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Effect of prism orientation and loading direction on contact stresses in prismatic enamel of primates Implications for interpreting wear patterns.

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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
Hominid Palaeontology Research Group, Department of Human Anatomy and Cell Biology, University of Liverpool,
Liverpool L69 3GE, UK
Sport and Exercise Subject Group, School of Social Sciences and Law, University of Teesside, Middlesbrough TS1
finite element stress analysis; tensile stress; friction; leading edge; trailing
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
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-
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: for DS; for GM.
Received 17 July 2003; accepted 11 December 2003.
DOI 10.1002/ajpa.20031
Published online 13 August 2004 in Wiley InterScience (www.
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.
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
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)
Crystal orientation x-y plane
Crystal orientation y-z plane
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
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).
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).
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).
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
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
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
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
Fig. 6. Illustration of chewing cycle and of what constitutes leading (L) and trailing (T) edge. Average prism orientation is also
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
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
the investigation of prism orientation in primates
can (with caveats) be usefully exploited to make
functional and behavioral inferences.
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).
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