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W. Pompe, M. Gelinsky: Biological Materials: Failure of Bone and Teeth.

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K. H. J. Buschow, R. W. Cahn, M. C. Flemings, B. Ilschner, E. J. Kramer, S. Mahajan (Hrsg.) Encyclopedia of Materials: Science and Technology

Elsevier (Pergamon), Oxford 2001. (Band 1, Seiten 580-584)

Biological Structures: Failure

Natural materials are the result of a long-term optimization controlled by the selection processes of evolution. Therefore, their relevant properties are well adapted and outstanding in comparison to other artificial materials. According to the ideas of Ashby et al. (1995) developed in their concept of materials property charts, it is helpful to evaluate the mechanical behavior of structural biomaterials such as wood, silk, cartilage, or bone on the basis of so-called performance indices. A combination of properties, such as Young's modulus, E, density, , strength, c, if maximized will optimize some aspect of the performance of the material. For instance, the stiffness of a lightweight beam with respect to bending is optimized with a maximum value for E\. In agreement with the Ashby concept, bone and enamel are characterized by high values of Gc and EGc, where Gc is the fracture toughness. Therefore, bone and enamel will resist better to fracture than any synthetic ceramic. Motivated by this observation an overview is given in this article on the understanding of the elastic behavior and the fracture toughness of bone and teeth. However, such a pure engineering view cannot include the complexity of a living structural material. Additional aspects such as remodeling and repair mechanisms are also considered.

Bone is composed of living cells, an organic matrix, and a mineral phase. About 95% of the organic matrix consists of collagen I, and the inorganic phase is mainly composed of calcium and phosphate in the form of crystalline hydroxyapatite. The collagenous matrix provides tensile strength, and the mineral content is responsible for the stiffness and the compressive (and shear) strength. In dependence on internal and external forces bone tissue is continuously remodeled by three different cell types: osteoblasts and osteoclasts are present on the bone surface, whereas osteocytes are localized in small spaces (lacunae) in the mineralized part of the bone. The osteoblasts are responsible for the production of the bone matrix and regulate the mineralization, whereas the osteoclasts dissolve and resorb bone material. The function of osteocytes is to maintain the bone matrix and they are therefore able to synthesize and to resorb bone material to a limited extend. Teeth consist of three different materials. The basic structural element is dentine, a composite of calcium phosphates (72%), collagen, and cells--the odontoblasts. The crown is covered with enamel, an extremely hard crystalline hydroxyapatite, and the root with cement for connection with the bone (Fig. 2).

2. Mechanical Behavior of Cellular Biomaterials The mechanical behavior of bone is strongly influenced by its porosity. There are pore structures of different size scales: intertrabecular pores up to 1 mm, vascular pores of the order of 20 µm, lacunar­ canalicular pores of about 0.1 µm, and collagen­ apatite pores of 10 nm. All four levels of bone porosity within cortical as well as cancellous bone are filled with fluids of significantly different viscosity. Thus, the mechanical response of bone to an external load is the deformation-driven bone fluid movement. The mechanical behavior of cancellous bone is determined mainly by the intertrabecular porosity. The characteristic lineal dimension of the intertrabecular pores varies with anatomical location. It is smaller near load-bearing surfaces and increases as the medullary canal is approached. The elastic interaction of the fluid and solid phase in the fluid-saturated porous medium can be described in the framework of poroelasticity (Cowin 1999). Different from soft tissue, it has to be included in such a model that the bulk modulus of the mineralized bone matrix is about six times stiffer than that of the fluid in the pores. Intuitively, it can be assumed that the microstructural anisotropy of the trabeculae of cancellous bone does not cause significant macroscopic elastic anisotropy. For instance, as shown experimentally, the elastic properties of cancellous whale bone under multiaxial compressive load can be predicted very well by using an ``effective isotropic tissue modulus.'' 1

1. Bone and Teeth Materials--Composition and Structure The structure and composition of bone and teeth is perfectly adapted to their function. The structure of long bones contains three major regions: compact (cortical) bone, spongy (trabecular) bone, and the marrow cavity. The compact bone obtains its high strength from a dense microstructure, whereas the spongy bone consists of a meshwork in which the spicules are arranged along the lines of force (Fig. 1).

Figure 1 Schematic structure of bone.

