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Aninvestigationintofracturedsurfacesof
enamelofmodernhumanteeth:Acombined
SEMandcomputervisualisationstudy
ArticleinArchivesofOralBiology·July2003
DOI:10.1016/S0003-9969(03)00040-2·Source:PubMed
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Archives of Oral Biology (2003) 48, 449—457
An investigation into fractured surfaces of enamel
of modern human teeth: a combined SEM and
computer visualisation study
Y. Jianga, I.R. Spearsb, G.A. Machoa,*
a
Hominid Palaeontology Research Group, Department of Human Anatomy and Cell Biology, The University
of Liverpool, The Sherrington Buildings, Liverpool L69 3GE, UK
b
School of Social Sciences, University of Teesside, Middlesbrough TS1 3BA, UK
Accepted 4 February 2003
KEYWORDS
Enamel microstructure;
3D computer model;
Prism arrangement
Summary It has long been recognised that the enamel microstructure may hold
important information with regards to phylogeny and masticatory biomechanics.
Further, the biophysical and adaptive processes involved in enamel formation and
in the creation of different microstructures are poorly understood. This lack of
understanding is in part due to technical difficulties when visualising the 3D structure
of enamel. Using modern visualisation techniques, models of various regions of
different modern human teeth were created. Underlying these models are consistent
mathematical representations of the interplay between cell-to-cell adhesion, integrity
of the advancing enamel front and (potentially decreasing) constraints on the prism
course from the dentino-enamel junction (DEJ) to the outer surface. Seven modern
human teeth (I1, 1 lower C, 1 P4, 1 M2, 2 M2 and 1 M3) were fractured longitudinally and
formed the basis for the creation of the models. For validation purposes the teeth were
then fractured transversely, thus allowing quantitative comparisons between the prism
pathways on the newly fractured transverse plane and the transverse pathways as
predicted by the model. It was found that these predictions were fairly accurate
provided that (a) the light position with respect to the model corresponds with the
beam position with respect to the scanned surface and (b) the path of prisms was
carefully reconstructed/extrapolated from SEM in cases where prisms were broken.
Given that these predictions were based on the mechanisms governing enamel formation as applied to the model, it is suggested that such theories must be reasonable.
In other words, biophysical processes, rather than complicated (genetic) positional
information, suffice to create different enamel microstructures. In addition, systematic differences were found in prism deviation from their c-axis in different enamel
pieces. Given the nature of these differences it is suggested that enamel formation is
not only the result of biophysical processes (proximal causes), but could be due to the
structures having been selected for in order to counteract masticatory stress exerted
during the lifetime of the species (ultimate causes). As to whether and to what extent
this may be the case is not yet clear but it is apparent that computer visualisation does
have potential to quantify enamel microstructure and to address such questions. Given
its non-destructive nature, computer modelling could have particular relevance for
studying fragmented fossilised remains.
ß 2003 Elsevier Science Ltd. All rights reserved.
Corresponding author. Tel.: þ44-151-794-5466; fax: þ44-151-794-5517.
E-mail address: [email protected] (G.A. Macho).
0003–9969/03/$ — see front matter ß 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0003-9969(03)00040-2
450
Introduction
Mature dental enamel is the hardest tissue of the
human body. On a macrostructural level it is composed of over 96 wt.% (85 vol.%) of inorganic, hydroxyapatite crystals, e.g.16 small quantities of other
minerals,2,6,22 water17 and about 1% organic material.14 On an ultra-structural level, the hydroxyapatite crystals are long, hexagonal rods and are
aligned along a common long-axis, thus forming
prisms; interprismatic matrix is formed by crystals
whose orientation differs from that of prisms.10 On
a microstructural level, enamel is made up of a
complicated arrangement of prisms and interprismatic matrix. Even within a single tooth, the prism
arrangement differs from region to region, i.e. from
the cusp tip to the cervical margin and between
cusps, e.g.3,18,21 This not only confounds cross-species comparisons, but also hampers interpretations
about the biomechanical behaviour of the tissue19
and the crack-resistance of teeth.5 While studies on
enamel structure are abundant in the published
literature, studies on a microstructural level are
mostly descriptive, e.g.4 At present, this is almost
certainly due to the technical difficulties associated
with ascertaining and quantifying the 3D enamel
microstructure.
