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 --> 00:00:06.320 Your support will help MIT OpenCourseWare 00:00:06.320 --> 00:00:10.680 continue to offer high quality educational resources for free. 00:00:10.680 --> 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. 00:00:25.792 --> 00:00:26.940 LORNA GIBSON: All right. 00:00:26.940 --> 00:00:29.460 So last time we were talking about tissue engineering 00:00:29.460 --> 00:00:30.664 scaffolds. 00:00:30.664 --> 00:00:32.330 And what we're going to talk about today 00:00:32.330 --> 00:00:34.200 still has to do with tissue engineering scaffolds, 00:00:34.200 --> 00:00:36.680 but we're going to look at it from a different perspective. 00:00:36.680 --> 00:00:38.054 So last time we were looking more 00:00:38.054 --> 00:00:39.580 at sort of a clinical perspective, 00:00:39.580 --> 00:00:41.740 and looking at those osteochondral scaffolds 00:00:41.740 --> 00:00:44.740 for repairing small defects in cartilage. 00:00:44.740 --> 00:00:46.430 And today what we're going to talk about 00:00:46.430 --> 00:00:48.800 are how cells-- how biological cells, 00:00:48.800 --> 00:00:50.600 interact with the scaffolds. 00:00:50.600 --> 00:00:52.660 And there's various kinds of interactions. 00:00:52.660 --> 00:00:54.620 So we're going to go through a bunch of these. 00:00:54.620 --> 00:00:56.310 So the first one I'm going to talk about 00:00:56.310 --> 00:00:58.830 is degradation of the scaffolds. 00:00:58.830 --> 00:01:01.220 Then we'll talk about the cell attachment. 00:01:01.220 --> 00:01:06.750 Cell morphology-- so the shape of the pores in the scaffold 00:01:06.750 --> 00:01:10.300 can affect the way the biological cells-- what 00:01:10.300 --> 00:01:12.020 shape they have. 00:01:12.020 --> 00:01:14.490 Biological cells could also contract the scaffold 00:01:14.490 --> 00:01:15.780 and apply mechanical forces. 00:01:15.780 --> 00:01:18.030 So we're going to talk about that. 00:01:18.030 --> 00:01:20.360 The stiffness of the scaffold and the pore size 00:01:20.360 --> 00:01:22.736 can affect the speed of cell migration. 00:01:22.736 --> 00:01:24.110 And the stiffness of the scaffold 00:01:24.110 --> 00:01:27.790 can affect the differentiation of cells, so from one cell type 00:01:27.790 --> 00:01:28.565 to another. 00:01:28.565 --> 00:01:30.190 So I thought today I'd talk about that. 00:01:30.190 --> 00:01:32.230 This probably won't take the whole hour. 00:01:32.230 --> 00:01:34.980 The next topic is on energy absorption in foams. 00:01:34.980 --> 00:01:38.100 And so we'll probably start that towards the end of the lecture. 00:01:38.100 --> 00:01:39.380 OK. 00:01:39.380 --> 00:01:41.000 So the idea here is that we're looking 00:01:41.000 --> 00:01:43.070 at how scaffolds are being used, really, 00:01:43.070 --> 00:01:46.380 to provide a 3D environment to characterize 00:01:46.380 --> 00:01:47.530 the behavior of cells. 00:01:47.530 --> 00:01:49.320 And in particular, how the cells interact 00:01:49.320 --> 00:01:50.960 with their environment. 00:01:50.960 --> 00:01:52.490 So let's write that down. 00:02:25.470 --> 00:02:28.460 So how the cell behavior is affected by the substrate 00:02:28.460 --> 00:02:28.970 it's on. 00:02:51.540 --> 00:02:52.040 OK. 00:02:52.040 --> 00:02:53.873 So the first thing we're going to talk about 00:02:53.873 --> 00:02:55.160 is scaffold degradation. 00:02:55.160 --> 00:02:58.850 And if you think of the native extracellular matrix, 00:02:58.850 --> 00:03:03.040 the cells secrete enzymes which resorb that matrix 00:03:03.040 --> 00:03:04.722 and then they also deposit new matrix. 00:03:04.722 --> 00:03:06.180 So it was kind of like what we were 00:03:06.180 --> 00:03:07.346 talking about with the bone. 00:03:07.346 --> 00:03:09.830 The bone is always being resorbed and deposited. 00:03:09.830 --> 00:03:12.270 And if there's a balance between that those two, 00:03:12.270 --> 00:03:14.110 then the density of the bone stays the same. 00:03:14.110 --> 00:03:16.770 And if one of the rates gets out of whack, 00:03:16.770 --> 00:03:19.200 then you get osteoporosis and you lose bone mass. 00:03:19.200 --> 00:03:25.670 So the idea is that in just the native extracellular matrix, 00:03:25.670 --> 00:03:28.970 the cells are producing enzymes that degrade the scaffold. 00:03:28.970 --> 00:03:31.610 And those enzymes are also going to degrade the tissue 00:03:31.610 --> 00:03:33.640 engineering scaffolds as well. 00:03:33.640 --> 00:03:35.360 And you want to be able to control 00:03:35.360 --> 00:03:37.680 the rate of degradation, versus the rate 00:03:37.680 --> 00:03:39.910 at which the native extracellular 00:03:39.910 --> 00:03:42.470 matrix gets deposited. 00:03:42.470 --> 00:03:44.880 Excuse me, sorry. 00:03:44.880 --> 00:03:47.880 So you can kind of imagine if the tissue engineering 00:03:47.880 --> 00:03:50.570 scaffold did not resorb quickly enough, 00:03:50.570 --> 00:03:52.020 you'd have scaffold there. 00:03:52.020 --> 00:03:53.330 And the cells would be trying to put down 00:03:53.330 --> 00:03:55.038 their own extracellular matrix, and there 00:03:55.038 --> 00:03:57.230 wouldn't be a place to put it. 00:03:57.230 --> 00:04:00.274 And if it resorbs too quickly, then the cells 00:04:00.274 --> 00:04:01.690 don't have something to attach to. 00:04:01.690 --> 00:04:04.500 So there has to be a balance between the rate at which 00:04:04.500 --> 00:04:08.470 the enzymes are resorbing the tissue engineering scaffold, 00:04:08.470 --> 00:04:11.130 versus the rate at which the cells are depositing 00:04:11.130 --> 00:04:12.947 their own extracellular matrix. 00:04:21.709 --> 00:04:25.650 So in the native extracellular matrix, 00:04:25.650 --> 00:04:32.670 the enzymes produced by the cells 00:04:32.670 --> 00:04:35.180 are resorbing the extracellular matrix. 00:04:47.130 --> 00:05:00.270 And then the cells are also synthesizing so they 00:05:00.270 --> 00:05:02.526 synthesize ECM to replace it. 00:05:11.410 --> 00:05:14.649 So the cells are also going to degrade the tissue engineering 00:05:14.649 --> 00:05:15.690 scaffold that you put in. 00:05:23.690 --> 00:05:27.850 And the length of time that the scaffold is insoluble, 00:05:27.850 --> 00:05:30.940 or so that it remains in the body as a solid, 00:05:30.940 --> 00:05:32.370 is called the residence time. 00:06:04.980 --> 00:06:09.180 And so then we require the scaffold degradation 00:06:09.180 --> 00:06:13.765 to occur over a time that balances with the new ECM 00:06:13.765 --> 00:06:14.265 synthesis. 00:06:52.540 --> 00:06:55.570 And so the scaffold residence time 00:06:55.570 --> 00:06:57.430 must be about equal to the time required 00:06:57.430 --> 00:07:00.258 to make new native extracellular matrix. 00:07:38.460 --> 00:07:41.820 So the degradation rate depends on the composition 00:07:41.820 --> 00:07:44.974 of the scaffold, on how much cross linking there is, 00:07:44.974 --> 00:07:46.140 and on the relative density. 00:07:46.140 --> 00:07:48.130 Obviously, the more scaffold there is, 00:07:48.130 --> 00:07:50.375 the longer it's going to take to degrade it. 00:08:22.960 --> 00:08:27.550 And with synthetic polymers you can vary the molecular weight 00:08:27.550 --> 00:08:28.670 of the polymer. 00:08:28.670 --> 00:08:30.460 And sometimes if you have copolymers, 00:08:30.460 --> 00:08:32.610 one may degrade faster than the other. 00:08:32.610 --> 00:08:35.919 And you can control the balance of how much of each copolymer 00:08:35.919 --> 00:08:36.419 you have. 00:09:07.360 --> 00:09:13.860 And for natural proteins, like collagen, 00:09:13.860 --> 00:09:16.920 you can control the amount of cross linking. 00:09:16.920 --> 00:09:19.700 So you can do the cross linking by various techniques. 00:09:19.700 --> 00:09:22.220 That's what's called physical methods. 00:09:22.220 --> 00:09:25.130 There's something called dehydrothermal treatment, where 00:09:25.130 --> 00:09:31.500 you heat the collagen up to 105 degrees C in a vacuum, 00:09:31.500 --> 00:09:33.170 in a dry environment. 00:09:33.170 --> 00:09:38.120 And that eliminates water and causes more cross linking. 00:09:38.120 --> 00:09:40.740 There's a UV treatment, ultraviolet light treatment, 00:09:40.740 --> 00:09:41.510 you can use. 00:09:41.510 --> 00:09:43.710 And there's also chemical cross linkers you can use. 00:11:29.900 --> 00:11:33.130 So there's different chemical methods you can also 00:11:33.130 --> 00:11:52.665 use to cross link the collagen. 00:11:52.665 --> 00:11:53.164 OK. 00:11:59.200 --> 00:12:03.220 So the next thing I wanted to talk about was cell adhesion. 00:12:03.220 --> 00:12:05.850 And let's just wait a minute for people to catch up. 00:12:15.670 --> 00:12:17.870 Are we just about there? 00:12:17.870 --> 00:12:20.500 So this next slide shows a sort of schematic 00:12:20.500 --> 00:12:23.260 of how a cell would adhere to a substrate. 00:12:23.260 --> 00:12:26.730 So down at the bottom here, all these little squiggly lines 00:12:26.730 --> 00:12:29.065 are representing the extracellular matrix 00:12:29.065 --> 00:12:29.940 in the native tissue. 00:12:29.940 --> 00:12:33.640 Or you can think of it as a, say, a collagen scaffold. 00:12:33.640 --> 00:12:35.500 But here we have the ECM. 00:12:35.500 --> 00:12:37.930 And this little blob here is our cell. 00:12:37.930 --> 00:12:40.470 This is the nucleus of the cell here, the little green blob 00:12:40.470 --> 00:12:41.550 in the middle. 00:12:41.550 --> 00:12:45.210 And the cell is attached to the ECM 00:12:45.210 --> 00:12:47.920 through something called focal adhesion points. 00:12:47.920 --> 00:12:52.070 And this schematic here is a blow up of that focal adhesion. 00:12:52.070 --> 00:12:54.060 And at the focal adhesion there's 00:12:54.060 --> 00:12:55.810 proteins called integrins. 00:12:55.810 --> 00:12:59.270 And integrins pass across the cell membrane. 00:12:59.270 --> 00:13:02.090 So the idea is the integrins attach to ligands 00:13:02.090 --> 00:13:03.950 on the extracellular matrix. 00:13:03.950 --> 00:13:06.560 And then they also attached to the sub membrane plaque 00:13:06.560 --> 00:13:07.760 within the cell. 00:13:07.760 --> 00:13:10.900 And then that plaque attaches to the side of skeleton. 00:13:10.900 --> 00:13:13.640 Things like actin filaments within the cell. 00:13:13.640 --> 00:13:15.800 So this is what attaches the cell 00:13:15.800 --> 00:13:18.390 as a whole to the extracellular matrix, 00:13:18.390 --> 00:13:22.610 is these focal adhesion sites here. 00:13:22.610 --> 00:13:28.680 And different kinds of cell behaviors-- obviously, 00:13:28.680 --> 00:13:30.250 things like cell attachment, but also 00:13:30.250 --> 00:13:32.690 things like cell migration, are affected 00:13:32.690 --> 00:13:34.458 by those focal adhesions there. 00:13:40.320 --> 00:13:48.400 So we have that the cells attach to the ECM at focal adhesions. 