Mechanical Design Strategies

Teeth: Structure/Mechanical Design Strategies Teeth fulfill a function that is almost always essential for survival—food procurement and processing. This constant evolutionary pressure ensures that their structures are finely tuned to their function. Furthermore, any benefits that might result from natural selection will readily be incorporated into the structure. Thus from the materials perspective, teeth can be regarded as cutting, piercing, and grinding tools whose structures and shapes have been finely honed over tens and even hundreds of millions of years. An understanding of the structure–function relations of teeth may therefore provide new ideas for the design of improved cutting, piercing, and grinding tools, and have implications for the development of novel dental and orthopedic materials. A wide variety of animals produce teeth, not all of which are mineralized. Presumably, the working surfaces of all, however, need to be hardened in one way or another to function well. The remainder of the tooth appears to provide a backing for the working surface. Thus, the very basic design strategy of most teeth seems to follow this intuitive division. Judging from the complexity of tooth structure, however, there are many more functional design features in teeth. Here we will briefly consider several tooth types whose structure–function relations have been investigated. For more information on mechanical properties of biological materials see Wainwright et al. (1976), and on biomineralization see Lowenstam and Weiner (1989) and Simkiss and Wilbur (1989).

1. Sea Urchin Teeth Sea urchins (phylum Echinodermata) produce five continuously growing teeth (Fig. 1(a)) that are used

for grinding the rocky substrate in order to extract the algae that tightly adhere to the surface. In fact, some of the rock itself is ground away. Amazingly, the tooth is composed of basically the same material as the rock that they usually grind, namely calcium carbonate. The tooth structure and modifications of the mineral phase are what makes it possible to grind away the rocky substrate. The tooth is continuously renewed as the scraping surface is worn down, and is self-sharpening (Fig. 1(a)) (Hyman 1955). For more information on the overall tooth structure see Markel et al. (1977) and Stock et al. (2002). Here we will consider only a few of the structural features. The basic structural elements of the tooth are long S-shaped fibers each of which is a single crystal of calcite. Each fiber is enveloped in an organic sheath. The fibers taper from 20 mm in diameter in the keel area to less than 1 mm or so in the working surface (Fig. 2(c)). There is also a reduction in the magnesium content from the keel side to the working surface (Wang et al. 1997). The reduction in size results in the hardness of the element increasing due to the decrease in the number of possible dislocations. The working surface (Fig. 2(b)) is composed of the tips of the fibers emerging perpendicular to the surface. Each fiber is embedded in a matrix of rounded and somewhat disordered crystals of diskshaped calcite that contain very large amounts (up to 35 mol.%) of magnesium within its lattice. The two phases are separated by an organic sheath (Wang et al. 1997). Resistance to fracture is presumably derived from the juxtaposition of the hard needles in a matrix of small rounded crystals. Furthermore, movement between the two can occur along the interface. In certain respects the tooth can be regarded as a gradient fiber-reinforced composite material in which both the fibers and the matrix are composed of mineral. For more information on structure and other design strategies built into the

Figure 1 SEMs of a sea urchin (Paracentrotus lividus) tooth. (a) The working tip of the whole tooth showing the self-sharpening profile. (b) The working tip showing the core composed of calcite needles embedded in a matrix of high-Mg calcite crystals. The core is surrounded by plates. (c) A crystal fiber that tapers in size from one end to the other. The thin end is embedded in the working tip. Micrographs are adapted from those in Wang et al. (1997).

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Teeth: Structure/Mechanical Design Strategies

Figure 2 Micrographs of the teeth of the limpet Lottia sp. (a) SEM of a mineralized tooth. (b) SEM of the hard outer working layer containing goethite in an organic matrix. (c) SEM of the softer inner layer containing opal in an organic matrix. Micrographs are from the collection of the late Prof. Heinz A. Lowenstam.

tooth structure, including the self-sharpening property, see Wang et al. (1997).