Biological Structures: Failure Thus poroelasticity and electrokinetics explain straingenerated potentials in wet bone. Experimental studies of the strain-generated potential of loaded bone can be used as a tool for investigating the influence of the bone microstructure on local stress development.

3.2 Strength and Fracture Toughness of Bone The structural anisotropy is reflected in the strength of bone. The remodeling capability of living bone means that bone develops optimal material properties in a particular orientation with minimum weight. Although bone is composed of collagen fibers with favored orientation in laminar structure, in Haversian bone the effect of morphology is less than assumed for a fiber-reinforced composite. Osteons as the natural unit element of bone show a weak dependence of the strength on fiber orientation (Table 2). In agreement with this, the strength and stiffness of compact bone can also be well modeled by a quasiisotropic material. Characteristic values for the strength of compact dense bone (e.g., cortical bone of mid-femur) are summarized in Table 3 (Einhorn 1996). However, studies of Liu et al. (1999) have shown that the fracture toughness significantly reflects the anisotropy on the microscopic scale. By using cylindrical miniature cantilever bending specimens (150 µm thickness) a strong anisotropy of the work-to-fracture is observed. A decrease of the work-to-fracture by a factor of 10­30 (depending on orientation) is measured when the osteons are oriented perpendicular to the specimen axis. For collagen fibril orientation along the sample axis, the work-to-fracture is in the region of 1 kJ m-# corresponding to a Kc value of about 4 MPa m"/#. Similar values have also been found for macroscopic samples. Assuming an average strength of about 100 MPa this leads to an ``intrinsic crack length'' of about 100­200 µm. Therefore, it can be concluded that cracks can start from defects like blood vessels, which are anything from 20 µm to 100 µm in diameter. Obviously there is a size dependence of the fracture toughness of bone. Fracture toughness tests conducted on miniaturized compact tension specimens made from human and bovine cortical bone (Vashishth et al. 1997) show that the fracture toughness (Kc) and the cumulative number of microcracks increase linearly with crack extension (Kc increases from 1.6 MPa m"/# to 2.5 MPa m"/# in human bone, and from 3.9 MPa m"/# to 7.2 MPa m"/# in bovine bone). This type of R-curve behavior can be explained by the formation of a growing zone of microcracks near the loaded macrocrack tip. The energy dissipation mechanism seems to be very similar to the microcrack toughening already proposed for polycrystalline ceramics (Kreher and Pompe 1981). As shown by Hellinger et al. (1982)

Figure 2 Schematic structure of teeth.

To a first approximation the influence of the fluid phase can be neglected for modeling the fracture of cancellous bone, as the critical strain of the mineralized matrix is less than 1%. Thus cancellous bone can be considered as a cellular material (Ashby et al. 1995). The compressive stiffness and strength of cancellous bone increases with the square or cube of the relative density depending on whether the cellular structure is built from open or closed pores.

3. Mechanical Behavior of Biomolecular Composites--Bone and Teeth 3.1 Elastic Properties of Bone From the mechanical point of view cortical bone can be understood as a composite material consisting of at least three phases: the mineralized matrix, the collagen fiber network, and the fluid-filled pore phase. The collagen fiber network can be neglected for modeling of the elastic behavior. The effective pore phase summarizes the vascular porosity, the lacunar­ canalicular porosity, and the collagen­apatite pores. Owing to the small pore sizes, the presence of the porefilling bone fluid cannot be neglected. Only the movement of the bone fluid in the very small collagen­apatite pores is negligible because most of the bone water is bound by interaction with ionic crystals. Generally, cortical bone shows anisotropic elastic behavior. However, it can be often approximated by a set of effective isotropic elastic constants. For human femoral cortical bone the poroelastic constants given in Table 1 can be applied. The strain-driven motion of the bone fluid is connected with charge transport owing to the existence of an electric double layer at the interface between the solid matrix and the bone fluid. The liquid transport causes an electrostatic potential in the pore channel. 2

Biological Structures: Failure

Table 1 Poroelastic constants for cortical bone with lacunar­canalicular porosity. Property Lacunar­canalicular porosity Effective shear modulus (GPa) Effective bulk modulus (GPa) Bulk modulus of the solid (GPa) Poisson's ratio of the solid Fluid pressure diffusion coefficient (m# s-") Compressibility coefficient

Source: Cowin (1999).