00:13:55.100 --> 00:13:57.300 And sometimes you see those referred to just as FA. 00:14:03.671 --> 00:14:06.370 And at the adhesion point the cell has integrins. 00:14:12.650 --> 00:14:15.890 And the integrins are transmembrane proteins, 00:14:15.890 --> 00:14:17.220 so they go across the membrane. 00:14:24.120 --> 00:14:28.790 And they bind to like ends on the ECM. 00:14:38.960 --> 00:14:40.770 And then the other end of the integrin 00:14:40.770 --> 00:14:43.980 is attached to the submembrane plaque within the cell. 00:15:10.370 --> 00:15:13.160 And then that connects to the cytoskeleton. 00:15:40.660 --> 00:15:44.520 And then different kinds of cell behaviors-- so 00:15:44.520 --> 00:15:48.040 for example, things like adhesion, 00:15:48.040 --> 00:15:49.744 and proliferation, and migration. 00:15:57.040 --> 00:15:59.330 And that cell contraction, we're going to talk more 00:15:59.330 --> 00:16:00.460 about that in a minute. 00:16:04.120 --> 00:16:07.442 They all depend in part on this adhesion between the cells 00:16:07.442 --> 00:16:08.650 and the extracellular matrix. 00:17:07.550 --> 00:17:11.900 And the biological activity depends on how many 00:17:11.900 --> 00:17:13.150 binding sites there are. 00:17:13.150 --> 00:17:15.000 So if you think of the extracellular matrix, 00:17:15.000 --> 00:17:16.930 it's got these ligands and it depends 00:17:16.930 --> 00:17:20.151 on the density of binding sites, how much interaction 00:17:20.151 --> 00:17:20.650 you can get. 00:17:20.650 --> 00:17:24.460 So things like how much cell attachment you can get, 00:17:24.460 --> 00:17:26.920 depends in part on just how many of these binding sites 00:17:26.920 --> 00:17:28.600 you've got for the cells to attach to. 00:17:53.430 --> 00:17:55.730 And that density of the binding sites 00:17:55.730 --> 00:17:58.230 or the density of the ligands depends on the composition 00:17:58.230 --> 00:17:59.210 of the scaffold. 00:17:59.210 --> 00:18:02.060 But also on the surface area per unit volume of the scaffold. 00:18:27.930 --> 00:18:29.970 So if you think of first, just the composition, 00:18:29.970 --> 00:18:33.060 if you have native proteins, like collagen, they 00:18:33.060 --> 00:18:34.700 have binding sites themselves. 00:18:34.700 --> 00:18:36.390 They have native binding sites. 00:18:36.390 --> 00:18:38.900 But if you think of synthetic polymers, 00:18:38.900 --> 00:18:41.570 like the resorbable sutured type of polymers 00:18:41.570 --> 00:18:43.890 that we talked about, they don't have binding sites 00:18:43.890 --> 00:18:46.530 and you have to coat the scaffold with some sort 00:18:46.530 --> 00:18:48.040 of adhesive protein. 00:19:57.480 --> 00:20:00.960 And then the surface area per unit volume of the scaffold 00:20:00.960 --> 00:20:04.950 is related to the pore size and the relative density. 00:20:04.950 --> 00:20:12.100 Let's call the specific surface area, 00:20:12.100 --> 00:20:13.645 surface area per unit volume. 00:20:31.800 --> 00:20:35.410 And if you think of having some scaffold that's 00:20:35.410 --> 00:20:39.150 like an open celled foam, you can roughly 00:20:39.150 --> 00:20:42.430 calculate what the surface area per unit volume is. 00:20:42.430 --> 00:20:44.860 So say each strut was a cylinder, 00:20:44.860 --> 00:20:47.290 then the surface area of each cylinder 00:20:47.290 --> 00:20:49.000 is going to be 2 pi rl. 00:20:49.000 --> 00:20:51.050 If each one has a radius r and a length l. 00:20:51.050 --> 00:20:54.480 Say we had n of them, that would be your surface area. 00:20:54.480 --> 00:20:58.240 And the volume of the whole scaffold, or one cell, 00:20:58.240 --> 00:21:02.240 would go as l cubed, the length of each strut cubed. 00:21:02.240 --> 00:21:05.200 So if we just forget about all the constants here. 00:21:05.200 --> 00:21:06.430 Forget about n. 00:21:06.430 --> 00:21:11.790 This just goes as r over l times 1 over l, 00:21:11.790 --> 00:21:17.270 and that goes as the relative density to the 1/2 power 00:21:17.270 --> 00:21:20.310 times 1 over the pore size. 00:21:20.310 --> 00:21:23.610 So the specific surface area depends on the relative density 00:21:23.610 --> 00:21:24.602 and on the pore size. 00:21:30.050 --> 00:21:33.645 And if you have a tetrakaidecahedron cell, 00:21:33.645 --> 00:21:35.770 you can work out exactly what that relationship is. 00:21:35.770 --> 00:21:36.790 It's sort of a model. 00:21:36.790 --> 00:21:38.910 And that gives you the relationship there. 00:21:38.910 --> 00:21:40.670 And in this particular case, I think 00:21:40.670 --> 00:21:43.200 the relative density was 0.5%. 00:21:43.200 --> 00:21:46.860 And so it's a constant over the cell size. 00:21:46.860 --> 00:21:49.290 So one of the things we did in my group 00:21:49.290 --> 00:21:52.090 was look at how cell attachment varied 00:21:52.090 --> 00:21:54.230 with this specific surface area. 00:21:54.230 --> 00:21:57.170 So we seeded cells onto scaffolds of different pore 00:21:57.170 --> 00:21:57.744 sizes. 00:21:57.744 --> 00:21:59.285 We kept the relative density constant 00:21:59.285 --> 00:22:01.440 and we changed the pore sizes. 00:22:01.440 --> 00:22:04.040 Remember I said, when we make these scaffolds by freeze 00:22:04.040 --> 00:22:05.800 drying we can control the pore size, 00:22:05.800 --> 00:22:07.920 by controlling the freezing temperature. 00:22:07.920 --> 00:22:11.060 And we see that it's just a linear relationship between how 00:22:11.060 --> 00:22:13.620 many cells attach, or the percentage of the cells 00:22:13.620 --> 00:22:17.430 that were seeded that attach, and the specific surface area. 00:22:17.430 --> 00:22:19.710 In here we used MC 3T3 cells. 00:22:19.710 --> 00:22:22.270 It's sort of a standard cell one that you can get. 00:22:22.270 --> 00:22:24.500 So Fergal O'Brien was the post-doc in my group 00:22:24.500 --> 00:22:28.080 who did that. 00:22:28.080 --> 00:22:37.030 So I'll just say we find cell attachment is 00:22:37.030 --> 00:22:39.300 proportional to the specific surface area. 00:22:47.841 --> 00:22:48.340 OK. 00:22:48.340 --> 00:22:54.672 So that's the cell attachment. 00:22:54.672 --> 00:22:56.630 So you can see how the scaffold design is going 00:22:56.630 --> 00:22:58.310 to affect how the cells attach. 00:22:58.310 --> 00:23:00.600 So there's some relationship between them there. 00:23:00.600 --> 00:23:03.770 Another thing people have looked at is cell morphology. 00:23:03.770 --> 00:23:06.630 And so if you change, the sort of, orientation of the pores, 00:23:06.630 --> 00:23:09.630 how does that change the orientation of the cells? 00:23:09.630 --> 00:23:11.380 So this was a study done in another group. 00:23:11.380 --> 00:23:14.087 So here we have randomly oriented fibers 00:23:14.087 --> 00:23:15.170 that make up the scaffold. 00:23:15.170 --> 00:23:17.430 And here they're not perfectly oriented this way, 00:23:17.430 --> 00:23:18.554 but more or less. 00:23:18.554 --> 00:23:19.970 And then these are cells that have 00:23:19.970 --> 00:23:22.630 been seeded onto them, so that the green staining is 00:23:22.630 --> 00:23:23.650 the cells. 00:23:23.650 --> 00:23:25.880 And you can see if the scaffold is random, 00:23:25.880 --> 00:23:29.040 the cells themselves line up with that fiber structure 00:23:29.040 --> 00:23:30.600 and become more or less random. 00:23:30.600 --> 00:23:32.450 And if the scaffold has fibers that 00:23:32.450 --> 00:23:34.380 are aligned, then the cells, they also 00:23:34.380 --> 00:23:36.030 line up and be aligned. 00:23:36.030 --> 00:23:38.040 So the morphology of the cells can 00:23:38.040 --> 00:23:41.040 be affected by the orientation of the scaffold pores. 00:23:46.400 --> 00:23:48.390 Also the cell morphology can be affected 00:23:48.390 --> 00:23:50.850 by the stiffness of the cells. 00:23:50.850 --> 00:23:52.880 Or the stiffness of the substrate. 00:23:52.880 --> 00:23:55.110 So this is a substrate. 00:23:55.110 --> 00:24:00.140 Here this was a PEG-fibrinogen hydrogel. 00:24:00.140 --> 00:24:03.340 And they varied the cross linking of this hydrogel. 00:24:03.340 --> 00:24:05.400 So they got different modularly for the hydrogel. 00:24:05.400 --> 00:24:08.730 So these numbers here, are all the stiffness of the four 00:24:08.730 --> 00:24:10.630 different hydrogels. 00:24:10.630 --> 00:24:13.040 And you can see the cell morphology changes 00:24:13.040 --> 00:24:19.130 from being a spread out thing on the least stiff substrate, 00:24:19.130 --> 00:24:22.310 to being just a little spherical or circular blob 00:24:22.310 --> 00:24:24.640 on the most stiff substrate. 00:24:24.640 --> 00:24:26.760 So the cells respond to the substrate. 00:24:26.760 --> 00:24:29.420 And so how the cells behave, depends 00:24:29.420 --> 00:24:30.695 in part on their environment. 00:24:35.060 --> 00:24:39.060 So I wanted to also talk about womb contraction. 00:24:39.060 --> 00:24:43.060 And talk about how cells contract scaffolds as well. 00:24:43.060 --> 00:24:45.900 So one of the things people have found 00:24:45.900 --> 00:24:48.990 when they look at say, skin and regeneration of skin-- 00:24:48.990 --> 00:24:52.260 so say you had somebody with a burn 00:24:52.260 --> 00:24:56.040 and the surgeons will clean the burnt out. 00:24:56.040 --> 00:24:59.140 And then what will happen as it heals, 00:24:59.140 --> 00:25:01.250 is scar tissue will form. 00:25:01.250 --> 00:25:04.240 And the scar tissue forms in conjunction 00:25:04.240 --> 00:25:05.660 with the wound contracting. 00:25:05.660 --> 00:25:08.170 So cells will actually migrate into the wound bed 00:25:08.170 --> 00:25:10.780 and they'll pull the edges of the wound 00:25:10.780 --> 00:25:12.350 together to try to close the wound. 00:25:12.350 --> 00:25:14.070 And they won't close it completely, 00:25:14.070 --> 00:25:15.680 but they'll partially close it. 00:25:15.680 --> 00:25:17.520 And that's called wound contraction. 00:25:17.520 --> 00:25:20.110 And that is thought to be associated with the formation 00:25:20.110 --> 00:25:21.420 of scar tissue. 00:25:21.420 --> 00:25:24.310 So the cells can actually apply mechanical loads. 00:25:24.310 --> 00:25:26.740 And they can contract the wound. 00:25:26.740 --> 00:25:29.190 And one of the things that Professor Yannas found 00:25:29.190 --> 00:25:32.160 was that if you use one of his collagen and gag scaffolds, 00:25:32.160 --> 00:25:34.010 you can inhibit that wound contraction. 00:25:34.010 --> 00:25:36.510 And if you can prevent the wound contraction from occurring, 00:25:36.510 --> 00:25:39.090 you also prevent the formation of the scar tissue. 00:25:39.090 --> 00:25:41.080 And that allows normal dermis to form. 00:25:41.080 --> 00:25:43.230 So you get normal skin. 00:25:43.230 --> 00:25:45.440 So this photograph here is of somebody 00:25:45.440 --> 00:25:49.470 who had burns over their entire torso. 