This is a comprehensive and accessible overview of what is known about the structure and mechanics of bone, bones, and teeth. In it, John Currey incorporates critical new concepts and findings from the two decades of research since the publication of his highly regarded The Mechanical Adaptations of Bones. Crucially, Currey shows how bone structure and bone's mechanical properties are intimately bound up with each other and how the mechanical properties of the material interact with the structure of whole bones to produce an adapted structure.
For bone tissue, the book discusses stiffness, strength, viscoelasticity, fatigue, and fracture mechanics properties. For whole bones, subjects dealt with include buckling, the optimum hollowness of long bones, impact fracture, and properties of cancellous bone. The effects of mineralization on stiffness and toughness and the role of microcracking in the fracture process receive particular attention. As a zoologist, Currey views bone and bones as solutions to the design problems that vertebrates have faced during their evolution and throughout the book considers what bones have been adapted to do. He covers the full range of bones and bony tissues, as well as dentin and enamel, and uses both human and non-human examples.
Copiously illustrated, engagingly written, and assuming little in the way of prior knowledge or mathematical background, Bones is both an ideal introduction to the field and also a reference sure to be frequently consulted by practicing researchers.
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BonesStructure and Mechanics
By John D. Currey
Princeton University PressCopyright © 2002 Princeton University Press
All right reserved.
Chapter OneTHE STRUCTURE OF BONE TISSUE
THROUGHOUT this book I shall be suggesting that the structure of bone tissue, and of whole bones, makes sense only if its function, particularly its mechanical function, is known or guessed. (As Rik Huiskes of Eindhoven is fond of saying : "If bone is the answer, then what is the question?") However, in this first chapter I shall deal only with the structure of bone, leaving almost all discussion of function until later. Of course, the mechanical properties of bone and bones are determined by their structure, and we cannot begin to understand the function without having a good idea of the structure. Much of the subject matter will be familiar to some readers, but not all to everyone. Indeed, some readers may be coming to bone for the first time, from say materials science, so I shall start with a single paragraph overview of bone structure.
Bone of present-day mammals and birds is a stiff skeletal material made principally of the fibrous protein collagen, impregnated with a mineral closely resembling calcium phosphate. Bone also contains water, which is very important mechanically. Bone is produced inside the body and is usually covered with cells throughout life,though in fish scales, for instance, the external lining of cells may be rubbed off. Most bone not only is covered by cells but has living cells and blood vessels within it. Bone, being hard, cannot swell or shrink; all changes in shape must take place at surfaces. Most bones are hollow and contain hema-topoietic or fatty marrow. Marrow probably has little mechanical significance. Tendons and ligaments insert into the bone substance, and the ends of bones are often covered by a thin layer of cartilage for lubrication. Some tissues, such as antler and dentin, are not called bone but are actually bone, or extremely like it. Horn, such as is found in cattle, is a completely different material, usually unmineralized, though the horn core, which supports the horn, is made of bone.
To start straight off talking about the structure of bone begs the question. It is not really at all clear what bone is. Consideration of a present-day mammal or bird would allow a clear distinction to be made, because bone is the only structure that is essentially collagen mineralized with calcium phosphate and containing cell bodies, though in antler bone the cells are all dead by the time the antler comes to be used. Dentin is collagen mineralized with calcium phosphate but it does not contain cell bodies, only tubular extensions of cells. The other significant tissue mineralized with calcium phosphate (as opposed to calcium carbonate) is enamel, and this is very different in that it has virtually no cells or cell processes or, indeed, much organic matrix. However, as soon as one looks outside the mammals and birds the situation becomes much more complex. Bone is found only in vertebrates. Many teleost fish have bone without bone cells, and the range of structures seen in scales of different fish species forms an almost complete spectrum from what is obviously "typical" bone or "'typical" dentin to what is obviously "typical" enamel. This situation is often found in biology, since nature is concerned not with categorization, but with producing effective results. (The great evolutionary biologist John Maynard Smith likes saying that "all biology is false," meaning, of course, that there are very few absolutes in biology.)
For the purposes of this book, the fact that there are so many different types of scales does not matter greatly because virtually nothing is known about the mechanical properties of scales. I shall be concerned almost entirely with the mechanics of typical bone, as found in mammals, but I shall devote some space to tissues such as dentin. Antler, which is dead when functioning, will figure prominently. A good account of the variation of structure in vertebrates is found in Francillon-Vieillot et al. (1990), which, though not an enthralling read, is very clear, comprehensive, and well illustrated.
Even "typical" bone is such a complex structure that there is no level of organization at which one can truly be said to be looking at bone as such. I shall start at the lowest level and work up to a brief description of the variety of shapes one sees in whole bones.