Technical advancements in computer hardware
and software have extended the possibilities of
exploring and reconstructing complicated 3D structures (e.g. trabecular architecture). However, to do
so usually requires that internal surfaces or boundaries can be identified which in turn requires that
differences in chemical composition and/or density
occur between regions. Unfortunately, as regards
enamel microstructure, the only distinctive boundary between prisms is a change in (crystal) orientation. In other words, prismatic and interprismatic
enamel are chemically identical, and can only be
distinguished optically as a result of different
reflection from the same light source, or through
beam reflection. This confounds 3D reconstruction
of enamel microstructure and, consequently, an
understanding of prism arrangement has so far
relied heavily on the subjective interpretation by
the observer.
Although the concept of computer visualisation is
relatively new, it is increasingly used for a wide
range of applications. By applying optical algorithms (e.g. position of light source, surface opacity, etc.) to a geometrical model, it is possible to
create a realistic visual representation of any given
object or combination of objects. Shading, possibly
the most important of these algorithms, can be
applied to surfaces depending on their orientation
with respect to the position of the light source and
Y. Jiang et al.
viewing direction. Given that the appearance of
prism orientation with respect to the light source
(or beam) underlies the identification of enamel
microstructure, such visualisation techniques may
have scope for an understanding, and quantification, of its microstructure. This may be particularly
so, as prism decussation does not appear to be
random. In modern humans, for example, prisms
follow a sinusoidal course from the dentino-enamel
junction (DEJ) towards the outer enamel surface
(OES), while prisms in adjacent rows are slightly
out of phase, e.g.11—13 Following these early studies, it was hypothesised that movements of ameloblasts are constrained and interdependent,
chiefly as a result of the advancing enamel front
retaining its integrity and exerting a force against
the increasing enamel volume (hydrostatic pressure sensu).13 If correct, it should be possible to
devise an algorithm which can recreate different
3D enamel microstructures.
The aims of this paper are two-fold: (a) to test the
feasibility of computer visualisation for the reconstruction of enamel and, in particular, whether outof-plane prism deviations can be understood from 2D
SEM images and (b) to test whether biophysical
processes as represented by mathematical algorithms, rather than complicated genetic (positional)
information, could underlie the complex 3D microstructure of modern human teeth. The long-term
aim is to develop a means of predicting enamel
microstructure from broken enamel surfaces
(e.g. fossil teeth) for comparative and biomechanical purposes.
Materials and methods
As regards the algorithms underlying the computer
model, a few biological mechanisms were considered (modified from13). Firstly, it was assumed that
the integrity of the advancing enamel front is
retained throughout odontogenesis. In other words,
adjacent prisms in one tangential plane must be
adjacent in the next. Secondly, the shape of prisms
must be retained, although the interprismatic
matrix between prisms can be slightly expanded
or reduced (i.e. no overlap of prisms); inspection
of SEM images suggests that this is case. Thirdly, it
was assumed that the movements of prisms close
to the DEJ are more constrained than they are
towards the outer enamel surface as a result of
the DEJ, on the one hand, and the advancing enamel
front, on the other (i.e. geometrically restricted).
Furthermore, it seems reasonable to suggest that
cell—cell adhesion remains either unchanged
throughout development or becomes more relaxed
A 3D model of enamel microstructure
as the enamel front advances and the cells age; this
would further constrain prism movement close to
the dentino-enamel junction. Consequently, the
frequency of prism undulation is higher at the DEJ
than it is towards the outer enamel surface. These
simple predictions form the basis for the mathematical algorithms developed for the graphical model.
The programming language Cþþ was used to call
up and create functions within the OpenGL graphics
architecture.23 The geometry of the enamel microstructure is created and the optical parameters
assigned by calling up these functions. When creating the geometry of the enamel microstructure
several steps are taken. The user is prompted to
position the viewing direction and light source
before the model is rendered. A row of speciesspecific prism cross-sections is then created, i.e.
the average proportion between prism height, prism
width and prism tail width is modelled (Fig. 1a—c).
