Comparative Mechanical Properties and Histology of Bone 1

Transcription

1 AMER. ZOOL., 24:5-12 (1984) Comparative Mechanical Properties and Histology of Bone 1 JOHN CURREY Department of Biology, University of York, York, Y01 5DD, England SYNOPSIS. Different bone tissues differ in their amounts of porosity, mineralization, reconstruction, and preferred orientation. All these have important effects on mechanical properties. Very porous, cancellous bone is always weaker and more compliant than compact bone on a weight for weight basis, yet it occurs in places where its energyabsorbing ability, or its low density, is advantageous. Bone varies considerably in its mineralization, and such variations have quite disproportionate effects on mechanical properties. These variations can be shown to be adaptive. In particular, there must always be a compromise between stiffness and resistance to fracture; these two properties run contrary to each other. The reason for secondary remodeling is an unresolved problem, though in a few places the role of such remodeling in changing the grain of the bone is clearly mechanically adaptive. The mechanical properties of non-mammalian bone are obscure, and as the histology of such bone is often quite different from that of mammalian bone, we are no doubt in for some surprises when the mechanical properties of nonmammalian bone are discovered. INTRODUCTION Bone material can vary in a number of ways that have important effects on its mechanical properties. Some of this variation is adaptive. Some, as far as we can tell, is not. I intend to show what this variation is, and how it is, or is not adaptive. There are four variables of importance whose effects are not impossibly difficult to quantify, though they do tend to be correlated with each other, and this produces problems. They are: a) Porosity b) Mineralization c) Reconstruction d) Orientation I shall first show the magnitude of their effects, and then discuss the adaptive or otherwise reasons for them. Porosity No bone is completely solid except, perhaps, that of some teleost fish which contains neither bone cells nor blood channels. However, compact bone does not often have more than a few percent of porosity, the cavities being those for blood cells, their 1 From the Symposium on Biomechanics presented at the Annual Meeting of the American Society of Zoologists, December 1982, at Louisville, Kentucky. canaliculi, blood channels, and erosion spaces. On the other hand, cancellous bone can have all degrees of porosity, from being effectively absent to being effectively compact bone. It is noticeable, however, that there is usually a fairly clear morphological distinction between compact and cancellous bone the one does not usually grade into the other. There have been many studies of cancellous bone, but the important ones here are those of Carter and his associates (Carter and Hayes, 1976, 1977; Carter et al, 1980). They have shown that over a wide range of values Young's modulus oc p i t and strength oc p 2, where p is the bulk density, that is the density with the spaces between the boney struts being counted as part of the volume but not adding the mass. This relationship holds for both tension and compression. The variation in values of p are such that there are very great variations in the values of strength and Young's modulus. Carter and Hayes (1977) found compressive strength varying between 2 and 200 MPa, and Young's modulus between 20 and 20,000 MPa. Cancellous bone is such an obvious feature of most bones that such wide variation in mechanical properties must be explained. It is interesting that theoretical and experimentally determined values in foams with interconnecting cavities, which is what in effect cancellous bone is, show that both

2 JOHN CURREY 40r o 30 whale bulla L tortoise crocodile//' /deer antler Ash(%) 80 FIG. 1. Relationship between Young's modulus and the ash content of different types of bone. The continuous lines enclose individual points, which are not shown. strength and modulus should follow a squared power relationship to density (Gibson and Ashby, 1982). Mineralization Although the variation in mineralization of bone is not as great as that of porosity, the mechanical effects are nearly as profound. Figure 1 shows variation of Young's modulus of elasticity of compact bone with the amount of mineralization, as determined by ashing. It must be admitted that the lower values for mineralization or ash, below about 50%, probably have some cross-talk from porosity as in these bones the vascular channels are rather large. Figure 2 shows the relationship between Young's modulus and bending strength. Figure 3 shows the relationship between the three important mechanical variables, and includes the very highly mineralized whale tympanic bulla. Young's modulus increases monotonically with mineral, as we have seen, and bending strength increases with Young's modulus except for Young's modulus (GPa) FIG. 2. Relationship between bending strength and Young's modulus. These points represent specimens of deer's antler, cow's femur, Galapagos tortoise's femur and crocodile's nasal. the values of highest Young's modulus. Work of fracture, which is a measure of the toughness of bone, rises to a maximum at about 59% mineral (Fig. 4), and then falls rapidly. Note that the range of mineralization over which great changes in mechanical properties take place is quite small; a ninefold increase in modulus takes place as the mineralization increases from 48% to 71%. frachre looojnt 2, FIG. 3. Relationship between three mechanical properties. It is not possible to test both work of fracture and bending strength of the same specimen. Therefore these values were taken from specimens close to each other in the bone, which also barely differed in their Young's modulus. The letter in the circle denotes the species, w: Fin whale bulla; b: Cow's femur; t: Galapagos tortoise femur; m: Muntjac deer antler; d: Red deer antler; c: Crocodile nasal.

