Download Dynamic analysis for clarifying occlusal force transmission during

J Med Dent Sci 2004; 51: 59–65
Original Article
Dynamic analysis for clarifying occlusal force transmission during orthodontic
archwire application: difference between ISW and stainless steel wire
K. Iramaneerat, M. Hisano and K. Soma
Orthodontic Science, Department of Orofacial Development and Function, Division of Oral Health Science,
Graduate School, Tokyo Medical and Dental University.
The purpose of our study was to utilize the
dynamic finite element analysis to clarify the difference between Improved Super-elastic Ti-Ni
alloy Wire (ISW) and Stainless Steel Wire (SSW) on
occlusal force transmission during orthodontic
treatment. ABAQUS/Standard was used to analyze
three finite models over a 30-ms period: ISW,
SSW, and wireless models; which consisting of
premolar, molar, periodontal ligament (PDL), and
alveolar bone. Wire model was established by
beam element. A Joint C, which exhibits viscoelasticity to buffer occlusal force, was applied
between the wire and bracket. The load was
applied on the occlusal surface. At load withdrawal point, the average amounts of von Mises stress
on PDL in three models were of the same value.
However as time progressed, the stress in wireless
model became higher than ISW and SSW models.
In contrast, as time progressed further, the stress
in SSW model became higher than the other two
models and maintained its higher level until the end
of analysis. Results showed that high damping
capacity of ISW had an ability to buffer the transmission of occlusal force to the PDL. Besides, the
dynamic analysis demonstrated an advantage to
investigate the stress alterative response between
Corresponding Author: K. Iramaneerat
Orthodontic Science, Department of Orofacial Development and
Function, Division of Oral Health Science, Graduate School, Tokyo
Medical and Dental University, 1-5-45 Yushima, Bunkyo-ku, Tokyo
113-8549, Japan.
Business phone: +81-3-5803-5530
Fax: +81-3-5803-5530
E-mail address: [email protected]
Received November 7; Accepted December 19, 2003
models versus time period.
Key words:
ISW, occlusal force, damping capacity,
dynamic analysis, Von Mises stress
Introduction
An Improved Super-elastic Ti-Ni alloy Wire (ISW) has
been developed with unique characteristics that offer
significant potential for orthodontic appliances. ISW
exhibits a shape memory property and a super-elasticity property, and recently its damping properties
have been highlighted. An experimental investigation of
the damping capacity of ISW in comparison with
stainless steel wire (SSW) showed that the damping
curve of ISW abruptly decreased while the damping
curve of SSW gradually decreased.1 This experiment
suggested that in clinical applications the damping
capacity of ISW would be able to buffer the occlusal
impact force transmitted to the tooth and supporting
structures. In vivo, it is difficult to investigate the biomechanical response of teeth and surrounding tissues
when occlusal forces are loaded on the teeth under
orthodontic treatment. Therefore, the finite element
method was chosen in our study, even though there are
various other methods. Because this technique has an
advantage to study the biomechanical response of the
internal structures and has been effectively used to calculate the structures with complicated shapes and different materials. Furthermore, the dynamic finite element method makes it possible to analytically apply various forces at any point over any calculation time
period.
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K. IRAMANEERAT, M. HISANO and K. SOMA
J Med Dent Sci
morphology.2 The PDL thickness was assumed to be
0.25 mm around the root. Three types of model were
established for comparative investigation: ISW
applied, SSW applied, and wireless models (Figure 1).
The wireless model was used as a control model.
The purpose of this study was to utilize the dynamic
finite element analysis to clarify the difference
between ISW and SSW on occlusal force transmission
to periodontal tissue (PDL) during orthodontic treatment. An influence of the damping capacity of ISW in
comparison with SSW on PDL was observed, when
teeth were subjected to occlusal force, associated
with vibration on the wire in time period.
Bracket and wire models
The bracket models consisting of 14 elements and
42 nodes were fixed by sharing the same nodes with
the teeth. One-dimensional beam elements consisting
of 12 elements and 13 nodes were used to assemble
the wire model. The size of applied wire in this study
was 0.016×0.022 inches.
