Effect of Enamel Prism Decussation and Chemical Composition on the Biomechanical Behavior of Dental Tissue: A Theoretical Approach to Determine the Loading Conditions to Which Modern Human Teeth are Adapted
Archaeological Sciences, Division of Archaeological, Geographical and Environmental Sciences, School of Life Sciences, University of Bradford, Bradford, England
Department of Evolution and Phylogeny, Primate Research Institute, Kyoto-University, Inuyama, Aichi, Japan
Enamel prism decussation is recognized to constitute a structural reinforcement of teeth, to guard against crack propagation and to reflect the dietary adaptations of species (Rensberger and von Koenigswald, 1980; von Koenigswald et al., 1987). Traditionally, differences in decussation are judged by their two-dimensional (2D) appearance, that is, Schmelzmuster (von Koenigswald and Sander, 1997), or by their optical appearance, the Hunter-Schreger bands (Kawai, 1955; Rensberger, 2000; Vieytes et al., 2007). Yet, enamel is a 3D structure (e.g., Hanaizumi et al., 1998). To more accurately quantify the 3D arrangement of prisms, a computer model has recently been developed (Jiang et al., 2003) that enables the reconstruction of prism decussation from scanning electron microscopic images of naturally broken surfaces (based on different fracture planes). Using this program, distinct differences in prism decussation between even closely related species could be identified, whereby the patterns appear comparable across nonhomologous aspects of teeth within the same tooth class (Macho et al., 2003). These differences are likely to result in biomechanical differences between species. For example, experimental studies have shown modern human molars to be better adapted to axial loading than pig molars (Popowics et al., 2001), which is apparently due to differences in dental microstructure, particularly with regard to the proportion of interprismatic matrix (IPM; Popowics et al., 2004). Similarly, a finite element (FE) study of enamel pieces reconstructed from hominoid teeth showed distinct patterns of stress concentration under axial loads (Macho et al., 2005). Although informative, the results of these studies are however limited, as they do not consider that teeth are subjected to a range of loading directions during mastication. To obtain a better understanding of the range of loading directions to which the microstructure in modern human molars may be adapted, the present study created FE models of enamel block and subjected them to differently angled loads. Although it is recognized that loads would change dynamically during mastication, while the contact area between tooth–food–tooth would change as food is broken down and formed into a bolus, the experiments are designed to yield insights into the functional adaptations of modern human enamel microstructure (i.e., within the tissue). However, the biomechanical behavior of the tissue may not be determined by its microanatomy alone.
Although the functional significance of enamel decussation is undisputed, albeit poorly understood, the biomechanical consequences of differences in mineralization are even more elusive. Throughout its thickness, the mineralization of the tissue apparently changes systematically from the dentinoenamel junction (DEJ) to the outer enamel surface (OES), at least in humans (Braly et al., 2007; Cuy et al, 2002). Enamel tends to be considerably harder toward the OES than at the DEJ, which will affect the biomechanical behavior of the tissue (Spears, 1997), the stress concentration at the DEJ (Shimizu and Macho, 2007) and may, together with the orientation of prisms at the OES, also influence the wear resistance at the OES (Braly et al., 2007; Shimizu et al., 2005). To explore the combined effects of mineralization, decussation, and loading direction a second set of models was created and tested, whereby only the material properties of the tissue were changed (Cuy et al., 2002), while all other aspects, such as crystal orientation, prism decussation, and loading directions, were kept the same as in the chemically homogenous enamel pieces. The effects of chemical composition were thus isolated.
Taken together, the objectives of the present study are twofold: First, it will be enquired whether the enamel microstructure of modern human teeth is adapted to a limited range of loading directions as inferred from experimental studies on whole cusps/teeth. Second, the effects of mineralization on the biomechanical behavior of the tissue is explored. The findings of this study are of heuristic relevance for clinical purposes, i.e., the fracture potential of modern human teeth, and for (paleo)biological enquiry, i.e., the determination of masticatory parameters and, hence, dietary adaptations, from isolated dental remains.
