Effect of prism orientation and loading direction on contact stresses in prismatic enamel of primates Implications for interpreting wear patterns.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 126:427– 434 (2005) Effect of Prism Orientation and Loading Direction on Contact Stresses in Prismatic Enamel of Primates: Implications for Interpreting Wear Patterns Daisuke Shimizu,1* Gabriele A. Macho,1* and Iain R. Spears2 1 Hominid Palaeontology Research Group, Department of Human Anatomy and Cell Biology, University of Liverpool, Liverpool L69 3GE, UK 2 Sport and Exercise Subject Group, School of Social Sciences and Law, University of Teesside, Middlesbrough TS1 3BA, UK KEY WORDS edge ﬁnite element stress analysis; tensile stress; friction; leading edge; trailing ABSTRACT The ability of prisms to effectively dissipate contact stress at the surface will inﬂuence wear rates in teeth. The aim of this investigation was to begin to quantify the effect of prism orientation on surface stresses. Seven ﬁnite element models of enamel microstructure were created, each model differing in the angulation of prism orientation with regard to the wear surface. For validation purposes, the mechanical behavior of the model was compared with published experimental data. In order to test the enamel under lateral loads, a compressed food particle was dragged across the surface from the dentino-enamel junction (DEJ) towards the outer enamel surface (OES). Under these conditions, tensile stresses in the enamel model increased with increases in the coefﬁcient of friction. More importantly, stresses were found to be lowest in models in which the prisms approach the surface at lower angles (i.e., more obliquely cut prisms), and highest when the prisms approached the surface at 60° (i.e., less obliquely cut). Finally, the direction of travel of the simulated food particle was reversed, allowing comparison of the difference in behavior between trailing and leading edge enamels (i.e., when the food particle was dragged either towards or away from the DEJ). Stresses at the trailing edge were usually lower than stresses at the leading edge. Taken together with what is known about prism orientation in primate teeth, such ﬁndings imply greater wear resistance at the intercuspal region and less wear resistance at the lateral enamel at midcrown. Such ﬁndings appear to be supported by archeological evidence. Am J Phys Anthropol 126:427– 434, 2005. © 2004 Wiley-Liss, Inc. Tooth wear is essential for the normal functioning of the masticatory apparatus (Osborn and Lumsden, 1978), and it has long been held that the pattern and rate of wear may provide information about the diet and feeding habits of extant and extinct species (e.g., King et al., 1999; Teaford et al., 2001) and populations (Smith, 1984; Ungar and Spencer, 1999). Despite a plethora of dental wear studies, however, insights gained into the dietary behavior of primates do not extend beyond broad dietary categorizations. The confounding factors are many (e.g., an understanding of the complexity of masticatory biomechanics or seasonal changes in food habits), but some fundamental issues are also unresolved. Speciﬁcally, although it is well-documented in the tribological literature that wear constitutes damage to a solid surface caused by the removal or displacement of material through mechanical forces (Archard, 1953; Marshek and Chen, 1989), the consequences of such mechanical forces on stresses in prismatic (crystalline) enamel remain to be explored. Based on experimental and theoretical grounds, it has been argued that crystal orientation within prisms and the interprismatic matrix may contribute to resisting dental wear (Rensberger and von Koenigswald, 1980; Boyde, 1984; Boyde and Fortelius, 1986; Young et al., 1987; Stern et al., 1989; Maas, 1991, 1994; Rensberger, 1997). The least wear is expected to occur when prisms, and therefore the predominant direction of crystals, are aligned parallel to the abrasion vector. However, intratooth variation in prism angulation was found to be considerable (Maas, 1991), and could be due to a num- © 2004 WILEY-LISS, INC. Grant sponsor: Japan Society for the Promotion of Science; Grant sponsor: Leverhulme Trust; Grant number: F/00025/A. *Correspondence to: Dr. Daisuke Shimizu or Dr. Gabriele A. Macho, Hominid Palaeontology Research Group, Department of Human Anatomy and Cell Biology, University of Liverpool, Liverpool L69 3GE, UK. E-mail: email@example.com for DS; firstname.lastname@example.org for GM. Received 17 July 2003; accepted 11 December 2003. DOI 10.1002/ajpa.20031 Published online 13 August 2004 in Wiley InterScience (www. interscience.wiley.com). 