Materials and Methods
Tooth, PDL, and alveolar bone models
A three-dimensional finite element model consisting
of left mandibular second premolar, first molar, PDL,
and alveolar bone, was constructed with 7,346 solid
elements and 14,414 nodes, based on the anatomical
Connection between bracket and wire models
To represent the damping capacity of the wire, the
connection between bracket and wire was constructed
Buccal view
a
Wireless model
Wire applied model
Wire
Distal
Mesial
Mesial
Distal
Bracket
Periodontal ligament
Alveolar bone
Periodontal ligament
Alveolar bone
b
Bracket
Lateral view
Wire
Joint C element
Spring element
Dashpot element
Fig. 1. a: On the left panel was an illustration of wire applied model; left mandibular second premolar and first molar with brackets and wire
on the buccal surface, on the right panel was an illustration of wireless model; no wire and bracket application on the teeth, b: Illustration
described the composition of wire applied model, joint C element was assembled between wire and bracket, which composed of dashpot and
spring.
DYNAMIC ANALYSIS ON OCCLUSAL FORCE TRANSMISSION IN ORTHODONTIC TREATMENT
by a joint C element, which composed of linear spring
and dashpot elements. The damping capacity of joint C
was derived from the dashpot portion, which had a
mechanism providing viscous energy dissipation
property.3 Accordingly, joint C was assembled with six
degrees of freedom on each tooth. The schematic
described joint C model is shown in Figure1b.
Dynamic analysis
ABAQUS/Standard Ver. 6.3 (HKS, INC., Rhode
Ireland, USA) was utilized for the dynamic finite element
calculation, and FEMAP Ver 6.0 (Enterprise Software
Products, INC., California, USA) was used to conduct
pre- and post-processing of the models.
The physical properties of the components in the
model were considered to be isotropic and elastic
materials, which were applicable since the material
4,5
parameters were based on their macro-behavior.
The tooth was simplified as a homogeneous material.5
The Young’s modulus, Poisson’s ratio, and density of
the components in the model, based on previous
studies,6-13 are listed in Table 1.
The boundary condition was set as fixed constraint
on the basal portion of alveolar bone. Assuming one
cycle of mastication, the loading condition of static force
was applied on the occlusal surfaces of the teeth supposedly as an occlusal force, and the dynamic analytical calculation was performed over 30-ms time period.
The loads, 30 N for premolar and 100 N for molar,14
were applied parallel to the long axis of the tooth models (the Z-axis), from time 0-5 ms (t0 - t5). Vibration on
the wire was generated from occlusal load on the
occlusal surface.
To determine the coefficient of joint C corresponding
to results from the wire-damping test that was reported
in previous study,1 the reproduction of wire finite element model was performed. The analysis results of the
ISW and SSW models are demonstrated in Figure 2a
and 2b respectively. The damping coefficient of joint C
in ISW and SSW applied models were 0.023 and
61
0.0085 Ns/ m, respectively, with the spring stiffness as
3.0×106 N/ m in both models.
Stress on the PDL surface
The von Mises stress on the PDL surface was
observed. These data were extracted every 1 ms in 25ms analysis period (t5 - t30). For a better understanding,
the results of the average stresses on the PDL in the
models were compared quantitatively in 3 divided
periods: (1) time t5 defined as the “load withdrawal
point”; (2) interval t6-t8 defined as the “initial phase”; and
(3) interval t8-t30 defined as the “late phase”.
The statistical significant differences of stresses on
elements between ISW applied, SSW applied, and
wireless models were assessed with t-test by using
SPSS statistical software (V.11.0 for Windows, SPSS
Inc, Chicago, I11).
a
Displacement (
)
b
Displacement (
)
ISW
t (ms)
SSW
Table 1. Mechanical properties of the components in the model used
in the present study were based on previous studies.6-13
t (ms)
Fig. 2. a: A displacement graph showing the damping capacity of
ISW finite element model, b: A displacement graph showing the
damping capacity of SSW finite element model.
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K. IRAMANEERAT, M. HISANO and K. SOMA
J Med Dent Sci
on the PDL compared between three models at time t6
are demonstrated in Figure 4a.
