journal of dental materials, 2011
TRANSCRIPT
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INTRODUCTION
The restoration of endodontically treated teeth is a
challenging task that usually involves the treatment of
teeth with signicant loss of tooth structure. It has been
suggested that a post should only be used when the
remaining coronal tooth tissue can no longer provide
adequate support and retention for restoration1,2).
Nowadays, we see a variety of metallic and non-metallic
materials such as gold, titanium, stainless steel, carbon,
ceramic, zirconia and bre reinforced composites being
used for dental posts that provide retention to the core
replacing the lost coronal part of the tooth structure.
Until the mid-1980s, the indirect cast, post-core system
was considered the safest way to restore an endodontically
treated tooth3). However, the fabrication of cast posts
and cores is often a time consuming and expensive
procedure as it entails an intermediate restorative
phase. In contrast, the utilization of prefabricated posts,
combined with different types of core materials, is a
much easier process that can be performed in one visit4).
In the past, it was thought that posts reinforced
endodontically treated teeth5,6), however, other studies
have shown otherwise a post may be a predisposing
factor for root fracture7,8).
Another issue which has been widely discussed inthe literature until today is the most appropriate
material for posts9). The most highly recommended
material for reducing the risk of root fracture is exible
material that has a exible dentine-like quality with a
high Youngs modulus, such as ber-reinforced composite
posts10,11); however stress concentration may be focused
at the post-dentine interface causing debonding of the
post and movement of the core, resulting in
microleakage12). Conversely, rigid posts allow minimal
tooth preparation due to the smaller post-diameters;
however this may lead to root fracture13,14). For this
reason, clinicians (dentists) are left with two choices:
continuing to use posts with a high modulus, which could
lead to irreparable failure, or choosing low modulus posts
that can result in reparable failure9). Needless to say,
post material should be similar to dentine in modulus
elasticity exhibiting different properties at the coronal
and apical portions of the tooth for better biomechanical
performance.
The concept of functionally graded materials
(FGMs) is a new approach for the improvement of dental
post material performance compared to traditional
homogeneous and uniform materials15). This technique
allows the production of materials with very different
characteristics within the same material at various
interfaces. FGM is an innovative new technology that is
progressing rapidly in terms of the processing of
materials and the computational modeling15). It has
been found that the development of functionally graded
biomaterials for implants in medical and dental
applications allows the integration of dissimilar
materials, without severe internal stress, by combining
diverse properties into a single material16-20).
The objective of this study was to investigate thestress distribution of functionally graded dental posts
along the root canal system as compared to homogenous-
type dental posts, as well as determining the stress-
strain distribution at the post-dentine interfaces.
MATERIALS AND METHODS
Finite element modeling
Model Geometry
A three-dimensional model of a maxillary central incisor
3D-FE analysis of functionally graded structured dental posts
Noor H. ABU KASIM1, Ahmed A. MADFA1, Mohd HAMDI2and Ghahnavyeh R. RAHBARI3
1Department of Conservative Dentistry, Faculty of Dentistry, University of Malaya, Kuala Lumpur, Malaysia2Department of Engineering Design and Manufacture, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia3Department of Physics, Faculty of Sciences, University of Malaya, Kuala Lumpur, Malaysia
Corresponding author, Noor Hayaty ABU KASIM; E-mail: [email protected]
This study aimed to compare the biomechanical behaviour of functionally graded structured posts (FGSPs) and homogenous-type
posts in simulated models of a maxillary central incisor. Two models of FGSPs consisting of a multilayer xTi-yHA composite design,
where zirconia and alumina was added as the rst layer for models A and B respectively were compared to homogenous zirconia post
(model C) and a titanium post (model D). The amount of Ti and HA in the FGSP models was varied in gradations. 3D-FEA was
performed on all models and stress distributions were investigated along the dental post. In addition, interface stresses between the
posts and their surrounding structures were investigated under vertical, oblique, and horizontal loadings. Strain distribution along
the post-dentine interface was also investigated. The results showed that FGSPs models, A and B demonstrated better stress
distribution than models C and D, indicating that dental posts with multilayered structure dissipate localized and interfacial stress
and strain more efciently than homogenous-type posts.
