,819 or just barely at the peak. 1023 01:08:16,819 --> 01:08:19,859 And then it decreases after that every year. 1024 01:08:19,859 --> 01:08:21,260 I'm considerably older than you. 1025 01:08:36,560 --> 01:08:38,670 And in women, when you go through menopause, 1026 01:08:38,670 --> 01:08:40,979 the cessation of estrogen production 1027 01:08:40,979 --> 01:08:42,260 increases the bone loss. 1028 01:08:42,260 --> 01:08:45,680 And so typically, osteoporosis is most common 1029 01:08:45,680 --> 01:08:47,200 in post menopausal women. 1030 01:09:23,200 --> 01:09:27,290 And osteoporosis is defined as a bone mass 2.5 1031 01:09:27,290 --> 01:09:30,029 standard deviations or more below that 1032 01:09:30,029 --> 01:09:31,850 of a young, normal mean. 1033 01:09:31,850 --> 01:09:33,960 So it's not like you fall and break your hip 1034 01:09:33,960 --> 01:09:35,720 and they say you have osteoporosis. 1035 01:09:35,720 --> 01:09:36,981 It's based on the bone mass. 1036 01:10:06,700 --> 01:10:08,910 And as I said, the trabeculae thin and then 1037 01:10:08,910 --> 01:10:09,870 they resorb completely. 1038 01:10:23,270 --> 01:10:25,780 So anybody here take Latin? 1039 01:10:25,780 --> 01:10:26,600 Yes. 1040 01:10:26,600 --> 01:10:29,140 I did Latin for one year in high school. 1041 01:10:29,140 --> 01:10:32,270 So trabeculae, with an E on the end here, 1042 01:10:32,270 --> 01:10:34,130 trabeculae, I suppose, is the plural. 1043 01:10:34,130 --> 01:10:36,120 Trabecula with an A is singular. 1044 01:10:36,120 --> 01:10:38,890 And that comes from Latin. 1045 01:10:38,890 --> 01:10:40,910 So you don't say trabeculas. 1046 01:10:40,910 --> 01:10:41,650 That's a no-no. 1047 01:10:46,660 --> 01:10:47,326 All right. 1048 01:10:49,930 --> 01:10:50,940 Let me get rid of these. 1049 01:10:56,750 --> 01:11:00,090 So if we saw that the strength of the bone 1050 01:11:00,090 --> 01:11:02,550 varies as the density squared, you 1051 01:11:02,550 --> 01:11:05,600 can begin to see how sensitive the strength is going 1052 01:11:05,600 --> 01:11:08,590 to be to this bone mass loss. 1053 01:11:08,590 --> 01:11:13,580 So say you went from a density of 0.2 to a density of 0.1, 1054 01:11:13,580 --> 01:11:15,560 then the densities changed by a factor of 2 1055 01:11:15,560 --> 01:11:17,260 so that the densities gone down by 1/2, 1056 01:11:17,260 --> 01:11:19,660 but the strength is going to go down by a factor of 4. 1057 01:11:19,660 --> 01:11:21,950 You're going to have the strength to be a 1/4. 1058 01:11:21,950 --> 01:11:25,920 And so you're going to have a big change in the strength. 1059 01:11:25,920 --> 01:11:27,780 And you can imagine is the trabeculae thins, 1060 01:11:27,780 --> 01:11:29,408 this buckling gets easier to happen. 1061 01:11:51,040 --> 01:11:52,570 And then once the trabeculae begin 1062 01:11:52,570 --> 01:11:56,030 to resorb as they disappear altogether, it's like I said. 1063 01:11:56,030 --> 01:11:59,100 it's like having a building's framework. 1064 01:11:59,100 --> 01:12:00,851 Now, you're removing beams and columns, 1065 01:12:00,851 --> 01:12:03,350 and the strength is going to go down even more dramatically. 1066 01:12:30,640 --> 01:12:33,880 And the way we model the osteoporotic bone 1067 01:12:33,880 --> 01:12:36,060 is we use finite element analysis. 1068 01:12:36,060 --> 01:12:38,660 So before we talked about using the unit cell 1069 01:12:38,660 --> 01:12:39,744 for the honeycomb. 1070 01:12:39,744 --> 01:12:41,160 But to use the unit cell, you have 1071 01:12:41,160 --> 01:12:43,890 to have repeating unit cells, and obviously, you 1072 01:12:43,890 --> 01:12:45,300 don't have that. 1073 01:12:45,300 --> 01:12:49,350 You've got local variations in what the structure looks like. 1074 01:12:49,350 --> 01:12:51,360 And we also used a dimensional analysis. 1075 01:12:51,360 --> 01:12:53,400 And the dimensional analysis relies 1076 01:12:53,400 --> 01:12:57,596 on the geometry being similar from one specimen to another, 1077 01:12:57,596 --> 01:12:58,970 and you can't really rely on that 1078 01:12:58,970 --> 01:13:01,760 either for the osteoporotic bone. 1079 01:13:01,760 --> 01:13:04,580 And so what we've done is-- and this 1080 01:13:04,580 --> 01:13:10,380 is what other people do as well, is use finite element modeling 1081 01:13:10,380 --> 01:13:11,420 to represent the bone. 1082 01:13:18,820 --> 01:13:21,805 So initially what we did was we used a 2D Voronoi model. 1083 01:13:21,805 --> 01:13:24,660 So remember we talked about Voronoi honeycombs and Voronoi 1084 01:13:24,660 --> 01:13:27,000 foams. 1085 01:13:27,000 --> 01:13:28,770 So I like to start out with simple things, 1086 01:13:28,770 --> 01:13:32,870 so we started out with 2D Voronoi model for a honeycomb. 1087 01:13:38,120 --> 01:13:42,160 Then we did a 2D representation of vertebral bone. 1088 01:13:51,510 --> 01:13:55,647 And then we had a 3D Voronoi. 1089 01:13:55,647 --> 01:13:57,480 And I had a couple of students who did this. 1090 01:13:57,480 --> 01:13:59,440 Matt Silver was the one who did the first two, 1091 01:13:59,440 --> 01:14:04,110 and Sereca Vagilla was the one who did the last one. 1092 01:14:04,110 --> 01:14:05,040 So let's see. 1093 01:14:05,040 --> 01:14:09,120 I think that's probably a good place to stop there for today. 1094 01:14:09,120 --> 01:14:13,450 So next time I'll talk about the modeling of osteoporotic bone, 1095 01:14:13,450 --> 01:14:15,450 and we might talk a little bit about metal bones 1096 01:14:15,450 --> 01:14:19,250 as a substitute for trabecular-- metal foams as a substitute. 1097 01:14:19,250 --> 01:14:21,210 I don't think we'll get to the evolution stuff. 1098 01:14:21,210 --> 01:14:23,920 We probably won't quite finish next time.