428 D. SHIMIZU ET AL. ber of reasons. Given that the abrasion vector is likely to change as a function of friction and mechanical properties of food stuff consumed (and hence the angle of approach of the mandible), the variability in prism (crystal) orientation may simply reﬂect an adaptation to varied functional demands. If this is the case, systematic differences in prism orientation within a tooth would not be expected. Alternatively, prism (crystal) orientation in different parts of the tooth could carry a functional signal, i.e., they may confer different properties to the tissue, thus making it either stronger or more wear-resistant, depending on the involvement of the area in question in predominantly shearing and crushing (Phase I) or grinding (Phase II) (Crompton et al., 1994). In support of these latter suggestions are observations that prism angulation differs systematically between leading and trailing edges in a number of animals (primates: Maas, 1993; opossum: Stern et al., 1989; koala: Young et al., 1987). Leading and trailing edges are not only differentiated by proportionately greater force being placed on the former (Kay and Hiiemae, 1974), but by shear forces occurring either away from the dentino-enamel junction (DEJ) or towards it. To contribute to a better understanding of the complex interrelationship between dental microstructure and wear was the aim of this study. The experimental method used was ﬁnite element stress analyses (FESA). Finite element stress analysis, a technique more commonly associated with engineering, has long been used to assess stress conditions during contact. Further, this technique was adopted for assessing the microstructural behavior of enamel under loads (Spears, 1997). By creating a modiﬁed version of this ﬁnite element (FE) model in which prism orientation was varied, and subjecting it to the types of loads exerted during hard-particle mastication, the aim of this study was to investigate the effect of prism orientation on contact stresses. Hence, it will 1) explore the mechanical processes underlying wear, and 2) determine the mechanical advantages of different prism orientations. MATERIALS AND METHODS This study builds on a previous attempt to determine Young’s modulus of prismatic enamel using FESA (Spears, 1997). The new model has the advantage of representing the geometry of keyhole-shaped prisms more accurately, while reducing the number of elements per prism from 24 to 14 (Fig. 1), thus optimizing processing time. Stiffness is the resistance of a material to deformation, and Young’s modulus (E) is the parameter used to quantify this resistance. For example, rubber has a low Young’s modulus because it undergoes a considerable amount of deformation when subjected to load, while steel has a high Young’s modulus because it undergoes little deformation under load. On an ultrastructural level, enamel is known to be composed of hydroxyapatite crystals held together by an inorganic matrix. Given that the crystals are considerably stiffer than the matrix, enamel (as most biological materials) behaves in a complex manner. Speciﬁcally, in cases where loads are applied along the direction of the crystals, most of the internal stresses are carried by the crystals, and hence the behavior of enamel is similar to that of crystals (i.e., higher stiffness). In contrast, when loads are applied across the direction of crystals, most of the internal stresses are carried by the inorganic matrix, and the behavior of enamel in this direction is more similar to that of the matrix. Consequently, the stiffness of enamel is different in different directions, i.e., it is anisotropic with respect to stiffness. Such dependence of stiffness on direction is more commonly encountered in unprocessed wood, where stiffness along the grain is greater than stiffness across it. For modeling purposes, this behavior of enamel can be simpliﬁed by assuming that the crystals are oriented in parallel within a small region, i.e., within one element (Fig. 1). This allows enamel to be modeled with orthotropic (i.e., a simple representation of anisotropy) behavior, in which the material properties are deﬁned along three directions (x-, y-, and z-axes). Following Spears (1997), the crystalline structure of enamel prism was considered to behave orthotropically with respect to stiffness (Fig. 1, Table 1). The stiffness in the three directions (Ex, Ey, Ez) was calculated using equations based on composite theory. In addition, any material which undergoes load will exhibit lateral deformation in the direction perpendicular to the direction of load. Such a phenomenon is commonly referred to as “barreling out,” and the parameter used to quantify this lateral deﬂection is Poisson’s ratio (). For example, a common sponge which collapses in on itself under load has a low Poisson’s ratio, while rubber, which always maintains a constant volume, has a high Poisson’s ratio. Given its composite structure, Poisson’s ratio for an orthotropic material, like