Finite element analysis of the

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ORIGINAL ARTICLE
Finite element analysis of the
biomechanical effect of clear aligners in
extraction space closure under different
anchorage controls
Guan-yin Zhu,a Bo Zhang,a Ke Yao,a Wen-xin Lu,a Jia-jia Peng,a Yu Shen,b and Zhi-he Zhaoa
Chengdu, China
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Introduction: Clear aligners (CAs) have attracted increasing attention from patients and orthodontists because
of their excellent esthetics and comfort. However, treating tooth extraction patients with CAs is difficult because
their biomechanical effects are more complicated than those of traditional appliances. This study aimed to
analyze the biomechanical effect of CAs in extraction space closure under different anchorage controls,
including moderate, direct strong, and indirect strong anchorage. It could provide several new cognitions for
anchorage control with CAs through finite element analysis, further directing clinical practice. Methods: A 3-
dimensional maxillary model was generated by combining cone-beam computed tomography and intraoral
scan data. Three-dimensional modeling software was used to construct a standard first premolar extraction
model, temporary anchorage devices, and CAs. Subsequently, finite element analysis was performed to
simulate space closure under different anchorage controls. Results: Direct strong anchorage was beneficial
for reducing the clockwise occlusal plane rotation, whereas indirect anchorage was conducive for anterior teeth
inclination control. In the direct strong anchorage group, an increase in the retraction force would require more
specific anterior teeth overcorrection to resist the tipping movement, mainly including lingual root control of the
central incisor, followed by distal root control of the canine, lingual root control of the lateral incisor, distal root
control of the lateral incisor, and distal root control of the central incisor. However, the retraction force could
not eliminate the mesial movement of the posterior teeth, possibly causing a reciprocating motion during treat-
ment. In indirect strong groups, when the button was close to the center of the crown, the second premolar pre-
sented less mesial and buccal tipping but more intrusion. Conclusions: The 3 anchorage groups showed
significantly different biomechanical effects in both the anterior and posterior teeth. Specific overcorrection or
compensation forces should be considered when using different anchorage types. The moderate and indirect
strong anchorages have a more stable and single-force system and could be reliable models in investigating
the precise control of future tooth extraction patients. (Am J Orthod Dentofacial Orthop 2023;-:---)
Key Laboratory of Oral Diseases and National Clinical Research Center for
iseases, and Department of Orthodontics, West China Hospital of Stoma-
y, Sichuan University, Chengdu, China.
ol of Basic Medical Sciences, Chengdu University, Chengdu, China.
-yin Zhu and Bo Zhang are joint first authors and contributed equally to
ork.
thors have completed and submitted the ICMJE Form for Disclosure of Po-
l Conflicts of Interest, and none were reported.
ork was supported by the Research and Development Program of West
Hospital of Stomatology Sichuan University (no. RD-03-202012).
ss correspondence to: Zhi-he Zhao, State Key Laboratory of Oral Diseases
ational Clinical Research Center for Oral Diseases, and Department of Or-
ntics, West China Hospital of Stomatology, Sichuan University, No. 14, 3rd
n, RenMinNan Rd Chengdu, Sichuan 610041, China; e-mail, zhzhao@scu.
n.
itted, September 2021; revised and accepted, February 2022.
5406/$36.00
2.
//doi.org/10.1016/j.ajodo.2022.02.018
Clear aligners (CAs), a new orthodontic appliance,have been widely used in the last 15 years.1Compared with fixed appliances, CA has the
main advantages of comfort, hygiene, and esthetics,
which endow patients with better quality of life; there-
fore, it has received great attention.2,3 However, ortho-
dontists need to care about the treatment experience
of patients and also clearly understand the effectiveness
of CA on different malocclusion types. The orthodontic
force of CA is derived from the resilience of the polymer
aligner worn on the teeth.4 Thus, its biomechanical or-
thodontic mechanism is completely different from that
of the traditional fixed appliance. CA is highly efficient
in molar distalization, anterior teeth alignment, and
space closure, as well as low efficiency in the correction
of a deep overbite, root movement control, and arch
1
Delta:1_given name
Delta:1_surname
Delta:1_given name
Delta:1_surname
Delta:1_given name
Delta:1_surname
Delta:1_given name
mailto:zhzhao@scu.edu.cn
mailto:zhzhao@scu.edu.cn
https://doi.org/10.1016/j.ajodo.2022.02.018
2 Zhu et al
expansion,5-8 making it suitable for handling simple
nonextraction patients, whereas higher requirements
are placed on orthodontists for relatively complex
extraction patients.9
In contemporary orthodontics, extraction patients
are very common, and nearly 30% of patients require
extraction of premolars to manage malocclusion.10 To
allow these patients to benefit from the CA treatment,
orthodontists have used the following methods to
compensate for CA control deficiency: (1) adding extra
overcorrection in the target position, (2) adding torque
compensation in anterior teeth and anchorage prepara-
tion in posterior teeth before extraction closure, (3) add-
ing attachments to ensure complete CA fit, and (4) using
a long-power arm to retract the anterior teeth in strong
anchorage patients.11-13 In fact, the deficiency of CA is
attributable to the characteristics of elastic polymer
material, which cannot simultaneously exhibit high
elasticity to generate proper orthodontic force, and
sufficient strength to ensure complete teeth movement
to the target position.