Value 0.05 5 Drained bone, 12; undrained bone, 13 13 0.325 0.51i10-' 0.4

Table 2 Variation of stiffness and strength of osteons with fiber orientation. Tension Orientation of fibers to long axis 90m 45m 10m Strength (MPa) 116.5 95.9 E (GPa) 11.9 5.59 Compression Strength (MPa) 112 137 167 E (GPa) 6.45 7.54 9.49

Source: Aszenzi and Bell (1970).

in connection with electrostimulation of bone growth, measurement of the bending strength together with monitoring of cumulative acoustic emission caused by microcrack formation yields a value for the increase of the fracture toughness during the formation of new mineralized bone. The strength and fracture toughness of bone are time dependent. There are two main mechanisms: (i) Biological aging. The strength and the modulus of elasticity decrease after maturation by approximately 2% per decade (Burstein et al. 1976). (ii) Viscoelastic effect. With increasing loading or strain rate the modulus of elasticity and the ultimate strength of cortical bone increase whereas the ultimate strain decreases. The modulus and the ultimate tensile strength of bone change with strain to the power of about 0.06 (Einhorn 1996). At low strain rate and strain bone behaves like a viscous material. Also, the fracture toughness shows a strong strain rate dependence. As reported by Behiri and Bonfield (1982), for instance the Gc value of cow leg bone increases from 0.63 kJ m-# to 2.88 kJ m-# while the crack velocity increases up to a value of 1.2 mm s-". When the propagation mode switches from stable to unstable crack growth the fracture changes from quasiplastic to brittle behavior and the fracture toughness decreases to about 0.2 kJ m-#. 3.3 Fatigue Failure of Bone Biological materials differ in one respect from other structural materials under repeated loading and un-

loading: they possess repair mechanisms. Under normal conditions cycling loading of a biomaterial will cause microdamage. However, damage accumulation will not occur in the case when the repair mechanism is active in a timely fashion. The repair activity can be slowed down for various reasons. Naturally there are age-related changes manifesting as a decrease of bone mineral density. Normal repair can also be impaired by metabolic diseases (e.g., osteoporosis) or by certain drugs. Furthermore, repeated loading without sufficient time for repair activity causes fatigue failure (Stanitski et al. 1978). Fatigue failure mainly occurs when bone is loaded repeatedly in the plastic region. However, fatigue failure has been observed in the elastic region as well in the case where the bone is denser. Under such conditions fatigue failure is caused by a large number of loading cycles with high frequency.

3.4 Mechanical Properties of Teeth The human tooth is a sandwich structure with a dentine core and enamel capping. The structure and properties of dentine are similar to compact bone. It is more uniformly grown than bone. The collagen fibrils are oriented in planes parallel to the surface of the dentine. The compressive strength (500 MPa) is higher than that of bone whereas the work-to-fracture is in the same range (1­10 kJ m-#) depending on the orientation of collagen fibrils. Enamel has a more complex structure. Rod-like carbonate apatite crystals of at least 100 µm in length are oriented from the surface of the tooth to the dentine core. The mineral volume fraction is about 95%. Two classes of proteins--the acidic enamelins associated with polysaccharides and hydrophobic amelogenins--are observed in enamel. Different from bone or dentine, they give no significant amount of toughening. The highly oriented crystalline structure creates a high Vickers hardness ( 300 kg mm-#) and stiffness (about 80 GPa). The fracture toughness is less than 1 kJ m-#. 3

Biological Structures: Failure

Table 3 Mean values for compact human bone material parameters (cortical tissue of mid-femur). Direction and type of load Longitudinal tension Longitudinal compression Longitudinal shear Transverse tension Transverse compression Apparent density (g cm-$) 1.85 1.85 1.85 1.85 1.85 Ultimate strength (MPa) 133 193 68 51 33 Modulus of elasticity (GPa) 17 17 3 11.5 11.5

