Artículos de Corticotomia

1. Biomechanical effects of corticotomy approaches
on dentoalveolar structures during canine
retraction: A 3-dimensional finite element
analysis
Chongshi Yang,a
Chao Wang,b
Feng Deng,c
and Yubo Fand
Chongqing and Beijing, China
Introduction: Corticotomy has proven to be effective in facilitating orthodontic tooth movement. There is,
however, no relevant study to compare the biomechanical effects of different corticotomy approaches on tooth
movement. In this study, a series of corticotomy approaches was designed, and their impacts on dentoalveolar
structures were evaluated during maxillary canine retraction with a 3-dimensional finite element method.
Methods: A basic 3-dimensional finite element model was constructed to simulate orthodontic retraction of
the maxillary canines after extraction of the first premolars. Twenty-four corticotomy approach designs were
simulated for variations of position and width of the corticotomy. Displacement of the canine, von Mises
stresses in the canine root and trabecular bone, and strain in the canine periodontal ligament were calculated
and compared under a distal retraction force directed to the miniscrew implants. Results: A distal corticotomy
cut and its combinations showed the most approximated biomechanical effects on dentoalveolar structures
with a continuous circumscribing cut around the root of the canine. Mesiolabial and distopalatal cuts had a
slight influence on dentoalveolar structures. Also, the effects decreased with the increase of distance between
the corticotomy and the canine. No obvious alteration of displacement, von Mises stress, or strain could
be observed among the models with different corticotomy widths. Conclusions: Corticotomies enable
orthodontists to affect biomechanical responses of dentoalveolar structures during maxillary canine retraction.
A distal corticotomy closer to the canine may be a better option in corticotomy-facilitated canine retraction.
(Am J Orthod Dentofacial Orthop 2015;148:457-65)
T
wo main challenges are often confronted in
orthodontic treatment for adult patients: long
duration and risk of side effects such as root
resorption and marginal bone loss.1,2
To cope with
these problems, surgical techniques are used to
facilitate orthodontic tooth movement, including
alveolar osteotomy, corticotomy, and distraction
osteogenesis.3-5
Compared with osteotomy and
distraction osteogenesis, corticotomy has become
popular gradually because of the minor surgical injury,
flexible approach, and operational simplicity.
Corticotomy has been demonstrated to facilitate
orthodontic tooth movement effectively in the clinic. It
has many advantages over more traditional orthodon-
tics, including reduced orthodontic treatment time,
more significant tooth movement, and less anchorage
required.5,6
Wilkco et al5
attributed these effects of
corticotomy to the regional acceleration phenomenon,
which is characterized by an increase in the rate of
bone turnover. The remodeling of alveolar bone and
periodontal ligament (PDL) would be activated and
aggravated after being exposed to an insult such as a
corticotomy or a cortical perforation. En-block
a
Graduate student, Chongqing Key Laboratory of Oral Diseases and Biomedical
Sciences, Stomatological Hospital of Chongqing Medical University, Chongqing,
China.
b
Assistant professor, Chongqing Key Laboratory of Oral Diseases and Biomedical
Sciences, Stomatological Hospital of Chongqing Medical University, Chongqing,
China.
c
Professor, Chongqing Key Laboratory of Oral Diseases and Biomedical Sciences,
Stomatological Hospital of Chongqing Medical University, Chongqing, China.
d
Professor, Chongqing Key Laboratory of Oral Diseases and Biomedical Sciences,
Chongqing Medical University, Chongqing; professor, Key Laboratory for Biome-
chanics and Mechanobiology of Chinese Education Ministry, International
Research Center for Implantable and Interventional Medical Devices, Beihang
University, Beijing, China.
Funded by the National Natural Science Foundation of China (numbers
11421202 and 11120101001).
Address correspondence to: Yubo Fan, Stomatological Hospital of Chongqing
Medical University, No. 426, Yubei District, Chongqing, China; e-mail,
yubofan@buaa.edu.cn.
Submitted, September 2014; revised and accepted, March 2015.