00:25:49.470 --> 00:25:51.770 And they put this tissue injury scaffold on this part 00:25:51.770 --> 00:25:54.000 at the bottom, but not on that part at the top. 00:25:54.000 --> 00:25:59.630 And you can see these lines here are contracture lines 00:25:59.630 --> 00:26:02.090 from the scar formation. 00:26:02.090 --> 00:26:06.380 And you can see this skin down here is relatively normal. 00:26:06.380 --> 00:26:09.420 And in fact, when people look at the histology of the skin 00:26:09.420 --> 00:26:11.430 the forms using these scaffolds, they 00:26:11.430 --> 00:26:14.349 find that it is pretty much the same as normal dermis. 00:26:14.349 --> 00:26:17.015 It doesn't have sweat glands and it doesn't have hair follicles. 00:26:17.015 --> 00:26:19.980 So you can't sweat from that skin and you don't grow hair. 00:26:19.980 --> 00:26:24.020 But apart from that, it's more or less normal dermis. 00:26:24.020 --> 00:26:26.714 So this observation that if you can inhibit 00:26:26.714 --> 00:26:28.880 the womb contraction, you can prevent scar formation 00:26:28.880 --> 00:26:30.782 and you can get normal dermis to form. 00:26:30.782 --> 00:26:32.240 That's led to some interest in just 00:26:32.240 --> 00:26:36.970 seeing how is it that the cells do this contract l process. 00:26:36.970 --> 00:26:40.417 I think hitting the thing and my battery is dead. 00:26:40.417 --> 00:26:42.000 So one of the things people have done, 00:26:42.000 --> 00:26:44.530 is they've just taken what's called, free floating scaffold. 00:26:44.530 --> 00:26:46.321 They've just taken little disks of scaffold 00:26:46.321 --> 00:26:50.160 and put it in a cell culture medium in a Petri dish. 00:26:50.160 --> 00:26:52.690 And they find that if you put, say fiberblast on it, 00:26:52.690 --> 00:26:55.096 the fiberblast will contract that scaffold. 00:26:55.096 --> 00:26:56.470 And people have measured how much 00:26:56.470 --> 00:26:58.490 the diameter of the scaffold changes. 00:26:58.490 --> 00:27:00.490 And so they've kind of measured this contraction 00:27:00.490 --> 00:27:03.030 just by-- it's almost like measuring a strain. 00:27:03.030 --> 00:27:04.680 And what we wanted to do is we wanted 00:27:04.680 --> 00:27:06.990 to try to measure the forces that were involved. 00:27:06.990 --> 00:27:09.640 So we first developed something called a cell force monitor, 00:27:09.640 --> 00:27:11.260 and I'll show you that. 00:27:11.260 --> 00:27:15.884 And then we tried to calculate how much an individual cell 00:27:15.884 --> 00:27:17.300 could apply in terms of the force. 00:27:19.960 --> 00:27:21.210 So we used this scaffold here. 00:27:21.210 --> 00:27:26.290 This is the same collagen GAG scaffold I showed you before. 00:27:26.290 --> 00:27:27.840 And here's the cell force monitor. 00:27:27.840 --> 00:27:30.690 So that's just a schematic of holding 00:27:30.690 --> 00:27:34.170 a piece of the scaffold between two clamps. 00:27:34.170 --> 00:27:37.017 So here it is in elevation view. 00:27:37.017 --> 00:27:38.850 And then I'll just build the whole thing up, 00:27:38.850 --> 00:27:40.016 so you can see how it works. 00:27:40.016 --> 00:27:41.560 So it's on a base plate. 00:27:41.560 --> 00:27:45.030 It's attached to a horizontal stage that's adjustable. 00:27:45.030 --> 00:27:47.612 Then there's a very thin beam here. 00:27:47.612 --> 00:27:49.320 So this is another adjustable stage here, 00:27:49.320 --> 00:27:51.190 and this very thin beam here. 00:27:51.190 --> 00:27:53.145 And that's attached to one end of this clamp. 00:27:53.145 --> 00:27:54.320 And here's the matrix. 00:27:54.320 --> 00:27:57.480 And this is attached to this other adjustable stage here. 00:27:57.480 --> 00:28:01.610 And then when we have a proximity sensor-- so 00:28:01.610 --> 00:28:05.210 what's going to happen is, this is fixed over here. 00:28:05.210 --> 00:28:06.830 The scaffold is going to contract 00:28:06.830 --> 00:28:11.410 with the cells applying these contract l forces. 00:28:11.410 --> 00:28:13.870 This beam here is going to bend and the proximity sensor 00:28:13.870 --> 00:28:15.495 is going to tell us how much it's bent. 00:28:15.495 --> 00:28:17.400 So we can measure how much that's bent. 00:28:17.400 --> 00:28:19.460 If we know how much that's bent, and we calibrate the beam, 00:28:19.460 --> 00:28:20.960 we can figure out the force in the beam. 00:28:20.960 --> 00:28:21.460 OK. 00:28:21.460 --> 00:28:24.220 So we can figure out how much is the total force that the cells 00:28:24.220 --> 00:28:26.020 are contracting with. 00:28:26.020 --> 00:28:28.070 And then this just is a little silicone well with 00:28:28.070 --> 00:28:28.903 some culture medium. 00:28:28.903 --> 00:28:30.240 So that's the whole setup there. 00:28:30.240 --> 00:28:32.770 Toby Fryman was a student who did that, who's 00:28:32.770 --> 00:28:34.360 married to Professor Van Vliet. 00:28:34.360 --> 00:28:38.110 And I have a very big soft spot for both of them. 00:28:38.110 --> 00:28:39.720 So anyway, that's the set up. 00:28:39.720 --> 00:28:43.500 And the thing that Toby measured was the force, 00:28:43.500 --> 00:28:46.600 by measuring how much that beam deflected. 00:28:46.600 --> 00:28:48.830 And he measured the force over time. 00:28:48.830 --> 00:28:52.900 And he found that if he put say, a certain number of fiberblasts 00:28:52.900 --> 00:28:56.580 onto the scaffold, the force would increase and then reach 00:28:56.580 --> 00:28:58.320 an asymptotic point. 00:28:58.320 --> 00:29:01.530 And you could describe these curves by this equation here. 00:29:01.530 --> 00:29:03.160 Here's the asymptotic force. 00:29:03.160 --> 00:29:06.870 And it's a 1 minus exponential of minus time over a time 00:29:06.870 --> 00:29:08.600 constant tao. 00:29:08.600 --> 00:29:11.260 And then this number here is the number of fiberblast 00:29:11.260 --> 00:29:12.820 that were attached at 22 hours. 00:29:12.820 --> 00:29:14.900 So he ran these tests for 22 hours. 00:29:14.900 --> 00:29:17.020 And when he was finished, he could 00:29:17.020 --> 00:29:19.690 count the number of cells that were attached in the scaffolds. 00:29:19.690 --> 00:29:22.650 So you would just wash off any cells that weren't attached 00:29:22.650 --> 00:29:26.180 and you can do accounting of how many cells are left. 00:29:26.180 --> 00:29:27.750 And one of the things that he found 00:29:27.750 --> 00:29:31.220 was that if you plot that asymptotic force-- if you plot 00:29:31.220 --> 00:29:35.470 through this force over here, against the number of cells 00:29:35.470 --> 00:29:38.760 that were attached, you just get a linear relationship. 00:29:38.760 --> 00:29:42.190 And the slope of that is roughly the force per cell. 00:29:42.190 --> 00:29:45.100 And that's about one nano neutron. 00:29:45.100 --> 00:29:47.930 Now this is a little deceptive because not all the cells 00:29:47.930 --> 00:29:49.044 are contracting. 00:29:49.044 --> 00:29:51.210 And not all the cells are lined up in one direction. 00:29:51.210 --> 00:29:53.085 So there are cells in different orientations. 00:29:53.085 --> 00:29:54.700 But just as an order of magnitude 00:29:54.700 --> 00:29:59.100 the cells are applying something like one minute per cell. 00:29:59.100 --> 00:30:00.900 So that's the effect of the cell number. 00:30:00.900 --> 00:30:02.350 Another thing he did was he looked 00:30:02.350 --> 00:30:05.000 at what happens if you change the stiffness of that beam if. 00:30:05.000 --> 00:30:08.090 You make that beam in the device different stiffnesses, 00:30:08.090 --> 00:30:09.880 how do the cells react. 00:30:09.880 --> 00:30:14.810 And so the stiffness here are the stiffness of the system. 00:30:14.810 --> 00:30:17.230 So there's 0.7 newtons per meter up to ten, 00:30:17.230 --> 00:30:19.830 so it's a factor of a little over ten difference. 00:30:19.830 --> 00:30:23.050 And you can see the displacement per cell changes. 00:30:23.050 --> 00:30:29.350 The stiffer the system is the less the cells can displace it. 00:30:29.350 --> 00:30:31.700 But if you then plot the force per cell, 00:30:31.700 --> 00:30:34.260 you find that the force per cell is about the same. 00:30:34.260 --> 00:30:36.320 So you develop about the same force. 00:30:36.320 --> 00:30:38.970 So that suggests the cells are capable of applying 00:30:38.970 --> 00:30:42.520 a certain amount of force, and not any more force. 00:30:42.520 --> 00:30:44.000 No larger force. 00:30:44.000 --> 00:30:45.874 So he did that. 00:30:45.874 --> 00:30:48.290 Then we were interested in what was the mechanism of this. 00:30:48.290 --> 00:30:50.200 How were the cells applying this force? 00:30:50.200 --> 00:30:52.550 Because I was kind of surprised to find out the cells 00:30:52.550 --> 00:30:54.247 even could apply forces. 00:30:54.247 --> 00:30:55.830 So we were interested in understanding 00:30:55.830 --> 00:30:58.549 the mechanism of this. 00:30:58.549 --> 00:31:01.090 And one of the things we knew that we didn't quite figure out 00:31:01.090 --> 00:31:02.850 how this all worked together was, 00:31:02.850 --> 00:31:04.496 we knew that the cells elongated. 00:31:04.496 --> 00:31:06.995 If you just take a substrate, like even just a 2d substrate, 00:31:06.995 --> 00:31:10.160 and you put cells on it they'll be rounded to start out with. 00:31:10.160 --> 00:31:12.490 And over time, over a few hours, they'll spread. 00:31:12.490 --> 00:31:14.230 And that's pretty standard. 00:31:14.230 --> 00:31:15.940 Many types of cells will do that. 00:31:15.940 --> 00:31:18.120 So we knew the cells were starting off as rounded 00:31:18.120 --> 00:31:19.967 and they were spreading. 00:31:19.967 --> 00:31:22.300 So the cells are getting longer, but our whole scaffolds 00:31:22.300 --> 00:31:23.060 getting shorter. 00:31:23.060 --> 00:31:25.640 And so it wasn't obvious how was the cells going longer, 00:31:25.640 --> 00:31:27.570 but the scaffold's getting shorter. 00:31:27.570 --> 00:31:29.810 And so the next thing we thought we would do 00:31:29.810 --> 00:31:32.450 is just watch the cells and see what they did. 00:31:32.450 --> 00:31:36.410 And so we measured the aspect ratio of the cells 00:31:36.410 --> 00:31:37.980 at different time points. 00:31:37.980 --> 00:31:41.320 And we did this by just impregnating 00:31:41.320 --> 00:31:43.280 the scaffold in the cells at different time 00:31:43.280 --> 00:31:46.200 points with a resin, and then using a stain, 00:31:46.200 --> 00:31:49.202 and then using digital image analysis. 00:31:49.202 --> 00:31:51.410 So what we found was that the fiber of the fiberglass 00:31:51.410 --> 00:31:53.050 morphology looked like this. 00:31:53.050 --> 00:31:55.430 So the long thready things of the scaffold, 00:31:55.430 --> 00:31:58.600 and these little blobs here are the fiberblast of the cells. 