2. Chiton and Limpet Teeth Chitons (phylum Mollusca, class Polyplacophora) and limpets (phylum Mollusca, class Gastropoda) also produce teeth for grinding the rocky substrate in order to extract the algae. Chitons and limpets wear down their teeth at the rate of approximately a row a day, and thus also produce new tooth rows at the same rate (Lowenstam 1962b). This occurs on a long tongue-like structure called a radula, which comprises more than 100 rows of teeth. Figure 2(a) shows a scanning electron micrograph (SEM) of a mineralized tooth of a limpet. The outer working layer is composed of goethite (iron hydroxide mineral) in an organic matrix (Fig. 2(b)), and the remainder of the tooth is composed of amorphous silica (opal) in an organic matrix (Fig. 2(c)) (Lowenstam 1962a, 1971). In chitons only two of the teeth in each row are mineralized. The mineral of the working surface layer is the relatively hard iron oxide magnetite—in fact the teeth are magnetic. Lowenstam (1962b) was the first to identify biogenic magnetite in the chiton tooth, or for that matter in any organism. It is now known to be widespread in biology (Kirschvink et al. 1985). The remainder of the tooth is comprised of softer and more pliable mineral phases, which in certain species is carbonated apatite (the same mineral present in vertebrate bones and teeth) or in other species an amorphous calcium iron phosphate mineral (Lowenstam and Weiner 1989). The two layers are separated by a thin third layer also 2

containing an amorphous mineral, ferrihydrite. This third layer possibly functions as a gasket allowing the two major layers with distinctly different mechanical properties to ‘‘work’’ together—a supposition that needs to be checked in chiton teeth, but has supporting evidence in human teeth (see below). van der Wal (1989) characterized the structure and materials design properties of the mineralized teeth of a limpet. Of particular interest is the manner in which the crystals in the working tip have two different orientations, and the hardness of the tip is about twice that of the other parts of the tooth. These properties are the key to the functioning of the tip as a self-sharpening grinding tool.

3. ‘‘Jaws’’ of Carnivorous Worms Various marine polychaete worms have sets of jaws which are a few millimeters long and sharp (Fig. 3). The tip is used by the worm as a syringe to inject venom into its prey. Bryan and Gibbs (1979) reported high levels of zinc in some species and copper in others. Lichtenegger et al. (2002) showed that in the case of the copper-containing species, Glycera, some of the copper is in the form of a most unusual mineral phase called atacamite (Cu2(OH)3Cl). The atacamite crystals are located in the region of the tips of the jaws. There are four polymorphs of this mineral phase, and the animals somehow induce the formation of only one (Lichtenegger et al. 2002). Lichtenegger et al. (2002) performed nanoindentation measurements as well as microprobe elemental analyses. They mapped the hardness and the elastic

Teeth: Structure/Mechanical Design Strategies modulus, and found that the areas with higher hardness and moduli are indeed those with high copper concentrations. In fact, the values measured were intermediate between dentin and enamel, the two materials of vertebrate teeth (see below). They also estimated the resistance of the worm teeth material to abrasion, and found that it is twice that of dentin and almost 80% of that of enamel, despite the fact that amount of mineral in the tissue is just one-seventeenth of that in dentin. Lichtenegger et al. (2002) also noted that the distribution of copper is higher in the inner part of the jaw, as compared to the surface. A gradual increase of stiffness from the surface to the interior is known to prevent crack formation and improve the ability of stiff materials to resist contact damage (Suresh et al. 1999). Thus, the jaw design strategy

Figure 3 Photograph of the jaw showing the sharp point used for injecting the venom. Scale: 0.2 mm (courtesy of Helga Lichteneggar).

integrates protein, copper ions, and copper minerals, and the authors point out that this may serve as a design prototype for new materials.

4. Human Teeth Human teeth, like most teeth of vertebrates, are composed of a hard thin working surface (enamel) that overlies the bulk of the tooth which is composed of a softer more pliant material called dentin (Fig. 4(a)). The mineral phase in both layers is composed of carbonated apatite (also known as dahllite), but the crystal sizes and shapes are very different. In enamel the crystals are highly elongated (spaghetti-shaped). They are arranged in bundles or prisms, and in many species, these bundles are aligned in no less than three different orientations (Fig. 4(b)). The mineral phase comprises B99% by weight of the material. The dentin, on the other hand, contains exceedingly small crystals (among the smallest known to be formed biologically). They are plate-shaped with a thickness of just 2–4 nm. The mineral comprises B65% by weight. A major portion of the dentin crystals are located inside fibrils of collagen, the protein that comprises the bulk of the matrix. They are arranged in layers that traverse across the fibril (reviewed in Lowenstam and Weiner 1989). The dentin and, to a certain extent, the enamel are graded materials in that their structural and hence mechanical properties continuously change. This has been demonstrated by microhardness profiles (Craig et al. 1959). One characteristic of dentin is the presence of numerous long and thin tubules (Fig. 4(c)). They usually have an internal diameter of 1 mm and extend from just below the dentin– enamel junction (DEJ) to the pulp cavity. The dentin immediately below the enamel layer in the crown of

Figure 4 Micrographs of human teeth. (a) View of a fractured cross-section of a human premolar. The arrow shows the outer enamel layer. (b) SEM of human enamel showing parts of prisms with elongated crystals oriented in different directions. (c) SEM of dentin in the crown of the tooth, showing the presence of peritubular dentin around the tubules (arrow).