MATERIAL AND METHODS
A graphic model of decussating enamel from the mid-crown area of the paracone of a modern human third molar (Jiang et al., 2003) was converted to a composite FE model using the FE software MSC.Mentat (MSC Software, 2005; Fig. 1). This involved recreating prism cross-section and extruding the section in the out-of-plane dimensions, in accordance with the graphical model of decussating enamel (Jiang et al., 2003). The model was expanded to create a cuboid enamel block encompassing more than one full cycle of deviating prisms in the z–y plane (i.e., 30 layers), with the angle between the DEJ and the prisms naturally being 27 degrees (Fig. 1). The length of the elements along the long axis of the prism, that is, c-axis, was based on the local curvature of the controlling splines, such that elements in regions of high prism deviations (i.e., toward the DEJ) were shorter in length than those in regions of low deviations. In cross-section, each prism was divided into four hexahedral elements (Fig. 2A), representing the prism head and the interprismatic matrix (IPM). Enamel is a composite material, whereby crystals in the prism head are oriented parallel to the long-axis of that prism (c-axis) and perpendicularly to it in the interprismatic matrix (IPM; e.g., Schroeder, 1992; Waters, 1980). To re-create this situation, the elements were given orthotropic properties with different crystal orientations (Macho et al., 2005; Shimizu et al., 2005; Spears, 1997; Table 1). This experimental setup has previously been validated for a small piece of enamel with parallel oriented prisms (Macho et al., 2005; Shimizu et al., 2005) and was deemed appropriate. The material properties inputted are shown in Figure 2 for both chemically homogenous and heterogeneous enamel.
Table 1. Crystal orientation used within each elementa
For an explanation of prism geometry, see Figure 3(A).
All models were fixed inferiorly at the x–z plane (Fig. 1), and a compressive face load of 3MPa was applied linearly to the elements parallel to the y-direction of the enamel blocks. Loading direction varied from −20 degrees (unphysiological) to 40 degrees (physiological), in 10-degree intervals; 0 degree corresponds to loading parallel to the DEJ (Fig. 1). To avoid artefacts and bending during loading, several modifications were made to the enamel block. First, to enable the application of differently-angled loads with regard to the prism arrangement, the rectangular block was retained while the enamel (i.e., decussating part) was taken from a rotated tooth (Fig. 1); this explains the different geometry of the blocks (Fig. 4). Second, to restrict lateral displacement and bending, mantle dentine (rather than dentine) was added to the DEJ with an isotropic Young's modulus of 50 GPa (Fong et al., 2000) and Poisson's ratio of 0.3. At the outer enamel side, elements with isotropic enamel properties of 85 GPa Young's modulus and Poisson's ratio of 0.3 were added (Marshall et al., 2001). The overall dimensions of the block were 1,800 μm (z-axis): 280 μm (y-axis): 280 μm (x-axis). Because of different enamel orientations, the total number of elements varied between models and was 317,000 elements for the 0 degree model, 326,376 elements (10 degree), 346,412 elements (20 degree), 380,028 elements (30 degree), 432,286 elements (40 degrees), 312,851 elements (−10 degrees), and 320,823 (−20 degree). In total, 14 models were tested.
For data collection, one prism was followed throughout its length (i.e., 28 elements) in six equally spaced layers within a cycle of decussating enamel (i.e., along y-direction), thus representing the entirety of the decussating cycle of enamel within the tissue (i.e., away from the loaded surface). The node chosen on the lateral side of the prism head is shown in Figure 3A, and its path throughout the tissue is illustrated in Figure 3B; data were collected from 29 nodes along each prism (for 6 prisms per model). For each node, only the normal stress perpendicular to the c-axis of that prism was calculated (Fig. 3B,C), as this is where tensile stress occurred almost exclusively (except for some isolated incidences). The average tensile stresses (MPa) for each prism is shown in Figure 4 for chemically heterogeneous (Fig. 4A) and homogenous (Fig. 4B) enamel, and the average for each enamel model is given in Figure 5A. The total number of nodes affected by tensile stress are also shown and are compared with the number of nodes in the outer third of enamel, where prisms are relatively straight and parallel to each other (and where stress concentration may more easily result in failure of the tissue).