4. Mechanisms of Mechanotransduction in Bone The remodeling and repair processes in bone are partially controlled by the mechanical loading regime. The microscopic mechanism connecting the mechanical signal with the cellular activity is not understood sufficiently. However, it is generally accepted that there are two types of cells that could be possible sensors for mechanical signals--the bone lining cells of osteoblastic origin and the osteocytes. There are indications that the osteocytes are the main cells responsible for the transduction of mechanical signals (Einhorn 1996). It is assumed that the osteocytes communicate with each other as well as with the osteoblasts and the bone lining cells via the canaliculi of unmineralized bone matrix. It has been shown that osteocytes, osteoblasts, and bone lining cells respond to mechanical strain with an increased RNA production and glucose consumption. The information transfer could occur owing to electric coupling between the cells as well as the intracellular and extracellular transport of signal molecules. Alternatively, mechanotransduction could be established through the cytoskeleton of cells. Wang et al. (1993) established such a model for endothelial cells. It is known that the cells interact via integrins with proteins of the extracellular matrix. Therefore, it can be assumed that mechanical strain in the extracellular matrix is transduced by integrins to the cytoskeleton, and via intracellular signal transduction to the cell nucleus. Furthermore, a stress sensitivity of fluid flow exists in the cell environment which can create a signal for the osteocytes. Mechanical loading of bone causes fluid flow in the canaliculi. Owing to the elastic mismatch between the mineral skeleton and the unmineralized regions, very small strain in the calcified matrix is connected with small shear stress as well as hydrostatic stress of the order of 1 Pa in the fluid, which could be detected by the osteocytes. It has been shown that purified osteocytes react to pulsating fluid stress with the release of prostaglandin, which stimulates the bone metabolism. 5. Summary The mechanical properties of bone and teeth are governed by a perfectly adapted composite structure. 4

Whereas the mineral phase creates a high stiffness and compressive strength, the collagenous matrix causes high fracture toughness. The strength and stiffness of compact bone can be modeled to a good approximation by a quasi-isotropic material. The high fracture toughness can be explained by microcrack accumulation near the loaded macrocrack tip. Other than synthetic ceramics, bone possesses repair mechanisms. Therefore, under normal conditions microdamage caused by cycling loading is not critical. The remodeling and repair processes in bone are controlled by cellular activity. The relevant mechanisms are not fully understood. See also: Bone and Natural Composites: Properties; Marine Teeth (and Mammal Teeth)

Bibliography

Ashby M F, Gibson L J, Wegst U, Olive R 1995 The mechanical properties of natural materials: I. Material property charts. Proc. R. Soc. London, Ser. A 450, 123­40 Aszenzi A, Bell G H 1970 Bone as a mechanical engineering problem. In: Bourne G H (ed.) The Biochemistry and Physiology of Bone. Academic Press, New York, pp. 311­52 Behiri J C, Bonfield W 1982 Fracture mechanics of cortical bone. In: Huiskes R, Van Campen D, De Wjin J (eds.) Biomechanics: Principles and Applications. Martinus Nijhoff, The Hague, The Netherlands, pp. 247­51 Burstein A H, Reilly D T, Martens M J 1976 Aging of bone tissue: mechanical properties. J. Bone J. Surg. 59A, 82­6 Cowin S C 1999 Bone poroelasticity. J. Biomech. 32, 217­38 Einhorn T A 1996 Biomechanics of bone. In: Bilezikian J P, Raisz L G, Rodan G A (eds.) Principles of Bone Biology. Academic Press, San Diego, CA, pp. 25­37 Hellinger J, Kleditzsch J, Muller Th, Pompe W, Six H-J, $ Schubert Th, Beere L, Guttler P 1982 Zum Einfluss der $ Elektrostimulation auf die Bildung und Organisation von Knochengewebe bei der Frakturheilung der Kaninchentibia. Beitr. Orthop. Traumatol. 29, 644­56 Kreher W, Pompe W 1981 Increased fracture toughness of ceramics by energy-dissipative mechanisms. J. Mater. Sci. 16, 694­706 Liu D, Weiner S, Wagner H D 1999 Anisotropic mechanical properties of lamellar bone using miniature cantilever bending specimens. J. Biomech. 32, 647­54 Stanitski C L, McMaster J H, Scranton P E 1978 On the nature of stress fractures. Am. J. Sports Med. 6, 391­6

Biological Structures: Failure

Vashishth D, Behiri J C, Bonfield W 1997 Crack growth resistance in cortical bone: concept of microcrack toughening. J. Biomech. 30, 763­9 Vincent J 1990 Structural Biomaterials. Princeton University Press, Princeton, NJ Wang N, Butler J P, Ingber D E 1993 Mechanotransduction across the cell surface and through the cytoskeleton. Science 260, 1124­7

W. Pompe and M. Gelinsky

Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 580­584 5

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