0889-5406/$36.00
Copyright Ó 2015 by the American Association of Orthodontists.
http://dx.doi.org/10.1016/j.ajodo.2015.03.032
457
ORIGINAL ARTICLE

2. movement of the bone segment was another
explanation for this technique.7,8
Corticotomy can
reduce the resistance of alveolar bone to orthodontic
tooth movement by breaking the continuity of the
bone layer, leading to a bone-bending effect,
and possibly even a greenstick fracture of the alveolar
bone.9
Orthodontic tooth movement is the result of
remodeling of the alveolar bone and the PDL around
the tooth.10
Two stages are included in this procedure:
the delivery of orthodontic force and the biologic
responses to the force.11
The force generated by the
orthodontic appliance is transmitted to the PDL by the
teeth and then to surrounding alveolar bone,
contributing to the change of the mechanical
environment of the dentoalveolar structure. The
mechanical stimulation can trigger a series of biologic
responses to regulate the deposition or resorption of
the alveolar bone temporarily and spatially to facilitate
tooth movement. The internal strength and distribution
of the mechanical stimulation can be denoted accurately
with stress and strain, rather than with orthodontic
force, in consideration of the shape and size of the den-
toalveolar units.12
The stress and strain in dentoalveolar
structure can be altered by breaking the continuity of the
cortical bone after a corticotomy.13
The change of stress
or strain can be calculated using 3-dimensional (3D)
finite element methods.
Three-dimensional finite element analysis is a
numeric technique for simulating mechanical processes
of a real physical system; it is considered to be a valid
and reliable approach for calculating stress, strain, and
displacement of dentoalveolar structures.14,15
This
technique can be used to simulate orthodontic
processes with different treatment plans and to
compare their biomechanical effects without
increasing the numbers of patients or animals in the
sample, unlike clinical or animal investigations.
The routine treatment plan for patients with
maxillary or bimaxillary protrusion is retraction of the
anterior teeth after extraction of the premolars. With
regard to these patients, a 2-step treatment can be
used to make the canine move first during space
closure.16
To shorten the treatment time and save
anchorage, corticotomies have been used to facilitate
canine movement in the clinic.17,18
Although these
studies have provided useful findings, the corticotomy
approach was limited. More importantly, little research
regarding the biomechanical effects of corticotomy
approaches on dentoalveolar structures has been done.
Therefore, the aims of this study were to design
different corticotomy approaches and compare their
biomechanical impacts on dentoalveolar structures
during retraction of the maxillary canine and to select
an optimal approach for clinical adoption.
MATERIAL AND METHODS
Construction of the basic finite element model was
based on computed tomography scans (120 kV;
175 mA; slice thickness, 0.625 mm) (LightSpeed VCT;
GE Healthcare, Wauwatosa, Wis) of the skull of an
adult with maxillary protrusion. A surface 3D model of
the maxillary alveolar bone and the dentition with the
first premolars extracted was constructed from the
scanned images through thresholding, region growing,
and calculating 3D operations with Mimics software
(version 9.0; Materialise, Leuven, Belgium). Scaling
and Boolean operations were performed on the surface
model of the alveolar bone and dentition to generate
the cortical bone with an average thickness of 2.0 mm
and the PDL around the tooth with an average thickness
of 0.2 mm based on the studies of Wang et al14
and Lim
et al19
with Rapidform software (version 6.5; INUS,
Seoul, Korea). The orthodontic appliances, including
edgewise brackets for the anterior teeth and premolars,
buccal tubes for the molars, square wires, and miniscrew
implants, were designed and modeled according to
clinical applications in computer-assisted design
software (version 2011; Solidworks, Velizy-Villacoublay,
France). The brackets and buccal tubes were placed on
the center of the labial or buccal surface of the clinical
crown of the teeth. The implants were placed in the
interradicular space between the first molar and the
second premolar. All components were saved in initial
graphics exchange specification format and imported
into Abaqus (version 6.11; Solidworks). The bases of
the brackets and buccal tubes were subtracted from
the corresponding teeth to create a matching geometry.
Then the alveolar bone, teeth, PDL and orthodontic
appliances were assembled to form the geometric model.
Volumetric meshes of these components in the model
were created separately. The types and numbers of
elements and nodes are listed in Table I
The first step of simulation of the corticotomy
approach was to design and build a shear band
Table I. Types of elements and numbers of nodes and
elements
Types of element Nodes (n) Elements (n)
Teeth C3D4 34037 166707
PDL C3D20R 589521 140402
Trabecular bone C3D4 29405 139600
Cortical bone C3D10 79619 40356
Bracket C3D4 28097 116846
Square wire C3D8R 1233 540
458 Yang et al
September 2015 Vol 148 Issue 3 American Journal of Orthodontics and Dentofacial Orthopedics

3. corresponding to the approach in Solidworks. Then
cortical bone was subtracted by the shear band to
generate the model in Abaqus. Twenty-four models
were built in this study. These models can be classified
as follows.