Figure 4 illustrates the distribution of maximum principal stress (MPa) in a cross-section of the respective enamel blocks, for heterogeneous enamel only. Note that stress is concentrated toward the DEJ in 0–20 degree loading, and shifts toward the OES at negative and very positive (oblique) angles. In Figure 5, the average tensile stresses (MPa) for each prism sampled is shown for chemically heterogeneous (A) and homogenous (B) enamel at different loading angles, respectively. While the overall tensile stress appears comparable across all analyses (Fig. 6A), the values obtained for the heterogeneous models are much more consistent across models. In contrast, the homogenous enamel block yielded relatively low tensile stresses for vertical and near-vertical loadings, but stress increased considerably at higher-angle loading, particularly at 40 degrees (Fig. 5B). In general, the distribution of affected nodes is comparable between both heterogeneous and homogenous models, whereby approximately 50% of all affected nodes are concentrated in the outer 1/3 (i.e., outer 10 nodes) of enamel. Importantly, although the values for tensile stress for 40 degree loading of homogenous enamel are relatively high (Fig. 5B), the number of nodes affected toward the OES is low (Fig. 6B). In contrast, in both heterogeneous and homogenous enamel tensile stress increases at more negative (i.e., unphysiological) loading angles, as does the number of affected nodes, both in total and in the outer part.
Depending on the diet and/or the stage of the chewing cycle, the lateral stroke of the mandible and, hence, the direction and position of external loads on the teeth will vary (Agrawal et al., 2000; Hiiemae et al., 1996); teeth are expected to dissipate the range of loads they are normally subjected to. For example, modern human teeth have been found to be well-suited to axial loading (Popowics et al., 2001, 2004), although the range of loading direction to which they may be adapted are unknown. The present study builds on these hypotheses and observations and proffers a nondestructive alternative for the study of the range of loading directions on teeth. Ascertaining the relationship between loading angle and microstructure would not only aid orthodontics for the assessment of fracture potential of teeth, but could also be exploited for wider (palaeo)biological research into the dietary adaptations of extinct species. However, before the findings of the present study can be interpreted within a wider biological framework, several methodological limitations need to be borne in mind. While most of these methodological limitations have been described elsewhere (Macho et al., 2005; Macho and Spears, 1999; Shimizu et al., 2005; Spears and Macho, 1998) and will therefore not be reiterated here, there are some additional shortcomings, specific to the present investigation.
Following Spears (1997), enamel was modelled as a hierarchical composite which, however, does not take into account the protein-rich prism sheaths and other micro- and nanostructural features (e.g., enamel tufts); these structures are likely to effect the elastic modulus and plastic behavior of enamel under loads (e.g., He et al., 2006). The DEJ was represented by a simple bond, despite recent findings that the complex nature of the DEJ may be biomechanically advantageous (Shimizu and Macho, 2007). This probably affected the apparently higher stresses toward the DEJ (Fig. 4). With regard to the chemical composition of the enamel block, the values chosen are those given in the published literature (Cuy et al., 2002) and do not relate to the tooth analyzed here; to what extent differences in mineralization exist between individuals, populations, or even species is uncertain. Furthermore, the complexity of dental tissue modelled here together with the computational limitations (in our lab) make it, at present, impossible to simulate the dynamic loading conditions encountered during mastication on a very large piece of enamel, let alone an entire tooth. In any case, such analyses will only become necessary when the kinematics (e.g., Koolstra, 2002) and the effects of foods on its parameters (e.g., Foster et al., 2006) are more fully understood, and the interactions between microstructure and biomechanical behavior of teeth have been explored. To contribute to the latter was the aim of the present study. To by-pass the influence of specific foods (e.g., hardness, friction) on stress within the dental tissue, the entire enamel block was placed under compressive face load. The static compressive load applied is thus theoretical, although it may approximate the conditions within the tissue at certain instances during the chewing cycle, especially once a food bolus has formed. Taken together, predictions of actual values of stress within the tissue and calculation of maximum sustainable load on enamel should thus be refrained from. Conversely, the consistency of all aspects of the models other than loading direction and material properties makes it possible to compare the relative magnitudes and locations of stress across models. When doing so, several biologically meaningful results emerge, and allow sharper biological hypotheses to be formulated.