In addition, CA is commonly made of a viscoelastic
polymer material, instead of superelastic materials,
such as nitinol springs. It undergoes creep and stress
relaxation during wearing, constantly losing elastic-
ity.4,14,15 Therefore, the tooth usually becomes more
deviated with the amount of toothmovement, becoming
obvious in patients with massive tooth movement, such
as extraction. Thus, an extra compensation force is
required to help the teeth reach the ideal target position.
To reasonably add such forces in a CA design system, or-
thodontists must clearly understand how the teeth move
in extraction space closure patients with regular CA
treatment.
We performed a finite element analysis (FEA) on a
first premolar extraction patient with moderate, direct
strong (using elastics to directly retract anterior teeth),
and indirect strong (fixing the second premolar with
metal wire ligation) anchorage groups to comprehen-
sively illustrate the tooth movement pattern of the
extraction space closure patient with CA treatment. In
addition, considering the direct strong anchorage was
relayed on the compliance of patients wearing the elas-
tics, the force was also varied. We also analyzed the
direct strong anchorage groups with different retraction
forces. The indirect strong anchorage group did not need
to wear and replace elastics, and the orthodontic force
was only derived from the CA, which was considered
relatively simple and reproducible. Thus, the analysis
of this group might be conducive to finding a reliable
overcorrection approach for strong anchorage. In addi-
tion, the biomechanical effect of the indirect strong
anchorage could be largely affected by the relative
- 2023 � Vol - � Issue - American
position of the ligation button and miniscrew. Thus,
we also analyzed the indirect strong anchorage group
with different second premolar button positions.
FEA has been widely used in solutions for complex
biomechanical questions, including the orthodontic
field,16 with outcomes containing an instantaneous
stress distribution and displacement, which are signifi-
cant in CA biomechanicalanalysis because the treatment
process can also be understood as the superposition of
multiple instantaneous mechanical effects. To increase
practicality, we illustrated the stress distribution in
different groups and converted the displacement data
as a tooth movement table, which was coordinated
with the mainstream CA design system, such as the Clin-
check of Invisalign (Align Technology, Santa Clara,
Calif). In this way, the 3-dimensional (3D) movement
of every tooth was displayed, which could facilitate
orthodontists to add force compensation in clinical
practice.
This study aimed to comprehensively demonstrate
the biomechanical effect of CA in extraction space
closure under different anchorage controls, which would
provide a new and clear understanding and lay a solid
foundation for future studies.
MATERIAL AND METHODS
A healthy orthodontic patient was included in the pa-
tient archive of the West China Stomatology Hospital.
This patient met the following inclusion criteria: (1) per-
manent dentition with normal tooth morphology, (2) no
obvious crowding, (3) normal anterior teeth torque, (4)
symmetrical arch with a normal occlusal curve, (5) no
periodontal disease, and (6) complete cone-beam com-
puted tomography (CBCT) and intraoral scan data. The
exclusion criteria were systemic diseases affecting bone
development. This study was approved by the Ethics
Committee of the West China Stomatology Hospital of
Sichuan University.
The maxillary model was generated by combining
CBCT and intraoral scan data. The CBCT image was
stored in the standard digital imaging and communica-
tions in medicine (DICOM) format, which was further
imported into Mimics Research (version 19.0; Materi-
alise NV, Leuven, Belgium). The soft tissues were
removed in Mimics via threshold segmentation on the
basis of gray value difference, and then the integrated
3D geometric surface model of the maxilla and denti-
tion were isolated. The obtained models were imported
into the Geomagic software (version 2017; 3D systems,
Rock Hill, SC) to refine the poor shape of the maxillary
model caused by DICOM data reconstruction and sur-
face model smoothening. Intraoral scan data were
Journal of Orthodontics and Dentofacial Orthopedics
Fig 1. Models for FEA: A, The maxillary tissues were constructed on the basis of patient data, and the
CA, miniscrew, and buccal buttons were constructed according to available products; B, The assem-
bled model structure in different views; C, Three main groups: moderate anchorage group (the extrac-
tion space was closed only by CA contraction), direct strong anchorage group (the extraction space
was closed by CA contraction, and an elastic [white] was used to retract the CA to enhance molar
anchorage), indirect strong anchorage group (the extraction space was closed by CA contraction,
and a metallic ligature [red] was placed from the miniscrew to the second premolar to negate the un-
wanted mesial force).