For the corticotomy approaches with the position of
the cuts varied, the corticotomy cuts were in cortical
bone around the maxillary canine. There were 4
basic cuts: mesiolabial, mesiopalatal, distolabial, and
distopalatal. Other approaches were the various
combinations of these cuts and combinations with labial
and palatal cuts. There were 20 corticotomy approaches
designed and modeled (Fig 1).
For the corticotomy approaches with the distance to
the canine varied, 2 other cuts parallel to the distal
corticotomy were designed at the extraction side. They
were 2 and 4 mm from the distal corticotomy cut,
respectively (Fig 1).
For the corticotomy approaches with the width of the
corticotomy cut varied, the width of the corticotomy cuts
above was set at 0.4 mm according to the diameter of the
bur used for corticotomies in the clinic. Two other cuts
with widths of 0.6 and 0.8 mm were designed on the
base of the distal corticotomy cut (Fig 1).
Five materials were used in this study. All materials
were assumed to be homogeneous, isotropic, and
linearly elastic. The material properties were determined
from the values documented in the literature (Table II).
Then the material properties were assigned to cortical
bone, trabecular bone, teeth, PDL, and orthodontic
appliances.
Canine distalization is the first step of space closure
in a 2-step treatment. To eliminate the complex
constraints of square wire on the canine and to facilitate
its movement, the segmented arch technique was used
in this study. The maxillary incisors, ipsilateral molars,
and second premolars were connected with 3 pieces of
square wire. The bilateral canines were not tied to the
Fig 1. Designs of corticotomy approaches for the maxillary canine: A, B, and C, continuous
circumscribing cut around the canine from the labial, lingual, and occlusal views; D, definition of canine
position for the designs of corticotomy approaches below; E, corticotomy approaches with the positions
of the cuts varied; F, corticotomy approaches with the distance to the canine varied; G, corticotomy
approaches with the width of the corticotomy cut varied.
Table II. Material properties
Young's
modulus (MPa)
Poisson's
ratio Reference
Cortical bone 10.7E3 0.3 Aversa et al20
Trabecular bone 9.7E2 0.3 Aversa et al20
Teeth 20.7E3 0.3 Lee and Baek21
PDL 50 0.45 Lin et al22
Brackets and stainless
steel wire
200E3 0.3 Canales et al23
American Journal of Orthodontics and Dentofacial Orthopedics September 2015 Vol 148 Issue 3
Yang et al 459

4. square wire to let them move freely. To prevent
separation and slippage, binding constraints were
used to define these interfaces: square wire-bracket,
tooth-bracket, PDL-tooth, trabecular bone-PDL, and
cortical bone-trabecular bone. The miniscrew implants
were not involved in calculations of finite element
models, and they were used to indicate the direction of
the orthodontic load (Fig 2).
All these models were restrained at the nodes on the
maxillary bone at the base of nasal cavity in all degrees of
freedom. To simulate retraction of the maxillary canine,
a 100-cN concentrated force was applied to the middle
points of the bracket slot toward the crown notch of
the miniscrew implant according to the clinical
condition (Fig 2). The displacement of the canine, stress
distributions in the canine root, and strain distributions
in the PDL and the trabecular bone were analyzed with
Abaqus software.
RESULTS
The displacements of the canines were observed in a
newly defined coordinate system: origin-anterior nasal
spine; x-axis, the line through posterior nasal spine;
and the x-y plane–middle sagittal plane. The initial
displacement of the canine showed distal movement
combined with clockwise rotation, and the largest
displacement of the canine was highly concentrated on
the cusp in all models (Fig 3). The position of the
corticotomy had an obvious effect on the displacement
of the canine. The maxillary canine in the model with
the continuous circumscribing cut showed the greatest
displacement, and larger displacements were found in
models with distal corticotomy cuts and their
combinations. However, no notable difference of canine
displacement was observed in models with distopalatal
and mesiolabial cuts and in the model with no
corticotomy. As the distance between the canine and
the corticotomy increased, the displacement of the
canine decreased gradually. The width of the
corticotomy cut had no obvious influence on the canine
displacement (Fig 3).