1.1 BONE AT THE MOLECULAR LEVEL
At the lowest level bone can be considered to be a composite material consisting of a fibrous protein, collagen, stiffened by an extremely dense filling and surrounding of calcium phosphate crystals. There are other constituents, notably water, some ill-understood proteins and polysac-charides, and, in many types of bone, living cells and blood vessels. The amount of water present in bone is an important determinant of its mechanical behavior, and I shall say more about it in chapter 4.
A word about terminology. In this book I use the word matrix to mean the water and the soft organic material, mostly collagen, in which the mineral crystals are deposited. This accords with what materials scientists would consider to be the matrix (though some might consider the mineral to be the matrix). However, bone biologists, who are focused almost entirely on the cells of bone, use the word matrix to mean the bone tissue itself, that is, the water, the organic material, and the mineral. There is no way round this possible source of confusion; one simply has to be aware of it.
Collagen is a structural protein found in probably all metazoan animal phyla. It is the most abundant protein found in animals, but only in the vertebrates does it undergo a wholehearted transformation into a mineralized skeletal structure, although some soft corals have traveled some way along the road. A classified bibliography of more than 3400 references to collagen, comprehensive up to that time, is given in Kadler (1994).
Unmineralized collagen is also found in the vertebrates, and in many invertebrates, in skin, tendon, ligament, blood vessel walls, cartilage, basement membrane, and in connective tissue generally, in those circumstances where the material is required to be flexible but not very extensible. Collagen makes up more than half the protein in the human body (Miller 1984). Collagen from different sites often has different amino acid compositions; in the mid 1990s 19 types of collagen were known throughout the animal kingdom, and the known number increases relentlessly (Prockop and Kivirikko 1995). The collagens of skin, tendon, dentin, and bone share the same type of composition, and are called type 1 collagen. The protein molecule tropocollagen, which aggregates to form the microfibrils of collagen, consists of three poly-peptides of the same length-two have the same amino acid composition, one a different one. These form on ribosomes, are connected by means of disulfide cysteine links, and leave the cell. Outside the cell the ends of the joined polypeptides are snipped off, the lost part containing the disulfide bonds. The three chains are by now held together by hydrogen bonds in a characteristic left-handed triple helix.
The primary structure of the polypeptides in the tropocollagen molecule is unusual, great stretches of it being repeats of glycine-X-Y, with X often being proline and Y sometimes hydroxyproline. The imino acids proline and hydroxyproline are unlike amino acids in that the nitrogen atom is included in the side chain as part of a five-membered ring. The effect of this is to reduce the amount of rotation possible between units of the polypeptide. It also prevents a-helix formation and limits hydrogen-bond formation. These constraints result in a rather inflexible polypeptide, 300 nm long (Olsen and Ninomiya 1993).
The tropocollagen molecules line up in files and bond, not with molecules in the same file, but with molecules in neighboring files, to form microfibrils. The tropocollagen molecules alongside each other are staggered by about one-fourth of their length. There is a gap between the head of one molecule and the tail of the next in the file, the hole region, and, because many tropocollagen molecules are stacked side by side, these gaps and other features of the molecules produce a characteristic periodicity, 67 nm long. The whole microfibril becomes stabilized by intermolecular cross-links. Microfibrils aggregate to form fibrils. Although the longitudinal arrangement of the tropocollagen molecules in the microfibrils is fairly well understood, the way in which the micro-fibrils themselves are arranged laterally to form fibrils is much less well understood. A clear introduction to the subject is provided by Prockop and Fertala (1998). Hulmes et al. (1995) produce evidence that the fibrils are arranged in concentric rings. Wess et al. (1998a,b) produce a rather different model that they claim will explain the way in which mineral is able to pack in bone. This is a difficult subject, with the majority view changing often as experimentation becomes ever more sophisticated. It could well be that when a stable view is formed the results will be useful in helping to model the mechanical behavior of bone, but at the moment this is not really the case.
Collagen comprises about 85 to 90% of the protein in bone. The proteins that are not collagen are called, negatively, noncollagenous proteins (NCPs). The literature on them is vast and expanding rapidly (Ganss et al. 1999; Gerstenfield 1999; Gorski 1998; Nanci 1999). Some NCPs are restricted to bone, and some are also found in other places in the body. Some of these proteins almost certainly have a role in the initiation and control of mineralization or reconstruction, and some may have a role in binding the collagen and mineral together (Roach 1994). However, we are almost completely in the dark at the moment about any quantitative effect NCPs may have on the mechanical properties of bone.
