WEBVTT 00:00:00.030 --> 00:00:02.470 The following content is provided under a Creative 00:00:02.470 --> 00:00:04.000 Commons license. 00:00:04.000 --> 00:00:06.330 Your support will help MIT OpenCourseWare 00:00:06.330 --> 00:00:10.690 continue to offer high quality educational resources for free. 00:00:10.690 --> 00:00:13.300 To make a donation or view additional materials 00:00:13.300 --> 00:00:17.025 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.025 --> 00:00:17.650 at ocw.mit.edu. 00:00:25.224 --> 00:00:26.874 LORNA GIBSON: So we're going to start 00:00:26.874 --> 00:00:28.540 talking about trabecular bone, and we're 00:00:28.540 --> 00:00:30.970 going to do a bone today and on Wednesday. 00:00:30.970 --> 00:00:34.120 And I'm hoping we can more or less finish it on Wednesday. 00:00:34.120 --> 00:00:36.000 So hello. 00:00:36.000 --> 00:00:37.137 Hold on a sec. 00:00:43.300 --> 00:00:45.960 So these are some images of trabecular bone, 00:00:45.960 --> 00:00:49.350 and you can see that it has a foam-like structure. 00:00:49.350 --> 00:00:52.560 And trabecular bone exists in certain places in the body. 00:00:52.560 --> 00:00:54.860 There's three main places that it exists. 00:00:54.860 --> 00:00:57.830 So it exists at the end of the long bones. 00:00:57.830 --> 00:01:00.830 And over here this is a femur. 00:01:00.830 --> 00:01:02.320 This is the very top of the femur, 00:01:02.320 --> 00:01:05.650 and you can see this is all trabecular bone in here. 00:01:05.650 --> 00:01:09.550 This is a tibia, and this is the top of your knee there. 00:01:09.550 --> 00:01:12.790 And you can see how the bone get more bulbous at the ends, 00:01:12.790 --> 00:01:14.770 and it's filled with a trabecular bone. 00:01:14.770 --> 00:01:15.820 This is a vertebrae. 00:01:15.820 --> 00:01:18.146 So vertebrae are actually mostly trabecular bone, 00:01:18.146 --> 00:01:19.520 and they have a really thin shell 00:01:19.520 --> 00:01:23.920 of what's called cortical bone, the dense bone, on top of it. 00:01:23.920 --> 00:01:27.530 So trabecular bone exists at the ends of the long bones, 00:01:27.530 --> 00:01:29.780 it exists in the core of the vertebrae, 00:01:29.780 --> 00:01:33.150 and it also exists in sort of shell or plate-like bones. 00:01:33.150 --> 00:01:35.140 So in your skull, for example, there's 00:01:35.140 --> 00:01:38.970 a layer of trabecular bone in between two layers 00:01:38.970 --> 00:01:41.010 of the compact dense bone. 00:01:41.010 --> 00:01:43.210 And in your pelvis, it's the same thing. 00:01:43.210 --> 00:01:45.199 So those of you who took 3032, you remember 00:01:45.199 --> 00:01:46.990 when I passed around the bird skulls, there 00:01:46.990 --> 00:01:49.273 was that very porous kind of trabecular bone. 00:01:52.360 --> 00:01:55.060 So trabecular bone is of interest medically 00:01:55.060 --> 00:01:57.520 in three main kind of medical situations. 00:01:57.520 --> 00:01:59.531 So the first one is osteoporosis. 00:01:59.531 --> 00:02:01.780 So I want to talk a little bit about osteoporosis now, 00:02:01.780 --> 00:02:05.020 and then we'll talk about it in more detail later on. 00:02:05.020 --> 00:02:06.670 I guess, we'll probably start today. 00:02:06.670 --> 00:02:10.729 Another medical issue is osteoarthritis, 00:02:10.729 --> 00:02:13.460 and the properties of the trabecular bone 00:02:13.460 --> 00:02:16.980 are important in arthritis, and the third issue 00:02:16.980 --> 00:02:18.370 is in joint replacements. 00:02:18.370 --> 00:02:21.000 And so we're going to talk a little bit about osteoporosis, 00:02:21.000 --> 00:02:23.670 osteoarthritis, and then joint replacements. 00:02:23.670 --> 00:02:25.170 And then I'll talk a little bit more 00:02:25.170 --> 00:02:28.310 about modeling bone like a foam and how it deforms 00:02:28.310 --> 00:02:30.290 and how it fails. 00:02:30.290 --> 00:02:34.020 And then we'll talk a little bit how we can model osteoporosis. 00:02:34.020 --> 00:02:37.605 So let me write down some of these things. 00:02:37.605 --> 00:02:39.450 I guess we'll start here. 00:02:47.830 --> 00:02:51.200 So trabecular bone has a foam-like structure, 00:02:51.200 --> 00:02:52.950 and what we're going to see is that we 00:02:52.950 --> 00:02:55.140 can use the models for foams to describe 00:02:55.140 --> 00:02:57.634 the mechanical behavior of the bone. 00:03:10.900 --> 00:03:13.104 It exists at the ends of the long bones. 00:03:13.104 --> 00:03:14.520 And at the ends of the long bones, 00:03:14.520 --> 00:03:16.760 the bones become more bulbous. 00:03:16.760 --> 00:03:20.190 And really what that's for is to increase the surface 00:03:20.190 --> 00:03:23.450 area so that there's cartilage between the ends of the two 00:03:23.450 --> 00:03:23.950 bones. 00:03:23.950 --> 00:03:25.430 So there would be a bone here and a bone there, 00:03:25.430 --> 00:03:26.971 and there's cartilage in between them 00:03:26.971 --> 00:03:29.150 that sort of lubricates that joint 00:03:29.150 --> 00:03:31.900 and makes low friction at the joint. 00:03:31.900 --> 00:03:35.760 And the bone gets larger to decrease the stresses 00:03:35.760 --> 00:03:36.506 on the cartilage. 00:03:36.506 --> 00:03:38.880 So if you have the same force and you have a larger area, 00:03:38.880 --> 00:03:40.500 you're going to have a smaller stress. 00:03:40.500 --> 00:03:43.320 So that's why the bone gets bulbous like that. 00:03:43.320 --> 00:03:45.780 And then by having the trabecular bone, because it's 00:03:45.780 --> 00:03:47.350 so porous and lightweight, you're 00:03:47.350 --> 00:03:49.140 not having a big, dense hunk of bone 00:03:49.140 --> 00:03:52.270 at the end of the long bones. 00:03:52.270 --> 00:03:56.367 So it exists at the ends of the long bones. 00:03:56.367 --> 00:03:58.950 And I'll just say the ends have a larger area than the shafts. 00:04:07.310 --> 00:04:10.872 And that's to distribute the loads on the cartilage 00:04:10.872 --> 00:04:12.580 or to reduce the stress on the cartilage. 00:04:21.300 --> 00:04:25.390 And then the trabecular bone reduces the weight. 00:04:33.680 --> 00:04:38.386 So it also exists in the core of the vertebrae, 00:04:38.386 --> 00:04:45.840 and in fact, it makes up most of the vertebrae 00:04:45.840 --> 00:04:49.460 and then in things like the skull and the pelvic bones 00:04:49.460 --> 00:04:51.469 in shell and plate-like bones. 00:05:14.060 --> 00:05:16.223 And so it's the core of a sandwich structure there. 00:05:27.350 --> 00:05:32.250 So it's of interest in osteoporosis, 00:05:32.250 --> 00:05:40.115 in osteoarthritis, and in joint replacements. 00:05:50.476 --> 00:05:57.780 So if we start by thinking about osteoporosis, 00:05:57.780 --> 00:05:59.430 you probably know that osteoporosis 00:05:59.430 --> 00:06:04.220 is a disease where the bone mass becomes reduced 00:06:04.220 --> 00:06:06.380 and there's a greater risk of fracture, 00:06:06.380 --> 00:06:09.070 so there's especially a greater risk of hip fractures 00:06:09.070 --> 00:06:10.774 and vertebral fractures. 00:06:10.774 --> 00:06:12.440 And it turns out in both of those sites, 00:06:12.440 --> 00:06:14.320 if you just look at these bones here, 00:06:14.320 --> 00:06:18.000 typically if you have a hip fracture, what happens is 00:06:18.000 --> 00:06:19.660 the neck of the femur breaks. 00:06:19.660 --> 00:06:21.000 So this is called the neck here. 00:06:21.000 --> 00:06:23.360 This is called the head, this spherical bit there. 00:06:23.360 --> 00:06:24.977 So the neck has a fracture, and you 00:06:24.977 --> 00:06:27.060 can see most of the bone there is trabecular bone, 00:06:27.060 --> 00:06:29.610 so it's really carrying most of the load and the same 00:06:29.610 --> 00:06:31.080 with the vertebrae. 00:06:31.080 --> 00:06:33.140 This sort of cylindrical part of the vertebrae 00:06:33.140 --> 00:06:35.090 here carries most of the load. 00:06:35.090 --> 00:06:37.410 It has a shell of really thin cortical bone, 00:06:37.410 --> 00:06:39.370 but it's mostly trabecular bone. 00:06:39.370 --> 00:06:42.064 And when the loads are vertical like this, 00:06:42.064 --> 00:06:43.730 that's really the trabecular bone that's 00:06:43.730 --> 00:06:45.210 carrying most of the load. 00:06:45.210 --> 00:06:48.240 And people get sometimes what are called wedge fractures 00:06:48.240 --> 00:06:50.970 where instead of having a sort of a cylinder with parallel 00:06:50.970 --> 00:06:54.000 faces like this, the trabecular bone fails, 00:06:54.000 --> 00:06:57.343 and the bone ends up like that so that there's-- yeah, I know. 00:06:57.343 --> 00:06:59.770 You make that wincing expression. 00:06:59.770 --> 00:07:00.492 It's like ouchy. 00:07:00.492 --> 00:07:02.894 And in fact, it's very ouchy for people who get that. 00:07:02.894 --> 00:07:04.810 And when you see little old ladies who are all 00:07:04.810 --> 00:07:06.210 hunched over, that's why. 00:07:06.210 --> 00:07:07.770 The bone has actually failed. 00:07:07.770 --> 00:07:10.840 It's actually been crushed into these wedge fractures, 00:07:10.840 --> 00:07:12.880 and there's no way they can straighten it out, 00:07:12.880 --> 00:07:14.560 and it's quite painful. 00:07:14.560 --> 00:07:17.359 So people who look at osteoporosis 00:07:17.359 --> 00:07:19.400 are quite interested in the mechanical properties 00:07:19.400 --> 00:07:22.340 of trabecular bone for this sort of reason. 00:07:22.340 --> 00:07:24.470 The hip fractures are particularly 00:07:24.470 --> 00:07:28.071 serious because people become immobilized and then sometimes 00:07:28.071 --> 00:07:30.070 because they're immobilized, they get pneumonia, 00:07:30.070 --> 00:07:32.430 and in elderly people they sometimes die. 00:07:32.430 --> 00:07:36.820 So something like 40% of elderly patients who are over 65 00:07:36.820 --> 00:07:39.470 die within a year of having hip fracture. 