Results
Stress on the PDL surface
1. Total data in time period
Figure 3a and 3b show the average amounts of
stress on the entire PDL surface of premolar and
molar respectively in wireless, ISW applied, and SSW
applied models, extracted every 1 ms in 30-ms period
of analysis from t5 to t30. As time progressed after t5, the
amounts of stress on premolar and molar decreased in
all models, however, the stress values were different on
each extracted investigation point in time period.
4. Late phase (t8-t30)
In the late phase, the average amount of stress in
SSW applied model increased higher than that in the
wireless and ISW applied models and maintained this
higher level until t30.
Since t10, our results showed that the average
amounts of stress in the ISW applied model were not
significantly different from those of the wireless
model, t-test at P＜0.05. The difference of average
amounts of stress between ISW applied and wireless
models was within the ranges of 0 to ±0.009 MPa on
premolar and within the ranges of 0 to ±0.02 MPa on
molar.
At t15, the middle time point of the analysis period, the
average amount of stress in SSW applied model was
higher than the other two models. The average
amounts of stress on the PDL compared between three
models at time t15 are shown in Figure 4b.
2. Load withdrawal point (t5)
The amounts of von Mises stress on PDL surface in
ISW applied, SSW applied, and wireless models were
of similar value.
3. Initial phase (t6-t8)
In the initial phase, the average amount of stress in
wireless model was higher than in the ISW applied and
SSW applied models. The average amounts of stress
b
a
Premolar
Stress (MPa)
Molar
Stress (MPa)
0.7
0.7
Wireless model
ISW model
SSW model
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
5
10
15
20
Wireless model
ISW model
SSW model
0
25
30
5
10
15
20
25
t (ms)
Initial phase
(t6-t8)
Load withdrawal
point (t5)
Late phase (t8-t30)
Initial phase
(t6-t8)
Load withdrawal
point (t5)
30
t (ms)
Late phase (t8-t30)
Fig. 3. a: Graph illustrated the average amounts of stress on the PDL of premolar in wireless, ISW, and SSW applied models from t5 to t30, b:
Graph illustrated the average amounts of stress on the PDL of molar in wireless, ISW, and SSW applied models from t5 to t30. Both graphs were
separated into three periods; load withdrawal point (t5), initial phase (t6-t8), and late phase (t8-t30).
DYNAMIC ANALYSIS ON OCCLUSAL FORCE TRANSMISSION IN ORTHODONTIC TREATMENT
Stress (MPa)
Time t6
*
*
*
*
*
*
* P < 0.05
ISW model
Wireless model
Time t15
Stress (MPa)
SSW model
*
*
*
*
* P < 0.05
Wireless model
ISW model
SSW model
Fig. 4. a: Graph demonstrated the average amounts of stress on the
PDL of premolar and molar at time t6 (t-test at P < 0.05), b: Graph
demonstrated the average amounts of stress on the PDL of premolar
and molar at time t15 (t-test at P < 0.05).
Discussion
Stress transmission versus time period
At load withdrawal point (t5), the von Mises stress on
the PDL in ISW applied, SSW applied, and wireless
models, were of similar value. However, during the initial phase (t6-t8), the average amounts of stress in wireless model were the highest, followed by ISW applied
model and lowest in SSW applied model. This result
was probably caused by the wire application on the
buccal surface. It implied that the attached wire had an
ability to absorb the occlusal force. Moreover, the
influence from the stiffness of the wire caused the teeth
in the wire applied model to return earlier to their original position and hence the amount of tooth displacement from the original position was of a lesser degree
than in the wireless model. This caused the pattern of
occlusal load transmission to the PDL to differ and the
stress on the PDL was affected consequently.
Furthermore, since the SSW was stiffer than the ISW,
the average amount of stress on the PDL in the SSW
applied model was found to be lesser than in the ISW
63
applied model.
At the end of the initial phase, the average stress in
all three models reached the same level. This implied
that the stiffness of the wire became of less influence,
while, alternatively, the remaining vibration on the
wire, which was created by the occlusal load, started to
show a more obvious influence to the stress alterative
response on the PDL.