Impregnating and surrounding the collagen is the bone mineral, which is some variety of calcium phosphate. The precise nature of the mineral of bone, both its chemistry and its morphology, is still a matter of some dispute. The problem is that the mineral in bone comes in very small crystals that have a very high surface-area-to-volume ratio. The size of the crystal is such that in one dimension it is only about 10 atomic layers thick (Lowenstam and Weiner 1989). This makes it reactive, and so most preparative techniques used for investigating it, such as, drying under vacuum for electron microscopy, may cause alterations from the living state. There is agreement that some of the bone mineral is the version of calcium phosphate called hydroxyapatite, whose unit cell (the smallest part of a crystal that is repeated uniformly throughout a crystal) contains [Ca.sub.10][(P[O.sub.4]).sub.6][(OH).sub.2]. The crystals are impure. In particular, there is about 4-6% of carbonate replacing the phosphate groups, making the mineral more truly a carbonate apatite (dahllite). This carbonate substitution takes place more near edges of the bone, close to vascular and marrow spaces and tends to reduce the crystallinity of the crystals (Ou-Yang et al. 2001). Various other substitutions may take place (Boyde and Jones 1998; McConnell 1962).
At the moment, we are ignorant of the mechanical properties of the mineral itself, and all modeling, such as that of Wagner and Weiner (1992) and Sasaki et al. (1991), which I discuss in section 3.7, makes use of somewhat insecurely based (though not necessarily far wrong!) estimates. The mineral is certainly stiff, but its strength, in such small blocks, is unknown.
The positioning of the mineral relative to the collagen fibrils, as well as its shape, is becoming clearer, though there is still controversy. There is some argument as to whether the crystalline mineral, which can be seen in electron micrographs, is needle-shaped or plate-shaped. Ascenzi et al. (1978) claimed that the mineralization process starts off with small granules, about 4.5 nm across, which coalesce or grow into needles about 40 nm long. However, the observations of Landis and his coworkers make it almost certain that in mineralized tendon (Landis et al. 1993) and in embryonic chick bone (Landis et al. 1996) the crystals are platelet-shaped. They have used the technique of taking multiple views of bone using high-voltage electron microscopy to produce a tomo-graphic image. This method shows very clearly the three-dimensional shape of the crystals and to some extent their spatial relationship to the collagen (fig. 1.1). These visualizations show that the crystals' thickness is rather unvarying at about 4-6 nm, their width is about 30-45 nm, and their length is typically 100 nm. Later, these mineral platelets seem to fuse sideways, and lengthways, producing at times sword-shaped blades that are quite long and broad. However, they do not seem to grow in the depth direction, remaining about 5 nm deep. Erts et al. (1994), using scanning probe microscopy, found similar values for turkey tendon.
Reports of the visualization of the crystals directly overwhelmingly supports this view that the crystals in all bone examined are platelet-shaped. Weiner and Price (1986) examined the size of bone mineral crystals, extracting them from the bone by a gentle procedure, and proposed values of about 50 x 20 x 2 nm. Kim et al. (1995) report platelet-shaped crystals from tissues of a taxonomically satisfyingly varied group of species: chickens, bovines, mice, and herring. The average length and breadth, in nanometers, for the four species are given in Table 1.1. Kim et al. did not measure the thickness, but suggested it was about 2 nm. Ziv and Weiner (1994) suggest that most estimates of the size of crystals are underestimates, because the plates are so fragile, and that crystals may be often hundreds of nanometers long in untreated bone.
Fratzl et al. (1992) have produced indirect evidence, using small-angle X-ray scattering, that the crystals in ossified tendon are indeed platelet-shaped but that in ordinary compact bone they are more likely to be needle-shaped. On the other hand, Wachtel and Weiner (1994) show that the small-angle X-ray scattering picture from crystals from rat bone is very similar to that from mineralizing turkey tendon, and suggest that it is probably reasonably safe to generalize about the crystal morphology from mineralizing turkey tendon.