00:07:39.470 --> 00:07:41.690 So it's not that the hip fracture kills them, 00:07:41.690 --> 00:07:44.980 it's that they become so immobile, and they can't move, 00:07:44.980 --> 00:07:47.930 and they can't walk around, and they end up getting pneumonia. 00:07:47.930 --> 00:07:49.780 So it's quite a serious thing. 00:07:49.780 --> 00:07:52.610 And there's something like 300,000 hip fractures a year 00:07:52.610 --> 00:07:55.790 in the US, and the cost of treating these hip fractures 00:07:55.790 --> 00:07:58.150 is something like $19 billion. 00:07:58.150 --> 00:08:00.290 So yeah, it's a huge problem. 00:08:00.290 --> 00:08:04.070 And as the population is aging, as baby boomers like 00:08:04.070 --> 00:08:07.880 me get older and older, there's going more people 00:08:07.880 --> 00:08:09.240 having hip fractures. 00:08:09.240 --> 00:08:13.510 So it's a huge deal, osteoporosis. 00:08:13.510 --> 00:08:24.050 So we'll say bone mass decreases with age, 00:08:24.050 --> 00:08:27.400 and osteoporosis is extreme bone loss. 00:08:35.247 --> 00:08:36.830 And a little later today I'll show you 00:08:36.830 --> 00:08:38.169 some pictures of what it looks like when 00:08:38.169 --> 00:08:39.210 people have osteoporosis. 00:08:44.950 --> 00:08:56.260 So the most common fractures are of the hip and the vertebrae, 00:08:56.260 --> 00:08:58.290 and at both sites, most of the load 00:08:58.290 --> 00:09:00.020 is carried by the trabecular bone. 00:09:18.750 --> 00:09:20.975 And the hip fractures you are the most serious. 00:09:26.980 --> 00:09:31.080 40% of elderly patients pass away within a year. 00:10:34.620 --> 00:10:38.420 So that's sort of a little introduction to osteoporosis. 00:10:38.420 --> 00:10:41.563 The next issue that people are interested in 00:10:41.563 --> 00:10:42.313 is osteoarthritis. 00:10:49.930 --> 00:10:52.310 And in osteoarthritis, there's a degradation 00:10:52.310 --> 00:10:56.210 of cartilage at the joints, and the stress on the cartilage 00:10:56.210 --> 00:10:58.260 is affected by the modulus of the bone that 00:10:58.260 --> 00:11:00.337 presses against the cartilage. 00:11:00.337 --> 00:11:02.420 You can kind of magic if you have a fiber compass, 00:11:02.420 --> 00:11:04.753 for instance, most of the stresses, if you're loading it 00:11:04.753 --> 00:11:07.030 along the fibers, is carried by the fibers 00:11:07.030 --> 00:11:08.170 because they're stiffer. 00:11:08.170 --> 00:11:10.970 So if you have like say trabecular bone that 00:11:10.970 --> 00:11:13.260 has varying density, the denser bits 00:11:13.260 --> 00:11:16.340 are going to have higher moduli, and it's 00:11:16.340 --> 00:11:19.020 there's going more stress associated with that. 00:11:19.020 --> 00:11:21.260 And so the modulus of the trabecular bone 00:11:21.260 --> 00:11:23.930 can affect how the loads are distributed in the cartilage, 00:11:23.930 --> 00:11:26.949 and that can affect the damage in the cartilage. 00:11:26.949 --> 00:11:28.490 And the shell, as I mentioned before, 00:11:28.490 --> 00:11:30.730 this sort of shell of cortical bone 00:11:30.730 --> 00:11:33.540 or the dense bone at the joints can be quite thin. 00:11:33.540 --> 00:11:35.420 It can be less than a millimeter. 00:11:35.420 --> 00:11:37.820 So I brought my little bones along with me again. 00:11:37.820 --> 00:11:41.050 So this is the head of a femur here, 00:11:41.050 --> 00:11:44.579 and this is a piece of a knee joint here from a tibia. 00:11:44.579 --> 00:11:46.120 And you can see just looking at these 00:11:46.120 --> 00:11:48.150 how thin the cortical shell is. 00:11:48.150 --> 00:11:51.147 So you can get an idea of how thin that is. 00:11:57.280 --> 00:12:02.650 So osteoarthritis involves a degradation 00:12:02.650 --> 00:12:04.130 of the cartilage at the joints. 00:12:21.780 --> 00:12:23.780 And the stress on the cartilage is 00:12:23.780 --> 00:12:33.630 affected by the moduli of the underlying bone, 00:12:33.630 --> 00:12:45.760 and the cortical shell, the totally dense bone, 00:12:45.760 --> 00:12:46.792 can be quite thin. 00:12:57.990 --> 00:13:00.474 So the mechanical properties of the trabecular bone 00:13:00.474 --> 00:13:02.640 can affect the stress distribution on the cartilage. 00:13:43.440 --> 00:13:46.570 And if osteoarthritis gets particularly bad, then 00:13:46.570 --> 00:13:48.810 sometimes people have joint replacements. 00:13:48.810 --> 00:13:51.190 So when it gets really bad, the cartilage 00:13:51.190 --> 00:13:54.260 is degraded completely, and the bone is rubbing on bone, 00:13:54.260 --> 00:13:55.760 and that's quite painful. 00:13:55.760 --> 00:13:58.490 And when it gets to that point, people generally 00:13:58.490 --> 00:14:00.800 have a joint replacement. 00:14:00.800 --> 00:14:02.760 And so the way the joint replacements are done 00:14:02.760 --> 00:14:06.490 is say somebody who is going to have a hip replacement, what 00:14:06.490 --> 00:14:09.490 they do is they chop off the top of the femur. 00:14:09.490 --> 00:14:12.580 So they would chop the femur off somewhere around here, 00:14:12.580 --> 00:14:14.950 and then they have a metal implant 00:14:14.950 --> 00:14:17.110 that has a spherical ball. 00:14:17.110 --> 00:14:18.770 That's like the head of the femur. 00:14:18.770 --> 00:14:21.250 And then it has a sort of stem and a shaft here 00:14:21.250 --> 00:14:24.140 that goes into the hollow part of the long part 00:14:24.140 --> 00:14:27.850 of the shaft of the femur. 00:14:27.850 --> 00:14:31.950 And so they use a number of different metals for this, 00:14:31.950 --> 00:14:33.710 titanium and stainless steel, and there's 00:14:33.710 --> 00:14:36.460 a cobalt-chromium alloy are also used. 00:14:36.460 --> 00:14:38.720 So you need metals that are biocompatible, 00:14:38.720 --> 00:14:40.261 aren't going to corrode, aren't going 00:14:40.261 --> 00:14:41.850 to have degradation products. 00:14:41.850 --> 00:14:44.930 And then the bone grows around that implant, 00:14:44.930 --> 00:14:48.240 and the bone grows in response to mechanical loads. 00:14:48.240 --> 00:14:50.750 So the density of the bone depends 00:14:50.750 --> 00:14:53.329 on the magnitude of the load, and the orientation 00:14:53.329 --> 00:14:55.870 of the trabeculae depends on the orientation of the principle 00:14:55.870 --> 00:14:57.800 stresses that are applied. 00:14:57.800 --> 00:14:59.300 So let me write that down. 00:15:38.360 --> 00:15:45.530 So they cut off the end of the bone, 00:15:45.530 --> 00:15:50.760 and they insert the implant into the hollow shaft 00:15:50.760 --> 00:15:52.090 of the remaining bone. 00:16:06.298 --> 00:16:18.930 And the metals they use are titanium, stainless steel, 00:16:18.930 --> 00:16:21.050 and a chromium-cobalt alloy. 00:16:28.250 --> 00:16:31.140 And then the bone grows into that implant. 00:16:36.970 --> 00:16:39.553 And the bone grows in response to mechanical loads. 00:16:52.974 --> 00:16:55.550 So the density of the bone depends 00:16:55.550 --> 00:17:07.940 on the magnitude of the stresses, 00:17:07.940 --> 00:17:13.829 and the orientation of the bone depends 00:17:13.829 --> 00:17:15.819 on the principle stresses. 00:17:56.430 --> 00:17:59.760 So one of the issues that comes up in joint replacements 00:17:59.760 --> 00:18:01.570 is that there's a mismatch in the moduli 00:18:01.570 --> 00:18:03.570 between the metal and the bone. 00:18:03.570 --> 00:18:06.220 So if you think the metal, like something like stainless steel, 00:18:06.220 --> 00:18:10.210 has a modulus of around 200, 210 gigapascals. 00:18:10.210 --> 00:18:11.890 And the cortical bone has a modulus 00:18:11.890 --> 00:18:15.330 of about 18 gigapascals, and the trabecular bone 00:18:15.330 --> 00:18:20.600 has a modulus between about 0.01 and 2 gigapascals, 00:18:20.600 --> 00:18:22.080 depending on its density. 00:18:22.080 --> 00:18:24.610 So you're taking the bone out, and you're replacing it 00:18:24.610 --> 00:18:26.710 with something that's much, much stiffer, and that 00:18:26.710 --> 00:18:30.850 changes the stress distribution around the remaining bone. 00:18:30.850 --> 00:18:33.040 And one of the things that can happen 00:18:33.040 --> 00:18:34.910 is you can get a loosening of the implant. 00:18:34.910 --> 00:18:37.070 So the bone can grow in initially, 00:18:37.070 --> 00:18:38.850 but over time, you get a different stress 00:18:38.850 --> 00:18:39.685 field in the bone. 00:18:39.685 --> 00:18:41.830 And if you have a different stress field, 00:18:41.830 --> 00:18:45.860 then the bone can resorb away from the implant and cause 00:18:45.860 --> 00:18:47.270 what's called loosening. 00:18:47.270 --> 00:18:49.600 So if the implant becomes loose, that's 00:18:49.600 --> 00:18:50.880 clearly not a good thing. 00:18:50.880 --> 00:18:52.400 It's a bad thing. 00:18:52.400 --> 00:18:54.515 And often orthopedic surgeons don't 00:18:54.515 --> 00:18:56.640 like to do these joint replacements in young people 00:18:56.640 --> 00:18:59.110 partly because they don't always loosen, 00:18:59.110 --> 00:19:00.690 but occasionally they do. 00:19:00.690 --> 00:19:03.300 And if they loosen they can go back and do a revision. 00:19:03.300 --> 00:19:05.076 But you can kind of imagine after they've 00:19:05.076 --> 00:19:06.450 chopped the head of the femur off 00:19:06.450 --> 00:19:08.340 and they put one implant in, it's 00:19:08.340 --> 00:19:11.117 not that easy to go back in and replace that with another one. 00:19:11.117 --> 00:19:12.700 You would need one with a longer stem, 00:19:12.700 --> 00:19:15.850 and the whole thing becomes a little bit more complicated. 00:19:15.850 --> 00:19:17.545 So this issue of stress shielding 00:19:17.545 --> 00:19:18.920 is what it's called when you have 00:19:18.920 --> 00:19:21.320 something much stiffer that's shielding 00:19:21.320 --> 00:19:23.502 the stresses in the bone. 00:19:23.502 --> 00:19:24.960 The issue of stress shielding means 00:19:24.960 --> 00:19:28.680 that they don't like to do the replacements on younger 00:19:28.680 --> 00:20:01.810 patients unless you can get stress shielding. 