Keywords: Heterogeneous structure, Functionally graded design, Multilayer post, Interfacial Stress, Simulated model
Color gures can be viewed in the online issue, which is avail-
able at J-STAGE.
Received Oct 4, 2010: Accepted Jul 25, 2011
doi:10.4012/dmj.2010-161 JOI JST.JSTAGE/dmj/2010-161
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was developed using Pro/Engineer software (Parametric
Technology Corporation, Kendrick St., Needham, USA),
based on the dimensions obtained from the
literature21-23). The relevant components such as the
alveolar bone, the periodontal ligament (PDL), dentine,
a post, the core, the crown and the gutta-percha were
also included in the geometric model (Fig. 1a) and their
dimensions is shown in Table 1. The geometry of the post
and core within the maxillary central incisor was
assumed to be axi-symmetrical along the vertical
centreline.
Mesh generation
Mesh generation is an important procedure that
subdivides the solid geometry of the incisor into smaller
elements. ABAQUS/CAE provides a number of different
meshing techniques. In the case of this study, a Free
meshing technique was followed that included
Table 1 Dimensions of the geometric model
Part Dimension (mm)
Crown
Height 10.5
Thickness at the top 2
Thickness at the bottom edge 1.5
Core
Height 8.5
Diameter 6
Thickness over the post 2
DentineLength 14.5
Width 8.5
Ferrule height 3
PostLength 16Diameter 1.5
Gutta-perchaLength 5Diameter 1.5
PDL Thickness 0.18
Bone Thickness 2
Fig. 1 (a) Schematic illustration of the geometric model and load directions. (b) Tetrahedral mesh structure of the geometric model.
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tetrahedral elements to separate the parts, because of
the complicated geometry of the models. This method
made it possible to achieve convergence. In addition, for
the purpose of this study, a four node, rst-order, linear
tetrahedral solid element was used (C3D4) for stress
analysis. This C3D4 incorporated a ne mesh in order to
obtain more accurate data, since constant stress on
tetrahedral elements exhibited low convergence24). After
conducting a pilot study, a tetrahedral mesh of 150465
(Fig. 1b) was used because the pilot study revealed an
error of below 0.1% for two different mesh sizes: 150465
and 239906.
Boundary condition
The boundary condition for the nodes was along the
bottom end line of the models, referred to as alveolar
bone as advocated by Yang et al.25). All components were
assumed to be perfectly bonded without any gapsbetween the components.
Three different types of loading conditions were
chosen as illustrated in Fig. 1a:
(i) A vertical load applied to the top of the crown to
simulate loading during bruxism; P1=100 N26,27).
(ii) An oblique load, angled at 45, to simulate the
masticatory force; P2=100 N26).
(iii) A horizontal load to simulate external traumatic
forces; P3=100 N26,27).
Materials and their elastic properties
A number of FGSP designs with various compositions
were investigated in a pilot study to ensure the best
combination for the FGSPs. The most signicant results
were seen in four layered FGSP, where the rst layer is
either zirconia (model A) or alumina (model B) and the
other three layers are made from xTi-yHA compositions,
as illustrated in Fig. 2. The elastic modulus of FGSPs
was estimated by applying the rule of mixture inspired
by the theory of composite materials as seen in the
following equation28):
where, (1)
1and 2are Poissons ratios for the rst and second
components in each layer.
E1 and E2 are the elastic modulus of the rst and
second components in each layer.
f1 and f2 are the volume fractions for the rst andsecond components in each layer.
The Poissons ratio for the FGSPs was also estimated
using the following formula:
(2)
The elastic properties of zirconia (in model C) and
titanium (in model D) posts and the other materials used
in the geometric models are presented in Table 2. Any
other stresses that may be introduced during the
endodontic treatment were ignored.
Ecomposite=
f1E1 +1
2
2
f2E2 2
1
=
+1 2
2
Fig. 2 Schematic illustration of the composition of the functionally graded structured posts.