00:31:58.600 --> 00:32:01.110 So here at time 0 you can see-- like I said, 00:32:01.110 --> 00:32:03.700 the cells are pretty rounded they're not very spread out. 00:32:03.700 --> 00:32:05.610 Here at eight hours you can see-- here's 00:32:05.610 --> 00:32:07.190 a cell that's gotten longer. 00:32:07.190 --> 00:32:08.040 Here's another one. 00:32:08.040 --> 00:32:10.400 This guy here is still rounded, it's not doing much. 00:32:10.400 --> 00:32:14.300 22 hours, again, some of the cells are quite elongated. 00:32:14.300 --> 00:32:16.290 Some of them are still not that elongated. 00:32:16.290 --> 00:32:18.405 So they don't all become active. 00:32:18.405 --> 00:32:19.780 But one of the things we noticed, 00:32:19.780 --> 00:32:22.680 if you look at this image here, you can see these cells 00:32:22.680 --> 00:32:24.666 are attached at one end, and at the other end. 00:32:24.666 --> 00:32:26.290 But they're not attached in the middle. 00:32:26.290 --> 00:32:29.480 There's sort of a gap between the cell and the strut. 00:32:29.480 --> 00:32:31.020 And this is another example here. 00:32:31.020 --> 00:32:34.740 Here's a cell here, and this is the collagen GAG strut 00:32:34.740 --> 00:32:36.204 that it's attached to. 00:32:36.204 --> 00:32:38.120 And you can see it's attached to the two ends, 00:32:38.120 --> 00:32:39.430 but not in the middle. 00:32:39.430 --> 00:32:42.420 And this starts to explain how it 00:32:42.420 --> 00:32:45.630 is that the cells are elongating but the scaffolds getting 00:32:45.630 --> 00:32:46.460 shorter. 00:32:46.460 --> 00:32:49.090 It's that the cells are just attached at two ends. 00:32:49.090 --> 00:32:51.070 And the cells are moving along a strut 00:32:51.070 --> 00:32:52.860 and they're attached to the two ends. 00:32:52.860 --> 00:32:55.300 And if you think of the cells attached 00:32:55.300 --> 00:32:57.320 through those focal adhesion points, 00:32:57.320 --> 00:33:00.500 they're applying tension to the cell. 00:33:00.500 --> 00:33:03.540 And the actin filaments in the cell are in tension. 00:33:03.540 --> 00:33:05.450 Obviously, filaments can't be in compression. 00:33:05.450 --> 00:33:06.960 They're only going to be in tension. 00:33:06.960 --> 00:33:09.990 And what happens is that puts the stress into compression. 00:33:09.990 --> 00:33:12.050 And if the struts in compression, at some point 00:33:12.050 --> 00:33:13.200 it's going to buckle. 00:33:13.200 --> 00:33:15.680 And you can see this strut here has basically 00:33:15.680 --> 00:33:17.710 buckled under that cell. 00:33:17.710 --> 00:33:19.830 And so if the cells are getting longer, 00:33:19.830 --> 00:33:22.860 and they're buckling the struts, then that's 00:33:22.860 --> 00:33:25.021 going to shorten the struts and the whole scaffold 00:33:25.021 --> 00:33:26.020 is going to get shorter. 00:33:28.630 --> 00:33:32.500 And so then Toby plotted the aspect ratio of the cell, 00:33:32.500 --> 00:33:35.690 so that is a measure of their elongation against the time. 00:33:35.690 --> 00:33:37.580 And again, he found one of these curves 00:33:37.580 --> 00:33:40.310 with the same kind of form as the curve 00:33:40.310 --> 00:33:42.220 for the forced development. 00:33:42.220 --> 00:33:44.210 And he found the time constant here 00:33:44.210 --> 00:33:47.550 for the change in the aspect ratio was about five hours. 00:33:47.550 --> 00:33:50.640 And for the development of the force it was about 5.7 hours. 00:33:50.640 --> 00:33:54.350 So the time constant for the elongation of the cells, 00:33:54.350 --> 00:33:56.200 more or less matches up with a time 00:33:56.200 --> 00:33:59.560 constant for developing the force. 00:33:59.560 --> 00:34:01.560 So that's what that says. 00:34:01.560 --> 00:34:04.280 And that suggests there's a link between the elongation 00:34:04.280 --> 00:34:07.170 of the cell population and the macroscopic contraction 00:34:07.170 --> 00:34:08.760 of the population. 00:34:08.760 --> 00:34:11.250 So then we wanted to take it one step further. 00:34:11.250 --> 00:34:13.849 And we wanted to look at what the cells were doing live. 00:34:13.849 --> 00:34:15.239 Like as they were doing it. 00:34:15.239 --> 00:34:18.429 So Toby devised this little schematic thing here. 00:34:18.429 --> 00:34:20.179 So he had just an optical microscope. 00:34:20.179 --> 00:34:26.449 He had a microscope slide with a fairly thick well in it, 00:34:26.449 --> 00:34:29.040 so that we could put culture medium in the well. 00:34:29.040 --> 00:34:31.800 We put a cell seeded matrix in here. 00:34:31.800 --> 00:34:34.290 And he had a heated stage here. 00:34:34.290 --> 00:34:37.067 And then he took little videos of what the cells were doing. 00:34:37.067 --> 00:34:39.400 And this required some patience because as you could see 00:34:39.400 --> 00:34:40.510 not all the cells did anything. 00:34:40.510 --> 00:34:42.179 Some of them just sat there and did nothing. 00:34:42.179 --> 00:34:43.960 So he would set this up for a day, and watch a cell, 00:34:43.960 --> 00:34:45.050 and it would do nothing. 00:34:45.050 --> 00:34:46.883 And then he would have to find another cell. 00:34:46.883 --> 00:34:48.810 But he did find some cells that were 00:34:48.810 --> 00:34:50.230 responsible for the contraction. 00:34:50.230 --> 00:34:52.560 And that was it was kind of neat. 00:34:52.560 --> 00:34:53.769 So here's the scaffold again. 00:34:53.769 --> 00:34:55.601 All these little bits here are the scaffold. 00:34:55.601 --> 00:34:57.090 This is a strut of the scaffold. 00:34:57.090 --> 00:35:00.710 And this is a fiberblast parked on the scaffold. 00:35:00.710 --> 00:35:03.340 And this has a little video here. 00:35:03.340 --> 00:35:06.780 And you can see what's happening is the strut here 00:35:06.780 --> 00:35:08.300 is starting to buckle. 00:35:08.300 --> 00:35:10.877 And you can see these two sides here, 00:35:10.877 --> 00:35:12.710 those two things are coming closer together. 00:35:12.710 --> 00:35:14.860 So they originally were this piece here, 00:35:14.860 --> 00:35:15.750 and that piece there. 00:35:15.750 --> 00:35:18.357 And now they're at that point there. 00:35:18.357 --> 00:35:20.190 And then if I let it go a little bit longer, 00:35:20.190 --> 00:35:23.290 it continues to do that process. 00:35:23.290 --> 00:35:27.860 And then the final thing-- this kind of smushed up mess 00:35:27.860 --> 00:35:31.740 here is these two things having me brought completely together. 00:35:31.740 --> 00:35:35.470 And this strut here is some strut down over here. 00:35:35.470 --> 00:35:39.110 So you can see how the cells are elongating and causing 00:35:39.110 --> 00:35:41.580 contraction of the scaffold. 00:35:41.580 --> 00:35:45.240 Here's a series of stills taken from another video that he did. 00:35:45.240 --> 00:35:47.840 So this sort of square thing is the scaffold. 00:35:47.840 --> 00:35:49.100 So b is the scaffold. 00:35:49.100 --> 00:35:52.510 And a, this little blob here, is the fiberblast. 00:35:52.510 --> 00:35:54.904 And you can see, even from this image to this one, 00:35:54.904 --> 00:35:57.070 you can see that the fiberblast has spread a little. 00:35:57.070 --> 00:35:59.730 Do you see how it's kind of oozed out along the scaffold 00:35:59.730 --> 00:36:00.930 there. 00:36:00.930 --> 00:36:03.186 And eventually it attaches over here. 00:36:03.186 --> 00:36:04.560 And you can see that it's buckled 00:36:04.560 --> 00:36:06.322 this strut underneath it. 00:36:06.322 --> 00:36:08.030 And here it's a little bit more deformed. 00:36:08.030 --> 00:36:10.420 It then grabs on down here somewhere 00:36:10.420 --> 00:36:11.560 and deforms it even more. 00:36:11.560 --> 00:36:13.920 So you can see that's more deformed. 00:36:13.920 --> 00:36:18.920 And then Toby put alcohol on the whole thing, 00:36:18.920 --> 00:36:20.829 which kills the cells and the cell let's go. 00:36:20.829 --> 00:36:22.995 And you can see you recover some of the deformation. 00:36:22.995 --> 00:36:26.920 You don't recover all of it, but you recover some of it. 00:36:26.920 --> 00:36:28.685 This was another example. 00:36:28.685 --> 00:36:30.060 And this was kind of interesting. 00:36:30.060 --> 00:36:32.780 Here there was a scaffold junction 00:36:32.780 --> 00:36:35.310 where there were three struts that came together, 00:36:35.310 --> 00:36:36.870 a little bit like a strut. 00:36:36.870 --> 00:36:38.890 And there was a little cell right there. 00:36:38.890 --> 00:36:40.570 And you can see the cell elongates. 00:36:40.570 --> 00:36:42.920 You see how this elongated and its grabbing 00:36:42.920 --> 00:36:44.670 on up here somewhere. 00:36:44.670 --> 00:36:47.680 But the amount of force the cell was 00:36:47.680 --> 00:36:52.930 kind of pulling with must have been less than the-- 00:36:52.930 --> 00:36:54.610 or rather must been more than the force 00:36:54.610 --> 00:36:55.720 of the focal adhesion. 00:36:55.720 --> 00:36:57.178 Because what happens was eventually 00:36:57.178 --> 00:36:58.860 the focal adhesion let go. 00:36:58.860 --> 00:37:01.630 And the cell kind of bounces back and ends up over here. 00:37:01.630 --> 00:37:03.130 So the cell was kind of snapped back 00:37:03.130 --> 00:37:05.430 on to the other focal adhesion over here. 00:37:05.430 --> 00:37:07.080 And here it's rounded again. 00:37:07.080 --> 00:37:08.770 And here it elongates again. 00:37:08.770 --> 00:37:10.860 And then this focal adhesion lets go 00:37:10.860 --> 00:37:14.260 and now it's moved back over to there. 00:37:14.260 --> 00:37:16.900 So these struts here are so stiff. 00:37:16.900 --> 00:37:18.770 They're much stiffer, I think, partly 00:37:18.770 --> 00:37:19.978 because they're triangulated. 00:37:19.978 --> 00:37:22.820 And it looks like they're just shorter and a lot thicker. 00:37:22.820 --> 00:37:25.340 The cell isn't being able to deform those. 00:37:25.340 --> 00:37:29.510 But it's elongating and then focal adhesion was letting go. 00:37:29.510 --> 00:37:32.720 So this is a little schematic of what we thinks going on. 00:37:32.720 --> 00:37:35.490 So the cell starts out-- it's some elongation here. 00:37:35.490 --> 00:37:36.810 It's attached at that point. 00:37:36.810 --> 00:37:38.460 It's attached at that point there. 00:37:38.460 --> 00:37:40.930 And the cell is getting longer. 00:37:40.930 --> 00:37:43.270 And if you think about it as the cell's getting longer-- 00:37:43.270 --> 00:37:46.260 if you think about the Euler Buckling formula, 00:37:46.260 --> 00:37:48.200 the buckling load goes as 1 over l squared. 00:37:48.200 --> 00:37:50.780 So the longer the length of this piece 00:37:50.780 --> 00:37:54.940 of the strut of the scaffold underneath the cell is, 00:37:54.940 --> 00:37:58.367 the smaller the load it takes to actually cause it to buckle. 00:37:58.367 --> 00:37:59.950 So at some point it buckles like this. 00:37:59.950 --> 00:38:02.060 And this is just a little force diagram. 00:38:02.060 --> 00:38:03.930 So the actin fibers are in tension 00:38:03.930 --> 00:38:05.870 and the matrix strut is in compression. 