Dental Materials Journal 2009; 28(2): 219－226
Three-dimensional finite element modeling from CT images of tooth and
Kiyoshi TAJIMA1, Ker-Kong CHEN2, Nobusuke TAKAHASHI1, Naoaki NODA3, Yuki NAGAMATSU1 and
1Division of Biomaterials, Kyushu Dental College, 2-6-1 Manazuru, Kokurakita, Kitakyushu 803-8580, Japan
2Division of Operative Dentistry, Kyushu Dental College, 2-6-1 Manazuru, Kokurakita, Kitakyushu 803-8580, Japan
3Mechanical Engineering Department, Kyushu Institute of Technology, 1-1 Sensui, Tobata, Kitakyushu 804-8550, Japan
Corresponding author, Kiyoshi TAJIMA; E-mail: email@example.com
The aim of this study was to develop a three-dimensional (3D) finite element (FE) model of a sound extracted human second
premolar from micro-CT data using commercially available software tools. A detailed 3D FE model of the tooth could be
constructed and was experimentally validated by comparing strains calculated in the FE model with strain gauge
measurement of the tooth under loading. The regression coefficient and its standard error in the regression analysis
between strains calculated by the FE model and measured with strain gauge measurement were 0.82 and 0.06, respectively,
and the correlation coefficient was found to be highly significant. These results suggested that an FE model reconstructed
from micro-CT data could be used as a valid model to estimate the actual strains with acceptable accuracy.
Key words: Finite element modeling, Tooth, CT
Received Sep 5, 2008: Accepted Oct 23, 2008
implemented in dentistry in the early 1970s and has
been increasingly used to analyze biomechanical
behaviors of dental materials
structures1-3). In FE analysis, it is necessary to
construct an FE model of the structures to be
examined. An FE model with a topological
description of geometrical and structural asymmetry
can be modeled in either a two-dimensional (2D) or
three-dimensional (3D) approach4-6). Recently, 3D
models for use in FE analysis have became popular
in the study of dental biomechanics, because they
allow better understanding of the mechanical and
fracture behavior of the dental tissues and structures,
providing more realistic and accurate results
resembling the actual occurrence in clinics6) than do
the simplified 2D models.
Accurate geometry is one of the important keys
to successful 3D modeling of both sound and restored
teeth in FE analysis. For complicated features of
teeth, there were two previous methods of manual
description: 1) use of standard anatomical data in the
literature, and 2) use of cross-sectional histological
images of teeth7,8). These conventional ways to
describe the 3D models often necessitated time-
consuming and labor-intensive effort, and resulted in
a generally glossy simplification of the model
geometry. Recently, an image acquisition method
using computed topography (CT) has been extensively
applied as a scanning tool for 3D-digitizing purposes
element (FE) analysis was initially
in modeling of teeth9-15), providing higher accuracy,
faster digitization and finer description. In addition,
several pioneering modeling techniques for CT data
have been originally developed as in-house programs
to extract the model geometry, because this method
requires the extraction of inner and outer contours
from CT data of teeth7-10). More recently, several
computer-aided techniques to extract the geometry
have become commercially available with the
industrial development of 3D image processing and
reverse engineering techniques, facilitating the
construction of FE models11-15).
Validation of the FE model, one of the important
problems in FE analysis17,18), has been previously
reported by experimental
comparison of the results with those of laboratory or
clinical tests of the teeth18-25). It is possible to
compare the strain calculated in FE models and
experimentally measured results using strain gauges,
although the process is very difficult and tedious.
Some researchers have previously indicated that 3D
FE models reconstructed
histological images showed good agreement with
experimental methods21-24). However, until now, the
resulting 3D FE models constructed from CT image
data of the teeth have not been fully validated18,25).