Zhu et al 3
used to refine the CBCT data, further improving the
precision of dentition modeling and constructing a
standard first premolar extraction model. Briefly, the
intraoral scan data with high precision were stored in
stereolithography (STL) format and imported into Or-
thoAnalyzer (3Shape, Copenhagen, Denmark) to align
the dentition on the basis of Andrews normal occlusion.
The aligned dentition was exported in STL format and
used as a template to adjust the CBCT dentition posi-
tion in Geomagic Studio. After aligning the CBCT
dentition, we replaced the CBCT crown with a high-
precision intraoral scan crown and integrated the
CBCT root through smooth modification. Finally, a
high-quality dentition model was developed. The first
premolars were then removed to generate the first pre-
molar extraction model. The tooth root was evenly
American Journal of Orthodontics and Dentofacial Orthoped
expanded 0.25 mm outward to construct a periodontal
ligament (PDL).17 A CA was developed, making a 0.5
mm external offset18 from dental crowns with Appli-
ance Designer (3Shape) (Supplementary Fig 1). To
further validate that the thickness parameter of PDL
and aligner were rational, extra physical experiments
were performed (Supplementary Table I;
Supplementary Figs 2-6). The buccal button and
miniscrew were constructed using SolidWorks
(Dassault Syst�emes Americas, Waltham, Mass). The
miniscrew was developed according to the Vector TAS
orthodontic implant (Ormco, Glendora, Calif), with a
total length of 10.7 mm and an implanted part of 8
mm, respectively (Fig 1, A). Unigraphics NX (UG,
Siemens PLM Software) was used to assemble the con-
structed parts into research models (Fig 1, B).
ics - 2023 � Vol - � Issue -
Table I. Discretization parameters
Group
Total no. of
nodes
Total no. of
elements
Moderate anchorage group 844,355 474,328
Direct strong anchorage
group
872,162 491,649
Indirect strong anchorage
group
872,162 491,649
Table II. Material properties
Material Young modulus, E (Mpa) Poisson ratio, v
Alveolar bone 1.37 3 104 0.30
Teeth 1.96 3 104 0.30
PDL 0.69 0.45
CA 528 0.36
Miniscrew 1.03 3 105 0.33
Buccal button 2.00 3 105 0.30
PDL, periodontal ligament; CA, clear aligners.
4 Zhu et al
This study included 3 major space closure groups
with different anchorage controls: group A, closing the
extraction space with moderate anchorage, in which
no extra anchorage was applied; group B, closing the
extraction space with direct strong anchorage, in which
elastic forces were applied from the miniscrew to the
canine appliance; and group C, closing the extraction
space with indirect strong anchorage, in which a metallic
ligature was placed from the miniscrew to the second
premolar to negate the unwanted mesial force. A sche-
matic diagram of the 3 groups is shown in Figure 1, C.
To further illustrate the factors that affect the biome-
chanical effect of strong anchorage groups, group B
was divided into several subgroups according to various
elastic retraction forces as follows: group B1, 150 g of
force; group B2, 300 g of force; and group B3, 500 g
of force. In addition, only the addition of elastic retrac-
tion forces (150 and 500 g of force) without adding a CA
contraction force was also analyzed (group B4-5). Group
C was further divided into 3 subgroups according to the
vertical location of the buccal buttons: group C1, high
position close to the gingival line; group C2, medium
position; and group C3, low position at the center of
the dental crown.
The model structures were imported into ABAQUS
(version 6.14; Dassault Syst�emes, Providence, RI) to
generate a 3D finite element model by a meshing process
and discretization. The models were meshed into tetra-
hedral elements (C3D10), suitable for irregular geome-
tries. The discretization parameters, including the
number of nodes and elements, are listed in Table I.
The maxilla, dentition, PDL, CA, buccal buttons, and
miniscrews were assigned isotropic, homogeneous, and
linearly elastic material properties, respectively. The
property parameters referenced from previous ortho-
dontic FEA studies have been commonly justified and
used18-22 (Table II). A fixed boundary condition was
set at the base of the maxilla to prevent the model
from body motion while the force was loaded. In addi-
tion, a frictional coefficient contact condition (m) of
0.2 was set between the CA and the dentition.22
The loading configuration was set according to the
abovementioned groups to simulate the different
- 2023 � Vol - � Issue - American
biomechanical effects in reality. The extraction closure
force of the CA was loaded by the thermal contraction
method, which was more suitable and practicable in sim-
ple extraction closure FEA (Supplementary Fig 6).