00:38:05.870 --> 00:38:07.980 Sometimes we saw some bending. 00:38:07.980 --> 00:38:11.040 So you could see if a cell was spanning between two struts, 00:38:11.040 --> 00:38:13.390 you could get the cell bending the struts as well. 00:38:13.390 --> 00:38:15.860 That was another possibility. 00:38:15.860 --> 00:38:18.310 And so we think that the cell elongation 00:38:18.310 --> 00:38:20.070 was related to the contraction. 00:38:20.070 --> 00:38:23.650 The time constants for the two things were almost the same. 00:38:23.650 --> 00:38:27.450 And as the cell elongates there's a gap between the cell 00:38:27.450 --> 00:38:30.060 and the matrix on the central portion. 00:38:30.060 --> 00:38:33.740 And then the cell is adhered at the periphery of the adhesion 00:38:33.740 --> 00:38:34.700 points. 00:38:34.700 --> 00:38:36.860 And then the tensile forces in these act. 00:38:36.860 --> 00:38:39.430 And filaments inside the cell induce compression 00:38:39.430 --> 00:38:42.690 in the strut, and that causes buckling. 00:38:42.690 --> 00:38:44.240 And then Toby graduated. 00:38:44.240 --> 00:38:46.310 And then I got another student, Brendan. 00:38:46.310 --> 00:38:49.620 And Brendan saw what Toby did and he wanted 00:38:49.620 --> 00:38:51.540 to do a little more with that. 00:38:51.540 --> 00:38:54.041 Brandon was also involved that osteochondral project 00:38:54.041 --> 00:38:55.290 that I talked about last time. 00:38:55.290 --> 00:38:57.940 And Brendan this other thing as well for his project. 00:38:57.940 --> 00:39:01.390 So he wanted to measure the force of an individual cell. 00:39:01.390 --> 00:39:03.460 So when we had that cell force monitor, 00:39:03.460 --> 00:39:06.540 that was the total force of all the cells in that one 00:39:06.540 --> 00:39:07.720 direction. 00:39:07.720 --> 00:39:09.670 But Brendan wanted to know if he could measure 00:39:09.670 --> 00:39:11.600 the force of a single cell. 00:39:11.600 --> 00:39:14.480 And now that we knew that the contractal process was related 00:39:14.480 --> 00:39:16.590 to buckling, We thought, well, we could just 00:39:16.590 --> 00:39:18.570 use Euler's formula. 00:39:18.570 --> 00:39:20.830 If we knew what the modulus of the solid 00:39:20.830 --> 00:39:24.690 was, and we knew what the dimensions of the struts were. 00:39:24.690 --> 00:39:27.220 So that would allow us to calculate the contractile force 00:39:27.220 --> 00:39:30.271 of a single fiberblast. 00:39:30.271 --> 00:39:32.020 So I think I've shown you this thing here. 00:39:32.020 --> 00:39:34.061 So Brendan was the one who did these experiments. 00:39:34.061 --> 00:39:37.840 He cut a single strut out of the scaffold. 00:39:37.840 --> 00:39:41.090 And the single strut is about 100 microns long. 00:39:41.090 --> 00:39:42.750 He used a microscope to do this. 00:39:42.750 --> 00:39:45.510 He then glued it onto a glass slide 00:39:45.510 --> 00:39:48.640 and he used the atomic force microscope probe 00:39:48.640 --> 00:39:51.140 to bend the strut like a cantilever beam. 00:39:51.140 --> 00:39:54.010 And he measured this displacement here. 00:39:54.010 --> 00:39:56.940 And from that he could back out what the modulus of the solid 00:39:56.940 --> 00:39:57.890 was. 00:39:57.890 --> 00:39:59.920 He did these tests in the dry state. 00:39:59.920 --> 00:40:02.340 But we could extrapolate to the wet state 00:40:02.340 --> 00:40:04.760 from looking at the behavior of the whole scaffold. 00:40:04.760 --> 00:40:10.190 So he had a modulus for the wet scaffold solid. 00:40:10.190 --> 00:40:13.760 And then this is our formula for Euler buckling here. 00:40:13.760 --> 00:40:17.240 So that's just the standard formula. 00:40:17.240 --> 00:40:20.590 I had a student from civil engineering, who 00:40:20.590 --> 00:40:24.067 looked at hydrostatic loading of a tetrakaidecahedral cell 00:40:24.067 --> 00:40:25.150 and he looked at buckling. 00:40:25.150 --> 00:40:27.310 If you had a tetrakaidecahedral cell and you 00:40:27.310 --> 00:40:29.397 load it in all three directions. 00:40:29.397 --> 00:40:30.480 He looked at the buckling. 00:40:30.480 --> 00:40:33.110 And he had calculated that the n constraint factor-- 00:40:33.110 --> 00:40:36.060 the n squared was point 0.34. 00:40:36.060 --> 00:40:39.010 So we have some idea of what that n squared value should be. 00:40:39.010 --> 00:40:41.750 Although it's somewhat of an estimate. 00:40:41.750 --> 00:40:44.000 I had a UROP student who took Toby's images 00:40:44.000 --> 00:40:46.420 and measured the dimensions of the struts. 00:40:46.420 --> 00:40:50.422 So he measured the diameter and the thickness of the struts. 00:40:50.422 --> 00:40:52.130 And from that, we just plugged everything 00:40:52.130 --> 00:40:53.480 into the Euler formula. 00:40:53.480 --> 00:40:56.070 And we found that the average single cell 00:40:56.070 --> 00:40:59.220 force is somewhere between about 11 and 41 nano neutron. 00:40:59.220 --> 00:41:01.169 It was something like 26 nano neutrons. 00:41:01.169 --> 00:41:03.460 So it would make sense that it's more than the one nano 00:41:03.460 --> 00:41:06.040 neutron per cell because not all of those cells were active 00:41:06.040 --> 00:41:08.850 and they weren't all going in the same direction. 00:41:08.850 --> 00:41:11.950 So Brendan Harley and Matt Wong did that part of the project. 00:41:16.070 --> 00:41:16.570 OK. 00:41:16.570 --> 00:41:17.710 So that's the contraction. 00:41:17.710 --> 00:41:19.220 Are we good with contraction? 00:41:19.220 --> 00:41:21.386 So it's kind of interesting that cells will contract 00:41:21.386 --> 00:41:23.490 and we can measure some forces. 00:41:23.490 --> 00:41:26.015 So the next type of interaction between the cells 00:41:26.015 --> 00:41:27.890 and the scaffolds that I wanted to talk about 00:41:27.890 --> 00:41:29.890 is cell migration. 00:41:29.890 --> 00:41:32.427 And these are some studies from the literature. 00:41:32.427 --> 00:41:33.760 These are two different studies. 00:41:33.760 --> 00:41:36.870 But the top one here, they've measured migration rate 00:41:36.870 --> 00:41:38.730 as a function of the cross linking 00:41:38.730 --> 00:41:40.790 treatment of a scaffold. 00:41:40.790 --> 00:41:44.327 And the decreasing stiffness goes this way. 00:41:44.327 --> 00:41:46.660 And so they're seeing that the speed of migration-- this 00:41:46.660 --> 00:41:48.810 is in millimeters per day. 00:41:48.810 --> 00:41:50.110 Cells don't move too quickly. 00:41:50.110 --> 00:41:52.330 They go millimeters per day. 00:41:52.330 --> 00:41:55.370 But you can see that the migration speed, the speed 00:41:55.370 --> 00:41:57.340 at which the cells can move, depends 00:41:57.340 --> 00:42:01.050 on the stiffness of the scaffold that they're attached to. 00:42:01.050 --> 00:42:03.790 And in this study on the bottom here, what they did was 00:42:03.790 --> 00:42:07.440 they had just a flat 2d substrate. 00:42:07.440 --> 00:42:09.550 Just a flat polymer. 00:42:09.550 --> 00:42:12.420 And what they did was they cross linked one part of the polymer 00:42:12.420 --> 00:42:14.660 more than the other part of polymer. 00:42:14.660 --> 00:42:17.600 So over here, this was the less cross linked. 00:42:17.600 --> 00:42:19.040 That was the soft part. 00:42:19.040 --> 00:42:20.790 And this was the more highly cross linked. 00:42:20.790 --> 00:42:22.460 This was the stiffer part. 00:42:22.460 --> 00:42:25.110 And they found that if they put a cell on the soft part 00:42:25.110 --> 00:42:27.730 it would migrate onto the stiff part. 00:42:27.730 --> 00:42:30.230 But if they put a cell on the stiff part, 00:42:30.230 --> 00:42:32.702 it would start going this way towards the soft part. 00:42:32.702 --> 00:42:34.160 But when it got to the interface it 00:42:34.160 --> 00:42:36.290 would just spread out along the interface. 00:42:36.290 --> 00:42:38.790 And it wouldn't go into the soft part. 00:42:38.790 --> 00:42:40.540 So the cells were somehow sensing 00:42:40.540 --> 00:42:42.152 the stiffness of the substrate. 00:42:42.152 --> 00:42:44.610 And for some reason, I don't know what, but for some reason 00:42:44.610 --> 00:42:46.450 these particular cells seem to prefer 00:42:46.450 --> 00:42:48.559 being on the stiff substrate. 00:42:48.559 --> 00:42:50.350 So this is just really showing that there's 00:42:50.350 --> 00:42:53.440 some interaction between the substrate stiffness and the way 00:42:53.440 --> 00:42:56.440 the cells are behaving and migrating. 00:42:56.440 --> 00:43:01.030 And then Brendan also wanted to study this. 00:43:01.030 --> 00:43:04.172 And he got some of the collagen GAG scaffold. 00:43:04.172 --> 00:43:05.380 He made some of the scaffold. 00:43:05.380 --> 00:43:08.000 And he stained that with a stain that made it turn red. 00:43:08.000 --> 00:43:12.660 So these lines here are all red struts in the scaffold. 00:43:12.660 --> 00:43:15.440 And then he put fiberblasts on to the scaffold 00:43:15.440 --> 00:43:16.530 and stained them green. 00:43:16.530 --> 00:43:20.430 So all these little blobs here that are green are the cells. 00:43:20.430 --> 00:43:22.290 And then he used confocal microscopy. 00:43:22.290 --> 00:43:24.170 And the confocal microscopy allowed 00:43:24.170 --> 00:43:27.560 him to look at a certain volume of the scaffold. 00:43:27.560 --> 00:43:29.210 And he had some software that would 00:43:29.210 --> 00:43:31.460 track the centroid of each cell as it 00:43:31.460 --> 00:43:33.230 moved through the scaffold. 00:43:33.230 --> 00:43:36.950 And so he had a thing he called spot tracking. 00:43:36.950 --> 00:43:40.310 So each of these little spheres here corresponds to a cell. 00:43:40.310 --> 00:43:43.115 And the white box is the volume of material 00:43:43.115 --> 00:43:45.150 that you could see in the scaffold. 00:43:45.150 --> 00:43:48.470 And this color scale here really corresponds to time. 00:43:48.470 --> 00:43:50.180 So I've forgotten which round. 00:43:50.180 --> 00:43:52.730 I think blue is the original time 0, 00:43:52.730 --> 00:43:55.360 and then red is maybe five seconds, 00:43:55.360 --> 00:43:56.520 and yellow was 10 seconds. 00:43:56.520 --> 00:43:59.360 The different colors correspond to different times. 00:43:59.360 --> 00:44:01.910 So he could track the path of each cell 00:44:01.910 --> 00:44:05.090 and also what the position was at different time points. 00:44:05.090 --> 00:44:08.145 So he knew what the position was at different time points. 00:44:08.145 --> 00:44:09.520 And obviously from that, he could 00:44:09.520 --> 00:44:12.200 get the speed of the scaffold. 00:44:12.200 --> 00:44:14.730 And he did these experiments on scaffolds 00:44:14.730 --> 00:44:18.170 of different stiffnesses, as well as, different pore size. 00:44:18.170 --> 00:44:21.110 And here you can see the cell speed. 