The von Mises stress distribution in the canine root is
illustrated in Figure 4. The maximum von Mises stress
was centered on the distolabial side of the cervix in all
models. The position of the corticotomy cuts had similar
variations on the distribution of the von Mises stresses to
the distribution of displacements of the canine. When
the distance and the width of the corticotomy cut were
increased, the maximum stress value was reduced,
especially for a corticotomy with the distance
increased. In general, the differences of the maximum
stress in the canine roots were not evident among these
models.
The maximum strain was concentrated mainly in the
cervical region of the PDL (Fig 5). There were significant
differences in the strain values in the PDL with the
changes of corticotomy position. The maximum strain
values decreased in the models with the continuous
circumscribing cut and the distal cut and its
combinations, but the values were enhanced in the
models with the mesial cut and its combinations
compared with the model with no corticotomy. The
maximum strain in the PDL increased gradually when
the distance to the canine increased. The influence of
the farthest corticotomy, which was about 5 mm from
the canine, got close to the effect with no corticotomy.
The width of the corticotomy had no remarkable
influence on the strain distribution in the PDL of the
canine.
von Mises stress in the trabecular bone was mainly
concentrated on the alveolar crest at the distal side of
the canine in the model without a corticotomy. But in
models with a corticotomy, the area of stress
concentration transferred to the alveolar crest near the
corticotomy. Thus, the position of the corticotomy can
affect the distribution of stress in trabecular bone
remarkably. The trabecular bone showed the maximum
stress value in the model with a continuous
circumscribing corticotomy cut, a lower stress value in
the model with the distal corticotomy cut and its combi-
nations, and still a lower stress value in the models with
mesial and minor cuts. When the distance between the
Fig 2. Basic geometric model and illustration of the boundary and load: A, frontal view; B, lateral view.
Diamonds, Boundary; arrow, orthodontic load.
September 2015 Vol 148 Issue 3 American Journal of Orthodontics and Dentofacial Orthopedics
460 Yang et al

5. corticotomy and the canine increased, the maximum
stress value was reduced. No obvious alteration of the
stress distributions was observed among the models
with different corticotomy widths (Fig 6).
DISCUSSION
The continuous circumscribing cut around the root
of the tooth proposed by Wilkco et al5
was reported in
many studies, and its effect on facilitating tooth
movement has been confirmed.18,24
In this approach, 4
vertical and 2 horizontal cuts around the root need to
be made after elevation of the full-thickness
mucoperiosteal flap, as for the canine. Although this
technique proved to be effective in shortening treatment
time, it was difficult for most orthodontic patients to
accept because of its postoperative discomfort and risk
of complications. To reduce the surgical injury and the
difficulty of the operation, new corticotomy approaches
with minor cuts were designed by changing the
continuous circumscribing cut in this study. The
biomechanical effects of these approaches on
dentoalveolar structures were studied and compared
with the models with the continuous circumscribing
corticotomy and with no corticotomy. At the same
time, we also considered the distance between the
corticotomy and the canine, and considered the width
of the corticotomy cut in this study.
Because of the deviations between the finite element
models and the actual situation in geometric and
mechanical similarities, and owing to material property
and boundary conditions, the results of this study should
be interpreted with caution. For instance, the PDL was
assumed to be isotropic, homogeneous, and linearly
elastic in this study, but the PDL is a nonlinear,
viscoelastic, and anisotropic material.25
Meanwhile, the
thickness of the PDL was set at 0.2 mm, and the
thickness of cortical bone was set at 2.0 mm. However,
the PDL and the cortical bone are not uniform in
thickness.26,27
In addition, it is difficult to simulate the
real situation of alveolar sockets after the extraction of
teeth. Because the healing of an alveolar socket is a
dynamic process, the morphology and mechanical
characteristics of alveolar bone in this area change
markedly. Therefore, the alveolar sockets were
excluded in these finite element models, and the
height and width of the alveolar process at the
Fig 3. Comparison of the maximum initial displacements of the canine in the models: A, with the
position of corticotomy cut varied; B, with the distance between the corticotomy cut and the canine
varied; C, with the widths of corticotomy varied; D, distribution of the initial displacements of the canine.
American Journal of Orthodontics and Dentofacial Orthopedics September 2015 Vol 148 Issue 3
Yang et al 461

6. extraction site were decreased slightly. Canine
movement occurred after the socket was well healed in
this study. Nevertheless, for comparisons, the relative
results have more value than the absolute results. In
this study, the different biomechanical responses of
the dentoalveolar structures with corticotomy
approaches were observed, and influences of these
approaches on orthodontic canine distalization were
seen.