More contentious is where the mineral is in relation to the collagen fibrils. For years, following a suggestion by Hodge and Petruska (1963), it was thought that the mineral is initially deposited in the holes between the heads and the tails of the tropocollagen molecules (the gap zones). This results in the initial mineralization having a 67-nm periodicity (Berthet-Colominas et al. 1979). Many studies seemed to confirm this, but nearly all were carried out on mineralizing turkey leg tendon, which, although very convenient to study because the collagen fibrils are so well arranged, is not typical bone, particularly in relation to the arrangement of the crystals (Wenk and Heidelbach 1999). It is probable that in some way the particular conformation of the collagen molecule allows it to act as a nucleation site, permitting the precipitation of lumps of mineral that, without the presence of the energetically favorable sites, could not come out of solution. There is some evidence that the mineral deposits preferentially in parts of the fibril that are high in hydrophilic residues (Maitland and Arsenault 1991). Later, the mineral is deposited all over the collagen fibrils, and also within them. Weiner and Traub (1986) have published stereopairs of mineralizing turkey leg tendon, showing how the crystals lie within the fibers. Landis et al. (1993, 1996) show similar pictures (fig. 1.1), and point out that the individual platelets seem to remain separated by a space in the depth direction of about 5 nm. This would, of course, allow collagen micro-fibrils to exist between the platelets. Jager and Fratzl (2000) suggest, though with no observations to back the suggestion up, that the crystals may be arranged circumferentially round the center of the fibril. This would accord with the radial fibril model of Hulmes et al. (1995).
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Table of ContentsPreface to the Second Edition xi
Preface to the First Edition xiii
CHAPTER ONE: The Structure of Bone Tissue 3
1.1 Bone at the Molecular Level 4
1.2 The Cells of Bone 11
1.3 Woven and Lamellar Bone 12
1.4 Fibrolamellar and Haversian Bone 14
1.5 Primary and Secondary Bone 20
1.6 Compact and Cancellous Bone 21
1.7 A Summary of Mammalian Bone Structure 24
1.8 Nonmammalian Bone 25
CHAPTER TWO: The Mechanical Properties of Materials 27
2.1 What Is Bone For? 27
2.2 Mechanical Properties of Stiff Materials 28
2.2.1 Stress, Strain, and Their Relationship 29
2.2.2 Anisotropy 37
2.2.3 Viscoelasticity 40
2.2.4 Modes of Loading 41
2.2.5 Fracture and Toughness 42
2.2.6 Fracture Mechanics 49
2.2.7 Creep Rupture 51
2.2.8 Fatigue Fracture 51
CHAPTER THREE: The Mechanical Properties of Bone 54
3.1 Elastic Properties 54
3.1.1 Orientation Effects 55
3.1.2 Strain Rate Effects 57
3.2 Strength 58
3.2.1 Orientation Effects 60
3.2.2 Strain Rate Effects 61
3.2.3 Modes of Loading 62
3.3 Inferring Bone Material Properties from Whole Bone
3.4 Fracture Mechanics Properties 64
3.5 Creep Rupture 67
3.6 Fatigue Fracture 69
3.7 Modeling and Explaining Elastic Behavior 74
3.8 Modeling Fracture in Tension 82
3.8.1 The Effects of Stress Concentrations 82
3.8.2 The Effects of Remodeling 86
3.8.3 Anisotropy in Fracture 88
3.9 Fracture of Bone in Compression 91
3.10 Fracture of Bone in Bending 93
3.11 Mechanical Properties of Haversian Systems 99
3.12 Cancellous Bone 104
3.13 Bone as a Composite 104
3.14 Microdamage 110
3.14.1 Microcracking Phenomena 110
3.14.2 The Mechanical Effects of Microcracking 112
3.15 Strain Rate, Creep, and Fatigue: Pulling the Threads
3.16 Fracture in Bone: Conclusions 122
CHAPTER FOUR: The Adaptation of Mechanical Properties to Different Functions 124
4.1 Properties of Bone with Different Functions 124
4.2 A General Survey of Properties 129
4.3 Mesoplodon Rostrum: A Puzzle 137
4.4 Property Changes in Ontogeny 138
CHAPTER FIVE: Cancellous Bone 146
5.1 Mechanical Properties of Cancellous Bone Material 146
5.2 Mechanical Properties of Cancellous Bone Tissue 150
5.3 Functions of Cancellous Bone 158
5.3.1 Principal Stresses 159
5.3.2 Arrangement of Trabeculae in Cancellous Bone 162
5.3.3 Joins Between Trabeculae 167
5.3.4 Energy Absorption of Cancellous bone 168
5.3.5 Cancellous Bone in Sandwiches and in Short Bones 170
5.3.6 Cancellous Bone in Tuberosities 170
5.3.7 Medullary Bone 170
5.3.8 The Size of Trabeculae 171
5.3.9 Cancellous Bone with No Compact Bone 172
5.4 Conclusion 173