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Finite element analysis
The generation of the nite element model, the
calculation of the stress distributions and the processingwere carried out using ABAQUS/CAE Professional
Version (Simulia, Valley St., Providence, USA). Stress
patterns were taken at various locations; (i) at the centre
of the posts; (ii) along the surface of the post at the
post-dentine interface and (iii) in the centre of the root
canal. The strain distribution was investigated at the
post-dentine interface and the maximum principal stress
in each component (X, Y and Z) was also studied. In
spite of this, no additional information was obtained
about the geometrical symmetry of the model along the
vertical axis (Y axis) and the direction of the exerted
loads; which are parallel, perpendicular, and oblique at
45.
RESULTS
Stress analysis under various load conditions
The maximum principle stress distributions at various
loading directions are shown in Fig. 3. The highest stress
regions are at the top of the crown and the apical part of
the root, when a vertical load was applied (Fig. 3a). On
the other hand, models C and D showed considerable
stress at the apical region of the posts (Fig. 3a).
Oblique loading caused stress to decrease
progressively from the outer to the inner part of the root
(Fig. 3b). However, it was evident that there were
differences between the stress distribution in FGSPmodels, A and B compared to models C and D, having
zirconia and titanium posts respectively. Figure 4a
shows the stress distribution in the centre of the root
canal indicating higher stress in models C and D.
Horizontal loading also showed a high level of stress
with a similar distributions pattern to oblique loading
(Fig. 3c). Moreover, stress concentration can be seen in
the centre of the root canal (Fig. 4b). When the posts
were removed, stress distribution was seen on the canal
walls, suggesting that the stress distribution was spread
over a larger area, yet the maximum principle stress was
s still within the same range (Figs. 4a and 4b).
The stress distribution along the dental posts in
models A, B, C and D when loaded vertically, obliquely
and horizontally are shown in Fig. 5. The maximumprinciple stress concentration along the post can be
observed in models C and D. In contrast, models A and
B showed a consistently lower stress distribution along
the dental posts.
Maximum principle stress and strain distributions at the
post-dentine interface
Figures 6 and 7 showed the stress and strain distributions
at the dentine-post interface. In the FGSP models, the
stress at the coronal area were negligible, while it
increased at the cervical part of the dentine ending with
gradual changes and uctuations at the apical part of
the post-dentine interface (Fig. 6). FGSP models
demonstrated less strain distribution under vertical
loading than model C and D at the apical part (Fig. 7a).
While at the junction between the middle and coronal
parts, FGSPs showed higher localized strain. For oblique
and horizontal loadings, the FGSP models demonstrated
less strain at the post-dentine interface from the cervical
part to the apical part of the dentine (Figs. 7b and c).
However, the strain distribution uctuated at the coronal
part of the FGSPs (Figs. 7b and c).
DISCUSSION
The Finite element method was used to investigate
stress in a human maxillary central incisor which hadbeen restored using various types of dental posts. A high
number of elements was used in this present study to
give a better estimation of the stress distribution.
Although Holmes et al.35), Lanza et al.36)and Zarone et
al.37)have included a cement layer in their nite element
analysis, others such as Cailleteau et al.38), Joshi et al.26)
and Toksavul et al.39) have omitted the cement layer. In
this study, the cement layer was not included as we
aimed to address the stress distribution of newly
designed dental posts. The highest value of stress
distribution was recorded at the post-dentine interface
when oblique and horizontal loadings were applied.
Table 2 Elastic properties
Materials Youngs Modulus (GPa) Poissons ratio References
Dentine 18.60 0.30 10, 29)
Titanium 116 0.33 30)
PDL 68.9103 0.40 31)
Alveolar bone 13.70 0.30 31)Gutta-percha 0.96103 0.40 10)
Zirconia 200 0.33 32)
Ceramic crown 120 0.28 33)
Composite resin core 16.60 0.24 26)
Hydroxyapatite 40 0.27 16)
Alumina 380 0.25 34)
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Fig. 3 Contour plots of the maximum principle stress distributions in models A [FGSP: zirconia/(xTi + yHA)]; B [FGSP:
alumina/(xTi + yHA)]; C [zirconia post]; D [titanium post].