Several studies have been published about the impact
of acceleration of canine movement and the histologic
findings. Aboul-Ela et al17
evaluated the clinical effects
of corticotomy-facilitated orthodontics during maxillary
canine retraction. Their results showed that the rate of
canine retraction with corticotomy was about twice
that of the control side in the first 2 months. Kim
et al28
investigated the biologic effects of corticotomy
on alveolar remodeling during canine retraction in an
animal study. Their histomorphometric analysis showed
an extensive direct resorption of bundle bone with less
hyalinization. Many researchers have attributed these
effects to the regional acceleration phenomenon, where
the acceleration of bone turnover was observed through
animal research.29,30
These studies confirmed the effects
of corticotomy as a stimulating factor that can increase
the rate of bone turnover. The change of the mechanical
situation in alveolar bone may be another stimulating
factor that can strengthen the remodeling of alveolar
bone, leading to rapid canine movement, which has
been proven in previous studies.31,32
In this study, we
found that the mechanical responses of dentoalveolar
structures can be affected by a corticotomy; the
responses were mainly reflected in the stress in
the trabecular bone. The maximum stress value in the
model with the continuous circumscribing cut
increased several times in the alveolar bone near the
corticotomy compared with the model with no
corticotomy.
The maximum displacement of the canine was
concentrated on the cusp of its crown under an
Fig 4. Comparison of the maximum stresses in the canine roots in the models: A, with the position of
the corticotomy cut varied; B, with the distance between the corticotomy cut and the canine varied;
C, with the widths of the corticotomy varied; D, distribution of the von Mises stress in the canine root
from the labial and distal views.
September 2015 Vol 148 Issue 3 American Journal of Orthodontics and Dentofacial Orthopedics
462 Yang et al

7. orthodontic load directed to the miniscrew implant. This
result demonstrated that the canine had clockwise
rotation, since the orthodontic force did not pass the
resistance center of the canine. This result is consistent
with the results reported by Xue et al.13
Alveolar bone
on the distolabial side of the canine was the main source
of resistance to its movement when the canine showed
clockwise rotation. Therefore, the maximum stress in
the canine root was focused on its cervix at the
distolabial side.
The effect of accelerated tooth movement and the
safety of the periodontal tissues are primary concerns
when performing a corticotomy. Changes of strain in
the PDL may have a significant influence on orthodontic
tooth movement. For one thing, the PDL is thought to be
the medium of orthodontic force transfer. For another,
the PDL itself takes part in the reactions promoting
orthodontic tooth movement.33
In this study, the distal
corticotomy approach and its combinations can reduce
the strain value of the PDL of the canine, but a mesial
corticotomy and its combinations can increase the strain
value. This result may contribute to the lower the rate of
orthodontic external root resorption, according to
Viecilli et al.12
In these models with different corticotomy
approaches, the model with the continuous circumscrib-
ing cut around the root of the canine affected the
mechanical responses of dentoalveolar structures the
most, and the distal corticotomy and its combinations
had similar impacts with the continuous circumscribing
cut compared with the model with no corticotomy.
These results can be generalized as to how corticotomy
cuts can greatly reduce the resistance to tooth move-
ment and how corticotomy cuts can affect the mechan-
ical responses of dentoalveolar structures greatly.
Therefore, a distal corticotomy approach may be a better
alternative to continuous circumscribing, and it can be
accepted readily by patients because of its minor injury
to dentoalveolar structures. A corticotomy cut closer to
the canine may benefit its distalization more because
the impact of the corticotomy decreased with the
increased distance between the cut and the canine.
Fig 5. Comparison of the maximum strains in the PDL of canine in the models: A, with the position
of the corticotomy cut varied; B, with the distance between the corticotomy cut and the canine varied;
C, with the widths of the corticotomy varied; D, distribution of strains in the PDL of the canine from the
labial and distal views.
American Journal of Orthodontics and Dentofacial Orthopedics September 2015 Vol 148 Issue 3
Yang et al 463

8. CONCLUSIONS
In this study, 24 corticotomy approaches used for
facilitating canine distalization were designed and
simulated, taking into consideration position, distance,
and width of the corticotomy. The biomechanical
responses of dentoalveolar structures were analyzed
and compared with 3D finite element analysis. From
the results of this study, the following conclusions can
be drawn.