00:20:01.810 --> 00:20:10.050 And if we just compare-- if we look at the cobalt and chromium 00:20:10.050 --> 00:20:16.650 alloy, the modulus of that in gigapascals is about 210. 00:20:16.650 --> 00:20:19.770 If we look at the titanium alloys that are used, 00:20:19.770 --> 00:20:22.380 the modulus is about 110. 00:20:22.380 --> 00:20:24.100 If we look at the stainless steel-- 00:20:24.100 --> 00:20:32.400 it's 316 stainless steel-- it has a modulus of around 210. 00:20:32.400 --> 00:20:38.080 And then if we look at the bone, the cortical bone 00:20:38.080 --> 00:20:45.870 has a modulus of about 18, and the trabecular bone 00:20:45.870 --> 00:20:50.160 has a modulus 0.01 to 2 gigapascals 00:20:50.160 --> 00:20:51.480 depending on the density. 00:20:56.310 --> 00:20:59.840 So after the joint replacement happens, 00:20:59.840 --> 00:21:02.176 the remodeling of the bone is affected. 00:21:25.820 --> 00:21:30.450 So the idea is that the stiffer metal carries more of the load, 00:21:30.450 --> 00:21:32.953 and then the bone carries less load, and then it resorbs. 00:21:49.620 --> 00:21:53.240 And that can lead to this thing called loosening, 00:21:53.240 --> 00:21:54.545 which is not desirable. 00:22:09.371 --> 00:22:11.620 Now, this typically doesn't happen till about 15 years 00:22:11.620 --> 00:22:13.240 after you've had the implant, so it's not 00:22:13.240 --> 00:22:14.865 something that would happen right away, 00:22:14.865 --> 00:22:16.056 but it can happen later on. 00:22:36.930 --> 00:22:38.760 So these are all sort of medical reasons 00:22:38.760 --> 00:22:40.926 why people are interested in trabecular bone because 00:22:40.926 --> 00:22:46.380 of osteoporosis, osteoarthritis, and joint replacements. 00:22:46.380 --> 00:22:48.870 So I wanted to start by talking about the structure 00:22:48.870 --> 00:22:50.310 of trabecular bone. 00:22:56.430 --> 00:23:01.240 And then we'll talk about what the stress-strain curves look 00:23:01.240 --> 00:23:03.330 like in compression and tension, what 00:23:03.330 --> 00:23:05.490 are the mechanisms of deformation and failure, 00:23:05.490 --> 00:23:09.580 and how we can apply our models for foams to the trabecular 00:23:09.580 --> 00:23:11.690 bone. 00:23:11.690 --> 00:23:14.140 So the idea is that the structure of the bone 00:23:14.140 --> 00:23:17.400 resembles a foam, and here's some SCM 00:23:17.400 --> 00:23:20.150 images of trabecular bone. 00:23:20.150 --> 00:23:23.950 And you can see that the bone has a varying structure. 00:23:23.950 --> 00:23:25.910 If it's relatively low density, this 00:23:25.910 --> 00:23:28.609 is a bone that's almost like an open-cell foam 00:23:28.609 --> 00:23:30.150 if I didn't tell you that was a bone, 00:23:30.150 --> 00:23:33.370 you might actually think it was an open-cell foam. 00:23:33.370 --> 00:23:36.100 And here's a denser piece of bone, 00:23:36.100 --> 00:23:39.840 and you can see there's still interconnections between all 00:23:39.840 --> 00:23:41.470 the openings, so it's not exactly 00:23:41.470 --> 00:23:45.160 like a closed-cell foam, but it's much denser, 00:23:45.160 --> 00:23:47.190 and it's almost like there's perforated plates 00:23:47.190 --> 00:23:48.370 in the structure. 00:23:48.370 --> 00:23:51.734 And then as I said the bone can grow in response to loads. 00:23:51.734 --> 00:23:53.900 So if you have loads that are more or less vertical, 00:23:53.900 --> 00:23:55.970 the trabeculae tend to line up and be 00:23:55.970 --> 00:24:00.420 more or less vertical with some sort of horizontal bracing. 00:24:00.420 --> 00:24:02.880 So this is a piece of bone from a knee, 00:24:02.880 --> 00:24:06.020 the condyle is sort of towards the top of the knee. 00:24:06.020 --> 00:24:10.310 And you can see these are sort of plate-like pieces of bone. 00:24:10.310 --> 00:24:13.370 They're almost parallel, and not too surprisingly in your knee, 00:24:13.370 --> 00:24:15.416 the loads are typically vertical, 00:24:15.416 --> 00:24:16.790 and then there's a little bracing 00:24:16.790 --> 00:24:18.752 bits that go horizontally here. 00:24:18.752 --> 00:24:20.210 So you can get different structures 00:24:20.210 --> 00:24:23.710 depending on the loading on the bone, 00:24:23.710 --> 00:24:26.370 and the density of the bone corresponds 00:24:26.370 --> 00:24:28.520 to the magnitude of the load, and the orientation 00:24:28.520 --> 00:24:34.954 of the trabeculae corresponds to the orientation of the load. 00:24:34.954 --> 00:24:35.870 AUDIENCE: [INAUDIBLE]. 00:24:40.416 --> 00:24:42.380 LORNA GIBSON: Resorb. 00:24:42.380 --> 00:24:45.686 So when the bone density goes down, when you lose bone mass, 00:24:45.686 --> 00:24:46.727 that's called resorption. 00:24:50.340 --> 00:24:54.140 So the idea is that the trabecular bone 00:24:54.140 --> 00:24:55.253 resembles a foam. 00:24:59.690 --> 00:25:06.030 And in fact, the word trabecular comes from Latin, 00:25:06.030 --> 00:25:08.421 and in Latin, it means little beam. 00:25:13.210 --> 00:25:15.179 So the foams to form by bending. 00:25:15.179 --> 00:25:17.220 They act like little beams, and so the trabeculae 00:25:17.220 --> 00:25:21.140 are like little beams, even in Latin. 00:25:21.140 --> 00:25:23.556 There's a range of relative densities, 00:25:23.556 --> 00:25:25.180 and you can see in that image up there, 00:25:25.180 --> 00:25:26.664 you can see that there's a range. 00:25:30.300 --> 00:25:33.630 And they range typically between about a 5% in dense 00:25:33.630 --> 00:25:35.090 and 50% in dense. 00:25:39.320 --> 00:25:43.450 So something like 0.1 or 0.2 might be typical. 00:25:43.450 --> 00:25:48.920 And the low-density bone resembles an open-cell foam. 00:25:56.890 --> 00:25:59.270 And the higher density, it becomes more 00:25:59.270 --> 00:26:00.510 like perforated plates. 00:26:17.120 --> 00:26:19.680 And the structure can be highly anisotropic 00:26:19.680 --> 00:26:21.140 depending on the stress field. 00:26:46.050 --> 00:26:50.610 And then I've got another image here of the trabecular bone. 00:26:50.610 --> 00:26:52.930 These images are using what's called 00:26:52.930 --> 00:26:54.940 micro computed tomography. 00:26:54.940 --> 00:26:57.610 So you've probably heard of computed tomography. 00:26:57.610 --> 00:27:00.710 Say somebody has cancer, they get put in a CT machine, 00:27:00.710 --> 00:27:02.240 and they do a scan. 00:27:02.240 --> 00:27:04.620 The micro CT is more of a research tool. 00:27:04.620 --> 00:27:06.360 It's the same kind of technology, 00:27:06.360 --> 00:27:08.410 but it's got a much finer resolution, 00:27:08.410 --> 00:27:11.230 and typically, you put a small specimen into a machine 00:27:11.230 --> 00:27:11.740 to do this. 00:27:11.740 --> 00:27:14.920 So the specimen might be half an inch 00:27:14.920 --> 00:27:17.910 in diameter and an inch tall, something like that. 00:27:17.910 --> 00:27:20.860 So these are done by a colleague, Ralph Muller, who's 00:27:20.860 --> 00:27:24.110 in Zurich, and this is one of his bread and butter things 00:27:24.110 --> 00:27:27.280 that he has these images, and he looks at osteoporosis. 00:27:27.280 --> 00:27:30.310 And you can see here the difference in the structure 00:27:30.310 --> 00:27:31.680 for the different densities. 00:27:31.680 --> 00:27:36.680 So here's a 26% dense piece of bone in the femoral head. 00:27:36.680 --> 00:27:38.980 It looks pretty sturdy and substantial. 00:27:38.980 --> 00:27:43.210 Here's an 11% dense piece from the lumbar spine, 00:27:43.210 --> 00:27:45.450 and here's a 6% dense piece. 00:27:45.450 --> 00:27:50.970 And you can kind of see when you go from 26 to 11, 00:27:50.970 --> 00:27:53.180 the struts get a little bit thinner. 00:27:53.180 --> 00:27:56.954 And when you go from 11 to 6, the struts get very thin, 00:27:56.954 --> 00:27:58.370 and in fact, if they get too thin, 00:27:58.370 --> 00:28:01.050 the struts resorb altogether, and some of their struts 00:28:01.050 --> 00:28:02.560 can just disappear. 00:28:02.560 --> 00:28:05.210 So when people get osteoporosis, what happens 00:28:05.210 --> 00:28:08.680 is they first lose bone mass by thinning the struts, 00:28:08.680 --> 00:28:12.270 but then at some point, the struts just resorb altogether. 00:28:12.270 --> 00:28:15.180 And if you think of the struts as a biological material, 00:28:15.180 --> 00:28:17.250 they have bone cells in them. 00:28:17.250 --> 00:28:20.760 So there's little osteoclasts and osteoblasts and osteocytes 00:28:20.760 --> 00:28:24.200 that live in the bone, the mineral thing, the bony thing. 00:28:24.200 --> 00:28:28.220 And those cells have dimensions of 10s of microns, so maybe 20, 00:28:28.220 --> 00:28:29.840 30 microns, something like that. 00:28:29.840 --> 00:28:31.780 So the struts can't get any thinner than that. 00:28:31.780 --> 00:28:34.154 If they get thinner than that, then the cells can't live, 00:28:34.154 --> 00:28:36.430 and the thing just disappears altogether. 00:28:36.430 --> 00:28:40.310 And you can think of from a mechanical point of view, 00:28:40.310 --> 00:28:43.160 if you lose density by thinning the struts, 00:28:43.160 --> 00:28:45.080 you can use our sort of foam equations. 00:28:45.080 --> 00:28:48.810 And say the density went from 0.2 to 0.1, 00:28:48.810 --> 00:28:51.160 you could make some estimate of how the modulus 00:28:51.160 --> 00:28:54.270 and how the strength would vary depending on our foam models. 00:28:54.270 --> 00:28:57.310 But if you lose density by resorbing the struts, 00:28:57.310 --> 00:28:59.490 the struts just disappear altogether, 00:28:59.490 --> 00:29:02.990 then it's as if you had a steel scaffold or a steel 00:29:02.990 --> 00:29:04.130 structure of a building. 00:29:04.130 --> 00:29:06.420 And now you're starting to remove columns and remove 00:29:06.420 --> 00:29:07.590 beams. 