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Effect of Enamel Prism Decussation and Chemical Composition on the Biomechanical Behavior of Dental TissueA Theoretical Approach to Determine the Loading Conditions to Which Modern Human Teeth are Adapted.

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THE ANATOMICAL RECORD 291:175–182 (2008)
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
DAISUKE SHIMIZU1,2 AND GABRIELE A. MACHO1*
Archaeological Sciences, Division of Archaeological, Geographical and Environmental
Sciences, School of Life Sciences, University of Bradford, Bradford, England
2
Department of Evolution and Phylogeny, Primate Research Institute, Kyoto-University,
Inuyama, Aichi, Japan
1
ABSTRACT
This theoretical study explored whether the directions of loads to
which modern human molars are commonly subjected to are reflected in
the biomechanical behavior of the tissue itself. A detailed finite element
model of a piece of decussating enamel (M3 paracone) was created, taking
into account differences in crystal orientation between the prism head and
the interprismatic matrix, and was tested under differently angled mediolateral loads (i.e., mimicking various stages of the chewing cycle). Second,
although teeth are highly mineralized, they also contain organic material
and water, while in modern humans, there are systematic differences in
chemical composition from the outer enamel surface to the dentinoenamel
junction. To test the biomechanical effects of this gradient in mineralization
a second set of models with gradually changing properties was created and
subjected to the same loads. Chemically heterogeneous enamel yielded overall lower stress levels than homogenous enamel, especially at extreme loading angles. However, the general trends regarding the increase in tensile
stresses at more oblique angles, and the number of nodes exhibiting tension, were comparable between the different set-ups. The findings support
suggestions that (a) the biomechanical behavior of dental tissue is the combined result of micromorphology and chemical composition and (b) that the
range of loading directions, to which teeth are normally subjected to, can be
inferred from dental microanatomy. For (palaeo)biological applications, the
findings suggest that the absolute strength of teeth (e.g., bite force) cannot
be predicted with certainty, whereas kinematic parameters of the masticatory apparatus can. Anat Rec, 291:175–182, 2008. Ó 2007 Wiley-Liss, Inc.
Key words: enamel prism decussation; human mastication; finite
element analyses; biomechanical behavior of dental
tissue
Grant sponsor: The Leverhulme Trust; Grant number: F/00
025/A; Grant sponsor: The Natural Environment Research
Council; Grant number: NER/A/S/2003/00347.
*Correspondence to: Gabriele A. Macho, Archaeological Sciences, Division of Archaeological, Geographical and Environmental
Sciences, School of Life Sciences, University of Bradford, BradÓ 2007 WILEY-LISS, INC.
ford BD7 1DP, UK. Fax: 44 (0)1274 235190.
E-mail: g.macho@bradford.ac.uk
Received 21 November 2006; Accepted 31 October 2007
DOI 10.1002/ar.20633
Published online 18 December 2007 in Wiley InterScience (www.
interscience.wiley.com).
176
SHIMIZU AND MACHO
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 midcrown 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-ofplane 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.
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
220 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 dis-
BIOMECHANICAL BEHAVIOR OF DECUSSATING ENAMEL
177
Fig. 1. A: Mediolateral cross-section of a maxillary molar showing the enamel pieces within the tissue
subjected to biomechanical testing. Arrow denotes direction of movement of the mandible. B: Creation of
the three finite element blocks of enamel, including boundary conditions and dimensions.
placement 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 mm (zaxis): 280 mm (y-axis): 280 mm (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 (210 degrees), and 320,823 (220 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).
RESULTS
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 rela-
178
SHIMIZU AND MACHO
Fig. 2. Material properties (Young’s modulus, Poisson’s ratio, Shear modulus) used for the creation of
the finite element models.
tively low tensile stresses for vertical and near-vertical
loadings, but stress increased considerably at higherangle 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
BIOMECHANICAL BEHAVIOR OF DECUSSATING ENAMEL
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.
DISCUSSION
Depending on the diet and/or the stage of the chewing
cycle, the lateral stroke of the mandible and, hence, the
TABLE 1. Crystal orientation used
within each elementa
Element number
x–z plane
y–z plane
a
1
2
3
4
90
90
90
75
90
30
90
5
For an explanation of prism geometry, see Figure 3(A).
Fig. 3. A: The geometry of the cross-section of a prism highlighting
the lateral node at the prism head from which the data were collected.
A small enamel block is also shown to illustrate the prism arrangement
and the crystal orientations within each element; further details about
the properties inputted are given in Table 1 and Figure 2. B: Illustration
of how one prism was tracked through the enamel block and how the
179
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
data were collected for the node highlighted in A. C: Given is the normal stress perpendicular to the c-axis of the prism on the star-plot for
two different positions within the tissue shown in B. Only tensile
stresses are analyzed in the present study, because of their potentially
damaging effect on the integrity of the tissue.
180
SHIMIZU AND MACHO
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);
Fig. 4. Cross-section through the finite element (FE) models with
chemically heterogeneous enamel at different angles. Note that for
computational reasons, that is, to apply surface-normal pressure, differently oriented enamel blocks were created and loaded.
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.
Fig. 5. The average tensile stress for each of the six layers (i.e., prism) through the depth of the
decussating enamel at different loading angles. A,B: Shown are the average values for chemically heterogeneous enamel (A), whereas B gives the values for chemically homogenous enamel.
BIOMECHANICAL BEHAVIOR OF DECUSSATING ENAMEL
Fig. 6. A: The average tensile stress values for each model (bar)
are plotted. B: The total number of nodes exhibiting tensile stress are
shown against the number of nodes in the outer third only. Note that,
on average, 50% of effected nodes are concentrated in the outer third
of enamel.
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
181
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 negativeangled 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,
182
SHIMIZU AND MACHO
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.
ACKNOWLEDGMENTS
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.
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