00:44:21.110 --> 00:44:23.680 He's measuring it in microns per hour now. 00:44:23.680 --> 00:44:25.760 The cell speed increases at first 00:44:25.760 --> 00:44:28.780 and then decreases with the strut stiffness. 00:44:28.780 --> 00:44:31.140 So we don't know exactly why this is. 00:44:31.140 --> 00:44:34.950 But there is an effect between the stiffness of the scaffold 00:44:34.950 --> 00:44:36.727 and the migration speed. 00:44:36.727 --> 00:44:38.310 And another thing he did was he looked 00:44:38.310 --> 00:44:42.070 at how the cell speed varies with the pore size. 00:44:42.070 --> 00:44:46.560 And as the pore size gets smaller, the speed goes up. 00:44:46.560 --> 00:44:48.310 And we're not entirely sure why that is. 00:44:48.310 --> 00:44:50.560 But I think that might be related to this binding site 00:44:50.560 --> 00:44:53.095 thing too. 00:44:53.095 --> 00:44:56.730 As the pore size goes down, the number of binding sites 00:44:56.730 --> 00:44:57.860 is going to go up. 00:44:57.860 --> 00:45:00.160 And if you think of the cells migrating 00:45:00.160 --> 00:45:02.940 by having these adhesion sites, and the adhesion sites are just 00:45:02.940 --> 00:45:05.700 at the ends of the cells, and the cells kind of putting out 00:45:05.700 --> 00:45:10.330 a little extension, and then looking for somewhere else 00:45:10.330 --> 00:45:10.996 it can bind. 00:45:10.996 --> 00:45:12.370 The more binding sites there are, 00:45:12.370 --> 00:45:14.100 the faster it's going to find a binding site. 00:45:14.100 --> 00:45:16.070 And the faster, I think, it's going to move on. 00:45:16.070 --> 00:45:19.910 So I think that the cell speed depends on pore size, at least 00:45:19.910 --> 00:45:23.290 in part because of the increase in the binding sites 00:45:23.290 --> 00:45:26.470 with smaller pore sizes. 00:45:26.470 --> 00:45:29.350 So pore size and the migration. 00:45:29.350 --> 00:45:31.300 And then the last thing I wanted to talk about 00:45:31.300 --> 00:45:33.470 was cell differentiation. 00:45:33.470 --> 00:45:35.870 And this is a study study by Engler. 00:45:35.870 --> 00:45:39.470 And one of the things he found was he put mesenchymal stem 00:45:39.470 --> 00:45:41.880 cells on 2d substrates. 00:45:41.880 --> 00:45:44.370 Just flat 2d substrates of different stiffnesses. 00:45:44.370 --> 00:45:48.200 And again, he could control the stiffness by cross linking. 00:45:48.200 --> 00:45:51.000 And what he's showing up here in the first bit 00:45:51.000 --> 00:45:55.330 is that he's looking at the stiffness of tissues 00:45:55.330 --> 00:45:56.450 of different kinds. 00:45:56.450 --> 00:45:59.270 So here's brain type tissue. 00:45:59.270 --> 00:46:00.790 Something like one kilo pascal. 00:46:00.790 --> 00:46:04.110 Muscle might be something like 10 kilo pascal. 00:46:04.110 --> 00:46:06.030 And collagenous bone-- this is sort 00:46:06.030 --> 00:46:08.790 of the osteoid that is the precursor of bone, not 00:46:08.790 --> 00:46:09.820 the bone itself. 00:46:09.820 --> 00:46:13.540 Is about 100 kilo pascals. 00:46:13.540 --> 00:46:16.210 And what he did was he put these mesenchymal 00:46:16.210 --> 00:46:20.150 stem cells-- so here's his cell onto his substrate. 00:46:20.150 --> 00:46:22.830 And he varied the stiffness of the substrate. 00:46:22.830 --> 00:46:25.010 And then he looked at the shape of the cells. 00:46:25.010 --> 00:46:28.400 So here's the least stiff substrate, 00:46:28.400 --> 00:46:30.930 so between point 1 and 1 kilo pascals. 00:46:30.930 --> 00:46:34.090 And here's 4 hours, 24 hours, 96 hours. 00:46:34.090 --> 00:46:39.280 And these cells formed long processes 00:46:39.280 --> 00:46:41.510 extending beyond the cell body. 00:46:41.510 --> 00:46:43.490 And they looked kind of like neurons. 00:46:43.490 --> 00:46:45.660 So they he called those neuron like. 00:46:45.660 --> 00:46:49.270 Then there's an intermediate stiffness of substrate here. 00:46:49.270 --> 00:46:53.330 And these cells became even more elongated. 00:46:53.330 --> 00:46:57.180 And became something like a muscle cell, myoblast like. 00:46:57.180 --> 00:47:01.115 And then cells that were put onto a substrate that 00:47:01.115 --> 00:47:04.270 was between about 25 and 40 kilo pascals, 00:47:04.270 --> 00:47:07.430 they developed a shape that was something like an osteoblast, 00:47:07.430 --> 00:47:09.460 like a bone cell. 00:47:09.460 --> 00:47:11.600 So one of the things he was looking at here, 00:47:11.600 --> 00:47:13.820 was how the stiffness of the substrate 00:47:13.820 --> 00:47:16.310 affected how a stem cell might differentiate 00:47:16.310 --> 00:47:18.250 into different cell types. 00:47:18.250 --> 00:47:23.680 And another thing that he did was he looked at different cell 00:47:23.680 --> 00:47:24.790 markers. 00:47:24.790 --> 00:47:28.490 And he found that the cells were expressing 00:47:28.490 --> 00:47:33.670 markers that were corresponding to the types of tissue. 00:47:33.670 --> 00:47:35.840 So I couldn't tell you the names of all these things 00:47:35.840 --> 00:47:36.590 and what they are. 00:47:36.590 --> 00:47:39.840 But I think the red here is expressing 00:47:39.840 --> 00:47:41.220 more of a particular marker. 00:47:41.220 --> 00:47:44.470 And I think these wounds were related to nerve tissue. 00:47:44.470 --> 00:47:46.860 These wounds here, were related more to muscle tissue. 00:47:46.860 --> 00:47:49.357 And these wounds here were related more to bone tissue. 00:47:49.357 --> 00:47:51.190 So the things the cells were expressing also 00:47:51.190 --> 00:47:54.380 seemed to correspond to the different types of tissue 00:47:54.380 --> 00:47:58.680 that they were corresponding to. 00:47:58.680 --> 00:48:01.500 So I'm just going to end this part by going 00:48:01.500 --> 00:48:02.890 through a little summary here. 00:48:02.890 --> 00:48:04.390 So what I've tried to show you today 00:48:04.390 --> 00:48:07.530 is different types of cell behavior 00:48:07.530 --> 00:48:09.400 that are affected by the scaffold. 00:48:09.400 --> 00:48:11.600 And they're affected by things like the number 00:48:11.600 --> 00:48:13.670 of binding sites, by the pore size, 00:48:13.670 --> 00:48:15.640 by the stiffness of the scaffold. 00:48:15.640 --> 00:48:17.410 So we started with a cell attachment. 00:48:17.410 --> 00:48:19.900 We saw that the cell attachment increases linearly 00:48:19.900 --> 00:48:21.655 with a specific surface area. 00:48:21.655 --> 00:48:24.260 We saw that the cell morphology depends on the orientation 00:48:24.260 --> 00:48:24.880 of the pores. 00:48:24.880 --> 00:48:26.296 And that kind of makes sense, they 00:48:26.296 --> 00:48:27.830 got to line up with the pores. 00:48:27.830 --> 00:48:29.679 We talked about the contraction behaviors. 00:48:29.679 --> 00:48:31.970 So the cells bind at the periphery, the cells elongate, 00:48:31.970 --> 00:48:33.490 and that causes this buckling. 00:48:33.490 --> 00:48:35.390 And you can calculate the buckling forces. 00:48:35.390 --> 00:48:39.870 It's around 10 to 40 nano neutrons. 00:48:39.870 --> 00:48:41.890 We looked at the cell migration speed. 00:48:41.890 --> 00:48:45.170 That increases with the stiffness of 1D fibers. 00:48:45.170 --> 00:48:49.360 And we looked at cell migration in the collagen gag scaffolds. 00:48:49.360 --> 00:48:51.802 So that depends on the stiffness of the pore size. 00:48:51.802 --> 00:48:53.260 And then there was this final study 00:48:53.260 --> 00:48:55.350 on the cell differentiation. 00:48:55.350 --> 00:48:57.400 So I wasn't going to write any notes on this 00:48:57.400 --> 00:48:59.710 because the slides I think pretty much explain it. 00:48:59.710 --> 00:49:01.251 So I was just going to put the slides 00:49:01.251 --> 00:49:03.970 on the website at the end after today's lecture. 00:49:03.970 --> 00:49:06.060 So are we good with how cells and the scaffolds 00:49:06.060 --> 00:49:08.892 of the environments interact? 00:49:08.892 --> 00:49:10.350 Because I think it's not so obvious 00:49:10.350 --> 00:49:14.230 that this actual mechanical environment makes a difference. 00:49:14.230 --> 00:49:18.756 People think of the chemical, the biochemical environment. 00:49:18.756 --> 00:49:20.130 That obviously affects the cells. 00:49:20.130 --> 00:49:22.690 But people don't think at first that something 00:49:22.690 --> 00:49:27.990 like the sort of structure of the pores, the pore size, 00:49:27.990 --> 00:49:31.062 or the orientation of the pores, or the mechanical properties 00:49:31.062 --> 00:49:32.770 are going to affect how the cells behave. 00:49:32.770 --> 00:49:34.530 But in fact, they do. 00:49:34.530 --> 00:49:35.110 So that's it. 00:49:35.110 --> 00:49:37.070 And this is all various people who worked 00:49:37.070 --> 00:49:38.580 with me on these projects. 00:49:38.580 --> 00:49:40.060 So it was a lot of fun. 00:49:40.060 --> 00:49:42.060 OK. 00:49:42.060 --> 00:49:46.310 So hang on a sec here. 00:49:46.310 --> 00:49:47.272 What's this all about? 00:49:47.272 --> 00:49:48.480 I'm going to get rid of that. 00:49:48.480 --> 00:49:49.560 Go away. 00:49:49.560 --> 00:49:50.160 Here we go. 00:49:50.160 --> 00:49:50.660 OK. 00:49:50.660 --> 00:49:54.640 So are we good with cells and substrates? 00:49:54.640 --> 00:49:55.310 Yeah? 00:49:55.310 --> 00:49:57.460 OK. 00:49:57.460 --> 00:49:59.585 So let's just take a little moment 00:49:59.585 --> 00:50:00.710 and I'll rub the board off. 00:50:00.710 --> 00:50:02.168 And then we can start the next bit. 00:50:43.616 --> 00:50:44.116 OK. 00:51:10.040 --> 00:51:10.540 OK. 00:51:10.540 --> 00:51:14.560 So that's the end of the medical material stuff. 00:51:14.560 --> 00:51:16.989 So we talked about the bone. 00:51:16.989 --> 00:51:19.030 We talked about the tissue engineering scaffolds. 00:51:19.030 --> 00:51:21.840 And then we talked about the cell scaffold interactions. 00:51:21.840 --> 00:51:25.200 So now we're going to go back to more engineering topics. 00:51:25.200 --> 00:51:27.310 And the next thing I wanted to talk about 00:51:27.310 --> 00:51:29.550 was energy absorption in foams. 00:51:29.550 --> 00:51:31.980 So foams are very widely used for energy absorption 00:51:31.980 --> 00:51:34.030 applications, things like bicycle helmets, 00:51:34.030 --> 00:51:35.400 different kinds of helmets. 00:51:35.400 --> 00:51:38.300 You buy a new computer, it comes in foam packaging. 00:51:38.300 --> 00:51:40.430 And the reason foams are used so much 00:51:40.430 --> 00:51:43.660 is they're extremely good at absorbing energy from impact. 00:51:43.660 --> 00:51:45.410 And in fact, they're better than the solid 00:51:45.410 --> 00:51:46.960 that they're made from. 00:51:46.960 --> 00:51:51.670 So let's just look at this curve here for a minute. 