1. Corticotomy surgery can influence the mechanical
responses of dentoalveolar structures during
maxillary canine retraction.
2. The position of the corticotomy can affect the
mechanical responses of dentoalveolar structures.
A distal corticotomy has similar biomechanical
effects as a continuous circumscribing cut around
the root of the canine.
3. When the distance between the corticotomy cut and
the canine increased, the biomechanical effects of
the corticotomy decreased gradually.
4. A distal corticotomy closer to the canine may be a
better option for rapid canine retraction, taking
into account of its biomechanical effects and
surgical injury.
SUPPLEMENTARY DATA
Supplementary data related to this article can
be found online at http://dx.doi.org/10.1016/j.ajodo.
2015.03.032
REFERENCES
1. Fisher MA, Wenger RM, Hans MG. Pretreatment characteristics
associated with orthodontic treatment duration. Am J Orthod
Dentofacial Orthop 2010;137:178-86.
2. Killiany DM. Root resorption caused by orthodontic treatment: an
evidence-based review of literature. Semin Orthod 1999;5:128-33.
3. Ren A, Lv T, Kang N, Zhao B, Chen Y, Bai D. Rapid orthodontic
tooth movement aided by alveolar surgery in beagles. Am J Orthod
Dentofacial Orthop 2007;131:160.e1-10.
4. Liou EJ, Huang CS. Rapid canine retraction through distraction of
the periodontal ligament. Am J Orthod Dentofacial Orthop 1998;
114:372-82.
Fig 6. Comparison of the maximum stresses in the maxillary trabecular bones in the models: A, with
the position of corticotomy cut varied; B, with the distance between the corticotomy cut and the canine
varied; C, with the widths of corticotomy varied; D, distribution of stresses in trabecular bone in the
models with the continuous circumscribing cut and with no corticotomy.
September 2015 Vol 148 Issue 3 American Journal of Orthodontics and Dentofacial Orthopedics
464 Yang et al

9. 5. Wilcko WM, Wilcko T, Bouquot JE, Ferguson DJ. Rapid
orthodontics with alveolar reshaping: two case reports of
decrowding. Int J Periodontics Restorative Dent 2001;21:9-19.
6. Mostafa YA, Fayed MM, Mehanni S, ElBokle NN, Heider AM.
Comparison of corticotomy-faciliated vs standard tooth-
movement techniques in dogs with miniscrews as anchor units.
Am J Orthod Dentofacial Orthop 2009;136:570-7.
7. K€ole H. Surgical operations on the alveolar ridge to correct
occlusal abnormalities. Oral Surg Oral Med Oral Pathol 1959;12:
515-29.
8. Chung KR, Oh MY, Ko SJ. Corticotomy-assisted orthodontics.
J Clin Orthod 2001;35:331-9.
9. Chung KR, Kim SH, Lee BS. Speedy surgical orthodontic
treatment using temporary anchorage devices as an alternative
to orthognathic surgery. Am J Orthod Dentofacial Orthop 2009;
135:787-98.
10. Henneman S, Von den Hoff JW, Maltha JC. Mechanobiology of
tooth movement. Eur J Orthod 2008;30:299-306.
11. Krishnan V, Davidovitch Z. Cellular, molecular, and tissue-level
reactions to orthodontic force. Am J Orthod Dentofacial Orthop
2006;129:469.e1-32.
12. Viecilli RF, Kar-Kuri MH, Varriale J, Budiman A, Janal M. Effects
of initial stresses and time on orthodontic external root resorption.
J Dent Res 2013;92:346-51.
13. Xue J, Ye N, Yang X, Wang S, Wang J, Wang Y, et al. Finite element
analysis of rapid canine retraction through reducing resistance and
distraction. J Appl Oral Sci 2014;22:52-60.
14. Wang C, Han JY, Li Q, Wang LZ, Fan YB. Simulation of bone
remodelling in orthodontic treatment. Comput Methods Biomech
Biomed Engin 2014;17:1042-50.
15. Ammar HH, Ngan P, Crout RJ, Mucino VH, Mukdadi OM.
Three-dimensional modeling and finite element analysis in
treatment planning for orthodontic tooth movement. Am J Orthod
Dentofacial Orthop 2011;139:e59-71.