3 MECHANICAL PROPERTIES OF BONE O CO Young's modulus (GPa) FIG. 4. Relationship between work of fracture and Young's modulus. Points represent the same range of species as in Figure 2. Reconstruction Compact bone, particularly that of mammals, often undergoes internal reconstruction, leading to the formation of secondary osteons, another name for which is Haversian systems. The effect of this on mechanical properties is nothing like as important as that of the previously discussed variables. What is interesting about reconstruction is that it seems to be mechanically deleterious (Currey, 1959, 1975; Reilly and Burstein, 1975; Carter and Hayes, 1976; Saha, 1982). This is true of properties measured under both static and dynamic loading, and of toughness. Completely primary, unreconstructed bone, is about one and a half times as strong as reconstructed bone. The effect on Young's modulus is rather small. Orientation Some bone is extremely anisotropic. Table 1, derived from Reilly and Burstein's work, shows this for mammalian compact bone. Particularly striking is the work done in fracturing a specimen in tension. This seven- to tenfold reduction is produced both by a reduction in the stress at fracture and also by a great reduction in strain at fracture. Specimens loaded in a direction at right angles to the long axis to the bone are very brittle. Many of the variations seen in bone are, of course adaptive. I shall consider the adaptive differences first, leaving until later the more awkward cases of apparantly unadaptive features. POROUS BONE Cancellous bone is very porous bone, and is fairly easy to explain. In mammals' and birds' skeletons, cancellous bone is found mainly in three characteristic places: (a) under the articulations in synovial joints; (b) all through the length of bones that are short relative to their length (such as wrist bones and vertebral centra); (c) in flat bones which are much longer in two dimensions than in the third (such as the bones of the pelvis, and the scapula). An important point to get clear is that although a block of cancellous bone is lighter than a block of compact bone it usually requires a greater mass of cancellous bone to produce a particular stiffness or strength. For instance, consider compressive strength. If a piece of bone is required to carry a compressive load of P newtons over a short distance L (a short distance avoids the complications of buck- TABLE 1. Anisotropy of the mechanical properties of compact bone ' Species Histology: Direction of loading relative to grain Young's modulus/gpa Tensile strength/mpa Ultimate tensile strain Yield tensile strain Work to fracture (arbitrary units) Derived from Reilly and Burstein (1975). Parallel Man Haversian Normal Parallel Cow Fibrolamellar Normal