00:51:51.670 --> 00:51:55.480 So here's a stress strain curve in compression for the foam. 00:51:55.480 --> 00:51:57.500 And the material that it's made from 00:51:57.500 --> 00:52:00.070 would have the stiffness something like this. 00:52:00.070 --> 00:52:02.450 It would be much, much stiffer than the foam. 00:52:02.450 --> 00:52:05.950 And if you think about how much energy you can absorb, 00:52:05.950 --> 00:52:08.020 the energy you can absorb is just the area 00:52:08.020 --> 00:52:09.390 under the stress/strain curve. 00:52:09.390 --> 00:52:12.280 That's the energy you can absorb in a given volume of foam. 00:52:12.280 --> 00:52:16.490 And so when you're thinking about these energy absorption 00:52:16.490 --> 00:52:18.380 problems, it's not just that you need 00:52:18.380 --> 00:52:19.640 to absorb a certain energy. 00:52:19.640 --> 00:52:22.110 You need to absorb it without exceeding a certain peak 00:52:22.110 --> 00:52:22.906 stress. 00:52:22.906 --> 00:52:25.280 So whatever it is you're trying to protect, at some point 00:52:25.280 --> 00:52:26.839 it's going to break. 00:52:26.839 --> 00:52:28.130 This is what you want to avoid. 00:52:28.130 --> 00:52:29.570 You want to avoid it breaking. 00:52:29.570 --> 00:52:31.659 So you don't want to have a stress bigger 00:52:31.659 --> 00:52:33.200 than the stress that's going to break 00:52:33.200 --> 00:52:36.540 whatever it is, your computer, or your head, or whatever. 00:52:36.540 --> 00:52:39.370 So say you have a given peak stress 00:52:39.370 --> 00:52:41.010 that you can tolerate here. 00:52:41.010 --> 00:52:43.450 And we've normalized things by the solid modules. 00:52:43.450 --> 00:52:45.730 But just say that's a peak stress here. 00:52:45.730 --> 00:52:47.910 The foam is going to absorb this amount of energy 00:52:47.910 --> 00:52:50.470 up here, this whole little shaded region. 00:52:50.470 --> 00:52:53.280 And the solid is going to absorb that little, teeny weeny bit 00:52:53.280 --> 00:52:54.160 in there. 00:52:54.160 --> 00:52:56.790 So what you want to do is absorb the energy 00:52:56.790 --> 00:52:58.970 without exceeding a certain peak stress. 00:52:58.970 --> 00:53:01.990 And the foam is always going to be better than the solid 00:53:01.990 --> 00:53:03.890 that it's made from. 00:53:03.890 --> 00:53:06.140 There's a couple other things that make the foams good 00:53:06.140 --> 00:53:09.020 because they're more or less isotropic, maybe not perfectly. 00:53:09.020 --> 00:53:11.562 But roughly, they have the same properties in all directions. 00:53:11.562 --> 00:53:13.728 Sometimes you don't know what direction the impact's 00:53:13.728 --> 00:53:14.530 going to come from. 00:53:14.530 --> 00:53:16.196 And so if you've got the same properties 00:53:16.196 --> 00:53:19.460 in all directions or roughly the same, that's a good thing. 00:53:19.460 --> 00:53:23.030 You also want the protective thing to be light. 00:53:23.030 --> 00:53:25.990 If you're paying for shipping for your computer or whatever, 00:53:25.990 --> 00:53:27.730 the fact that the packaging is light 00:53:27.730 --> 00:53:29.732 makes the shipping easier. 00:53:29.732 --> 00:53:31.190 If you have a helmet for your head, 00:53:31.190 --> 00:53:32.690 you don't want some big heavy thing. 00:53:32.690 --> 00:53:34.100 You want something fairly light. 00:53:34.100 --> 00:53:35.070 And foams are cheap. 00:53:35.070 --> 00:53:39.040 So the fact that they're roughly isotropic, they're light, 00:53:39.040 --> 00:53:42.080 they're cheap, this all helps as well. 00:53:42.080 --> 00:53:44.670 But from a mechanical point of view, 00:53:44.670 --> 00:53:47.130 foams are very good at absorbing energy. 00:53:47.130 --> 00:53:49.870 And so what we're going to do in the next-- 00:53:49.870 --> 00:53:52.530 the rest of this lecture and on Wednesday-- we're 00:53:52.530 --> 00:53:55.700 going to see how we can convert these stress/strain 00:53:55.700 --> 00:53:59.010 curves into what are called energy absorption diagrams. 00:53:59.010 --> 00:54:01.446 We're going to look at some energy absorption diagrams 00:54:01.446 --> 00:54:03.570 that we just measure from the stress/strain curves. 00:54:03.570 --> 00:54:05.530 And we're going to look at how we can predict the energy 00:54:05.530 --> 00:54:07.027 absorption diagrams as well. 00:54:09.760 --> 00:54:12.560 OK. 00:54:12.560 --> 00:54:17.950 So the main idea here is that the impact protection 00:54:17.950 --> 00:54:19.960 has to absorb the energy from the impact 00:54:19.960 --> 00:54:22.056 but without exceeding a certain peak stress. 00:55:12.300 --> 00:55:14.630 So the direction of loading may not be predictable. 00:55:24.350 --> 00:55:26.570 And foams are good because they're roughly Isotropic. 00:55:33.234 --> 00:55:35.150 And they would have the same energy absorption 00:55:35.150 --> 00:55:36.502 capacity from any direction. 00:55:45.040 --> 00:55:46.689 And foams are also light and cheap. 00:56:07.110 --> 00:56:13.840 We can say for a given peak stress the foam is always 00:56:13.840 --> 00:56:16.750 going to absorb more energy than the solid it's made from. 00:56:41.380 --> 00:56:42.920 So other things that make foams good 00:56:42.920 --> 00:56:45.567 are that they have a capacity to undergo large deformations. 00:56:59.790 --> 00:57:02.300 And they do that at roughly constant stress. 00:57:08.580 --> 00:57:10.540 So that if you look at the stress strain 00:57:10.540 --> 00:57:17.780 curve for the foam, you're going to be 00:57:17.780 --> 00:57:21.220 able to absorb all this energy under here. 00:57:21.220 --> 00:57:23.250 And these strains that the foam might go to 00:57:23.250 --> 00:57:28.210 might be 0.08 to 0.09, so huge strains on an engineering 00:57:28.210 --> 00:57:30.930 scale. 00:57:30.930 --> 00:57:34.240 And then this is your energy-- would absorb 00:57:34.240 --> 00:57:39.160 is that area under the stress/strain curve. 00:57:39.160 --> 00:57:41.716 So I wanted to say something about strain rates too. 00:57:45.340 --> 00:57:47.260 So typically we're going to be talking 00:57:47.260 --> 00:57:48.580 about problems of impact. 00:57:48.580 --> 00:57:51.080 And in impact, the strain rates are typically 00:57:51.080 --> 00:57:55.090 on the order of 10 to 100 per second, something like that. 00:57:55.090 --> 00:57:57.410 We're not going to talk about things like blast. 00:57:57.410 --> 00:57:59.229 If you have a blast loading, then you 00:57:59.229 --> 00:58:01.020 have to take inertial effects into account. 00:58:01.020 --> 00:58:02.910 And blasts involves strain rates, 00:58:02.910 --> 00:58:06.890 which are 1,000 to 10,000 per second, much, much higher. 00:58:06.890 --> 00:58:08.810 So we're going to talk about strain rates that 00:58:08.810 --> 00:58:13.530 are about 10 to 100 per second, maybe a bit more than that. 00:58:13.530 --> 00:58:16.099 And for instance, you can roughly 00:58:16.099 --> 00:58:18.140 estimate what one of these impact rates would be. 00:58:18.140 --> 00:58:20.960 So you had something that you dropped 00:58:20.960 --> 00:58:22.210 from a height of 1 meter. 00:58:28.110 --> 00:58:32.260 Then the velocity on impact is just if you just 00:58:32.260 --> 00:58:34.430 equate the potential energy with a kinetic energy. 00:58:34.430 --> 00:58:36.730 The velocity and impact is just the square root of 2gh. 00:58:36.730 --> 00:58:39.920 So g's the gravity acceleration. 00:58:39.920 --> 00:58:41.850 And h is the height. 00:58:41.850 --> 00:58:45.030 So that's the square root of 2 plus 9.81 meters 00:58:45.030 --> 00:58:48.050 per second times 1 meter. 00:58:48.050 --> 00:58:53.490 And that comes out to 4.4 meters per second. 00:58:53.490 --> 00:58:55.400 And say you had some foam packaging that 00:58:55.400 --> 00:58:57.422 was 100 millimeters thick. 00:59:02.570 --> 00:59:05.935 Then you could say roughly that the strain rate would 00:59:05.935 --> 00:59:13.160 be approximately equal to that velocity over the thickness, so 00:59:13.160 --> 00:59:19.500 4.4 per second over 0.1 meters. 00:59:19.500 --> 00:59:22.350 That' would be 44 per second. 00:59:22.350 --> 00:59:23.869 So it's somewhere in that range. 00:59:23.869 --> 00:59:26.160 Obviously, the thickness could be a little bit smaller, 00:59:26.160 --> 00:59:27.140 it could be bigger. 00:59:27.140 --> 00:59:29.050 But it's in that ballpark. 00:59:29.050 --> 00:59:31.950 And if you do tests on servo controlled instrons 00:59:31.950 --> 00:59:33.392 or you do a drop hammer test, you 00:59:33.392 --> 00:59:34.975 can get strain rates in that ballpark. 00:59:59.220 --> 00:59:59.840 OK. 00:59:59.840 --> 01:00:02.726 So we're talking about impact and not blast. 01:00:39.660 --> 01:00:41.670 OK. 01:00:41.670 --> 01:00:45.060 So most of the energy that's absorbed 01:00:45.060 --> 01:00:47.700 is really absorbed in that stress plateau. 01:00:47.700 --> 01:00:52.464 So if you think of the stress/strain curve, 01:00:52.464 --> 01:00:54.380 most of the area under the stress/strain curve 01:00:54.380 --> 01:00:58.150 comes from the area from underneath the stress plateau. 01:00:58.150 --> 01:01:00.219 So the mechanisms of absorbing the energy 01:01:00.219 --> 01:01:02.760 are going to be mechanisms that are associated with a plateau 01:01:02.760 --> 01:01:03.530 stress. 01:01:03.530 --> 01:01:06.000 So for elastomeric foams, we've got 01:01:06.000 --> 01:01:07.500 elastic buckling of the cells. 01:01:17.610 --> 01:01:21.530 And one of the advantages or disadvantages-- depending 01:01:21.530 --> 01:01:24.600 on what you want-- of this is that the deformation 01:01:24.600 --> 01:01:26.450 is recoverable and you got to have rebounds. 01:01:26.450 --> 01:01:29.380 So if you have an object and you drop it onto elastomeric foam, 01:01:29.380 --> 01:01:31.270 it's going to bounce around like that. 01:01:36.380 --> 01:01:41.913 So the elastic deformation is going to be recovered, 01:01:41.913 --> 01:01:43.246 and you're going to get rebound. 01:02:02.730 --> 01:02:05.880 If you have a foam that has a plastic yield point 01:02:05.880 --> 01:02:08.200 or is brittle, then the deformation 01:02:08.200 --> 01:02:11.177 is going to be largely from dissipating plastic work 01:02:11.177 --> 01:02:12.010 or work of fracture. 01:02:31.060 --> 01:02:34.100 And in that case, there's no rebound. 01:02:34.100 --> 01:02:36.340 But once you've loaded it, you've crushed the thing, 01:02:36.340 --> 01:02:40.070 and you've permanently deformed it, and you can't use it again. 01:02:40.070 --> 01:02:42.870 So sometimes if you ride your bicycle like I do, 01:02:42.870 --> 01:02:45.880 if you have a helmet, you should wear your bicycle helmet. 01:02:45.880 --> 01:02:48.460 If you have a problem, if you have an accident, 01:02:48.460 --> 01:02:50.192 and your helmet get smooshed, that's it. 01:02:50.192 --> 01:02:51.650 You have to throw your helmet away. 01:02:51.650 --> 01:02:52.608 You can't use it again. 01:02:52.608 --> 01:02:53.695 And this is why. 01:02:53.695 --> 01:02:55.175 [INAUDIBLE], even if it doesn't get 01:02:55.175 --> 01:02:57.300 smooshed, if you hit your head at all, [INAUDIBLE]. 