The purpose of this study was to develop a 3D
FE model via a CAD model reconstructed from CT
data of the extracted tooth, using commercially
available software tools. Furthermore, the accuracy
of the created FE model was experimentally validated
by comparing strains calculated from the FE model
Dent Mater J 2009; 28(2): 219－226220
with strain gauge measurements of the tooth under
MATERIALS AND METHODS
Tooth FE modeling from CT data
The geometrical model was obtained by 3D recon-
struction from CT images of a sound extracted
human maxillary second premolar. The process
required to reconstruct the 3D FE model of the tooth
was comprised of the following steps: 1) image
acquisition, 2) geometry extraction, 3) surface
modeling, 4) solid modeling, and 5) FE meshing.
For image acquisition, the tooth was scanned
with an industrial micro-focus 3D X-ray system
(HMX225-ACTIS+3, TESCO, Tokyo, Japan). The
scan conditions were as follows: tube voltage, 131kV;
exposure dose, 57 μA; image matrix, 512 x 512;
geometric magnification, 14.3; slice thickness, 50
μm. The obtained CT data were converted into a
series of CT slice images with 8-bit tagged image file
(TIF) format. The CT slice images were visualized
with a free 3D DICOM viewer (INTAGE Realia,
KGT, Tokyo, Japan).
For geometry extraction, the grayscale slice
images were imported into a light-weight tool for the
generation of 3D point clouds from the multi-slice
images (Pilamaster, ISID, Tokyo, Japan). Three
point clouds of the contours of the outer tooth and
dentin region, and the boundary of the dentine and
pulp were extracted from the CT slices. The
cementum layer was included in the dentin portion
of the tooth because of its thinness. Enamel was
created in the following solid modeling. Each region
was manually determined according to their different
threshold values for a given grayscale image. Then,
for the multi-slices, threshold-based segmentation
and 3D stacking of the point clouds were automati-
cally performed, resulting in the separate generation
of 3D point clouds for the three regions. The
respective point cloud data were exported in initial
graphics exchange specification (IGES) format.
These points were then imported into an
application tool for 3D reverse engineering and
surface reconstruction (LeiosMesh,
Nagoya, Japan) to generate the surface models. The
input points were filtered to reduce their number to
a level in which the accuracy of the models could be
maintained, followed by triangular mesh creation,
mesh healing by smoothing, and triangular mesh
decimation. The finally obtained triangle mesh
models were then fit with a stitched set of untrimmed
nonuniform rational B-spline (NURBS) surfaces,
resulting in surface models. The operations with this
tool were performed completely automatically by
clicking command menus.
Surface models of three regions were imported in
IGES format into a 3D CAD package (Rhinoceros,
Robert McNeel & Assoc., WA, USA) for manual
creation of the respective volumetric (solid) models of
tooth, dentin and pulp. After creating these solid
models, a solid model of the enamel was created
using Boolean operations26) for the tooth and dentin
solid models. Finally, to assemble a solid model of
the tooth consisting of enamel, dentin and pulp, the
dentin model was added to the enamel model, while
the pulp model was subtracted from the dentin model
using Boolean operations. After assembly, unsuitable
geometric features such as overlapping surfaces and
small surfaces were manually corrected. The
resulting assembled solid model of the tooth was
finally exported in IGES format into a finite element
pre- and post-processor (HyperMesh, Altair Engineering,
MI, USA) to reconstruct an FE mesh model with a 3D
10-node tetrahedral structural solid element. This
element is defined by 4 nodes at the corners of a
triangular gimlet and 6 midside nodes. The meshing
program caused some errors in meshing due to the
unsuitable geometric features, which were manually
Strain measurement with strain gauge technique
Five sound extracted second premolars with similar
dimensions were selected. The teeth were stored in
1.0％ chloramines to prevent dehydration. The
actual strains of the
compressive loading with conic-type indentation were
measured using the strain gauge technique27) to
verify the FE model. Figure 1 shows a diagram of
the locations of strain gauges and loading points of
the tooth. A uniaxial strain gauge (KFG-1N-120-C1-
11 L1M2R, Kyowa, Tokyo, Japan) with a gauge
length of 1 mm was bonded to the surface of the
teeth. The bonded locations of strain gauge were
four regions; the bucco-lingual cervical third regions
of the crown and root while placing them below and
above the cementoenamel junction (CEJ). The strain
was measured in only one direction along the long
axis of the tooth. Stainless rings (30 mm in diameter
and 26 mm in height) were filled with die stone, and
the tooth was embedded to a level 2 mm apical to the
CEJ, without covering the strain gauges as shown in
Fig. 2. Following the embedding of the tooth, gauge
leads were attached to a dynamic strain amplifier
(DPM-711B, Kyowa, Tokyo, Japan).