Briefly, a 1-mm area was selected in the extraction re-
gion. The selected area contracted according to the
linear expansion coefficient when the temperature was
loaded. Thus, a proper temperature difference and linear
expansion coefficient were applied to the selected area
to make it accurately contracted by 0.2 mm,thereby
achieving the closing effect. In the direct strong
anchorage group, elastic forces were applied bilaterally
from the miniscrew to the canine appliance. In the indi-
rect strong anchorage group, a fixed distance boundary
condition was set between the buccal button of the sec-
ond premolar and the miniscrew to simulate metal wire
ligation. The finite element models were calculated us-
ing ABAQUS software to generate a series of nodal dis-
placements and von Mises stress distributions.
Three-dimensional coordinates were separately set
on every tooth to determine the displacements as fol-
lows: x (labial lingual direction), y (mesiodistal direc-
tion), and z (tooth long axis). The origins, which
could reflect the body movement of the crown and
root, were separately set on the body center point of
the clinical crown and the root apex (Fig 2). In this
way, the displacement of the dentition could
be exported as a “teeth movement table,” which was
coordinated with the available CA design system,
making them more comprehensible with clinical
reference values.
Statistical analysis
Descriptive and Pearson product-moment correla-
tion analyses were used to test the correlations between
the elastic forces and biomechanical effects in the direct
strong anchorage group. Prism (version 8; GraphPad
Software, San Diego, Calif) was used for the statistical
analyses.
Journal of Orthodontics and Dentofacial Orthopedics
Fig 2. The 3D coordinates set for each tooth. A-C, 3D coordinates set in different views. The global
coordinates were on the lower left side. The local coordinates were separately set on every tooth: x
(mesiodistal direction), y (labial lingual direction), and z (tooth long axis). The origins, which could
reflect the body movement of the crown and root, were separately set on the facial axis of the clinical
crown and the root apex point.D, The root origin of the molars, which hadmultiroots, was located at the
center point (black) of the 3 apical points.
Zhu et al 5
RESULTS
The FEA results of the 3 different anchorage groups
are presented in Figure 3, including the periodontal
stresses and tooth displacements. No obvious peri-
odontal stress distribution variation was found among
the 3 groups (Figs 3, D-F) because the major stresses
concentrated on the dental cervix (red), and the rest of
the stresses (blue) on the teeth root surfaces did not
show obvious differences. However, there was still a
slight tendency for the lingual periodontal ligament of
the anterior teeth in the strong anchorage groups to pre-
sent a higher stress distribution, while the stresses in the
posterior teeth (particularly the molars) were smaller and
more uniform. The displacement of the dentition (Figs 3,
G-O) showed a similar tendency and more intuitive dif-
ferences. Compared with the moderate anchorage
group, both the direct and indirect strong anchorage
groups showed effective anchorage protection, in which
more anterior teeth retraction and smaller molar mesial
movement were found. Apart from the amount of
displacement, no apparent change in displacement di-
rection was found in the anterior teeth and molars.
Interestingly, the displacement of the second premo-
lar presented a distinctive difference between the 2
strong anchorage groups. The displacement direction
of the second premolar in the direct strong anchorage
group was similar to that of the moderate group,
whereas the second premolar in the indirect strong
American Journal of Orthodontics and Dentofacial Orthoped
anchorage group presented an obvious intrusion ten-
dency. To illustrate this phenomenon, we investigated
the biomechanical mechanism of the indirect strong
anchorage and its factors in the following section.
As shown in Table III, comprehensive tooth move-
ment data were extracted to quantitatively analyze the
crown and root movement patterns among the 3 groups,
and the tooth tipping movement forms were calculated
using the crown relative movement ratio. The potential
meaning of the crown relative movement ratio is pre-
sented in Supplementary Fig 7. From the vertical view,
in contrast to the moderate anchorage group, direct
strong anchorage groups could reduce the anterior teeth
extrusion, whereas the indirect strong anchorage group
could aggravate the extrusion. The posterior teeth
showed a different movement tendency than the moder-
ate anchorage group. The second premolar and first
molar of the direct strong anchorage group showed
decreased intrusion, and the second molar presented
decreased extrusion. Although the second molar of the
indirect strong anchorage group also tended to reduce
extrusion, the second premolar and first molar showed
an increased intrusion, in which the second premolar
had an approximately 2-fold intrusion. Given the relative
vertical change of the incisor and the molars, the direct
strong anchorage might be beneficial to decrease the
clockwise rotation of the occlusal plane, whereas the in-
direct group had the opposite effect. From the sagittal
ics - 2023 � Vol - � Issue -
Fig 3. FEA of different anchorage groups: A-C, Schematic diagram of 3 different anchorage groups;
D-F, Von Mises stress distribution at PDL of the different groups; G-I, Teeth displacement magnitude
of the different groups; J-O,Resultant displacement of anterior teeth and posterior teeth of the different
groups. FEA, finite element analysis; PDL, periodontal ligament.
6 Zhu et al
view, both strong anchorage groups could successfully
increase anterior teeth retraction and protect the molar
anchorage at a similar level. However, neither of them
completely prevented the molar from mesial movement.