00:29:07.590 --> 00:29:08.280 Yes, I know. 00:29:08.280 --> 00:29:09.810 That's not good, not good. 00:29:09.810 --> 00:29:11.270 And so we'll talk a little bit more 00:29:11.270 --> 00:29:13.820 about that when we talk more about osteoporosis, 00:29:13.820 --> 00:29:15.700 and you can see the consequences of that. 00:29:15.700 --> 00:29:17.241 But this image here kind of gives you 00:29:17.241 --> 00:29:20.870 a little bit of a picture of what the bone structure looks 00:29:20.870 --> 00:29:23.280 like as it gets less dense. 00:29:23.280 --> 00:29:24.820 So I want to talk a little bit more 00:29:24.820 --> 00:29:27.410 about the bone growing in response to load. 00:29:27.410 --> 00:29:28.850 Let me rub off the board. 00:30:06.980 --> 00:30:09.720 So you're probably already a little bit familiar 00:30:09.720 --> 00:30:10.400 with this idea. 00:30:10.400 --> 00:30:13.670 So when astronauts go up into space, 00:30:13.670 --> 00:30:16.252 they often do exercises where they have a treadmill, 00:30:16.252 --> 00:30:18.710 and they've got springs, and they're pulling on the springs 00:30:18.710 --> 00:30:20.049 to try to exercise themselves. 00:30:20.049 --> 00:30:21.840 And the reason they do that is when they're 00:30:21.840 --> 00:30:25.450 in microgravity, if they were doing some kind of exercise, 00:30:25.450 --> 00:30:27.280 they would lose bone mass. 00:30:27.280 --> 00:30:30.900 And they will get back to Earth where we have Earth gravity, 00:30:30.900 --> 00:30:32.160 and they would have a problem. 00:30:32.160 --> 00:30:35.650 So you see it in astronauts, in microgravity. 00:30:35.650 --> 00:30:38.660 The other place you see this just in everyday life 00:30:38.660 --> 00:30:41.020 is in professional tennis players. 00:30:41.020 --> 00:30:44.100 People have done like x-rays of the bones 00:30:44.100 --> 00:30:46.320 of professional tennis players, and obviously, they 00:30:46.320 --> 00:30:49.420 have one arm that they hit the ball with their racquet. 00:30:49.420 --> 00:30:50.890 The bones in that arm actually get 00:30:50.890 --> 00:30:54.500 bigger because they're loading that bone over and over 00:30:54.500 --> 00:30:57.020 again pretty much every day when they're playing tennis, 00:30:57.020 --> 00:30:58.700 and they're not loading the other arm. 00:30:58.700 --> 00:31:01.350 So their two arms are not symmetrical because 00:31:01.350 --> 00:31:04.760 of this loading from hitting the racquet over and over. 00:31:04.760 --> 00:31:07.480 And the people in 3032 have already seen this, 00:31:07.480 --> 00:31:10.210 but I couldn't resist bringing up the Guinea fowl experiments 00:31:10.210 --> 00:31:11.580 again. 00:31:11.580 --> 00:31:14.270 So obviously, you can only do x-rays on human. 00:31:14.270 --> 00:31:16.590 You can't sacrifice the humans and look at their bones, 00:31:16.590 --> 00:31:18.050 but you can with Guinea fowl. 00:31:18.050 --> 00:31:20.600 And so people have done experiments 00:31:20.600 --> 00:31:23.470 where they run Guinea fowl on treadmills, 00:31:23.470 --> 00:31:25.700 and they have one set of Guinea fowl 00:31:25.700 --> 00:31:27.950 that they run on the treadmill that's horizontal. 00:31:27.950 --> 00:31:29.450 They have another set of Guinea fowl 00:31:29.450 --> 00:31:31.949 that they run on a treadmill that's inclined to 20 degrees, 00:31:31.949 --> 00:31:34.490 so one would think they might have more stress on their bones 00:31:34.490 --> 00:31:36.550 from that, and then they have a control group 00:31:36.550 --> 00:31:38.580 that they don't run on the treadmill at all. 00:31:38.580 --> 00:31:41.170 And then what they do is they have a forced 00:31:41.170 --> 00:31:44.360 plate on the treadmill so as the Guinea fowl is running, 00:31:44.360 --> 00:31:46.320 they measure the maximum force in they're 00:31:46.320 --> 00:31:47.820 taking high-speed video. 00:31:47.820 --> 00:31:49.850 And then they measure the angle of the knee 00:31:49.850 --> 00:31:52.490 at that point at which the force is maximum. 00:31:52.490 --> 00:31:53.940 And they can see there's a change 00:31:53.940 --> 00:31:57.160 in the angle of the knee when they put them on the inclined 00:31:57.160 --> 00:31:59.290 treadmill, not too surprisingly. 00:31:59.290 --> 00:32:01.870 And then these are juvenile Guinea fowl 00:32:01.870 --> 00:32:03.856 that haven't completely matured their bones. 00:32:03.856 --> 00:32:05.480 And then after about six weeks of this, 00:32:05.480 --> 00:32:09.070 they sacrifice the Guinea fowl, and they do scans on the bone, 00:32:09.070 --> 00:32:11.250 and they look at the orientation of the bone, 00:32:11.250 --> 00:32:14.560 and they measure what's called the orientation 00:32:14.560 --> 00:32:16.150 of the peak trabecular density, which 00:32:16.150 --> 00:32:19.600 is a way of characterizing the orientation of the bone. 00:32:19.600 --> 00:32:22.510 And they find that the angle of the knee when 00:32:22.510 --> 00:32:26.490 the Guinea fowl are running changes by about 14 degrees. 00:32:26.490 --> 00:32:28.130 And it turns out the angle of the bone, 00:32:28.130 --> 00:32:31.520 the orientation of the bone also changes by about 14 degrees. 00:32:31.520 --> 00:32:34.910 So the bone has remodeled to match that change 00:32:34.910 --> 00:32:37.710 in the forces that are applied as the Guinea fowl are running 00:32:37.710 --> 00:32:38.780 on a treadmill. 00:32:38.780 --> 00:32:40.410 So this is all a demonstration just 00:32:40.410 --> 00:32:43.410 to show that bone grows in response to load. 00:32:43.410 --> 00:32:47.230 So let me write down some of this stuff. 00:32:47.230 --> 00:32:51.840 So I will say astronauts-- did you 00:32:51.840 --> 00:32:55.600 see Michael Collins is going to come to the talk at MIT? 00:32:55.600 --> 00:32:58.840 When I was a kid in '60s, he was one of the Apollo astronauts. 00:32:58.840 --> 00:33:02.830 He was like one of the first NASA astronauts. 00:33:02.830 --> 00:33:11.232 Anyway astronauts, so in microgravity, 00:33:11.232 --> 00:33:13.065 they would lose bone if they don't exercise. 00:33:20.100 --> 00:33:41.330 And tennis players, the bones get larger in the arm 00:33:41.330 --> 00:33:43.982 that they hold the racket with. 00:33:43.982 --> 00:33:46.109 And then I'll just write a little bit 00:33:46.109 --> 00:33:47.900 of notes about the Guinea fowl experiments. 00:33:58.200 --> 00:34:09.934 So this was done by-- it's in a paper, Ponzer et al 2006. 00:34:09.934 --> 00:34:11.600 So they have one set of Guinea fowl that 00:34:11.600 --> 00:34:15.880 run on a level treadmill, they have 00:34:15.880 --> 00:34:22.900 another set that run on a inclined treadmill, 00:34:22.900 --> 00:34:25.590 and it's inclined at 20 degrees. 00:34:25.590 --> 00:34:27.322 And then they have a control group that 00:34:27.322 --> 00:34:28.530 doesn't run on the treadmill. 00:34:44.129 --> 00:34:52.400 And then they measure the angle at the knee at the moment 00:34:52.400 --> 00:34:54.238 of peak force on the treadmill. 00:35:06.450 --> 00:35:16.310 And after six weeks, they sacrificed the Guinea fowl, 00:35:16.310 --> 00:35:19.580 and they measured the orientation 00:35:19.580 --> 00:35:21.475 of the peak trabecular density. 00:35:38.600 --> 00:35:40.530 And they find that the knee flexion 00:35:40.530 --> 00:35:55.011 angle changed by 13.7 degrees. 00:35:55.011 --> 00:36:08.640 And if you compared the inclined versus the level treadmill, 00:36:08.640 --> 00:36:11.170 and they found the orientation of the peak trabecular 00:36:11.170 --> 00:36:28.690 density, which they called OPDD, also changed by 13.6 degrees. 00:36:28.690 --> 00:36:31.000 So the idea is that the orientation of the trabeculae 00:36:31.000 --> 00:36:33.870 changed to match the orientation of the loading. 00:37:12.990 --> 00:37:14.420 Then I have a little video here. 00:37:18.390 --> 00:37:19.490 Do you like video? 00:37:19.490 --> 00:37:22.170 So I have a colleague who's at Harvard who studies animal 00:37:22.170 --> 00:37:25.160 locomotion, and they didn't do this set of experiments, 00:37:25.160 --> 00:37:27.250 but they do do experiments on Guinea fowl running 00:37:27.250 --> 00:37:30.250 on treadmills, and thought you might find this amusing. 00:37:30.250 --> 00:37:34.220 So let me see if I can make this work. 00:37:34.220 --> 00:37:36.830 [VIDEO PLAYBACK] 00:37:36.830 --> 00:37:39.340 -Sometimes you walk into a lab and you just 00:37:39.340 --> 00:37:46.026 think this is what science is all about. 00:37:46.026 --> 00:37:47.900 -I just put the Guinea fowl on the treadmill, 00:37:47.900 --> 00:37:50.090 and this is something that we commonly do. 00:37:57.360 --> 00:37:59.480 -Welcome to the Concord Field Station, 00:37:59.480 --> 00:38:04.650 a defunct Nike missile base turned scientific menagerie. 00:38:04.650 --> 00:38:07.630 It's owned by Harvard, and biologist Andy Biewener 00:38:07.630 --> 00:38:08.800 is the director here. 00:38:08.800 --> 00:38:10.070 So think of it as-- 00:38:10.070 --> 00:38:13.270 -A research lab facility for doing comparative biomechanics 00:38:13.270 --> 00:38:16.350 and physiology of largely animal movement. 00:38:16.350 --> 00:38:19.920 -And the birds are just the tip of the iceberg. 00:38:19.920 --> 00:38:22.751 -So do you want to see the baby goat and the emu? 00:38:22.751 --> 00:38:23.250 -Obviously. 00:38:23.250 --> 00:38:23.749 -OK. 00:38:38.660 --> 00:38:42.330 We keep it because it's sort of like a mascot. 00:38:42.330 --> 00:38:44.780 There used to be a lizard colony. 00:38:44.780 --> 00:38:46.876 You can hear the African greys. 00:38:46.876 --> 00:38:50.400 Then the jerboas are housed in this room here. 00:38:50.400 --> 00:38:53.580 This is where we originally did our pigeon flight studies. 00:38:53.580 --> 00:38:56.815 So usually the ones with claws and sharp teeth 00:38:56.815 --> 00:38:59.190 and aggressive behaviors, you want to watch out for them. 00:38:59.190 --> 00:39:00.440 -As you might expect. 