Each prism cross-section is created by square Bspline (four points) (Fig. 1c). These cross-sections
are then extruded along another square B-spline in
the z-direction, thus defining the c-axis of the prism
(Fig. 1d—f). The geometry of the square B-spline
along the long-axis is controlled by 29 points
(Fig. 1d). At this stage, the user is prompted to
nudge the curve, i.e. superimpose a curve, until
the model appears similar to the SEM image (Fig. 1f).
451
In doing so, the user can simulate the out-of-plane
sinusoidal course of the prisms axis as it passes from
the dentino-enamel junction towards the outer
enamel surface. Adjacent layers are slightly out
of phase (Fig. 1g), as a result of successive differentiation of rows of ameloblasts during odontogenesis, on the one hand, secretion rate and the
cohesion of the advancing enamel front, on the
other. The number of rows between same-phased
layers can be assessed from longitudinal breaks/
sections and can be inputted in the model. Fig. 2
illustrates the capabilities of the model with regards
to changes in frequency (Fig. 2a—c), amplitude
(Fig. 2a—d), distribution of the maximum amplitudes (Fig. 2a,e and f), and position of prisms at
the DEJ with regard to the OES (Fig. 2a and g). In
lateral view (longitudinal break) the angle of the
prism long-axis with respect to the DEJ and its
(possible) upward/downward curvature can also
be changed if required. Some further features
(e.g. possible curves in vertical plane, secondary
curves, etc.) were built into the model, but were
not found to be necessary for the recreation of
modern human enamel microstructure and are
therefore not discussed further. Thus far, only limited provisions have been made to change the curvature of the DEJ/OES and, consequently, the prism
width remains constant throughout its length.
Figure 1 Illustration of how the model was created. In (a) and (b) the distinctive key-hole cross-sectional geometry of
modern human enamel prisms is recorded10 and modelled (c). In this example, the maximum width and height of 20
prism heads were measured, as was the cross-sectional width of the prism tail, and an average size is assigned to the
model. For the creation of the 3D computer model, one prism is first created (d) and the control points are then
manipulated (e), so that the shading pattern of the model (f) matches that of the SEM image. Then the rows of prisms
between prisms with the same phase are inputted and the model is created (g). The number of prisms in the x- and
y-axis are then increased.
452
Y. Jiang et al.
Figure 2 Illustration of various shapes of prism courses along the c-axis and one (simplified) completed cycle (grey).
In (a) a generalised prism course is shown; while (b) and (c) indicate the effects of an increase and increase in
frequency, respectively. The change in amplitude is shown in (d). Pictures (a); (e); and (f) depict how the position of
the greatest amplitude(s) can be varied across the thickness of the enamel. The origin of the prisms may not always be
in the same plane as the straight part towards the outer enamel surface (g); both the disparity and the position of
curvature can be modelled.
A number of teeth were chosen from our teaching
collection. Longitudinal fractures were induced in
the teeth, using small chisels and hammer. As
enamel has the tendency to break along prisms,1
this method was considered most appropriate for
the present purposes. Subsequently, the pieces
were broken transversely as far apically as possible:
usually, the transverse breaks were approximately
at mid-crown (at the beginning of imbricational
enamel). It was attempted to create breaks through
the middle of the cusps, but this was not always
possible, especially in unworn teeth. For the teeth
presented here, and except for one molar (mesial
aspect), the breaks were through the (presumptive)
cusp tips along a bucco-lingual plane. While the
incisor and the canine could be broken with ease,
posterior teeth were more resistant to breakage.
The premolar exhibited a fairly clean, i.e. along the
A 3D model of enamel microstructure
453
Figure 3 In (a) and (b) the longitudinal break of the enamel block is shown and recreated in (c). Subsequently, the
transverse section of the enamel block (d) is analysed and the tracked prism course (black line) is compared with the
predicted prisms in the model.
prisms, break (Fig. 3a and b) and was thus deemed
particularly suited for the assessment of light position for the creation of the model. The purpose of
the other teeth/models was chiefly to assess the
accuracy when dealing with prisms that were broken across as well as along the c-axis. When making
the models, the SEM images were assessed carefully
and cutting planes were introduced in the models to
cross-check the images obtained from the model
with the SEM. The range of variation in prism deviation among modern human molars was subsequently
appraised.