Moreover, from the buccal-lingual crown relative
movement ratio, compared with the moderate
anchorage group, the addition of elastics in the direct
- 2023 � Vol - � Issue - American
anchorage group could aggravate the lingual tilt of the
central incisor, whereas the indirect anchorage was rela-
tively conducive to reducing this movement. From the
mesial-distal crown relative movement ratio, compared
with the direct strong anchorage group, the metal wire
ligature in the indirect strong anchorage group was
more effective in preventing the crown of the premolar
Journal of Orthodontics and Dentofacial Orthopedics
Table III. Teeth movement in different anchorage groups
Group
Anterior teeth Posterior teeth
1 2 3 5 6 7
Moderate anchorage group
Extrusion/intrusion (310�2 mm) 1.207 E 0.720 E �0.082 I �0.634 I �0.200 I 0.854 E
Buccal/lingual movement: crown (3 10�2 mm) �3.030 L �2.273 L �0.704 L 0.129 B �0.053 L 0.101 B
Buccal/lingual movement: root (3 10�2 mm) 1.476 B 1.007 B 0.325 B �0.159 L 0.051 B 0.114 B
Mesial/distal movement: crown (3 10�2 mm) 0.608 D 1.513 D 2.671 D �1.531 M �1.219 M �1.111 M
Mesial/Distal movement: root (3 10�2 mm) �0.270 M �0.706 M �1.571 M 0.813 D 0.535 D 0.424 D
Buccal/lingual crown relative movement ratio �3.053 L �3.257 L �3.166 L �1.816 B �2.035 L �0.114 L
Mesial/distal crown relative movement ratio �3.252 D �3.145 D �2.700 D �2.883 M �3.278 M �3.618 M
Direct strong anchorage group (150 g of force)
Extrusion/intrusion (310�2 mm) 1.075 E 0.377 E �0.462 I �0.529 I �0.162 I 0.724 E
Buccal/lingual movement: crown (310�2 mm) �3.278 L �2.393 L �0.646 L 0.107 B �0.044 L 0.100 B
Buccal/lingual movement: root (310�2 mm) 1.606 B 0.963 B 0.255 B �0.157 L 0.021 B 0.083 B
Mesial/distal movement: crown (310�2 mm) 0.701 D 1.729 D 2.985 D �1.300 M �1.040 M �0.747 M
Mesial/distal movement: root (310�2 mm) �0.284 M �0.796 M �1.757 M 0.698 D 0.437 D 0.345 D
Buccal/lingual crown relative movement ratio �3.041 L �3.485 L �3.537 L �1.679 B �3.078 L 0.207 B
Mesial/distal crown relative movement ratio �3.470 D �3.172 D �2.699 D �2.863 M �3.380 M �3.163 M
Indirect strong anchorage group
Extrusion/intrusion (310�2 mm) 1.292 E 0.749 E �0.116 I �1.237 I �0.197 I 0.699 E
Buccal/lingual movement: crown (310�2 mm) �3.216 L �2.409 L �0.760 L 0.143 B 0.002 B 0.076 B
Buccal/lingual movement: root (310�2 mm) 1.563 B 1.060 B 0.349 B �0.203 L 0.024 B0.392 B
Mesial/distal movement: crown (310�2 mm) 0.626 D 1.579 D 2.811 D �1.047 M �1.008 M �0.924 M
Mesial/distal movement: root (310�2 mm) �0.277 M �0.734 M �1.642 M 0.606 D 0.453 D 0.362 D
Buccal/lingual crown relative movement ratio �3.058 L �3.273 L �3.181 L �1.707 B �0.937 L �0.805 L
Mesial/distal crown relative movement ratio �3.261 D �3.152 D �2.712 D �2.729 M �3.225 M �3.550 M
Note. Positive values indicate extrusion, buccal, and distal direction in tooth movement, whereas negative values indicate intrusion, lingual, and
mesial direction in tooth movement; Positive and negative values in crown relative movement ratio have no specific displacement direction (ie,
direction are also marked after the value); Crown movement is the movement of the midpoint of the facial axis of the clinical crown, whereas
root movement, the movement of the root apex; Crown relative movement ratio is the value of the crown displacement minus the root displacement
divided by the root displacement, which partially reflects the tooth tipping movement pattern.
E, extrusion referenced to the occlusal plane; I, intrusion referenced to the occlusal plane; B, buccal direction; L, lingual direction; M, mesial di-
rection; D, distal direction; 1, central incisor; 2, lateral incisor; 3, canine; 5, second premolar; 6, first molar; 7, second molar.