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These ndings are in agreement with Zarone et al.37),
who recorded a high stress concentration at the
post-dentine interface. They also stated that when the
dental post is made from a material with a high modulus,
it will adversely alter the natural biomechanical
behaviour of the restored tooth when functioning.
Ideally, dental posts should stabilize the core and
not weaken the root40). When occlusal force is applied
coronally, the force is transferred to dentine through thecore and post system. In such situations, stress
concentrates at the cervical and apical part of the tooth.
Stress concentration at the cervical region is likely to be
due to an increase in the exure of the compromised
tooth structure, while stress concentration at the apical
region is generally due to tapering of the root canal and
the characteristics of the post41). High stress
concentrations were also observed at the apical
termination of the post42). The stiffness mismatch
between the intra-radicular post and the dental tissue
also resulted in high stress concentrations along the
post-dentine interface27). It has therefore been suggested
that an ideal dental post would have high stiffness at the
cervical region and that this stiffness should be gradually
reduced to match the dentine stiffness at the apical
end43). The compositional gradient of multilayer materials
achieved in FGMs has been identied as a possible
solution for this problem of mismatch of material
properties. Drake et al.44) used the law of power
distribution to show that signicant reduction in stress
and plastic strain can be achieved by increasing thegradient of thickness of ceramic materials and tailoring
the exponent to provide a gradual compositional change
near the parts exhibiting high modulus and little
plasticity. Matsuo et al.45) reported a reduction in the
concentration of stress at the apical area when FGM
dental posts were used.
Vertical load analysis
The highest value of maximum principle stress was
observed at the apical part of the posts in models C and
D under vertical loading. However for models A and B,
there was lower stress concentration at the apical part
Fig. 4 Contour plots of the maximum principle stresses distribution in dentine under oblique and horizontal loads for
models A [FGSP: zirconia/(xTi +yHA)]; B [FGSP: alumina/(xTi + yHA)]; C [zirconia post] and D [titanium post].
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Fig. 5 Maximum principle stress distributions along the center of the posts from coronal to
apical when loaded vertically (a), obliquely (b) and horizontally (c).
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Fig. 6 Maximum principle stress distributions at the interface between the posts and
surrounding structures from coronal to apical when loaded vertically (a), obliquely (b)
and horizontally (c).
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Fig. 7 Strain distributions at the interface between the posts and surrounding structures
from coronal to apical when loaded vertically (a), obliquely (b) and horizontally (c).
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as shown in Fig. 3a. This is due to the functionally graded
structural design of models A and B. The variation of Ti
concentration in xTi-yHA provides a smooth change in
the property of FGSPs, providing a reduction in the
stress concentration46). Thus, FGSPs were successful in
improving the stress dissipation and barring stress
propagation in the tooth structure. Figure 5a shows the
maximum principle stress concentrations along the
dental posts. FGSPs displayed better stress distribution
at the coronal and apical parts compared to homogenous
posts. Although higher stress was observed at the middle
portion of models A and B as shown in Fig. 5a, this value
can be considered as negligible compared to models C
and D. A considerably high stress concentration was
detected at the apical parts of the posts in models C and
D, which could be the reason for failure at the apical
parts and the fracture of the root in commercially
produced dental posts.
The maximum principle stress distribution in the
interface of the posts and their surrounding structure
can be seen in Fig. 6a. FGSPs dissipated interface stressexcellently from the coronal to the apical parts of the
posts. The homogenous posts, on the other hand,
transferred the stress through the whole interface, with
two points of maximum stress located at the coronal and
apical parts. The behaviour of models A and B was very
similar, while models C and D only demonstrated similar
behaviour towards the apical part of the post interface.
The strain distribution in the interface of the post
and its surrounding structure is shown in Fig. 7a.
Compared to homogenous posts, FGSPs showed less
strain values at the apical part. Localized strain values
in FGSPs showed a peak at the junction between the
coronal and the middle third, when a vertical load was
applied. The occurrence of this peak may be due to the
limitations of the FEA program where an estimate of 1
mm thickness has been used for the transition layer
between the rst and second layers (Fig. 2), assuming a
uniform composition. However, this may be inaccurate
when FGMs are fabricated. In reality, a gradual change
in the composition of the rst and second layers is
normal, resulting in what is called a transition zone.