4 8 JOHN CURREY ling), the cross sectional area of the bone required will be P/S where S is the compressive strength. The total mass will be plp/s Now as we saw above S oc p 2 Therefore mass is proportional to LP/p; as L and P are fixed Mass is proportional to 1/p Therefore the mass required is inversely proportional to the density, so if mass is to be minimized, density should be maximized. It can be shown that for various loading systems, and possible failure modes, cancellous bone is never superior to compact bone, and is usually inferior, on a mechanical property per mass basis. The situation is even worse if the mass of mechanically useless fat in the interstices of the cancellous bone is taken into account. If all this is so, then at first sight it seems strange that cancellous bone should be adaptive, yet it is a frequent constituent of bones. I think that the mechanical function of cancellous bone is rather different in the three kinds of places in which it is found. Cancellous bone under synovial joints The bone forming half of a synovial joint has a thin layer of cartilage overlying a very thin layer of subchondral bone. Beneath this are struts of cancellous bone leading the loads from the often expanded ends of the bone to the compact bone of the shaft. If the compact cortical bone were merely continued round under the cartilage, and there were no cancellous bone underlying it, it would be carrying the load in bending, and would therefore have to be quite thick if the contours of the joint surface were not to distort under load. But, if the bone were thick, there would be a different difficulty. Synovial cartilage is weak and very compliant. If the cartilage were sandwiched between two layers of rigid bone, then when the joint was loaded in impact during locomotion the energy distribution would be such that the cartilage would be squashed. Cancellous bone, being much more compliant, will absorb much of the energy of the impact, and so spare the cartilage, yet will also deform as a whole, and keep the shape of the end of the bone fairly constant, so allowing the correct amount of congruity between the surfaces. This solution is also slightly lighter than a structure made of solid bone. Short wide bones Bones like vertebral centra and wrist bones often consist of a thin shell of compact bone surrounding the cancellous bone which stretches right along the length of the bone. The design criterion to be met here is that loads must be transmitted over the length of the bone. There must, presumably, be some limit to the distortion allowed, and the structure should be as light as possible. One solution to satisfy these criteria would be a box. (Assume, initially, that the side walls are rigid, and distortion comes from flexure of the end walls, the "lid.") Another solution would be an entirely cancellous bone. Clearly, the wider the bone the more a box lid will deflect for a given load because it is being loaded over a greater span, so the deflection as a proportion of the length of the bone will be greater. So, if the deflection is to be kept to some particular value, the lid of the box must become thicker and thicker as the bone gets wider. The cancellous bone, on the other hand, is not affected by the width, each part of the cross section bearing its own share of the load, and deflecting accordingly. Figure 5 shows the results of calculations. It shows that, for a particular set of reasonable constraints the cancellous bone solution is lighter than the box solution when the ratif breadth to depth is 1.5. This is at least in the region in which we do see one solution changing over to another, though the point of changeover comes when the bones are somewhat too flat. If we allowed the sidewalls of the box solution to deflect, then the changeover would approach even more closely the situation found in real bones. Sandwich bones Bones such as the ilium are classical sandwich structures. Two sheets of compact bone are separated by a cancellous filling. The cortices bear the bending load; one is in tension, the other in compression. The

5 MECHANICAL PROPERTIES OF BONE to to S.8h.05 Breadth/Length FIG. 5. Comparison of the box solution and the cancellous bone solution. A cylindrical bone is loaded with a uniform stress on twpposite faces. The solid lines show the relative mass of the box solution having the same maximum deflection as the cancellous bone solution, whose mass is taken as unity. The sidewalls are considered completely stiff. The lower curve assumes the lid fixed firmly to the sidewalls; the upper curve assumes the lid is simply supported by the sidewalls. The pictures at the ends of the wavy lines show the appearance of half the bone, the marrow cavity being represented by dots. filling keeps the cortices apart, so ensuring that the second moment of area remains large, and preventing the cortices from buckling. The filling also has to bear some shear stresses. Again it is possible, by making some simplifying assumptions, to calculate the relative masses of various solutions to this problem. The results are shown in Figure 6. There are two variables; the proportion of the depth occupied by cancellous bone, and the density (or porosity) of the cancellous bone. (In the previous section the density of the cancellous bone was uniquely determined by the allowable strain.) There is again some, though not spectacular, saving in mass by adopting a sandwich construction, and the total proportion of the depth occupied by cancellous bone does agree quite well with what is found in mammals generally. In both the sandwich bone and the short bone, the potential saving in mass would be much greater if there were no mechanically useless fat to add to the mass of the cancellous bone Cancellous proportion of depth FIG. 6. Weight of sandwich bone relative to a solid plate of the same stiffness. Abscissa: proportion of the depth of the sandwich occupied by cancellous bone. Dotted lines: assuming no marrow; continuous lines: assuming marrow present. The numbers on the lines refer to the porosity. (A porosity of unity means that the cancellous bone is absent, and the sandwich has no filling except marrow.) Minimum weight frameworks So far I have talked about cancellous bone merely as a uniform lump that obeyed two power laws: strength oc p 2, Young's modulus <x p 3. In fact it is often obviously exquisitely adapted to the stresses falling on it. It is possible to generate, mathematically, so-called minimum weight frameworks which are, as the name suggests, frameworks that will bear a particular load with the minimum weight possible. Figure 7 shows a minimum weight cantilever, and a cross section of the ilium of a horse. The correspondence of the two structures is seductive, and shows that the reconstruction mechanism in cancellous bone is accurately responsive to the stresses falling on the bones. (Proving that this is so is, in fact, rather difficult.) MINERALIZATION The compact bone of mammals shows a great range of mechanical properties, and these seem to be produced mainly by dif-