Zhu et al 7
and the first molar from mesial tipping. Because the
aligner contraction and elastic forces were mainly paral-
lel to the sagittal direction, the force component acting
on the horizontal plane was relatively small. However,
the elastic force component in the direct strong
anchorage group still caused a buccal inclination ten-
dency of the second molar, whereas the indirect strong
anchorage group presented a movement pattern similar
to that of the moderate anchorage group. The biome-
chanical effects of the 3 groups are summarized in
Figure 4.
Compared with the moderate and indirect strong
anchorage groups, the direct strong anchorage group
was highly variable and dynamic owing to the addition
of elastic force. Twomain factorsmight affect the biome-
chanical effect of this group: the strength of the elastic
force and its relationship with the aligner contraction
force. To clearly illustrate this issue, direct strong
anchorage with various elastic force groups (the addition
of 300-g and 500-g groups) and a single 150 g elastic
American Journal of Orthodontics and Dentofacial Orthoped
force without aligner contraction force group were
further analyzed via FEA (Fig 5). In contrast to the 150-
g elastic force in Figure 3, the increased retraction forces
(300-g and 500-g) increased the periodontal stresses in
the anterior teeth, especially on the lingual side, and a
significant stress difference was observed between the
anterior teeth and posterior teeth (Figs 5, D and E). The
tooth displacement also demonstrated that a larger ante-
rior teeth crown retraction was present in the high-
retraction force group, and the displacement direction
rotated counterclockwise owing to the decreased extru-
sion (Figs 5, J and K). The posterior teeth had a slightly
smaller mesial movement in the higher retraction force
group. However, mesial posterior tooth movement still
existed in the 500-g retraction force group (Figs 5, M
and N). To further illustrate this result, 150-g retraction
forces without aligner contraction were performed (Fig
5, C), which reflected the biomechanical effect of the
pure retraction elastic force on the dentition with CA
and the biomechanical status of a patient wearing a CA
ics - 2023 � Vol - � Issue -
Fig 4. Biomechanical effects of the 3 anchorage groups: A, The biomechanical effect of the indirect
strong anchorage group, compared with the moderate anchorage group; B, The biomechanical effect
of the direct strong anchorage group, compared with the moderate anchorage group; C, The biome-
chanical difference between the indirect strong anchorage group and the direct strong anchorage
group.
8 Zhu et al
for several days when the CA contraction force was atten-
uated, but the elastics still maintained a similar force.
Compared with the instantaneous aligner contraction
force (Fig 3, A), 150 g of elastic retraction force was
slighter, and the biomechanical effects differed in both
anterior and posterior teeth. Compared with the aligner
contraction force, the elastic retraction force could
distinctively reduce extrusion, slightly increase retraction
on the anterior teeth, and have almost opposite effects on
the posterior teeth (Figs 5, L and O). Thus, a preliminary
conclusion can be drawn: the anchorage protection of
the posterior teeth by direct strong anchorage is dynamic
and manifests as a 2-stage reciprocating motion (mesial
followed by distal movement).
Exhaustive tooth movement data were extracted to
quantitatively analyze the effect of retraction force on
tooth movement, as shown in Table IV. Combined with
Table III, several keys could be intuitively summarized:
(1) a larger elastic retraction force was conducive to
reducing the anterior teeth extrusion and reduce the
posterior teeth intrusion, thereby decreasing the ten-
dency of the clockwise occlusal plane rotation; and (2)
- 2023 � Vol - � Issue - American
a larger elastic retraction force was beneficial for anterior
teeth retraction and molar anchorage protection, but
could not completely prevent molar mesial movement,
which is consistent with the results shown in Figure 5.
The crown relative movement ratio was not intuitive
data but partially reflected the tipping movement
change of each tooth in a specific plane. Pearson’s test
was performed on the movement ratio in various retrac-
tion force groups to further investigate the effects of
retraction force on teeth movement patterns (Table V).
Notably, the increase in elastic retraction force had
increased effects on buccal root control of the central
incisor, lingual crown tipping of the lateral incisor and
second premolar, and lingual root control of the canine
and molars. In addition, from the mesial/distal plane, it
had increased effects on distal crown tipping of the
incisor and second premolar and mesial root control of
the canine and molars. There is also noted increased
negative displacement effects in space closure, including
the lingual tipping of the incisors, the lingual-buccal
tipping of the molars, the distal tipping of the anterior
teeth, and the overcorrection suggestions were further
Journal of Orthodontics and Dentofacial Orthopedics
Fig 5. FEA of direct strong anchorage groups with different elastic forces:A-C,Schematic diagram of 3
different anchorage groups; D-F, Von Mises stress distribution at the PDL of the different groups; G-I,
Teeth displacement magnitude of the different groups; J-O, Resultant displacement of anterior teeth
and posterior teeth of the different groups. FEA, finite element analysis; PDL, periodontal ligament.