In the late phase (t8-t30), the stress in SSW applied
model turned out to be higher than the other two models. This implied that the remaining vibration on the
SSW, due to its lower damping capacity, affected the
stress alterative response on the PDL in the model. The
ISW with higher damping capacity exhibited higher
competence to buffer the transmission of force to the
PDL. This result implied that in a clinical situation, different types of wire will result in differences in stress
concentration in the PDL area and may therefore
affect the incidence of root resorption during orthodontic movement. As there are many other contributing factors to the incidence of root resorption, our result may
be one of relative factors of those aspects.
Comparing ISW applied and wireless models since
t10 until t30, the average amount of stress in the ISW
applied model had a narrow difference range to the
stress in the wireless model. This suggested that the
ISW had a damping capacity to buffer the force transmission to the PDL. As a result, the stress pattern on
PDL in the ISW applied model had a minute difference
from that of the wireless model. This result corresponded to the previous study.15,16 They stated that the
transmitted pulse through Ti-Ni alloy would be
depressed, as compared with those through titanium
and stainless steel which suggested that the loading
stress to adjacent tissues could be decreased with the
use of Ti-Ni alloy as component material in an implant
system.
The stress-decreasing patterns from t5 to t30 in
Figure 3a and 3b, on premolar and molar respectively,
were in wave-liked pattern that decreased from the
higher stress level to almost 0 MPa at the end of analysis, which showed similar patterns to the previous
study.17 Besides, the stress-decreasing pattern of premolar was different from the pattern of molar, which
implied that the tooth configuration also affected the
stress-decreasing pattern.
The joint C elements were utilized in this study in
order to generate and demonstrate the damping
capacity of two types of wires. The joint C element provided the node on the wire to displace and rotate slightly with respect to the node on the bracket. The simplifi-
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K. IRAMANEERAT, M. HISANO and K. SOMA
cation of the connection between bracket and wire
models was achieved, otherwise, the three-dimensional movement of the wire in the bracket slot space,
which is a complicated movement, should be considered together in the model construction.
In this study, only one time of static load supposedly
as one stroke of mastication was applied on the
occlusal surface. However in human body, several
strokes of mastication continuously take place; therefore, the stress-decreasing pattern and the alteration of
an amount of stress should be different, which is an
interesting aspect to be investigated in the future
study.
When lighter forces are transmitted to the roots of the
teeth, there is less patient discomfort and root resorption.18 The high damping capacity of ISW could contribute to previously mentioned properties. Therefore, in
clinical application, the wire selection should be considered carefully, in order to use appropriate wire that
will minimize unsatisfactory consequence in the
orthodontic treatment.
Advantage of dynamic analysis
There are various static finite element studies performed to investigate the stress levels induced in the
periodontal tissue by orthodontic forces. However, the
use of dynamic finite element technique to evaluate the
stress pattern was rarely performed. In this study, the
dynamic finite element method provided a mathematical model that allowed quantification of the stress on
the PDL over consecutive 30-ms period. In addition, the
amount of stress in wireless model was different from
those of ISW and SSW applied models as time progressed. These results implied that the application of
dynamic finite element analysis had an advantage to
clarify the difference of stress alterative response on the
PDL against the occlusal force in progressed time period of these three models.
The limitation of this study involved the approximations of material behaviors and tissue geometry. The
tooth model was simplified as homogeneous, and the
complicated modeling of the internal tooth structure
was considered unnecessary. Further investigation in
the condition that the teeth are crowded and activated
by the wire during orthodontic treatment should be
studied in the future.
wireless, ISW applied and SSW applied models, the
results showed that high damping capacity of ISW had
an ability to buffer the transmission of occlusal force to
the PDL. Furthermore, the dynamic analysis demonstrated its advantage over static analysis in clarifying
the difference of stress alterative response in three
models.
Acknowledgments
The authors would like to thank Dr. Kazuo
Takakuda from Institute of Biomaterials and
Bioengineering at Tokyo Medical and Dental
University for his suggestions and helpful discussions
toward this work.
This study was financially supported by Grants-in-Aid
for Scientific Research (14370688) from the Ministry of
Education, Culture, Sports, Science and Technology of
Japan.
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