Oblique and horizontal load analysis
The maximum principle stress was more prominent at
the outer sides of the root canal for models C and D,
compared to models A and B, as shown in Fig. 3b, c. This
is probably due to the low stiffness of the FGSPs at theapical part of the root canal. The results therefore further
substantiate the claim that FGSPs help to reduce and
dissipate stress concentration.
Stress distributions at the post-dentine interface are
illustrated in Fig. 6b, c. FGSPs dissipated or even
eliminated the interface stress from the coronal portion
to the middle part of the post. However, the interface
stress was high in the middle part of the post and
increased progressively at the apical part, uctuating in
value. In models C and D, maximum principle stress
increased dramatically throughout the interface, with a
higher intensity and uctuations in stress values at the
apical part. Similar trends were observed for oblique and
horizontal loadings for all models (Fig. 6b, c). The strain
behaviour at the middle and apical parts (Fig. 7b, c)
corresponded to the stress analyses when oblique and
horizontal loadings were applied. In the horizontal
plane, the material was distributed uniformly, i.e.there
were no changes in composition in a radial direction.
Therefore, FGSPs showed slightly more shear strain
distribution than the homogenous posts in the coronal
part.
Comparison between vertical, oblique and horizontal
loadings
Under horizontal and oblique loadings, the higher values
of maximum principle stress are distributed mainly at
the coronal and middle parts of the homogeneous posts.
Then the stress reduces dramatically in the middle part
of the posts, and becomes almost negligible at the apical
part. However under vertical loading, the concentration
of stress was low at the coronal parts but was noticeably
high at the apical parts of the model C and model Dposts. Vertical loading caused a high concentration of
stress at the apical portion of the tooth, yet under
horizontal and oblique loading, the stress became
concentrated at the outer sides of the root. Also, the
interface stress and strain increased in the middle of the
tooth and grew progressively, uctuating at the apical
part under horizontal and oblique loadings. On the
contrary, under vertical loading, the interface stress and
strain increased at the coronal part and reached its
maximum level at the apical part with little uctuation.
The concentration of stress caused by horizontal and
oblique loading was higher than that caused by vertical
loading at the apical part of the simulated posts. Thus,
horizontal loading should be avoided as much as possible.
These ndings concurred with the results reported by
Yang et al.47), who observed that greater deection and
higher stress is generated by horizontal loading. Under
horizontal and oblique loadings, post material should be
chosen carefully to ensure that the posts support the
restored tooth and prevent high stress along the inner
canal wall (Fig. 4). Ramakrishna et al.48)suggested that
dental posts should be stiff in the coronal region, i.e.the
core, so that the core is not stressed excessively when
occlusal force is applied to the crown. Hence, an ideal
dental post is one that has a high degree of stiffness at
the coronal region, and which gradually reduces to a
value similar to that of dentine at the apical end. Thishigh stiffness eradicates stress from the core, and the
gradual reduction in stiffness dissipates stress from the
post to the dentine uniformly. This gradual dissipation of
stress eliminates the concentration of stress and reduces
interfacial shear stress. For vertical loading, materials
that prevent a high concentration of stress at the apical
portion of the tooth should be chosen. In addition, the
stiffness of the entire post-core system must be able to
resist the forces of mastication, with the least possible
deformation49).
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CONCLUSION
This study shows that FGSPs exhibited several
advantages in terms of stress distribution compared to
posts fabricated from homogeneous material. The stress
and strain distribution at the post-dentine interface of
FGSPs was better than that of homogenous posts.
Functionally graded materials approach can be used to
design new dental posts that enhance the success of
endodontically treated teeth.
ACKNOWLEDGMENTS
The authors wish to sincerely thank Mr. Bernard Saw
Lip Huat, at the Department of Engineering Design and
Manufacture, Faculty of Engineering, University of
Malaya for his invaluable advice in FEA. This study was
funded by PS354/2008C, University of Malaya.
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