stiffness, has to be deﬁned in three directions (xy (the amount it barrels out in the y-direction when load is applied along the x direction), yz, and zx). Finally, in addition to deformation along the axes of crystals, the overall shape of enamel can be distorted. For example, a square-shaped specimen can be distorted into the shape of a diamond. These distortional components of stress are known as shear, and the resistance to such distortion is the shear modulus (G). Again, in an orthotropic representation of enamel, the shear modulus must be speciﬁed for three directions Gxy, Gyz, and Gzx). In order to represent the orthotropic behavior of enamel, these nine variables were assigned to the model where Ex or Ey were Young’s moduli along the x and y axis in the plane perpendicular to the c-axis of the crystal. Ez was the Young’s modulus along the c-axis. xy and Gxy were the Poisson’s ratio and the shear modulus within the x-y plane, respectively. yx and zx refer to the Poisson’s ratio within a plane along the long axis. Gyz and Gzx were shear moduli within a plane along the 429 PRISM ORIENTATION AND STRESS IN PRISMATIC ENAMEL Fig. 1. Creation of FE model. a: Dimensions of prism and elements. b: Entire enamel block created for analyses. c: Numbering of elements is that used in Table 1, which lists coordinates of crystal orientations. d: Differences in crystal orientation. TABLE 1. Prism orientation within each element1 Element no. (see Fig. 1c) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Crystal orientation x-y plane Crystal orientation y-z plane 93° ⫺15° 87° ⫺15° 97° 0° 90° 0° 83° 0° 90° 0° 97° 30° 90° 30° 83° 30° 93° 80° 90° 75° 87° 80° 93° 85° 87° 85° 1 Positive direction of y-axis is 90°, and the positive directions of x- or z-axes are 0°. Numbers of elements refer to those shown in Figure 1c. long axis. A Young’s modulus of 103.0 GPa was assigned to represent the properties along the long axis (Ez), whereas a Young’s modulus of 32.1 GPa was assigned to represent the properties across the long axis (Ex) (Spears, 1997). Young’s moduli are expected to vary depending on the volumetric fraction of crystals, and for the present study, the volumetric proportion was assumed to be 0.9 (Spears, 1997). A value of 31.0 GPa was used to deﬁne shear moduli in two planes along the crystallites (Gyz) (Arikawa, 1989). Poisson’s ratios were assumed to be 0.313 (zx in the plane along the long axis) and 0.177 (xy in the plane perpendicular to the long axis). The orientation of crystals within each element was deﬁned following Waters (1980) (Fig. 1, Table 1). All calculations were carried out using MSC.MARC ﬁnite element software (MSC Software Corp., 2002). Once the crystal orientation was deﬁned for one prism (Fig. 1c,d, Table 1), an enamel block was created (Fig. 1b) by reproducing a single prism. The block was then compressed using displacement-controlled (1 ⫻ 10⫺10 m) loading in various directions. Reaction forces were used to determine the bulk modulus of the enamel block (e.g., Spears, 1997). The bulk behavior of the specimen (E ⫽ 74.1 gigapascals (GPa) for loading along the prism orientation, and E ⫽ 55.9 GPa and 31.6 GPa for loading across the prism orientation) compared well with Young’s moduli derived experimentally (Stanford et al., 1960; Craig et al., 1961) and numerically (Spears, 1997) (Fig. 2). 430 D. SHIMIZU ET AL. Fig. 2. Results for validation of enamel block are compared with values of experimental studies (Craig et al., 1961; Stanford et al., 1960). Pictures of small enamel pieces along x-axis illustrate direction of loading. Satisﬁed that the behavior of this microstructural model was realistic, new models with differently angled prisms were created (Fig. 3a,b). The approach of the prisms to the wear surface varied from 0 –90°, in intervals of 15°. A small, half-spherical food particle of Mezzettia seeds (diameter, 200 m) was then modeled and pushed onto the new surface. The Young’s modulus of the food particle was 7.8 GPa, with a Poisson’s ratio of 0.3 (Spears and Macho, 1998). For all analyses, a total load of 180 N was applied to the food particle (Fig. 3c), which in turn was transmitted to the enamel model; this accords well with experimental data on maximum bite forces in modern humans (Fernandes et al., 2003). The food particle was deliberately placed so that the initial point of contact was at the middle of the head of the most central prism. Surface-parallel loads were simulated by displacing the compressed food particle tangentially with respect to the enamel surface, i.e., it was dragged across without rolling. The parameter used to quantify the resistance of one body against sliding over another contacting body is the coefﬁcient of friction (), deﬁned as the ratio of resistive force to compressive force. As food items differ quite considerably with regard to their friction