Differences in chemical composition of dental tissue have long been noted (Weatherell et al., 1974) and have recently become subject of investigation again (Cuy et al., 2002; Braly et al., 2007). The systematic pattern of chemical distribution across the tooth would suggest that such differences do not occur at random as a result of enamel maturation (or local environment), but may confer a functional advantage to the tooth. Although such propositions can only be explored once more data have accumulated in the published literature, the present study provides a theoretical framework for such functional hypotheses to be investigated further. Softer enamel is expected to reduce the stress level within the tissue (Spears, 1997), but the combined effects of enamel decussation, material properties, and loading direction appear more complex. While the stress levels are somewhat higher for more axial loading when compared with the results from the homogenous enamel blocks, they are lower at greater angles (Fig. 5). Consequently thus, the stress values for heterogeneous enamel are more comparable across the entire range of loading directions applied in this study than they are for chemically homogenous enamel. These observations suggest that the systematic change in chemical composition from the DEJ to the OES may safeguard the tooth against extreme loading angles not habitually encountered, although experimental studies are needed to further confirm or refute this proposition.
Morphologically, modern human enamel microstructure typically consists of slightly apically curved parallel prisms in the outer half to third of enamel, while the inner part close to the DEJ consists of layers of prisms exhibiting a sinusoid curve, whereby consecutive layers of prisms are out of phase (Jiang et al., 2003; Risnes, 1986). This arrangement results in decussating layers of prisms close to the DEJ, where microcracks are common (Boyde, 1989; Schroeder, 1992) but not harmful. The outer arrangement of relatively straight prisms, together with the high Young's modulus (Cuy et al., 2002), probably confers strength and wear resistance to the tissue (Shimizu et al., 2005). Given the simplistic arrangement of prisms in the outer enamel, however, cracks induced in this part of enamel are more likely to propagate through the tissue resulting in catastrophic failure. In light of such considerations, it is noteworthy that tensile stresses increase at negative loading angles, while the number of nodes affected also increases, especially in the outer third of enamel (Fig. 6B). Such localized high stresses in parallel-arranged prisms are potentially damaging to the tooth and may explain the relative high occurrence of fractures when biting on hard (unexpected) food (e.g., Bader et al., 2001; Cavel et al., 1985; Eakle et al., 1986), that is, at a negative angle. Conversely, although tensile stresses similarly increase at extreme positive loading angles, i.e., at 30 degrees and 40 degrees (Fig. 6A), the number of nodes affected, particularly in the outer enamel region, remains low (Fig. 6B). Hence, whereas positive oblique loading angles may be disadvantageous, they are not necessarily as detrimental to the integrity of the tooth as are negative-angled loads.
For both chemically heterogeneous and homogenous enamel, the lowest overall tensile stresses and fewest number of nodes affected were yielded for angles between 0 and 20 degrees. This range of loads accords well with experimental studies on kinematic parameters (Agrawal et al., 2000; Anderson et al., 2002; Wintergeist et al., 2004) and with what was predicted from whole tooth analyses using an FE approach also (Spears and Macho, 1998). Although tentative, the apparent concordance between the FE analyses of enamel microstructure presented here and kinematic parameters thus highlights the integrated nature of the masticatory apparatus as a whole. If confirmed further, the study of enamel microstructure may hold important information with regard to kinematic parameters otherwise unavailable, for example, in fossil material.
In summary, the findings of the present study shed light on the importance of chemical composition for a biomechanical assessment of teeth and raise questions about the systematic nature of material properties between individuals, populations, and species. Despite its importance in equalizing stress across different loading directions however, the pattern of stress concentration, as well as distribution, is comparable between experimental setups, that is, between chemically heterogeneous and homogenous enamel. From these observations, it logically follows that, unless the chemical composition is known, the absolute strength of the tissue (and -by proxy- bite force magnitude, properties of food, and so on) cannot be inferred with certainty, whereas kinematic parameters apparently can. This finding offers novel possibilities for the study of dietary adaptations across species.
We thank Yong Jiang for writing the software to create the graphical models of decussating enamel upon which this study is based, and Iain Spears for discussion at an earlier stage of the project. We thank the reviewers for their constructive comments on an earlier draft of the manuscript.