All breakages were cleaned and the surfaces
etched for 20 s in 5% HCL. The fractured surfaces
were then viewed with the SEM (ISS) using backscattered mode (BSE).
Results
Utilising the computer model described above, the
associated microstructural appearance was first
recreated in a P4 (Fig. 3a—c). In doing so, predictions were made by the model in the out-of-plane
transverse direction (Fig. 3d). Given that light
position affected our interpretation of enamel
microstructure, lighting position/orientation was
varied (Fig. 4a). The best prediction occurred
when the light source position in the model (208)
corresponded with the collector angle to the beam
in the SEM (Fig. 4b). In this case, the amplitude
(i.e. the perpendicular distance of the prisms away
from its long-axis) of the predicted model was
always within 1 mm of the tracked prism, while
the overall error was consistently less than 2%.
Interestingly, the model consistently underestimated the true prism length. Once the correct light
position had been established for the premolar, outof-plane prism deviation was predicted for the
other six specimens and, subsequently, compared
with the tracked prisms in the transverse planes.
Good agreement was found between the predicted
and the actual prism course in all instances, despite
the greater prism deviation in posterior teeth; the
overall error in amplitude was about 5%. Correct
models of enamel pieces of all teeth were then
created and compared. Fig. 5 shows the models
created from longitudinal and transverse breaks
(approx. mid-crown) of the modern human teeth
analysed here. For each recreated piece of enamel,
a simplified view of one cycle in transverse view is
also presented (sensu Fig. 2). Molars consistently
exhibit more deviation than anterior teeth, while
the outer straight enamel (with one exception) is
off-set with regards to the origins of the prisms at
the DEJ (Figs. 5 and 6).
Discussion
It is evident that the shading algorithms together
with the theories adopted in the creation of the
454
Y. Jiang et al.
Figure 4 (a) The positions of four different lighting arrangements used in predicting out-of-plane dimensions of
prisms are shown. Viewing direction is orientated along the x-axis. Also shown are the angles of the light-rays with
respect to the viewing direction (x-axis). The angles given are in accordance with the expected range in the SEM, i.e.
198 (1); 258 (2); 458 (3); and 558 (4). (b) Comparisons of the out-of-plane deviations predicted from the longitudinal
surface of the model are made with the tracked deviations from the transverse view of the enamel block. Each point
represents a single control point.
model give realistic predictions of enamel microstructure. However, in doing so there are several
limitations of this protocol which affect both reliability and reproducibility of the results. Most notably, despite our intentions of reducing the
subjectivity involved in predicting enamel microstructure, the overall procedure adopted is still
reliant on the user being able to match up what is
viewed under a microscope with what is seen on a
computer-rendered model. Despite this, the model
has potential for use as an analytical tool and allows
translation of previously observed patterns into a
quantifiable format. However, care must be taken
that the direction of light used when setting up the
model is comparable to the angle between the beam
and the collector in the SEM. When done so, the
error margin of the amplitude was within 2% in cases
of clean breaks (e.g. P4) and within 5% in cases
where prisms were broken across the c-axis. It is
noteworthy that the true prism length was always
underestimated, but never overestimated. The
greatest error margins were found in posterior
teeth, which exhibit substantial prism deviation/
decussation.