coefﬁcient (shaded bars in Fig. 4), simulations with various coefﬁcients ( ⫽ 0.1– 0.7) were performed for food being dragged from the DEJ to the outer enamel surface (OES); this corresponds with the direction of wear at the leading edge (Fig. 3d, ii). Once the effects of friction on the leading edge were established, a constant friction coefﬁcient of 0.5 was Fig. 3. a: Graph showing creation of enamel and food model. b: Three blocks with differently angled prisms are given, while bar at right gives schematic representation of seven enamel blocks used. c: Relationship between force, force vector, and friction (d). PRISM ORIENTATION AND STRESS IN PRISMATIC ENAMEL 431 Fig. 5. Maximum tensile stresses reached in leading and trailing edge with differently angled prisms (coefﬁcient of friction ⫽ 0.5) Fig. 4. Maximum tensile stresses within enamel blocks with differently angled prisms and using different friction coefﬁcients. Presumptive food particle is dragged from DEJ toward OES. Shaded bars indicate friction coefﬁcients for some foods: i, rose fruit (Demir and Özcan, 2001); ii, hackberry (Demir et al., 2002); iii, gorgon nut (Jha, 1999); iv, lupin (Öğüt, 1998). Stippled line indicates values for saliva reported in literature. used in the model; this value corresponds closely with the friction coefﬁcient of saliva (e.g., Reeh et al., 1995). The direction of travel of the food particle was then reversed and the analyses repeated, thus simulating the behavior of enamel at a trailing edge (Fig. 3d, i). RESULTS For all models, the highest values of tensile stress occurred when prisms were orientated at 60° to the wear surface. The lowest values occurred when prisms approached the surface at 15°, followed by 30°. Varying the coefﬁcient of friction had a marked effect on the maximum tensile stresses reached within the enamel (Fig. 4). The maximum tensile stresses were generally lowest at angulations between 0 –30°. At 45° and 60°, maximum tensile stresses increased most dramatically as friction increased (Fig. 4). Although overall relatively high, the maximum tensile stresses obtained for prism angulations between 75–90° increased only moderately at higher frictions, comparable to enamel blocks with 0 –30° angulations. Figure 5 shows the maximum tensile stresses in enamel blocks when food was dragged either from the DEJ to the OES (i.e., leading edge) or from the OES to the DEJ (i.e., trailing edge). At low prism angulations (i.e., below 30°), maximum tensile stresses did not differ as a result of direction of food movement. Although the overall values were generally higher at 75° and 90°, the difference between leading edge and trailing edge was negligible, with the leading edge yielding somewhat higher maximum tensile stress values. The greatest difference was found for prism angulations of 60°. For this angulation, the stress values in the leading edge enamel were more than double those in the trailing edge. DISCUSSION Dental wear (i.e., abrasion) is a mechanical process, whereby microfracture at the enamel surface may cause the demise of a tooth (Zheng et al., 2003). Even when the experimental wear design is kept constant, microwear features on the surface may vary between regions of a tooth as a result of differential prism orientation (Maas, 1991). This compounds interpretation of microwear features for the reconstruction of diet in extant and extinct species, but also raises questions as to the functional adaptations of primate teeth to resist wear. As a case in point, while it is evident from these and earlier experimental studies (e.g., Rensberger and von Koenigswald, 1980; Gordon, 1984; Maas, 1991) that prism (crystal) orientation affects surface damage, the exact mechanisms causing wear are poorly understood. This FE study was designed to address these questions and to determine the possible functional consequences of differences in prism orientation between leading and trailing edges, as well as throughout the lifetime of the tooth (i.e., apico-cervically). While the ﬁndings of the present study allow us to explore the interrelationship between enamel microstructure and surface stresses, there are limitations to both the model and the validation procedure. With regard to the former, it is acknowledged that not all primate enamels are keyhole-shaped (e.g., von Koenigswald and Sander, 1997), and that there are proportionate differences between prism head and interprismatic matrix. Such differences would affect the way in which the surface of enamel deforms under loads, and could have profound effects on the magnitudes and patterns of stress distribution. With regard to the validation procedure, it was chosen to compare bulk values of Young’s moduli as calculated by the model with those measured experimentally. Despite good agreement of these bulk values, it is recognized that the