00:39:00.440 --> 00:39:02.780 But did you know that Guinea fowl-- 00:39:02.780 --> 00:39:04.357 -They're really lovely to work with. 00:39:04.357 --> 00:39:04.856 -Sometimes. 00:39:07.590 --> 00:39:08.410 Or that-- 00:39:08.410 --> 00:39:10.210 -Rats are not very good on treadmills. 00:39:10.210 --> 00:39:10.830 -Yes. 00:39:10.830 --> 00:39:12.690 That's what a rat treadmill looks like. 00:39:12.690 --> 00:39:13.330 And this? 00:39:13.330 --> 00:39:15.200 -And this was historically a treadmill 00:39:15.200 --> 00:39:18.260 of note, the treadmill that they first taught kangaroos 00:39:18.260 --> 00:39:20.819 on and showed that kangaroos stored energy in their tendons 00:39:20.819 --> 00:39:23.360 enough that they don't actually increase their metabolic rate 00:39:23.360 --> 00:39:25.580 when they hop at faster speeds. 00:39:25.580 --> 00:39:27.490 -These are the kind of discoveries made here 00:39:27.490 --> 00:39:31.150 with the use of high-speed video and x-ray machines 00:39:31.150 --> 00:39:34.400 and semi cooperative animals. 00:39:34.400 --> 00:39:37.230 But beyond the basic biology, Biewener 00:39:37.230 --> 00:39:39.310 says engineers are using this research 00:39:39.310 --> 00:39:41.340 to build better robots, and it can 00:39:41.340 --> 00:39:43.470 help improve medical treatment for people 00:39:43.470 --> 00:39:45.250 with movement disorders. 00:39:45.250 --> 00:39:48.160 Today the big excitement at the lab is happening here. 00:39:48.160 --> 00:39:51.810 Ivo Ros is studying how heart rate changes when cockatiels 00:39:51.810 --> 00:39:53.020 fly at different speeds. 00:39:53.020 --> 00:39:56.450 So this is a way to look at how much energy it takes to fly, 00:39:56.450 --> 00:39:58.640 and that cord is measuring heart rate. 00:39:58.640 --> 00:40:02.228 But instead of the birds flying faster, the wind changes speed. 00:40:02.228 --> 00:40:03.478 -I'm going to turn it on then. 00:40:10.460 --> 00:40:14.430 -It's hard to fly fast, and it's hard to fly slow, Ros says. 00:40:14.430 --> 00:40:16.800 So the expectation is that the heart rate should 00:40:16.800 --> 00:40:20.090 be shaped like a U. But so far Ros is 00:40:20.090 --> 00:40:22.240 finding that it's a flat line. 00:40:22.240 --> 00:40:25.520 It's like the bird goes into a stress reaction 00:40:25.520 --> 00:40:27.090 when it takes off. 00:40:27.090 --> 00:40:28.920 Is that just because of the wind tunnel? 00:40:28.920 --> 00:40:30.045 What Ros wants to know is-- 00:40:30.045 --> 00:40:32.670 - --whether or not they need to be stressed to fly in the first 00:40:32.670 --> 00:40:33.220 place. 00:40:33.220 --> 00:40:35.810 -That's something that Ros is looking into, 00:40:35.810 --> 00:40:38.150 but today is mostly about training. 00:40:38.150 --> 00:40:38.770 -Keep going. 00:40:38.770 --> 00:40:39.530 Come on. 00:40:39.530 --> 00:40:40.940 -Imagine you're a cockatiel. 00:40:40.940 --> 00:40:43.590 A wind tunnel is kind of a strange experience. 00:40:43.590 --> 00:40:45.720 -A bird in a wind tunnel has to confront the fact 00:40:45.720 --> 00:40:48.150 that the world is not moving past, which 00:40:48.150 --> 00:40:50.290 defies its normal sensory cues. 00:40:50.290 --> 00:40:52.781 -Which pretty well sums up the Concord Field Station 00:40:52.781 --> 00:40:53.280 generally. 00:41:03.110 --> 00:41:04.940 For Science Friday, I'm Flora Lichtman. 00:41:04.940 --> 00:41:05.080 [END PLAYBACK] 00:41:05.080 --> 00:41:07.030 And if read The New York Times, Flora Lichtman 00:41:07.030 --> 00:41:10.920 used to work for NPR and would make these Science Friday 00:41:10.920 --> 00:41:12.530 videos for them. 00:41:12.530 --> 00:41:15.870 But now she has a gig doing things for The New York Times, 00:41:15.870 --> 00:41:17.900 and she does science videos still. 00:41:17.900 --> 00:41:19.776 I don't know if you quite call them videos, 00:41:19.776 --> 00:41:22.150 but what they do is they have these little paper puppets, 00:41:22.150 --> 00:41:24.930 and the paper puppets are animated and re-enact 00:41:24.930 --> 00:41:27.250 different episodes in science. 00:41:27.250 --> 00:41:31.200 And it's kind of amazing how they do these little science 00:41:31.200 --> 00:41:32.030 videos. 00:41:32.030 --> 00:41:33.710 So if you Google Flora Lichtman, you'll 00:41:33.710 --> 00:41:37.107 see more Science Videos with all sorts of things. 00:41:37.107 --> 00:41:38.690 I guess the other interesting anecdote 00:41:38.690 --> 00:41:40.790 is I went to the Concord Field Station once. 00:41:40.790 --> 00:41:44.090 And I had done a study on quills and animals 00:41:44.090 --> 00:41:47.937 that have quills because the quills have a foamy structure 00:41:47.937 --> 00:41:48.520 in the middle. 00:41:48.520 --> 00:41:49.620 So they're carrot, and they have sort 00:41:49.620 --> 00:41:50.930 of like carrot-like structures. 00:41:50.930 --> 00:41:52.680 And they have an outer shell that's dense, 00:41:52.680 --> 00:41:54.730 and then they have a foamy thing in the middle. 00:41:54.730 --> 00:41:56.950 Anyway I did this paper on quills 00:41:56.950 --> 00:41:58.550 and how they work mechanically. 00:41:58.550 --> 00:42:00.709 And Technology reviewed a little article about it, 00:42:00.709 --> 00:42:02.750 and they said they wanted to take a picture of me 00:42:02.750 --> 00:42:03.769 with a hedgehog. 00:42:03.769 --> 00:42:05.560 The hedgehogs are little European-- they're 00:42:05.560 --> 00:42:08.320 like little small, cute things. 00:42:08.320 --> 00:42:10.360 And I said, well, if you can find a hedgehog, 00:42:10.360 --> 00:42:12.300 I'm happy to have my photograph taken. 00:42:12.300 --> 00:42:14.540 And they had a hedgehog at the Concord Field Station. 00:42:14.540 --> 00:42:17.070 So we went out there, and we had these big leather gloves 00:42:17.070 --> 00:42:18.030 and took a picture. 00:42:18.030 --> 00:42:20.280 And I don't if it was Andy or I don't know who it was, 00:42:20.280 --> 00:42:21.760 but I said one of the people there, 00:42:21.760 --> 00:42:23.093 what did you do with a hedgehog? 00:42:23.093 --> 00:42:26.570 And he said, well, we tried to do the treadmill study. 00:42:26.570 --> 00:42:28.020 But hedgehogs are like porcupines. 00:42:28.020 --> 00:42:30.269 When they get scared, they curl up into a little ball. 00:42:30.269 --> 00:42:32.172 And so they said they would put the hedgehog 00:42:32.172 --> 00:42:34.380 down under the treadmill, and they would start it up, 00:42:34.380 --> 00:42:35.970 and it would make a noise, and it would get scared it. 00:42:35.970 --> 00:42:38.345 And it would just go into a little ball and kind of slide 00:42:38.345 --> 00:42:41.040 along to the end, and then it would kind of get flopped off. 00:42:41.040 --> 00:42:43.609 So that was the end of the hedgehog experiments. 00:42:43.609 --> 00:42:45.650 But they did have wallabies there the day I went. 00:42:45.650 --> 00:42:47.390 So they have all sorts of animals 00:42:47.390 --> 00:42:50.610 that they put on to treadmills, birds that they fly, 00:42:50.610 --> 00:42:53.090 so it's kind of interesting to go there. 00:42:53.090 --> 00:42:55.370 But the main idea here is that there 00:42:55.370 --> 00:42:57.480 was this set of experiments with Guinea fowl that 00:42:57.480 --> 00:43:00.970 showed just how precisely the orientation of the bone 00:43:00.970 --> 00:43:02.810 matches the orientation of the loads. 00:43:02.810 --> 00:43:05.310 AUDIENCE: Was there a difference between the control groups? 00:43:05.310 --> 00:43:07.120 LORNA GIBSON: Ah, so I have slides. 00:43:07.120 --> 00:43:07.950 I have slides. 00:43:07.950 --> 00:43:09.220 Hang on a sec. 00:43:09.220 --> 00:43:11.990 I got distracted by my video. 00:43:11.990 --> 00:43:14.730 Sorry. 00:43:14.730 --> 00:43:18.220 So here's the sort of schematic of Guinea fowl on treadmill. 00:43:18.220 --> 00:43:22.540 And where's the little doo-da here? 00:43:22.540 --> 00:43:24.490 So on the level, the knee flexion angle 00:43:24.490 --> 00:43:28.480 was whatever this is, 76.3, and here was the 62.6, 00:43:28.480 --> 00:43:30.790 so the difference is 13.7. 00:43:30.790 --> 00:43:34.200 And then this kind of table here summarizes these results. 00:43:34.200 --> 00:43:38.970 So this is the maximum trabecular density, 00:43:38.970 --> 00:43:40.280 and this is the angle. 00:43:40.280 --> 00:43:43.007 And here we have the incline. 00:43:43.007 --> 00:43:44.590 Let's see, the control was the yellow, 00:43:44.590 --> 00:43:47.000 and the level was the blue, and they've 00:43:47.000 --> 00:43:51.020 got the values for that peak trabecular density orientation. 00:43:51.020 --> 00:43:52.650 So they've got that for the level. 00:43:52.650 --> 00:43:54.510 And then they looked at the difference 00:43:54.510 --> 00:43:58.340 between the incline and the level in the knee angle. 00:43:58.340 --> 00:44:00.809 That's what this thing here is. 00:44:00.809 --> 00:44:02.600 And then between the level and the control, 00:44:02.600 --> 00:44:04.860 there wasn't really any difference in the knee 00:44:04.860 --> 00:44:10.040 angle because the control ones, they were just walking around. 00:44:10.040 --> 00:44:15.460 So that's the sort of slide that has the actual data on it. 00:44:15.460 --> 00:44:16.190 All right. 00:44:16.190 --> 00:44:18.360 And then I showed you the video. 00:44:18.360 --> 00:44:18.860 All right. 00:44:18.860 --> 00:44:21.287 So we need to do a couple more things before we 00:44:21.287 --> 00:44:22.120 get to the modeling. 00:44:26.050 --> 00:44:27.200 Let me get a drink. 00:44:34.200 --> 00:44:37.020 So if we want to use the models for foams 00:44:37.020 --> 00:44:38.920 to try to describe the trabecular bone, 00:44:38.920 --> 00:44:41.420 we need to know something about the properties of the solid. 00:44:41.420 --> 00:44:44.550 Remember we used the properties of the solid in the models. 