A compressive load of 9 kg was applied to the
loading points of the embedded tooth, as shown in
Fig. 1, with an apparatus modified to apply a
constant load. Loading points were as follows: buccal
cusp (BC), the outer incline of the buccal cusp (BO),
the inner incline of the buccal cusp (BI), lingual
cusp (LC), the outer incline of the lingual cusp (LO)
and the inner incline of the lingual cusp (LI). For
BC and LC loading, the load was applied along the
extracted tooth under
Dent Mater J 2009; 28(2): 219－226221
tooth axis bucco-lingually in the sagittal plane of the
tooth. For the other loading points, the embedded
tooth was secured in the apparatus so that it was
aligned bucco-lingually at an angle of -45° or 45° to
the tooth axis for application with a load of 9 kg.
Strain calculation with the FE model
The obtained FE mesh model was exported with the
application program interface of HyperMesh to a
general purpose FE program for engineering analysis
(ANSYS Academic Teaching Introductory, CYBERNET,
Tokyo, Japan). In the FE model, boundary conditions
were applied to represent the conditions of
experimental measurement with a strain gauge. The
nodes on the root surface corresponding to the
portion embedded with die stone in the strain gauge
technique were constrained in the x, y, and z
directions. A load of 88.26 N (9 kg) was applied to
the nodes according to the loading points of the tooth
in the strain gauge technique26). Material properties
of enamel and dentin (Young’s modulus, Poisson’s
ratio) were as follows: enamel 60.6 GPa, 0.30; dentin:
18.3 GPa, 0.3028), and all materials were assumed to
be homogeneous, isotropic and linear elastic. The
pulp was modeled as void inside the dentin because
the Young’s modulus of pulp is negligibly small in
comparison to those of
Calculation for the FE model was performed with a
workstation computer (Xeon 3.8 GHz processor,
3.25 GB RAM, running Microsoft Windows XP
enamel and dentin.
For the strains calculated with the FE model,
maximum and minimum principal strains at the
nodes corresponding to the gauge-bonded locations on
the tooth were determined. The strain values
obtained from the FE model were compared with the
strain values from the strain gauge technique using
linear regression analysis to validate the FE model
results. The independent variable was the strain in
the FE model, and the dependent variable was the
average strain measured with the strain gauge
Figure 3 shows a multiplanar reconstruction image,
CT slice images and semi-transparent reconstruction
imaging of the tooth. In this study, 337 2D grayscale
images were obtained with an image resolution of 27
μm per pixel from the CT data. The slice images
showed clearly distinct differences in grayscale for
regions of enamel, dentin and pulp. The semi-
transparent colored image was acquired by volume
rendering of three data set, which were extracted
based on a certain range of grayscales. Pulp in the
tooth tissues and CEJ on the tooth surface (white
line in green region) were visible in the image, while
a thinly overlapped cementum layer could be
observed around the cervical root. Figure 4 shows
the models generated from the CT data. The
numbers of point clouds set for the tooth, dentin and
pulp were 110,148, 92,007 and 22,160, respectively.
For the final assembled solid model of the tooth, an
FE mesh model comprising 20,773 elements and
30,718 nodes was generated.