predictions of localized behavior of the enamel model under load, although based on well-proven algorithms, remain theoretical. Given the nature of the model, it may seem appropriate to compare the ﬁndings with data 432 D. SHIMIZU ET AL. from indentation studies. Unfortunately, indentation experiments on enamel have focused on the nanolevel (indenter radius ⫽ 100 nm; Willems et al., 1993; Habelitz et al., 2001; Cuy et al., 2002). Behavior at this level would be too localized for validation purposes, and it is therefore acknowledged that the quantitative nature of the results should be interpreted with caution. However, the results are internally consistent such that the limitations are identical regardless of prism orientation. This, together with the fact that bulk behavior compares well with experimental data, should allow conclusions to be drawn. The types of stress attributed to wear in contacting surfaces are many. Given enamel’s weakness under tension (Rasmussen et al., 1976), the most dangerous types of stress considered in the present study are tensile. There are two mechanical processes contributing to the development of these tensile stresses in the models. Firstly, as with any structure which is subjected to surface-tangential loads, tensile stresses develop at the surface in the region behind the contact area. The magnitude of these stresses depends largely on the coefﬁcient of friction assigned. Secondly, and possibly more important with regard to the effect of prism orientation on stresses, is the disparity in localized surface deformation. As the food particle is pushed onto the surface, large deformations in the area of contact and low deformations around the periphery result in an imbalance of surface deformation, which in turn causes tensile stresses in the intermediate regions (similar tensile stresses occur in the springs of a trampoline during a trampolinist’s landing). The magnitude of these tensile stresses depends largely on how much the surface deforms under load, and consequently, on the stiffness of the surface with respect to loading direction and magnitude. While the tensile stresses presented here are a combination of both types of stress, and while the frictional forces can be explained in light of the friction coefﬁcients assigned, the stresses due to surface deformation are fundamental in understanding the more interesting aspects of the ﬁndings. Overall, maximum tensile stresses tend to be lower in the trailing-edge than the leading-edge simulations. This difference is most pronounced when prisms approach the surface between 45– 60° (Fig. 5). At these angles, the abrasive vector is orientated more or less parallel to the prisms (i.e., along the direction of high stiffness) in the trailing edge. Consequently, surface deformation is expected to be low. Conversely, when applied to the leading edge, the abrasive vector acts across the predominant orientation of the crystals (i.e., prism head), particularly when the prisms are angled at 60° and 45°. Given that this is the direction of lowest stiffness, surface deformation is high and tensile stresses reach their highest levels (Fig. 5). These ﬁndings and considerations have implications for an understanding of tooth behavior during mastication. Primate (mammalian) mastication is characterized by two distinct stages, which leave characteristic wear facets (e.g., Kay and Hiiemae, 1974) (Fig. 6). During Phase I, the teeth are brought into occlusion and the food is predominantly sheared and crushed, whereas grinding occurs mainly during Phase II of mastication (Mills, 1963). Although the forces generated during the ﬁrst part of the power stroke (Phase I) are considered to be higher, the forces during chewing remain substantial (Kay and Hiiemae, 1974). These latter forces, together with the relative movement of the contacting surfaces (i.e., tooth-food-tooth), combine to cause greater volumetric loss of enamel. The results of the model indicate that tensile stresses are greater in the leading edge than in the trailing edge. If these stresses are sufﬁcient to cause microdamage to the surface, it would logically be expected that resistance to wear would be region-speciﬁc. Notably, differences would occur between the (inter)cuspal area and the side enamel. Such suggestions, if taken further, may help to explain the formation of angled wear facets observed for functional cusps in macrowear studies (Smith, 1984). Whether this oblique wear pattern constitutes an adaptation to increased grinding (Shimizu, 2002) or is simply a by-product of prism orientation (crown formation) needs to be investigated. Regardless, our ﬁndings may also explain why complicated surface topography is retained throughout varies stages of wear (Ungar and M’Kirera, 2003). Furthermore, although it may be argued that such inferences are, at present, only