01:02:57.300 --> 01:02:58.690 Exactly. 01:02:58.690 --> 01:03:00.150 [INAUDIBLE] 01:03:00.150 --> 01:03:00.650 Yeah. 01:03:00.650 --> 01:03:01.670 You need a new helmet. 01:03:01.670 --> 01:03:03.280 Yeah. 01:03:03.280 --> 01:03:04.070 Go ahead. 01:03:04.070 --> 01:03:07.741 Talk about helmets because I'm on a helmet conversion thing. 01:03:07.741 --> 01:03:08.240 Yes. 01:03:08.240 --> 01:03:09.720 You've got to wear your helmet. 01:03:09.720 --> 01:03:11.770 And you should change it every now and then. 01:03:11.770 --> 01:03:15.050 Anything else you'd like to add about bicycle helmet safety? 01:03:15.050 --> 01:03:15.950 No, absolutely. 01:03:15.950 --> 01:03:16.680 You've got to wear your helmet. 01:03:16.680 --> 01:03:18.929 So I know several people who would have had their head 01:03:18.929 --> 01:03:21.270 smooshed had they not been wearing their helmet. 01:03:21.270 --> 01:03:24.031 So you have to wear your helmet. 01:03:24.031 --> 01:03:24.530 Let's see. 01:03:24.530 --> 01:03:27.290 OK. 01:03:27.290 --> 01:03:30.230 If you think about natural cellular materials, things 01:03:30.230 --> 01:03:37.150 like wood, they often have cell walls 01:03:37.150 --> 01:03:38.330 that are fiber compensates. 01:03:38.330 --> 01:03:41.980 And you can dissipate energy by mechanisms related to the fiber 01:03:41.980 --> 01:03:45.210 nature, so by things like fiber pull out fracture. 01:04:17.594 --> 01:04:21.660 And then you can also have open cell foams with fluids. 01:04:21.660 --> 01:04:23.506 You can have fluid within the cells. 01:04:28.870 --> 01:04:34.670 And if the cells are open cells, the fluid effect 01:04:34.670 --> 01:04:36.170 is really only going to be important 01:04:36.170 --> 01:04:39.690 if the cells are extremely small or the fluid is particularly 01:04:39.690 --> 01:04:42.280 viscous, or the strain rates are very high. 01:05:09.750 --> 01:05:11.880 So in most cases, the fluid effects 01:05:11.880 --> 01:05:14.260 aren't important in open cell foams. 01:05:14.260 --> 01:05:16.520 But, for example, you could try to make an open cell 01:05:16.520 --> 01:05:19.570 foam that had more energy absorption by putting 01:05:19.570 --> 01:05:20.410 a fluid into it. 01:05:20.410 --> 01:05:22.600 So you could put glycerin into the fluid, 01:05:22.600 --> 01:05:25.262 and that would increase how much energy it would absorb. 01:05:25.262 --> 01:05:26.720 Or, you can put this honey into it. 01:05:26.720 --> 01:05:30.250 That would make it more energy absorption. 01:05:30.250 --> 01:05:38.040 And enclosed cell foams, you may have an effect 01:05:38.040 --> 01:05:39.847 of the gas within the cells. 01:05:39.847 --> 01:05:41.680 But it's really only going to be significant 01:05:41.680 --> 01:05:43.220 if you have elastimeric foams where 01:05:43.220 --> 01:05:44.860 the cell faces don't rupture. 01:05:44.860 --> 01:05:46.380 The cell faces rupture, then the gas 01:05:46.380 --> 01:05:48.310 is just going to flow out of them, 01:05:48.310 --> 01:05:50.200 and that's not going to do much. 01:07:08.640 --> 01:07:11.140 So the next step is I want to go from having 01:07:11.140 --> 01:07:13.240 the stress/strain curve that we've become very 01:07:13.240 --> 01:07:16.110 familiar with, and make something 01:07:16.110 --> 01:07:19.930 with that that is a little easier to see graphically 01:07:19.930 --> 01:07:21.842 that shows how much energy we can absorb. 01:07:21.842 --> 01:07:24.050 Remember, what I said what we're really interested in 01:07:24.050 --> 01:07:25.675 is absorbing a certain amount of energy 01:07:25.675 --> 01:07:28.760 without exceeding a certain peak stress. 01:07:28.760 --> 01:07:31.550 So what I'm going to do is plot another plot 01:07:31.550 --> 01:07:33.280 that's based on that. 01:07:33.280 --> 01:07:35.940 It's going to be the energy absorbed. 01:07:35.940 --> 01:07:38.840 So w is going to be energy absorbed per unit volume. 01:07:49.080 --> 01:07:52.235 And I'm going to plot that against the peak stress. 01:08:04.220 --> 01:08:05.360 OK. 01:08:05.360 --> 01:08:08.290 So we're going to look at three different regimes here. 01:08:08.290 --> 01:08:10.050 We're going to look at what happens 01:08:10.050 --> 01:08:13.930 in the linear elastic part, what happens in the stress plateau, 01:08:13.930 --> 01:08:16.779 and then what happens in the densification part. 01:08:16.779 --> 01:08:21.740 So let's think about the elastic regime first. 01:08:21.740 --> 01:08:25.720 And if I moved up-- say I moved up to some point 01:08:25.720 --> 01:08:29.319 right there where the little x is on the stress/strain curve. 01:08:29.319 --> 01:08:31.050 Then the amount of energy I absorbed 01:08:31.050 --> 01:08:35.580 would just be equal to this little bit here. 01:08:35.580 --> 01:08:38.920 And if I moved up, and then the peak stress would be this peak 01:08:38.920 --> 01:08:39.840 stress there. 01:08:39.840 --> 01:08:43.880 We'll call that sigma p1 and w1. 01:08:43.880 --> 01:08:48.970 And if I moved up over here, I'd be at w2. 01:08:48.970 --> 01:08:51.250 And that would be sigma p2, right? 01:08:51.250 --> 01:08:54.170 And if I know the modulus, I know what that relationship is. 01:08:54.170 --> 01:08:56.057 And I get a relationship. 01:08:56.057 --> 01:08:58.640 And these are going to be-- I'm going to do this on log scales 01:08:58.640 --> 01:08:59.140 here. 01:08:59.140 --> 01:09:03.140 There's going to be log, and that's going to be log. 01:09:03.140 --> 01:09:07.510 I'm going to get in that linear elastic regime. 01:09:07.510 --> 01:09:15.260 The energy is going to go as the peak stress squared over 2 01:09:15.260 --> 01:09:17.720 times the modulus of the foam. 01:09:17.720 --> 01:09:22.920 Remember, energy is a half stress times strain. 01:09:22.920 --> 01:09:26.550 And I can say strain is sigma p over e. 01:09:26.550 --> 01:09:30.000 So it's 1/2 sigma p squared over e. 01:09:30.000 --> 01:09:31.790 So on my log1 plot here, this is just 01:09:31.790 --> 01:09:35.260 going to be a straight line like that. 01:09:35.260 --> 01:09:37.430 And then I'm going to get to this value here. 01:09:37.430 --> 01:09:42.492 I'm going to get to my collapse stress here. 01:09:42.492 --> 01:09:44.609 So let's call that single star. 01:09:44.609 --> 01:09:49.270 And at that point, the more I go along here, 01:09:49.270 --> 01:09:51.620 every point I go along, like that, 01:09:51.620 --> 01:09:53.859 I'm going to absorb more and more energy. 01:09:53.859 --> 01:09:56.590 But the stress isn't going to go up at all. 01:09:56.590 --> 01:10:01.009 So then this thing here is going to go like that because I'm 01:10:01.009 --> 01:10:02.300 absorbing more and more energy. 01:10:02.300 --> 01:10:04.740 But the stress just stays the same. 01:10:04.740 --> 01:10:08.930 So this is good news if we want to absorb energy. 01:10:08.930 --> 01:10:11.690 And then once I get to the densification point, 01:10:11.690 --> 01:10:14.010 then it's going to do the opposite thing. 01:10:14.010 --> 01:10:17.220 As I go along here, at each increment 01:10:17.220 --> 01:10:19.180 I'm not absorbing that much more energy. 01:10:19.180 --> 01:10:21.130 But the stress is going up. 01:10:21.130 --> 01:10:25.730 So at some point it turns and starts to look like that. 01:10:25.730 --> 01:10:28.930 So this part here corresponds to linear elasticity. 01:10:31.470 --> 01:10:37.560 This bit here corresponds to the stress plateau. 01:10:37.560 --> 01:10:44.770 And this bit here corresponds to densification. 01:10:48.150 --> 01:10:51.410 And the point where I would like to be 01:10:51.410 --> 01:10:53.120 is right here, because here I'm going 01:10:53.120 --> 01:10:55.470 to absorb the most energy possible 01:10:55.470 --> 01:10:57.710 through the peak stress. 01:10:57.710 --> 01:11:01.480 So you can think of that as sort of an optimal point. 01:11:01.480 --> 01:11:08.736 And I'm going to refer to that as a shoulder 01:11:08.736 --> 01:11:10.360 because it's the shoulder between where 01:11:10.360 --> 01:11:11.955 the curve bends over again. 01:11:15.750 --> 01:11:21.460 So I've only got a couple minutes left. 01:11:21.460 --> 01:11:23.800 But let me just show you one thing 01:11:23.800 --> 01:11:26.960 and then we'll talk about this more next time. 01:11:26.960 --> 01:11:30.250 So I've just done this for one relative density. 01:11:30.250 --> 01:11:32.740 But if you look at the screen, you 01:11:32.740 --> 01:11:35.810 can imagine I would have stress/strain curves for lots 01:11:35.810 --> 01:11:37.165 of different relative densities. 01:11:37.165 --> 01:11:39.290 And let's say these are all at the same temperature 01:11:39.290 --> 01:11:41.220 and all at the same strain rate. 01:11:41.220 --> 01:11:43.860 And I could draw a curve that looks like that 01:11:43.860 --> 01:11:45.940 for each stress/strain curve. 01:11:45.940 --> 01:11:48.200 And if I did that, I'd get a family of them. 01:11:48.200 --> 01:11:50.770 So this is our energy absorbed here. 01:11:50.770 --> 01:11:53.480 I've normalized it by dividing by the solid modulus. 01:11:53.480 --> 01:11:55.360 This is our peak stress here. 01:11:55.360 --> 01:11:57.902 And I've normalized that by dividing by a solid modulus. 01:11:57.902 --> 01:12:00.110 And I've got a sort of family of these things, right? 01:12:00.110 --> 01:12:01.318 They all have the same shape. 01:12:01.318 --> 01:12:03.810 But they shift depending on the relative density. 01:12:03.810 --> 01:12:06.600 And then the thing that makes life good is 01:12:06.600 --> 01:12:10.370 that these shoulder points you can connect with a line. 01:12:10.370 --> 01:12:12.360 And you can mark off the relative density 01:12:12.360 --> 01:12:14.600 for those shoulder points on each line. 01:12:14.600 --> 01:12:16.990 And then the last step you can do 01:12:16.990 --> 01:12:19.045 is you can just plot these lines. 01:12:19.045 --> 01:12:21.170 And you can repeat this for different strain rates. 01:12:21.170 --> 01:12:24.850 So this would be a family of these guys here. 01:12:24.850 --> 01:12:27.272 There's a family of those lines at different strain rates. 01:12:27.272 --> 01:12:29.480 And then you would join up the points that correspond 01:12:29.480 --> 01:12:30.610 to each relative density. 01:12:30.610 --> 01:12:32.110 So you can make a drawing that looks 01:12:32.110 --> 01:12:37.040 like this that summarizes the most energy you can absorb 01:12:37.040 --> 01:12:39.004 for a certain peak stress for foams 01:12:39.004 --> 01:12:41.420 of different relative densities tested at different strain 01:12:41.420 --> 01:12:42.011 rates. 01:12:42.011 --> 01:12:44.510 You could do it for different temperatures if you wanted to. 01:12:44.510 --> 01:12:46.180 So next time, we'll talk about that. 01:12:46.180 --> 01:12:48.280 But I'm going to stop there for today. 01:12:48.280 --> 01:12:48.780 OK? 01:12:48.780 --> 01:12:50.520 Are we good?