00:44:44.550 --> 00:44:47.360 So we want to get the properties of the solid in the trabeculae, 00:44:47.360 --> 00:44:49.530 and there's a couple of ways you can do this. 00:44:49.530 --> 00:44:53.480 To get the moduli, you can use an ultrasonic wave propagation 00:44:53.480 --> 00:44:56.165 method, and you can measure a modulus that way. 00:44:56.165 --> 00:44:57.540 And if they do that, they measure 00:44:57.540 --> 00:45:00.680 a modulus between about 15 and 18 gigapascals. 00:45:00.680 --> 00:45:03.610 Another way to do it is to take a piece of bone, 00:45:03.610 --> 00:45:07.690 do a compression test on it, measure the modulus. 00:45:07.690 --> 00:45:10.670 Before you do the test, you put it in the micro CT machine, 00:45:10.670 --> 00:45:13.060 and you get a picture of the structure, 00:45:13.060 --> 00:45:14.650 and then you use that as the input 00:45:14.650 --> 00:45:16.390 to a finite element analysis. 00:45:16.390 --> 00:45:17.830 So the finite element analysis is 00:45:17.830 --> 00:45:22.080 a computer numerical analysis to do mechanical calculations. 00:45:22.080 --> 00:45:26.260 And if you know what the modulus of the structure is, 00:45:26.260 --> 00:45:28.640 you can back out what the modulus of the solid 00:45:28.640 --> 00:45:31.020 must have been from the fine element thing. 00:45:31.020 --> 00:45:33.210 And those sorts of experiments also 00:45:33.210 --> 00:45:35.400 showed that the modulus was around 18. 00:45:35.400 --> 00:45:37.940 And it turns out that moduli is about the same as cortical 00:45:37.940 --> 00:45:41.820 bone, and the properties of the solid trabeculae 00:45:41.820 --> 00:45:44.860 are very similar to the solid cortical bone. 00:45:44.860 --> 00:45:46.260 So let me scoot over here. 00:46:51.560 --> 00:47:00.800 So if you use an ultrasonic wave propagation, 00:47:00.800 --> 00:47:04.200 people have measured a modulus for the solid in trabecular 00:47:04.200 --> 00:47:14.650 bone of 18 gigapascals, or you can do a finite element 00:47:14.650 --> 00:47:22.420 calculation based on micro CT data for the structure. 00:47:35.540 --> 00:47:38.140 And then you measure the overall modulus for the trabecular 00:47:38.140 --> 00:47:48.380 bone, and then you back out the modulus of the solid. 00:47:52.150 --> 00:47:54.660 And people who've done that have gotten values 00:47:54.660 --> 00:48:01.700 of around 18 gigapascals too, and that's very similar to what 00:48:01.700 --> 00:48:02.900 the cortical bone is. 00:48:10.780 --> 00:48:14.650 And so we're going to use the following properties 00:48:14.650 --> 00:48:17.380 for the solid in the trabecular bone. 00:48:17.380 --> 00:48:19.690 We're going to say the density is 1,800 00:48:19.690 --> 00:48:21.770 kilograms per cubic meter. 00:48:21.770 --> 00:48:26.930 The Young's modulus is 18 gigapascals. 00:48:26.930 --> 00:48:30.960 The yield strength has different values 00:48:30.960 --> 00:48:32.780 in tension and compression. 00:48:32.780 --> 00:48:35.680 It's about 182 megapascals in compression. 00:48:39.670 --> 00:48:45.310 And it's about 115 megapascals in tension. 00:48:53.109 --> 00:48:54.525 So those are the solid properties. 00:49:48.280 --> 00:49:50.440 So then if we look at the compressive stress-strain 00:49:50.440 --> 00:49:54.760 curves, they have the shape shown on the screen there. 00:49:54.760 --> 00:49:57.090 And you can see how similar the stress-strain curves 00:49:57.090 --> 00:49:58.420 are for those for a foam. 00:49:58.420 --> 00:50:00.400 So there's the same three regimes 00:50:00.400 --> 00:50:01.930 that we see for the foam. 00:50:01.930 --> 00:50:04.060 There is a linear elastic regime over here, 00:50:04.060 --> 00:50:06.120 there's a stress plateau here, and there's 00:50:06.120 --> 00:50:08.310 some densification regime here. 00:50:08.310 --> 00:50:11.000 These are three curves for three different relative densities. 00:50:11.000 --> 00:50:14.280 As the relative density goes up, the stiffness goes up, 00:50:14.280 --> 00:50:17.380 the plateau stress goes up, and the densification strain 00:50:17.380 --> 00:50:17.880 goes down. 00:50:17.880 --> 00:50:22.410 So is the same as the foams that we've looked at before. 00:50:22.410 --> 00:50:27.570 And if we look at the mechanisms of deformation and failure, 00:50:27.570 --> 00:50:29.570 people have looked at this. 00:50:29.570 --> 00:50:31.650 These are on a whale vertebrae. 00:50:31.650 --> 00:50:35.440 So these are tests that are done in a micron CT machine, 00:50:35.440 --> 00:50:37.590 again, by Ralph Muller's group. 00:50:37.590 --> 00:50:39.600 And here the specimen is unloaded, 00:50:39.600 --> 00:50:41.190 and here's the same specimen loaded. 00:50:41.190 --> 00:50:43.580 So you can see this platen has come down a little bit. 00:50:43.580 --> 00:50:45.800 And if you look at this column here, 00:50:45.800 --> 00:50:48.780 this trabecular here, you can see it's bent out 00:50:48.780 --> 00:50:50.240 and bowed out more. 00:50:50.240 --> 00:50:51.810 And people have found that usually 00:50:51.810 --> 00:50:54.060 the linear elastic behavior is controlled 00:50:54.060 --> 00:50:57.410 by bending of that trabeculae, and the plateau 00:50:57.410 --> 00:51:00.570 stress is usually controlled by some sort of buckling. 00:51:00.570 --> 00:51:01.880 But it's not elastic buckling. 00:51:01.880 --> 00:51:02.670 You don't recover it. 00:51:02.670 --> 00:51:04.670 If you take a piece of bone and you compress it, 00:51:04.670 --> 00:51:07.200 it's going to have a permanent deformation. 00:51:07.200 --> 00:51:10.010 So it's inelastic buckling. 00:51:10.010 --> 00:51:12.310 And I think we have some more pictures. 00:51:12.310 --> 00:51:14.120 This is another example from whale bone 00:51:14.120 --> 00:51:17.510 from Ralph Muller's group. 00:51:17.510 --> 00:51:19.670 So here's the bone unloaded. 00:51:19.670 --> 00:51:22.390 Here it's loaded to 4% strain, here it's to 8%. 00:51:22.390 --> 00:51:25.250 And you can start seeing right in this area here 00:51:25.250 --> 00:51:29.310 if you compare with up there, it's starting to form. 00:51:29.310 --> 00:51:31.700 And if you go up here to 12% strain, 00:51:31.700 --> 00:51:33.440 you see that strut right there. 00:51:33.440 --> 00:51:35.900 That was this guy up here, and you can see 00:51:35.900 --> 00:51:37.210 that it's buckled right over. 00:51:37.210 --> 00:51:39.740 So people have made measurements like this in observations, 00:51:39.740 --> 00:51:41.550 and you can actually see the buckling. 00:51:41.550 --> 00:51:44.810 And people have also done finite element modeling. 00:51:44.810 --> 00:51:48.170 They can take a micro CT scan and input that 00:51:48.170 --> 00:51:49.412 to the fine element model. 00:51:49.412 --> 00:51:50.870 And then if they do the compression 00:51:50.870 --> 00:51:52.720 and they input the properties of the solid, 00:51:52.720 --> 00:51:55.590 they can see that they get a buckling kind of failure. 00:51:55.590 --> 00:52:01.150 If you have trabeculae that are very aligned-- we have more. 00:52:01.150 --> 00:52:02.590 Here's one more in the buckling. 00:52:02.590 --> 00:52:04.660 So this is one of Ralph's little movies. 00:52:04.660 --> 00:52:07.040 So when it unloads, it looks like it recovers, 00:52:07.040 --> 00:52:09.880 but this is all just an animation. 00:52:09.880 --> 00:52:12.270 He takes several stills and puts them together, 00:52:12.270 --> 00:52:13.627 and it doesn't actually recover. 00:52:13.627 --> 00:52:14.960 It's just the way that it shows. 00:52:14.960 --> 00:52:17.490 But again, these are two different specimens 00:52:17.490 --> 00:52:19.050 of different densities. 00:52:19.050 --> 00:52:23.390 You can see how the struts deform. 00:52:23.390 --> 00:52:24.772 They bend and then they buckle. 00:52:27.451 --> 00:52:29.784 Let me stop there, and I'll put some stuff on the board. 00:52:35.000 --> 00:52:40.430 So we'll say the compressive stress-strain curve 00:52:40.430 --> 00:52:43.570 has the characteristic shape of cellular solids. 00:53:06.240 --> 00:53:09.060 And the mechanisms of deformation and failure, 00:53:09.060 --> 00:53:15.310 usually there is bending followed by, usually, 00:53:15.310 --> 00:53:16.825 inelastic or plastic buckling. 00:54:00.770 --> 00:54:03.860 And sometimes if the trabeculae are 00:54:03.860 --> 00:54:05.930 aligned like that knee that I showed you, 00:54:05.930 --> 00:54:08.346 or if the trabecular are aligned or if they're very dense, 00:54:08.346 --> 00:54:11.760 then the actual deformation is important. 00:54:11.760 --> 00:54:13.850 And I'll just say people have found this 00:54:13.850 --> 00:54:23.230 by making observations using micro computer tomography 00:54:23.230 --> 00:54:27.788 or by finite element calculations. 00:55:09.410 --> 00:55:11.540 And this is a stress-strain curve and tension 00:55:11.540 --> 00:55:14.760 here, a tension you get failure at small strains, then 00:55:14.760 --> 00:55:16.447 you get micro cracks in the bone. 00:55:35.880 --> 00:55:39.320 And these next plots just show some data for the bone. 00:55:39.320 --> 00:55:43.930 So we're plotting the Young's modulus here. 00:55:43.930 --> 00:55:46.030 So this is a relative Young's modulus, 00:55:46.030 --> 00:55:48.400 the modulus of the bone divided by the solid cell wall 00:55:48.400 --> 00:55:49.430 material. 00:55:49.430 --> 00:55:50.960 Here's the relative density. 00:55:50.960 --> 00:55:54.130 Here's data for lots of different specimens of bone. 00:55:54.130 --> 00:55:56.250 So some of this data is for human bones, 00:55:56.250 --> 00:55:59.190 some is for bovine bone. 00:55:59.190 --> 00:56:01.860 Sometimes the data is taken where 00:56:01.860 --> 00:56:03.657 the orientation of the trabeculae 00:56:03.657 --> 00:56:05.740 doesn't line up with the direction of the loading. 