16. Vig PS, Weintraub JA, Brown C, Kowalski CJ. The duration of
orthodontic treatment with and without extraction: a pilot study
of five selected practices. Am J Orthod Dentofacial Orthop 1990;
97:45-51.
17. Aboul-Ela SM, El-Beialy AR, El-Sayed KM, Selim EM,
El-Mangoury NH, Mostafa YA. Miniscrew implant-supported
maxillary canine retraction with and without corticotomy-
facilitated orthodontics. Am J Orthod Dentofacial Orthop 2011;
139:252-9.
18. Iino S, Sakoda S, Miyawaki S. An adult bimaxillary protrusion
treated with corticotomy-facilitated orthodontics and titanium
miniplates. Angle Orthod 2006;76:1074-82.
19. Lim JE, Lee SJ, Kim YJ, Lim WH, Chun YS. Comparison of cortical
bone thickness and root proximity at maxillary and mandibular
interradicular sites for orthodontic mini-implant placement.
Orthod Craniofac Res 2009;12:299-304.
20. Aversa R, Apicella D, Perillo L, Sorrentino R, Zarone F, Ferrari M,
et al. Non-linear elastic three-dimensional finite element analysis
on the effect of endocrown material rigidity on alveolar bone
remodeling process. Dent Mater 2009;25:678-90.
21. Lee NK, Baek SH. Stress and displacement between maxillary
protraction with miniplates placed at the infrazygomatic crest
and the lateral nasal wall: a 3-dimensional finite element analysis.
Am J Orthod Dentofacial Orthop 2012;141:345-51.
22. Lin TS, Tsai FD, Chen CY, Lin LW. Factorial analysis of variables
affecting bone stress adjacent to the orthodontic anchorage
mini-implant with finite element analysis. Am J Orthod
Dentofacial Orthop 2013;143:182-9.
23. Canales C, Larson M, Grauer D, Sheats R, Stevens C, Ko CC. A
novel biomechanical model assessing continuous orthodontic
archwire activation. Am J Orthod Dentofacial Orthop 2013;143:
281-90.
24. Kim SH, Kim I, Jeong DM, Chung KR, Zadeh H. Corticotomy-
assisted decompensation for augmentation of the mandibular
anterior ridge. Am J Orthod Dentofacial Orthop 2011;140:720-31.
25. Fill TS, Toogood RW, Major PW, Carey JP. Analytically determined
mechanical properties of, and models for the periodontal ligament:
critical review of literature. J Biomech 2012;45:9-16.
26. Toms SR, Eberhardt AW. A nonlinear finite element analysis of the
periodontal ligament under orthodontic tooth loading. Am J
Orthod Dentofacial Orthop 2003;123:657-65.
27. Ozdemir F, Tozlu M, Germec-Cakan D. Cortical bone thickness of
the alveolar process measured with cone-beam computed
tomography in patients with different facial types. Am J Orthod
Dentofacial Orthop 2013;143:190-6.
28. Kim SJ, Park YG, Kang SG. Effects of corticision on paradental
remodeling in orthodontic tooth movement. Angle Orthod 2009;
79:284-91.
29. Baloul SS, Gerstenfeld LC, Morgan EF, Carvalho RS, Van Dyke TE,
Kantarci A. Mechanism of action and morphologic changes
in the alveolar bone in response to selective alveolar
decortication-facilitated tooth movement. Am J Orthod
Dentofacial Orthop 2011;139(4 Suppl):S83-101.
30. Wang L, Lee W, Lei DL, Liu YP, Yamashita DD, Yen SL. Tissue
responses in corticotomy- and osteotomy-assisted tooth
movements in rats: histology and immunostaining. Am J Orthod
Dentofacial Orthop 2009;136:770.e1-11:discussion, 770-1.
31. Melsen B. Tissue reaction to orthodontic tooth movement—a new
paradigm. Eur J Orthod 2001;23:671-81.
32. Kawarizadeh A, Bourauel C, Zhang D, G€otz W, J€ager A. Correlation
of stress and strain profiles and the distribution of osteoclastic cells
induced by orthodontic loading in rat. Eur J Oral Sci 2004;112:
140-7.
33. McCormack SW, Witzel U, Watson PJ, Fagan MJ, Gr€oning F.
The biomechanical function of periodontal ligament fibres in
orthodontic tooth movement. PLoS One 2014;9:e102387.
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