6 10 JOHN CURREY Fie. 7. Above: a mathematically generated minimum weight cantilever, supported at A and B, and loaded at its free end at C. The continuous lines represent parts of the framework loaded in compression, the interrupted lines those parts loaded in tension. Below: cross section of part of the ilium of a horse. This is a flat plate sandwich structure. The main part of the pelvis is around B. The ilium is loaded by adductor muscles near its free end A. ferences in mineralization. The most heavily mineralized bone I know is the tympanic bulla of the whale. This has a high modulus of elasticity (31 GPa) and a derisible work of fracture and bending strength. However the high modulus is adaptive, because it increases the input impedance of the otic bone, and prevents the sound from reaching the inner ear except via the tympanic membrane. Isolating the ear is very important for marine mammals because the body in water is almost transparent to sound and the usual cues for locating the direction of sound are therefore vague (Currey, 1979). The mineralization of the antlers of deer is rather variable, ranging from quite low values in some specimens of red deer to values in muntjac nearly as high as those in cow's femora. The monotonic increase shown in the relationship between Young's modulus and mineralization is not shown by the bending strength or work of fracture. It would be fascinating to know what bending strengths bone could achieve with somewhat higher values of mineralization than the most highly mineralized cow bones shown here. Unfortunately, there are no natural experiments intermediate between the cow's bone and the bulla to tell us. The bulla has given up the struggle to be strong, in the pursuit of stiffness. The adaptive reason for the upper limit on bending strength is that, at the highest strength, the toughness as shown by the work of fracture is declining rapidly. Natural selection has balanced the competing needs for stiffness and strength, which go together, with that for toughness. The balance achieved is different in the cow and in the red deer. For the deer the more important feature is the resistance to impact, because the antler is used in fighting, and the toughness can achieve very high values. For the cow's femur, locomotory efficiency is needed, and therefore stiffness becomes relatively more important. The red deer antler shows considerable variation in all four of the properties we measured, and indeed some values for work of fracture are quite low. These different properties seem to vary regionally over the antler, and I am not yet sure of the significance of this variation. The muntjac antler is not used seriously for fighting (Chapman, 1981) and its properties are intermediate between those of red deer and cow bone, but the work of fracture is not as high as one would expect from a bone with such a relatively low Young's modulus. Finally, the bone with the consistently highest values for work of fracture was the femur of the Galapagos Tortoise Geochelone elephantopus. The mineralization was at the upper end of the range seen in red deer. Unfortunately, we have essentially no data about the mechanical properties of reptile bone, so we do not know whether the Galapagos Tortoise is typical of reptiles, or whether reptiles show a similar range of values to that of mammals. Whether the high work of fracture of the tortoise, with the corresponding low value of Young's modulus, is adaptive is difficult to say. Tortoises are not notable for fast locomotion, but Galapagos Tortoises are notoriously clumsy. For a very long-lived