The process of crack propagation is a complicated
dynamic process7 depending largely on the unknown
orientation of prisms, and exact orientations of
fractured surfaces are difficult to control for. Nonetheless, teeth have a tendency to break along, rather
than across, the prism long-axis,15 whereby the
plane of fracture may hold important information
with regard to prism organisation. However, prism
A 3D model of enamel microstructure
455
Figure 5 Enamel blocks created from six modern human teeth (transverse and longitudinal breaks at mid-crown). The
pieces are not to scale and are intended only for illustration of differences in prism amplitude, frequency, distribution
and cycle length between teeth: (a) bucco-lingual break through a lower central incisor; (b) lower canine; (c) upper
second molar (paracone); (d) mesial aspect of a second upper molar (different individual to (c)); (e) protoconid of a
lower second molar; (f) metacone of a third upper molar.
decussation has probably evolved as a crack stopping mechanism5 thus making it virtually impossible
to obtain clean breaks in heavily decussating
enamel. As a case in point, in all molars (except
for the paracone of an upper second molar) the start
of the prisms at the DEJ is off-set in relation to the
plane of the outer 1/3 of straight prisms. Any longitudinal crack initiated at the outer enamel surface
must therefore travel across the undulating prism
path if forced (Figs. 5c,e,f and 6a), although this
is not the case for transverse breaks (Fig. 6b). These
systematic changes in the amount of prism deviation concur with expected increases in bite force
towards the posterior of the mouth, e.g.9 This,
together with the findings that these cusps are
apparently designed to sustain higher loads,
i.e.8,20 would add support to the growing consensus
that enamel microstructure is, at least in part,
adapted to meet the functional demands expected
during the individual’s lifetime.
456
Y. Jiang et al.
Figure 6 Differences in prism course between teeth shown in Fig. 5: (a) shows the projected prism outline in
transverse plane (x—z-axis); while (b) illustrates the orientation of the prisms with regard to the DEJ (y—z-axis).
The mathematical algorithms employed to write
the computer programme are based on three simple, but biological meaningful, assumptions about
the biological/physical mechanisms underlying
enamel formation. To reiterate, it was assumed
that the movements of ameloblasts during odontogenesis are constrained and interdependent as a
result of cell differentiation and extension rate
(i.e. number of layers within a cycle), the volume
secreted#1 and cell—cell adhesion of the advancing
1
This should not be confused with the ‘secretion rate’
commonly reported in the anthropological literature (see, for
example, contributions in Journal of Human Evolution 4/5
(1998), special issue). The latter is a 2D measure of the 3D prism
structure. Yet, prism diameter differs between species, and
changes from the DEJ towards the OES in order to accommodate
the larger surface area of the OES. Without due regard of these
factors (i.e. proper scaling) the 2D secretion rates reported in
the literature are meaningless for the description of (a) the
volume of material secreted; (b) cell activity; and (c) growth
rates.
enamel front (i.e. frequency and amplitude of sinus
curves). In making these assumptions, modern
human enamel microstructure could be successfully
reconstructed for different teeth and in different
locations. Although we were unable to directly
verify the enamel structure hidden below the fracture planes, the regularity with which the prisms
approach (and go out of) the broken longitudinal
and transverse breaks, and our ability to mimic this
appearance in the models, would imply that the
models reflect reality. Consequently, the success of
the model should be attributed to previous theories
of enamel formation in modern humans.13 Interestingly, ongoing work on other species indicates that
these theories may not only hold for the formation
of modern human dental microstructure, but
(at least) across primates, although provisions have
to be made for prisms deviating in more planes. It is
apparently not necessary to invoke complicated
genetic mechanisms, based on positional information of cells, to account for the different enamel
A 3D model of enamel microstructure
microstructures. Biophysical processes suffice as the
proximal causes for their development, whereas the
expected biomechanical demands during the animal’s lifetime may be regarded as the ultimate
causes for the selection of different microstructures.
In conclusion, technical advancements in visualisation technology have great potential for the
study of dental material. Although the technique
presented here has shortcomings, in particular with
regards to subjectivity, it allows the quantification
of enamel microstructure for comparative purposes. Furthermore, it facilitates the generation
of models, which can be used for biomechanical
testing.19 As such, it may provide a valuable tool in
biological enquiry.
Acknowledgements
This study was supported by The Leverhulme Trust
(F/00025/A). We thank Dr. Brian Boothroyde for his
help with the SEM, and Dr. Daisuke Shimizu for
discussion. The comments of Dr. R. Holland and
an anonymous referee are appreciated.
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