00:56:05.740 --> 00:56:08.073 So you might have trabeculae that are oriented this way, 00:56:08.073 --> 00:56:09.370 but you're loading it this way. 00:56:09.370 --> 00:56:13.310 There's sometimes different strain rates. 00:56:13.310 --> 00:56:13.830 Let's see. 00:56:13.830 --> 00:56:17.280 There's different groups, and so there's a huge scatter 00:56:17.280 --> 00:56:19.500 in the range of the data. 00:56:19.500 --> 00:56:21.370 But you can see if you look at it broadly 00:56:21.370 --> 00:56:23.780 and you look at that whole cluster of data, 00:56:23.780 --> 00:56:28.040 the data lie close to a line of a slope of 2. 00:56:28.040 --> 00:56:30.000 And if you think of the open-celled foam model 00:56:30.000 --> 00:56:31.460 and you had bending of the cell walls, 00:56:31.460 --> 00:56:32.935 you'd expect that the modulus would vary 00:56:32.935 --> 00:56:34.260 [? to the ?] density squared. 00:56:34.260 --> 00:56:37.107 So that's kind of the limit of how we do the modeling. 00:56:37.107 --> 00:56:39.690 We're really just interested in seeing how the properties vary 00:56:39.690 --> 00:56:40.947 with density. 00:56:40.947 --> 00:56:42.530 If you had a particular piece of bone, 00:56:42.530 --> 00:56:44.904 I don't think you could use the models to exactly predict 00:56:44.904 --> 00:56:46.900 what the modulus of that bone would be. 00:56:46.900 --> 00:56:48.995 And here's the compressive strength here. 00:56:48.995 --> 00:56:50.870 So this is the relative compressive strength. 00:56:50.870 --> 00:56:52.980 Here we've normalized it with the yield 00:56:52.980 --> 00:56:57.480 stress of the solid bone, and here's the relative density. 00:56:57.480 --> 00:57:00.340 And you can see, again, this line is of slope 2, 00:57:00.340 --> 00:57:03.890 so that kind of speaks to the buckling-type failure mode. 00:57:03.890 --> 00:57:05.970 And I think I have another one here. 00:57:05.970 --> 00:57:07.680 This is the tensile strength. 00:57:07.680 --> 00:57:09.200 So if you pull the bone in tension, 00:57:09.200 --> 00:57:10.699 you wouldn't expect to get buckling, 00:57:10.699 --> 00:57:13.120 you'd expect to get plastic yielding. 00:57:13.120 --> 00:57:16.030 And if you got yielding and you use the open-cell foam model, 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. 00:57:19.980 --> 00:57:22.480 And this line is sort of towards the upper bound 00:57:22.480 --> 00:57:23.450 of that set of data. 00:57:23.450 --> 00:57:26.650 You can imagine a line that went through it a little bit lower 00:57:26.650 --> 00:57:28.080 but the same slope. 00:57:28.080 --> 00:57:30.360 And so these open-celled foam models, 00:57:30.360 --> 00:57:32.140 they don't predict the properties 00:57:32.140 --> 00:57:34.130 of a particular piece of bone because the bone 00:57:34.130 --> 00:57:36.900 can have some anisotropy to it. 00:57:36.900 --> 00:57:39.950 The orientation of these things may not be perfectly lined up 00:57:39.950 --> 00:57:41.520 with the loading. 00:57:41.520 --> 00:57:44.100 But overall the models give you a sense 00:57:44.100 --> 00:57:49.450 of how the bone is deforming and failing. 00:57:49.450 --> 00:57:51.330 So let me write some of this down. 00:58:02.455 --> 00:58:04.920 So that's data for the modulus, the compressive strength, 00:58:04.920 --> 00:58:06.840 and the tensile strength. 00:58:06.840 --> 00:58:10.350 And those have been on those plots. 00:58:10.350 --> 00:58:16.310 Those values are normalized by data for cortical bone. 00:58:27.229 --> 00:58:28.520 I thought somebody was talking. 00:58:28.520 --> 00:58:29.770 It's just the chair squeaking. 00:58:37.520 --> 00:58:40.580 And as I said the spread in the data is large, 00:58:40.580 --> 00:58:50.120 and that's due to anisotropy in the bone and misalignment 00:58:50.120 --> 00:58:52.640 between the bone orientation and the loading direction. 00:59:07.430 --> 00:59:10.950 So when people first started doing tests on trabecular bone, 00:59:10.950 --> 00:59:13.710 they typically were orthopedics labs. 00:59:13.710 --> 00:59:16.970 And the orthopedics labs tended to initially cut the bone 00:59:16.970 --> 00:59:19.840 specimens on anatomical axes. 00:59:19.840 --> 00:59:22.180 So they would do you know the superior-inferior, 00:59:22.180 --> 00:59:25.190 or the medial-lateral, or the posterior-anterior. 00:59:25.190 --> 00:59:28.469 But the bone orientation didn't line up with those directions. 00:59:28.469 --> 00:59:30.010 So the bone might have been this way, 00:59:30.010 --> 00:59:31.440 but they were loading it this way, 00:59:31.440 --> 00:59:34.856 and so that gave this misalignment. 00:59:34.856 --> 00:59:36.230 And there could be some variation 00:59:36.230 --> 00:59:37.470 in the solid properties too. 00:59:40.550 --> 00:59:43.070 So you could imagine some solid might have more micro cracks 00:59:43.070 --> 00:59:45.470 than another. 00:59:45.470 --> 00:59:49.195 So if you took say human bone of different ages, 00:59:49.195 --> 00:59:50.820 you might expect the older bone to have 00:59:50.820 --> 00:59:51.960 more micro cracks in it. 00:59:56.830 --> 01:00:01.725 So these plots put a lot of data together, 01:00:01.725 --> 01:00:05.800 and then the lines are based on models for open-cell foams. 01:00:14.690 --> 01:00:16.660 So the relative modulus goes roughly 01:00:16.660 --> 01:00:21.565 as a relative density squared, and the cell walls are bending. 01:00:24.250 --> 01:00:29.450 And the compressive strength goes roughly 01:00:29.450 --> 01:00:36.590 as the modulus squared, and that's 01:00:36.590 --> 01:00:39.880 related to this plastic buckling. 01:00:39.880 --> 01:00:45.470 And then the tensile stress or tensile strength 01:00:45.470 --> 01:00:48.620 depends on the formation of plastic hinges, 01:00:48.620 --> 01:00:51.600 and it goes roughly as the density to the 3/2 power. 01:01:00.840 --> 01:01:08.310 And one observation that people have made 01:01:08.310 --> 01:01:13.690 is that in compression, if the modulus and the strength both 01:01:13.690 --> 01:01:16.040 go as a density squared, then the ratio 01:01:16.040 --> 01:01:19.180 of the strength to the modulus is just a constant, and that, 01:01:19.180 --> 01:01:22.260 in fact, is just the strain at failure, 01:01:22.260 --> 01:01:24.950 or the strain for that say, the plateau. 01:01:32.310 --> 01:01:35.190 And that's a strain of about 0.7%, 01:01:35.190 --> 01:01:37.370 and that's pretty consistent in trabecular bone. 01:01:41.476 --> 01:01:42.155 Let's see. 01:01:56.260 --> 01:01:58.815 And we said sometimes the bone was relatively aligned. 01:01:58.815 --> 01:02:00.560 So here's that picture of the femoral 01:02:00.560 --> 01:02:04.770 condyle again in the knee, and you can see the bones lined up. 01:02:04.770 --> 01:02:06.900 If you have bone that's lined up like that 01:02:06.900 --> 01:02:09.660 and you load it along the direction of alignment, 01:02:09.660 --> 01:02:13.460 then you can get axial deformation in the trabeculae. 01:02:13.460 --> 01:02:15.940 And then you would expect the moduli would go linearly 01:02:15.940 --> 01:02:17.800 with the density. 01:02:17.800 --> 01:02:20.980 And here's some data for the Young's modulus 01:02:20.980 --> 01:02:24.430 and the compressive strength of bone that was fairly aligned. 01:02:24.430 --> 01:02:26.160 So this was selected to be aligned. 01:02:26.160 --> 01:02:27.950 So here's the modulus here. 01:02:27.950 --> 01:02:33.630 And the square data points are the longitudinal direction, 01:02:33.630 --> 01:02:37.160 and the little diamond, these little stars, are transverse. 01:02:37.160 --> 01:02:40.800 So here's a line of slope 1, and again, they don't all 01:02:40.800 --> 01:02:43.810 lie perfectly on that line, but roughly the slope is about 1 01:02:43.810 --> 01:02:44.400 there. 01:02:44.400 --> 01:02:47.520 And then similarly here, this is the compressive strength. 01:02:47.520 --> 01:02:51.140 Now the little squares are the longitudinal data, 01:02:51.140 --> 01:02:53.420 and they're not exactly on a slope of 1, 01:02:53.420 --> 01:02:55.170 but they're more or less on a slope of 1. 01:02:58.480 --> 01:03:00.140 So I'll just say in some regions, 01:03:00.140 --> 01:03:01.193 the bone may be aligned. 01:03:12.000 --> 01:03:14.040 And then axial deformation is important. 01:03:18.660 --> 01:03:22.700 And then you would expect the modulus to go linearly 01:03:22.700 --> 01:03:26.110 with the density and the strength 01:03:26.110 --> 01:03:29.120 to go linearly with the density in the longitudinal direction. 01:03:43.640 --> 01:03:46.190 Then finally I wanted to finish up the bit on the modeling 01:03:46.190 --> 01:03:48.160 by making one of these plots a little bit 01:03:48.160 --> 01:03:49.890 like we did for wood. 01:03:49.890 --> 01:03:52.470 So here's the Young's modulus of bone plotted 01:03:52.470 --> 01:03:53.920 against the density. 01:03:53.920 --> 01:03:55.600 The trabecular bone is down here. 01:03:55.600 --> 01:03:57.710 It's sort the lowest density. 01:03:57.710 --> 01:04:00.040 And then this is the collagen that's 01:04:00.040 --> 01:04:01.850 in the solid part of the bone, and this 01:04:01.850 --> 01:04:04.200 is hydroxyapatite, the mineral. 01:04:04.200 --> 01:04:07.640 So the modulus of hydroxyapatite is around 120 gigapascals, 01:04:07.640 --> 01:04:10.800 and the modulus of collagen is somewhere around 5. 01:04:10.800 --> 01:04:13.560 And if you make composites of collagen and hydroxyapatite, 01:04:13.560 --> 01:04:17.380 their moduli are going to be in this envelope here, 01:04:17.380 --> 01:04:19.910 and compact bone, the modulus fits in around here. 01:04:19.910 --> 01:04:22.694 Remember I said it was around 18 gigapascals. 01:04:22.694 --> 01:04:24.110 So then if you take a compact bone 01:04:24.110 --> 01:04:25.920 and you turn it into trabecular bone, 01:04:25.920 --> 01:04:30.020 you'd expect the modulus would go down along a slope of 2. 