Zhu et al 9
presented. Table VI ranked the negative effects in Table
V on the basis of the crown-root displacement difference
to clarify which negative displacement effect had the
greatest impact when using elastics to enhance
anchorage. The order of the overcorrection requirements
was as follows: (1) lingual root control of the central
incisor, (2) distal root control of the canine, (3) lingual
root control of the lateral incisor, (4) distal root control
of the lateral incisor, (5) distal root control of the central,
and (6-7) lingual-buccal root control of the molars. The
American Journal of Orthodontics and Dentofacial Orthoped
overcorrection needs of the anterior teeth were deter-
mined, but the needs of the posterior teeth varied de-
pending on the strength of the retraction force, in
which lingual root control was needed in low-
retraction force and buccal root control was needed in
high-retraction force. Based on the above results, a dy-
namic biomechanical process of closing the space with
a direct strong anchorage can be summarized (Fig 6).
Compared with the direct strong anchorage, theindirect strong anchorage was relatively stable because
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Table IV. The impact of retraction force on teeth movement
Group
Anterior teeth Posterior teeth
1 2 3 5 6 7
Direct strong anchorage (300 g of force)
Extrusion/intrusion (310�2 mm) 0.930 E �0.061 I �0.869 I �0.425 I �0.128 I 0.594 E
Buccal/lingual movement: crown (310�2 mm) �3.525 L �2.530 L �0.595 L 0.083 B �0.070 L 0.097 B
Buccal/lingual movement: root (310�2 mm) 1.739 B 0.938 B 0.196 B �0.151 L �0.005 L 0.055 B
Mesial/distal movement: crown (310�2 mm) 0.807 D 1.946 D 3.299 D �1.067 M �0.859 M �0.782 M
Mesial/distal movement: root (310�2 mm) �0.307 M �0.895 M �1.950 M 0.583 D 0.338 D 0.265 D
Buccal/lingual crown relative movement ratio �3.027 L �3.697 L �4.043 L �1.550 B 11.971 L 0.782 B
Mesial/distal crown relative movement ratio �3.631 D �3.174 D �2.692 D �2.831 M �3.543 M �3.945 M
Direct strong anchorage (500 g of force)
Extrusion/intrusion (310�2 mm) 0.709 E �0.395 I �1.410 I �0.287 I �0.084 I 0.261 E
Buccal/lingual movement: crown (310�2 mm) �3.842 L �2.660 L �0.534 L 0.053 B �0.024 L 0.096 B
Buccal/lingual movement: root (310�2 mm) 1.916 B 0.850 B 0.123 B �0.142 L �0.041 L 0.016 B
Mesial/distal movement: crown (310�2 mm) 0.960 D 2.248 D 3.736 D �0.755 M �0.616 M �0.560 M
Mesial/distal movement: root (310�2 mm) �0.346 M �1.008 M �2.229 M 0.429 D 0.204 D 0.158 D
Buccal/lingual crown relative movement ratio �3.005 L �4.129 L �5.344 L �1.373 B �0.405 B 5.052 B
Mesial/distal crown relative movement ratio �3.774 D �3.230 D �2.676 D �2.762 M �4.013 M �4.535 M
Direct strong anchorage (150 g of force) without aligner contraction
Extrusion/intrusion (310�2 mm) �0.184 I �0.307 I �0.248 I 0.156 E 0.012 E �0.051 I
Buccal/lingual movement: crown (310�2 mm) �0.240 L �0.157 L �0.083 L �0.115 L �0.070 L �0.064 L
Buccal/lingual movement: root (310�2 mm) 0.124 B �0.041 L 0.039 B 0.067 B �0.011 L 0.018 B
Mesial/distal movement: crown (310�2 mm) 0.110 D 0.238D 0.451 D 0.267 D 0.225 D 0.215 D
Mesial/distal movement: root (310�2 mm) �0.025 M �0.098 M �0.288 M �0.155 M �0.128 M �0.126 M
Buccal/lingual crown relative movement ratio �2.939 L �2.873 L �3.129 L �2.710 L 5.573 L �4.464 L
Mesial/distal crown relative movement ratio �5.434 D �3.436 D �2.565 D �2.721 D �2.758 D �2.708 D
Note. Positive values indicate extrusion, buccal, and distal direction in tooth movement, whereas negative values indicate intrusion, lingual, and
mesial direction in tooth movement; Positive and negative values in crown relative movement ratio have no specific displacement direction (ie,
direction are also marked after the value); Crown movement is the movement of the midpoint of the facial axis of the clinical crown, whereas
root movement, the movement of the root apex; Crown relative movement ratio is the value of the crown displacement minus the root displacement
divided by the root displacement, which partially reflects the tooth tipping movement pattern.
E, extrusion referenced to the occlusal plane; I, intrusion referenced to the occlusal plane; B, buccal direction; L, lingual direction; M, mesial di-
rection; D, distal direction; 1, central incisor; 2, lateral incisor; 3, canine; 5, second premolar; 6, first molar; 7, second molar.