Figure 5 shows vector plots of calculated
Fig. 1 Diagrams of four strain gauges bonded to the tooth
and six occlusal points loaded.
BC, buccal cusp; BO, the outer incline of the buccal
cusp; BI, the inner incline of the buccal cusp; LC,
lingual cusp; LO, the outer incline of the lingual
cusp; LI, the inner incline of the lingual cusp; SG,
Fig. 2 Tooth-bonded strain gauges, embedded with dental
stone in a stainless ring.
Dent Mater J 2009; 28(2): 219－226222
principal strain distributions in bucco-lingual cervical
regions at BO, BC and BI under loading. The strain
data from the FE model and strain gauge technique
are listed in Table 1. For the FE model, when a load
was applied to the BO point, strains longitudinally
estimated in the buccal and lingual cervical regions
were maximum principle strain in tension and
minimum principle strain
respectively, and vice versa when the BC and BI
points were subjected to loading. Similar behavior
was also observed when a load was applied to the
LO, LC and LI points for the FE model. The strains
of the root cervical regions were larger than those of
the coronal cervical regions. These strain behaviors
estimated in the FE model were similarity observed
in the measured strains.
Figure 6 shows the correlation between the
strains calculated by the FE model and average
Fig. 3 CT images of the tooth.
Left: multiplanar reconstruction image. Center: representatives of CT slice images. Right: semi-transparent
image. Pulp=red; dentin=white; enamel=green
Fig. 4 Original tooth and models of each step.
Upper left original tooth. Upper center: point cloud of outer tooth. Upper right: surface model. Lower left: solid
models. Lower center: FE mesh model. Lower right: close-up view of the mesh.
Dent Mater J 2009; 28(2): 219－226223
Fig. 5 Vector plots of calculated principal strain displacements at bucco-lingual cervical regions.
Black and blue vectors show maximum and minimum principal strains, respectively. Upper row: BO loading.
Middle row: BC loading. Lower row: BI loading. Left column: buccal view. Center column: mesial view. Right
column: lingual view.
Buccal cervical regionLingual cervical region
－4.2 -52.1 ( 48.8)187.4 127.8 (135.8)
－17.5 ( 25.2)
－457.4 (184.3)26.8 59.8 ( 28.5)119.0 255.9 (196.1)
－708.7 (325.5)65.9 68.6 ( 44.1)563.7 353.8 (170.7)
LI49.7 122.3 ( 29.4)484.3 451.9 (101.8)
－202.5 ( 57.9)
LC27.7 71.6 ( 19.3)111.6 224.4 ( 91.0)
－190.3 ( 82.1)
－22.7 ( 24.7)
－69.5 ( 58.7)
ε(cal): calculated strain
ε(mea): measured strain( ):SD, n=5
Table 1 Measured (average and SD) and calculated strains at bucco-lingual cervical regions
Dent Mater J 2009; 28(2): 219－226224
strains measured by the strain gauge method. The
result of the linear regression analysis showed that
there is a significantly strong positive correlation
between the calculated and measured strain (r=0.94,
p<0.001) with a standard error of 0.0001. The
regression slope and its standard error are 0.82 and
0.06, respectively, while the regression slope with a
95％ confidence interval of 0.70 to 0.94 is signifi-
cantly different from 1 (Y=X).
The results of FE analysis require experimental
validation, due to the effects of the FE model
assumputions16,17). In the field of tooth biomechanics,
however, there are few reports on the validation of
FE models of the teeth18-25). Reeh et al. have
validated tooth FE models with the strain gauge
technique, although for 2D models19). Parmard et
al.21,22) and Lee et al.23) have validated 3D FE models
reconstructed using cross-sectional
images. However, these reports have not clearly
demonstrated the statistical correlation between the
results with the FE models and experimental
methods. In this study, according to the high
correlation coefficient (0.94) and the low standard
error (0.06) of the regression analysis, the FE model
reconstructed from the CT image shows qualitatively
good agreement with the result of the experimental
model. This indicates that the FE model can be
considered valid with acceptable accuracy for use as
a simulation model of the actual strain in the tooth.