CHAPTER SIX: The Properties of Allied Tissues 174
6.1 Calcified Cartilage 174
6.2 Collagenous Tissues of Teeth 176
6.2.1 Cement 176
6.2.2 Dentin 177
6.2.3 Narwhal Dentin 180
6.3 Enamel 183
6.4 Fish Scales 191
6.5 Dentin vs. Bone 191
CHAPTER SEVEN: The Shapes of Bones 194
7.1 Shapes of Whole Bones 194
7.2 Designing for Minimum Mass 196
7.3 Long Bones 197
7.3.1 Why Are Long Bones Hollow? 197
7.3.2 How Hollow Should Bones Be? 199
7.3.3 How Stiff Should Bones Be? 210
7.4 Flat or Short Bones with Cancellous Bone 212
7.4.1 Sandwich Bones 212
7.4.2 Short Bones 217
7.4.3 Synergy Between Cortical and Cancellous Bone 219
7.5 Paying for Strength with Mass 220
7.5.1 Minimum Mass of Compact Bone Material 220
7.5.2 Minimum Mass of Cancellous Bone 224
7.6 The Swollen Ends of Long Bones 225
7.7 Euler Buckling 231
7.8 Interactions Between Bone Architecture and Bone
Material Properties 236
7.9 The Mechanical Importance of Marrow Fat 239
7.10 Methods of Analyzing Stresses and Strains in
Whole Bones 241
7.11 Conclusion 243
CHAPTER EIGHT: Articulations 245
8.1 The Synovial Joint 247
8.2 The Elbow 248
8.3 The Swelling of Bones Under Synovial Joints 254
8.4 Intervertebral Disks 261
8.5 Sutures 262
8.6 Epiphyseal Plates 263
8.7 Joints in General 268
8.8 Conclusion 271
CHAPTER NINE: Bones, Tendons, and Muscles 272
9.1 Tendons 273
9.2 Sesamoids and Ossified Tendons 277
9.3 Attachment of Tendons to Bone 280
9.4 Muscles Produce Bending Stresses in Bones 283
9.5 Why Do Tendons Run Close to Joints? 285
9.6 Muscles as Stabilizing Devices 294
9.7 Curvature of Long Bones and Pauwels' Analyses 294
9.8 Skeletons in General 299
9.8.1 Pelvic and Pectoral Girdles 300
9.8.2 Limbs 301
9.8.3 Fusion and Loss of Bones 302
9.8.4 The Vertebral Column 304
9.8.5 The Skull 307
9.9 Conclusion 307
CHAPTER TEN: Safety Factors and Scaling Effects in Bones 309
10.1 Safety Factors 309
10.2 Size and Shape 327
10.2.1 Scaling 327
10.2.2 Elastic Similarity 329
10.2.3 Geometric Similarity 331
10.3 Conclusion 336
CHAPTER ELEVEN: Modeling and Reconstruction 337
11.1 The Need for Feedback Control 337
11.2 What Do We Need to Know? 341
11.3 Classic Experiments 343
11.4 The Nature of the Signal 345
11.4.1 Electrical Effects 345
11.4.2 Direct Measurement of Strain 349
11.5 How Does Bone Respond to the Signal? 350
11.6 Postclassical Experiments 354
11.7 In Search of the Algorithm 357
11.8 Precision of Response 364
11.9 Modeling of Cancellous Bone 367
11.10 The Functions of Internal Remodeling 368
11.10.1 Removing Dead Bone 369
11.10.2 Improving the Blood Supply 370
11.10.3 Mineral Homeostasis 371
11.10.4 Changing the Grain 372
11.10.5 Taking out Microcracks 374
11.10.6 It's a Pathological Mistake 377
11.11 Bone Cell Biology 378
11.12 Conclusion 378
CHAPTER TWELVE: Summing up 380
What People are Saying About This
Written by a highly respected biologist, this work is unique in that it integrates a comprehensive treatment of skeletal biology at the tissue and organismal levels with principles of evolutionary biology, zoology, and animal locomotion. It is written in a uniquely interesting way that is understandable to both experts and relative novices in the field.
David D. Burr, Indiana University School of Medicine
This is a highly readable book with excellent illustrations. It will be required reading for all those interested in the mechanical testing of mineralized tissues or in a biological understanding of bone adaptation to mechanical loading. The author's evaluations of the topics that form the leading edge of bone research are remarkably thoughtful, well reasoned, and nicely documented.
Steve Cowin, City University of New York
"This is a highly readable book with excellent illustrations. It will be required reading for all those interested in the mechanical testing of mineralized tissues or in a biological understanding of bone adaptation to mechanical loading. The author's evaluations of the topics that form the leading edge of bone research are remarkably thoughtful, well reasoned, and nicely documented."Steve Cowin, City University of New York"Written by a highly respected biologist, this work is unique in that it integrates a comprehensive treatment of skeletal biology at the tissue and organismal levels with principles of evolutionary biology, zoology, and animal locomotion. It is written in a uniquely interesting way that is understandable to both experts and relative novices in the field."David D. Burr, Indiana University School of Medicine