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Teeth: Structure/Mechanical Design Strategies the tooth contains yet another material type called peritubular dentin. This is a dense collar of mineral that surrounds each of the tubules (Fig. 4(c)). It contains crystals of the same shape, size, and basic organization as in the bulk of the dentin, but almost no collagen (Weiner et al. 1999). It is much harder than intertubular dentin and presumably much stiffer. Various materials properties of enamel and dentin have been measured separately. These include both elastic and fracture properties (Kinney et al. 1996). Surprisingly, very little is known about the design strategy of whole teeth. Some human teeth (canines for example) function mainly as cutting tools, whereas others are mainly for grinding. During mastication the forces applied to the tooth are not only exerted in a direction perpendicular to the cutting surface, but can be from oblique directions. Furthermore, the manner in which the stress is applied can vary greatly depending upon the nature of the food being chewed. Thus, the tooth structure presumably has many design strategies for dealing with different mechanical challenges. Here we identify a few. The position and orientations of the tubules surrounded by peritubular dentin location below the enamel working surface point to a buttressing function for peritubular dentin such that it supports the enamel cap. The tubules with their collar of hard peritubular dentin provide added stiffness to the crown dentin. Strangely, the peritubular dentin does not extend all the way to the dentin–enamel interface or junction (DEJ). Nor do the tubules extend all the way to the DEJ. Both are absent in a transition zone some 100–200 mm below the DEJ. In this same zone, the hardness decreases significantly as compared to the bulk dentin below. All these structural properties point to a unique role for this area of the dentin (Weiner et al. 1999). Wang and Weiner (1998) reasoned that because of the marked differences in stiffness between the enamel and the dentin, some sort of soft intermediate layer must be present to allow the two materials to ‘‘work’’ together. The microhardness profiles supported this supposition. They used Moire! interferometry to map the strain on the surface of a human tooth slice subjected to compressive forces comparable to those incurred during mastication. They found that indeed the highest strains were measured in the 200 mm zone below the DEJ. Furthermore, the extent of the strain was asymmetric when comparing the labial (external) and the lingual (internal) sides of the tooth. It was postulated that this soft zone is actually the working part of the tooth (Wang and Weiner 1998). It apparently acts as a gasket to allow the very hard and stiff enamel to ‘‘work’’ together with the softer more pliant dentin. Similar experiments were repeated at much higher resolution, but instead of using compressive forces, the tooth slices 4

were subjected to changes of humidity. In one experimental configuration the enamel confined the dentin and prevented it from contracting as a function of dehydration, whereas in another configuration the dentin contracted and expanded freely. Most of the expansion was in the same soft zone below the DEJ (Wood et al. 2000). Much more remains to be understood about the manner in which whole human teeth are designed to fulfill their functions. This information may have farreaching implications on treatment regimes and on the design of new dental materials.

5. Concluding Comment Teeth structures throughout the animal kingdom appear to have some common design features, but in general are very different. All, however, probably fulfill vital functions and, therefore, have interesting structure–function relations. Much can be learned from the study of these relations that may produce new ideas for the design of improved synthetic materials.

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Teeth: Structure/Mechanical Design Strategies contact damage through controlled gradients in elastic properties at contact surfaces. Acta Mater. 14, 3915–26 van der Wal P 1989 Structural and material design of mature mineralized radula teeth of Patella vulgata (Gastropoda). J. Ultrastruct. Mol. Struct. Res. 102, 147–61 Wainwright S A, Biggs W D, Currey J D, Gosline J M 1976 Mechanical Design in Organisms. Princeton University Press, Princeton Wang R, Weiner S 1998 Strain–structure relations in human teeth using Moir!e fringes. J. Biomech. 31(2), 135–41 Wang R Z, Addadi L, Weiner S 1997 Design strategies of seaurchin teeth—structure, composition and micromechanical

relations to function. Phil. Trans. R. Soc. Ser. B 352(1352), 469–80 Weiner S, Veis A, Beniash E, Arad T, Dillon J, Sabsay B, Siddiqui F 1999 Peritubular dentin formation: crystal organization and the macromolecular constituents in human teeth. J. Struct. Biol. 126, 27–41 Wood J D, Wang R Z, Weiner S, Pashley D H 2000 Mapping of tooth deformation caused by moisture change using Moir!e interferometry. Dent. Mater. 19, 159–66

S. Weiner and P. Zaslansky

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