In this study, the FE model constructed from CT
showed a tendency to quantitatively underestimate
the strains as compared with the experimentally
measured ones, as indicated by the value of the
regression slope in Fig. 6, which was less than 1.
Some of the causes for this underestimation of the
strain magnitudes may be due to both the
uncertainty in correlating experimental conditions
and that in the FE model. Obviously from the
scattering in the measured strains shown in Table 1,
the experimental method has unavoidable uncertain-
ties in both geometry29) and material properties28,30) of
the tooth, and experimental conditions such as strain
gauge position and loading position. The strain
gauge technique, therefore, would present practical
challenges in that it is difficult to adjust the gauges,
possibly resulting in the unavoidable scattering of
On the other hand, the accuracy of the results of
the FE model depends on the accuracy of input
parameters; the error depends on geometry, materials
properties, boundary conditions, and loads applied.
The FE analysis is a deterministic approach in that
the output is determined once the set of selective
input parameters and the geometry of the model
have been specified. In this study, one geometric
model, reconstructed from CT data for a specific
tooth and the average elastic modulus of enamel and
dentin in the literature, was selected. Furthermore,
we made the assumptions that both dentin and
enamel were homogeneous, isotropic and elastic
despite full representation of the tooth tissues in
order to simplify the calculations for the model. Such
a deterministic and assumptive
constructing FE models may be attributed to the
inaccuracy of the FE results. Therefore, a statistical
approach incorporating these uncertainties in FE
analysis of biological tooth tissues is important to
provide a more accurate evaluation. Furthermore,
the accuracy of FE results is also dependent on
element and node sizes of the FE model. The
element size of the FE model in this study was finer
than compared with the FE models previously
reported22,23). The FE analysis program used in this
study has an allowable limit of 32,000 nodes. It
appears, therefore, that the size limit had been
generated in the FE mesh model, which could be
reconstructed with acceptable accuracy. The effect of
element size on accuracy of the FE model requires
This study shows that an FE model of a tooth
can be reconstructed
modeling, in which a combination of several
commercially available computer-aided techniques
are used to extract geometrical information from CT
Fig. 6 Correlation between the strains calculated by the
FE model and average strains measured by the
strain gauge method (n=5).
Solid line shows the regression line. Short and
long dashed lines show the 95％ confidence
interval for the regression and population,
respectively. Vertical lines show the SD of
measured strains (n=5).
Dent Mater J 2009; 28(2): 219－226225
data and to generate the model. Previously, several
successful works on FE modeling of teeth from CT
data have applied some efficient geometry extraction-
CAD modeling combinations11-13,16).
combinations might result in a considerable reduction
in the time consumed in creation of FE models, as
compared with traditional methods of modeling from
CT data. In this study, however, manual operations
in both CAD and FE mesh modeling were very time-
consuming and required both considerable experience
and skill, although segmentation and surface
modeling were mostly automated. Therefore, fully
automated and more efficient modeling techniques
using CT data of the teeth would facilitate creation
of FE models without considerable skill.
In conclusion, a 3D FE tooth model could be
constructed using micro-CT data and a combination
of several commercially
techniques with acceptable accuracy, although the
FE modeling process starting from CT data was not
fully automated. The FE model presented here
provides a useful means to three-dimensionally
explore the biomechanical characteristics of tooth
abfraction lesions under occlusal loading.
We express our sincere thanks to Mrs. Hirohide
Kaida and Masaaki Koganemaru of Fukuoka
Industrial Technology Center for supplying the CT
system used in this study and their important contri-
butions to the experiments. This work was supported
in part by the Grant-in-Aid for Scientific Research
(C) 18592095 from the Ministry of Education,
Culture, Sports, Science and Technology of Japan,
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