01:04:30.020 --> 01:04:32.840 So here's our little slope of 2, and more or less that's 01:04:32.840 --> 01:04:35.330 what you see with the trabecular bone. 01:04:35.330 --> 01:04:37.260 So the idea is that the models give you 01:04:37.260 --> 01:04:40.241 kind of a general idea of how the bone is behaving, 01:04:40.241 --> 01:04:41.740 but it's not really meant to predict 01:04:41.740 --> 01:04:42.980 a particular piece of bone. 01:04:42.980 --> 01:04:44.438 Because a particular piece is going 01:04:44.438 --> 01:04:46.470 to have a particular geometry. 01:04:46.470 --> 01:04:49.830 Typically they're not equi ax and isotropic. 01:04:49.830 --> 01:04:50.600 All right. 01:04:50.600 --> 01:04:53.400 So are we good with the general overview? 01:04:53.400 --> 01:04:55.440 Are we good with how fewer equations there 01:04:55.440 --> 01:04:57.790 are now that we got past the first part of the course? 01:05:02.760 --> 01:05:05.552 So I'm going to talk a bit more about osteoporosis, 01:05:05.552 --> 01:05:07.260 and I'm going to talk about some modeling 01:05:07.260 --> 01:05:11.707 that my group did to look at the consequences of osteoporosis. 01:05:11.707 --> 01:05:13.790 And then later on we're going to talk a little bit 01:05:13.790 --> 01:05:17.030 about using metal foams as a possible replacement material 01:05:17.030 --> 01:05:18.970 for a trabecular bone as well. 01:05:18.970 --> 01:05:20.860 And I have a little bit of a talk 01:05:20.860 --> 01:05:25.280 on using trabecular bone in evolutionary studies 01:05:25.280 --> 01:05:29.144 to see whether or not a species was bipedal or quadrupedal. 01:05:29.144 --> 01:05:31.310 So I think I talked about this a little bit in 3032, 01:05:31.310 --> 01:05:35.800 but I have more slides and more stuff I'm going to talk about. 01:05:35.800 --> 01:05:37.555 So let me get myself organized. 01:06:18.880 --> 01:06:21.420 So osteoporosis comes from the Latin, 01:06:21.420 --> 01:06:23.450 and it actually means porous bones. 01:06:23.450 --> 01:06:26.910 So osteo means bone, and not too surprisingly 01:06:26.910 --> 01:06:31.700 porosis means porous. 01:06:31.700 --> 01:06:34.180 So this next slide gives you some idea what 01:06:34.180 --> 01:06:36.510 osteoporotic bone looks like. 01:06:36.510 --> 01:06:39.770 So the top slide is normal bone in a 55-year-old woman. 01:06:39.770 --> 01:06:42.590 These are sections from the lumbar spine. 01:06:42.590 --> 01:06:45.130 And that bone up here is 17% dense, 01:06:45.130 --> 01:06:47.520 so the relative density is point 0.17. 01:06:47.520 --> 01:06:51.550 And this is a section from the same area 01:06:51.550 --> 01:06:55.770 of bone in an 86-year-old woman, and it's 7% dense. 01:06:55.770 --> 01:06:58.180 So you can see there's a huge difference in the density, 01:06:58.180 --> 01:06:59.721 and you can start to see what happens 01:06:59.721 --> 01:07:01.930 when you lose bone mass. 01:07:01.930 --> 01:07:06.282 So if you look at this bone up here, it's all well connected. 01:07:06.282 --> 01:07:07.740 Each little trabeculae is connected 01:07:07.740 --> 01:07:09.470 to its neighboring friends. 01:07:09.470 --> 01:07:11.790 And you can see down here, I mean, you look at this 01:07:11.790 --> 01:07:13.670 and you kind of go ouch just looking at it. 01:07:13.670 --> 01:07:16.970 Because this piece of bone here is just kind of dangling off, 01:07:16.970 --> 01:07:18.680 not connected to anything. 01:07:18.680 --> 01:07:20.840 And you can see the struts have gotten thinner, 01:07:20.840 --> 01:07:23.290 so they've lost bone mass by thinning. 01:07:23.290 --> 01:07:25.980 And then as I said when the thickness gets 01:07:25.980 --> 01:07:29.710 less than they are roughly equal to the size of the cells, 01:07:29.710 --> 01:07:31.190 then the cells can't live anymore, 01:07:31.190 --> 01:07:34.720 and the bone strut just disappears altogether. 01:07:34.720 --> 01:07:37.330 So it's not too surprising that if you lose this much bone 01:07:37.330 --> 01:07:40.980 mass, there's mechanical consequences, 01:07:40.980 --> 01:07:43.110 and there's a greater risk of fracture. 01:07:43.110 --> 01:07:47.880 And as I said the two most common types of fractures 01:07:47.880 --> 01:07:50.000 are hip fractures and vertebral fractures. 01:07:53.890 --> 01:07:56.240 So let's see here. 01:07:56.240 --> 01:08:00.735 So as people age, everybody loses bone mass. 01:08:07.000 --> 01:08:09.580 And happily for you and not so happily for me, 01:08:09.580 --> 01:08:12.200 the bone mass peaks at about 25 years old. 01:08:12.200 --> 01:08:14.440 So you're probably either not at the peak 01:08:14.440 --> 01:08:16.819 or just barely at the peak. 01:08:16.819 --> 01:08:19.859 And then it decreases after that every year. 01:08:19.859 --> 01:08:21.260 I'm considerably older than you. 01:08:36.560 --> 01:08:38.670 And in women, when you go through menopause, 01:08:38.670 --> 01:08:40.979 the cessation of estrogen production 01:08:40.979 --> 01:08:42.260 increases the bone loss. 01:08:42.260 --> 01:08:45.680 And so typically, osteoporosis is most common 01:08:45.680 --> 01:08:47.200 in post menopausal women. 01:09:23.200 --> 01:09:27.290 And osteoporosis is defined as a bone mass 2.5 01:09:27.290 --> 01:09:30.029 standard deviations or more below that 01:09:30.029 --> 01:09:31.850 of a young, normal mean. 01:09:31.850 --> 01:09:33.960 So it's not like you fall and break your hip 01:09:33.960 --> 01:09:35.720 and they say you have osteoporosis. 01:09:35.720 --> 01:09:36.981 It's based on the bone mass. 01:10:06.700 --> 01:10:08.910 And as I said, the trabeculae thin and then 01:10:08.910 --> 01:10:09.870 they resorb completely. 01:10:23.270 --> 01:10:25.780 So anybody here take Latin? 01:10:25.780 --> 01:10:26.600 Yes. 01:10:26.600 --> 01:10:29.140 I did Latin for one year in high school. 01:10:29.140 --> 01:10:32.270 So trabeculae, with an E on the end here, 01:10:32.270 --> 01:10:34.130 trabeculae, I suppose, is the plural. 01:10:34.130 --> 01:10:36.120 Trabecula with an A is singular. 01:10:36.120 --> 01:10:38.890 And that comes from Latin. 01:10:38.890 --> 01:10:40.910 So you don't say trabeculas. 01:10:40.910 --> 01:10:41.650 That's a no-no. 01:10:46.660 --> 01:10:47.326 All right. 01:10:49.930 --> 01:10:50.940 Let me get rid of these. 01:10:56.750 --> 01:11:00.090 So if we saw that the strength of the bone 01:11:00.090 --> 01:11:02.550 varies as the density squared, you 01:11:02.550 --> 01:11:05.600 can begin to see how sensitive the strength is going 01:11:05.600 --> 01:11:08.590 to be to this bone mass loss. 01:11:08.590 --> 01:11:13.580 So say you went from a density of 0.2 to a density of 0.1, 01:11:13.580 --> 01:11:15.560 then the densities changed by a factor of 2 01:11:15.560 --> 01:11:17.260 so that the densities gone down by 1/2, 01:11:17.260 --> 01:11:19.660 but the strength is going to go down by a factor of 4. 01:11:19.660 --> 01:11:21.950 You're going to have the strength to be a 1/4. 01:11:21.950 --> 01:11:25.920 And so you're going to have a big change in the strength. 01:11:25.920 --> 01:11:27.780 And you can imagine is the trabeculae thins, 01:11:27.780 --> 01:11:29.408 this buckling gets easier to happen. 01:11:51.040 --> 01:11:52.570 And then once the trabeculae begin 01:11:52.570 --> 01:11:56.030 to resorb as they disappear altogether, it's like I said. 01:11:56.030 --> 01:11:59.100 it's like having a building's framework. 01:11:59.100 --> 01:12:00.851 Now, you're removing beams and columns, 01:12:00.851 --> 01:12:03.350 and the strength is going to go down even more dramatically. 01:12:30.640 --> 01:12:33.880 And the way we model the osteoporotic bone 01:12:33.880 --> 01:12:36.060 is we use finite element analysis. 01:12:36.060 --> 01:12:38.660 So before we talked about using the unit cell 01:12:38.660 --> 01:12:39.744 for the honeycomb. 01:12:39.744 --> 01:12:41.160 But to use the unit cell, you have 01:12:41.160 --> 01:12:43.890 to have repeating unit cells, and obviously, you 01:12:43.890 --> 01:12:45.300 don't have that. 01:12:45.300 --> 01:12:49.350 You've got local variations in what the structure looks like. 01:12:49.350 --> 01:12:51.360 And we also used a dimensional analysis. 01:12:51.360 --> 01:12:53.400 And the dimensional analysis relies 01:12:53.400 --> 01:12:57.596 on the geometry being similar from one specimen to another, 01:12:57.596 --> 01:12:58.970 and you can't really rely on that 01:12:58.970 --> 01:13:01.760 either for the osteoporotic bone. 01:13:01.760 --> 01:13:04.580 And so what we've done is-- and this 01:13:04.580 --> 01:13:10.380 is what other people do as well, is use finite element modeling 01:13:10.380 --> 01:13:11.420 to represent the bone. 01:13:18.820 --> 01:13:21.805 So initially what we did was we used a 2D Voronoi model. 01:13:21.805 --> 01:13:24.660 So remember we talked about Voronoi honeycombs and Voronoi 01:13:24.660 --> 01:13:27.000 foams. 01:13:27.000 --> 01:13:28.770 So I like to start out with simple things, 01:13:28.770 --> 01:13:32.870 so we started out with 2D Voronoi model for a honeycomb. 01:13:38.120 --> 01:13:42.160 Then we did a 2D representation of vertebral bone. 01:13:51.510 --> 01:13:55.647 And then we had a 3D Voronoi. 01:13:55.647 --> 01:13:57.480 And I had a couple of students who did this. 01:13:57.480 --> 01:13:59.440 Matt Silver was the one who did the first two, 01:13:59.440 --> 01:14:04.110 and Sereca Vagilla was the one who did the last one. 01:14:04.110 --> 01:14:05.040 So let's see. 01:14:05.040 --> 01:14:09.120 I think that's probably a good place to stop there for today. 01:14:09.120 --> 01:14:13.450 So next time I'll talk about the modeling of osteoporotic bone, 01:14:13.450 --> 01:14:15.450 and we might talk a little bit about metal bones 01:14:15.450 --> 01:14:19.250 as a substitute for trabecular-- metal foams as a substitute. 01:14:19.250 --> 01:14:21.210 I don't think we'll get to the evolution stuff. 01:14:21.210 --> 01:14:23.920 We probably won't quite finish next time.