based on theoretical models rather than cross-species comparisons, the interpretations proffered here are in accord with studies which reported systematic differences between functionally distinct regions of the tooth (Rensberger and von Koenigswald, 1980; Young et al., 1987; Stern et al., 1989; Maas, 1993), as well as with observations about rates of wear. It has long been known that the attitude of prisms in modern human (primate) teeth changes from being cuspally inclined apically towards being more horizontally orientated cervically (e.g., Kraus et al., 1969). If propositions regarding the rate of wear derived from our experiments are reasonable, stresses in the enamel should increase initially as the wear facet approaches the midenamel (i.e., for prisms cut between 60 –75°), and then decrease as the tooth becomes increasingly worn (i.e., for prisms cut between 15– 45°). Such propositions would be valid irrespective of possible changes in metabolic requirements and dietary preferences with age (e.g., Bosy-Westphal et al., 2003). Indeed, these predictions seem to be borne out by archaeological data, which document a decrease in rates of wear as individuals age, resulting in a curvilinear relationship between crown height and age (Walker et al., 1991) (Fig. 7). Given that the amount of tooth material is greatest at midcrown level, the proportionally greater loss of enamel through wear would not be recognized if changes in tooth crown heights were the focus of study. In other words, the higher PRISM ORIENTATION AND STRESS IN PRISMATIC ENAMEL 433 Fig. 6. Illustration of chewing cycle and of what constitutes leading (L) and trailing (T) edge. Average prism orientation is also highlighted. volumetric loss of enamel at midcrown level in posterior teeth is probably compensated for by the amount of material available (Fig. 7). Changes of rates of wear observed in anterior teeth of Pleistocene hominins (Bermúdez de Castro et al., 2003) could thus also be explained and, if correct, could alter predictions made about the average life expectancy of this population (Bermúdez de Castro et al., 2003). Hence, the actualistic data are clearly in support of interpretations made from the theoretical models, but comparisons of wear patterns among primates need further consideration. Although tooth formation follows the same basic principles in all primates, differences exist in the average attitude of prisms from the DEJ as well as the vertical path taken by these prisms (Macho et al., 2003). Such differences are likely to affect the rates of wear between species, but also between different regions of the same tooth. Whether such differences in prism pathways have been selected for to predomi- Fig. 7. Summary of prism angulation, tensile stresses, and rate of wear (data from Walker et al., 1991) throughout life. nantly confer greater resistance to abrasion or to resist crack propagation (or both) has yet to be determined (Jiang et al., 2003; Macho et al., 2003). Regardless, on the basis of the present ﬁndings and interpretations, it seems that primate teeth may be well-designed to cope with the demands of mastication, but inferences about dietary adaptations on the basis of prism arrangement, particularly among extinct primates, may not be straightforward. Prinz and Lucas (2000) suggested that tooth wear may be increased as a result of higher friction. The ﬁndings of the present study clearly support such propositions (Fig. 4). As the angulation between main crystal orientations and abrasion vector will change with frictional force, the amount of tensile stress concentrated within the tissue will also be changed. Consequently, foods with the same internal mechanical properties (e.g., stiffness) can induce different rates of wear, depending on their frictional behavior with enamel alone. Only when the properties of habitual foods, including friction when paired with enamel, are known will it be possible to relate enamel microstructure to speciﬁc diets. To conclude, the engineering approach (FESA) adopted in the present study has shed light on the mechanisms underlying wear, and has provided possible insights into the functional adaptations of primate postcanine teeth. Although grounded largely in theoretical considerations, the ﬁndings of the present study are in accord with comparative anatomy and archaeological evidence, and suggest that 434 D. SHIMIZU ET AL. the investigation of prism orientation in primates can (with caveats) be usefully exploited to make functional and behavioral inferences. ACKNOWLEDGMENTS D.S. was supported by the Japan Society for the Promotion of Science, and G.M. and I.S. by the Leverhulme Trust (F/00025/A). LITERATURE CITED Archard JF. 1953. Contact and rubbing of ﬂat surfaces. J Appl Physics 24:981–988. Arikawa H. 1989. 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