7 animal, the selection pressures on not breaking a bone may be considerable. HISTOLOGY, RECONSTRUCTION, AND ANISOTROPY MECHANICAL PROPERTIES OF BONE 11 There is a great range of histological types of bone, but we know extremely little about the mechanical properties of the different types. We do know in mammalian bone that the Haversian bone, which replaces by reconstruction the primary fibrolamellar bone is weaker and less stiff than the primary bone. It is not really clear why this should be so, indeed what we know of fracture processes in bone might make us guess that Haversian bone would be stronger than primary bone, because it looks, superficially anyhow, more like a composite material. Probably its weakness has to do with the insertion of tubes of bone of lower Young's modulus in pre-existing bone. What is interesting about Haversian bone is why it should form at all. Various reasons have been produced, from a need to take calcium from the bone to the need to prevent the bone from becoming over-mineralized. All these non-mechanical explanations would seem to fall down because of peculiar distribution of Haversian remodelling. For instance, why should a homeostatic mechanism, involving a reduction in strength of the bone, proceed with great vigor in healthy young Americans, who can rarely be short of calcium in their diet, yet be absent in the bones of small wild rodents who must often undergo great fluctuations in calcium intake? The mechanical explanations would not seem to fare much better. Secondary remodeling takes place more vigorously towards the marrow cavity than towards the subperiosteal side, yet the greatest stresses, and therefore the greatest likelihood of microfracture, will be near the subperiosteal surface. Also, as shown in Figure 8, Haversian remodeling occurs remarkably symmetrically in paired bones, rather as if a program of reconstruction were being carried out. It stretches the imagination to think that these symmetrically arranged reconstruction events are FIG. 8. Paired sections of a tibia of a cat, to show symmetry of remodeling. Fine stippling: Haversian bone; plain: Primary bone; black splodges: Haversian systems actively forming. taking out symmetrically placed microfractures. One instance in which remodeling may be mechanically adaptive is when Haversian remodelling occurs when the grain of the bone is changed. Both primary bone and Haversian bone are very anisotropic (Table 1). Bones can grow only by accretion, and therefore bone that was originally well-oriented can be found in a position where it is loaded at a large angle to its grain, which makes it weak. This is particularly likely tccur under muscle insertions and here, indeed, Haversian remodeling is very common. Remodeling also occurs actively in compact coarse-cancellous bone. This is bone produced by the filling in of cancellous bone that was originally at the ends of long bones, but which becomes incorporated into the main shaft during growth. Compact coarse-cancellous bone has a low bending strength, is rather compliant, and has a low work of fracture. This weakness must be caused by the almost random distribution of the grain of the bone. The replacement of this jumble of fossilized trabeculae by adaptively oriented Haversian systems, which themselves are weaker than a neatly produced fibrolamellar bone is a classic case of making the best of a bad job. Biewener (1982) has shown that the bone of small mammals, of body mass in the region 0.1 to 1 kg, has bending strengths very similar to that of cows and humans.

8 12 JOHN CURREY It may well be that the other mechanical properties will be similar too. At the moment we are almost totally ignorant of the mechanical properties of non-mammalian bone. There are good indications that at least some birds' bones are similar mechanically to mammalian bones (Biewener, 1982), but good information about the reptiles and anamniotes is lacking. The histology of these bones is often rather different from that of mammals and birds. For instance, the bone of Geochelone, with its very high work of fracture, seems mainly to consist of compact coarse cancellous bone, which in mammals has a rather low work of fracture. Much reptile bone consists of very fine textured circumferential lamellae; most teleost fish have acellular bone, and sn. When the mechanical properties of these bony types are determined we shall probably be in for some surprises. However, I would be very surprised if it were not possible, in the end, to show that the mechanical properties, and the histology that produces them, are mainly determined by the selective balance between stiffness, and resistance to fracture. These two properties are both important, yet require contrary design features in the bone material. REFERENCES Biewener, A. A Bone strength in small mammals and bipedal birds: Do safety factors change with body size?j. Exp. Biol. 98: Carter, D. R. and W. C. Hayes Bone compressive strength: The influence of density and strain rate. Science, N.Y. 194: Carter, D. R. and W. C. Hayes The compressive behaviour of bone as a two-phase porous structure. J. Bonejt. Surg. 59-A: Carter, D. R., G. H. Schwab, and D. M. Spengler Tensile fracture of cancellous bone. Acta Onhop. Scand. 51: Chapman, D. I Antler structure and function a hypothesis. J. Biomech. 14: Currey.J.D Differences in the tensile strength of bone of different histological types. J. Anat. 93: Currey, J. D The effect of strain rate, reconstruction and mineral content on some mechanical properties of bovine bone. J. Biomech. 8: Currey.J.D Mechanical properties of bone tissues with greatly differing functions. J. Biomech. 12: Gibson, L. J. and M. F. Ashby The mechanics of three-dimensional cellular materials. Proc. R. Soc. A 382: Reilly, D. T. and A. H. Burstein The elastic and ultimate properties of compact bone tissue. J. Biomech. 8: Saha, S The dynamic strength of bone and its relevance. In D. N. Ghista (ed.), Osteoarthromechanks, pp McGraw-Hill, New York.