10 Zhu et al
it had only aligner contraction forces. The anchorage
protection of the posterior teeth was derived from
the metallic wire ligation; therefore, the relative posi-
tion of the miniscrew and the buccal button was the
essential factor that could affect the anchorage pro-
tection effect. FEA of the impact of the buccal button
position on posterior teeth movement is shown in
Supplementary Figure 8. However, there was no intu-
itive displacement difference among the 3 groups, as
the difference was too slight, and the FEA only re-
flected the instant effect. Therefore, accurate tooth
movement data were further extracted from the FEA
(Table VII), demonstrating that the largest displace-
ments occurred in the second premolar, and the
mesial tipping and intrusion were the 2 most signifi-
cant movement types. The movement change ten-
dency of the table is summarized in Table VIII. The
premolar not only had the largest displacement but
also had an unchanged movement tendency. When
the position was located from the high to the low,
- 2023 � Vol - � Issue - American
the premolar presented decreasing mesial and buccal
tipping but increased intrusion. In contrast, the move-
ment tendency of the molars was unstable and could
be reversed.
DISCUSSION
Extraction patients, particularly strong anchorage
patients, are relatively complicated in orthodontic
treatments. The core problem is how to compensate
for the insufficient control of the CA, which causes un-
wanted tipping movement. To address this issue, a
basic question needs to be answered: what are the
insufficient controls of the CA in space closure, and
to what extent? Clinical observations and trials are usu-
ally affected by many confounding factors unsuitable
for answering this question. FEA is based on a stable
and reproducible model, which can be used to investi-
gate the biomechanical effects and their change ten-
dency. In recent years, several FEA studies have been
conducted on orthodontic biomechanics.22-24
Journal of Orthodontics and Dentofacial Orthopedics
Table V. The correlation between the elastic retraction force and the teeth tipping movement
Plane
Anterior teeth Posterior teeth
1 2 3 5 6 7
Buccal/lingual
Tipping direction Lingual Lingual Lingual Buccal Lingual/Buccal Lingual/Buccal
Crown relative
movement ratio
Y [ [ Y [/Y [/Y
Pearson correlation
coefficient, r
0.9972 �0.9944 �0.9744 0.9999 – –
P value (significance) 0.0028** 0.0056** 0.0256* \0.0001**** – –
Crown displacement
tendency
Lingual[ Lingual[[ LingualY BuccalYY LingualY BuccalY
Root displacement
tendency
Buccal[[ BuccalY BuccalYY LingualY BuccalYY/
Lingual[[
BuccalYY
Teeth displacement
tendency
Buccal root
control
Lingual crown
tipping
Lingual root
control
Lingual crown
tipping
Lingual root control Lingual root control
Negative displacement
effect
[ [ Y Y Y/[ Y/[
Overcorrection
requirements
Lingual root
control[
Lingual root
control[
Lingual root
controlY
Buccal root
control[
Lingual /Buccal root
control[
Lingual /Buccal root
control[
Mesial/distal
Tipping direction Distal Distal Distal Mesial Mesial Mesial
Crown relative
movement ratio
[ [ Y Y [ [/Y
Pearson correlation
coefficient, r
�0.9864 �0.9512 0.9498 0.9796 �0.9628 �0.8140
P value (significance) 0.0136* 0.0488* 0.0502 (NS) 0.0204* 0.0372* 0.1860 (NS)
Crown displacement
tendency
Distal[[ Distal[[ Distal[ MesialYY MesialY MesialY
Root displacement
tendency
Mesial[ Mesial[ Mesial[[ DistalY DistalYY DistalYY
Displacement tendency Distal crown
tipping
Distal crown
tipping
Mesial root
control
Distal crown
tipping
Mesial root control Mesial root control
Negative displacement
effect
[ [ [ Y Y Y
Overcorrection
requirements
Distal root
control[
Distal root
control[
Distal root
control[
– – –
NS, no significance.
*P\0.05; **P\0.01; ****P\0.0001.
Table VI. Ranking of overcorrection needs for direct strong anchorage
Rank I II III IV V VI VII
Tooth 1 3 2 2 1 7 6
The need for
overcorrection
Lingual root
control
Distal root
control
Lingual root
control
Distal root
control
Distal root
control
Lingual / buccal
root control
Lingual / buccal
root control
Crown-root displacement
difference
4.506-5.758 4.242-5.965 3.280-3.5 10 2.219-3.256 0.878-1.306 �0.104 to 0.08 �0.288 to 0.017
Note. The molars need lingual root control in the low-retraction strong anchorage group but buccal root control in the high-retraction direct strong
anchorage group. Crown-root displacement differences are the displacement difference of the crown-root from 0 g to 500 g of force in a specific
plane (mesial-distal or buccal-lingual).
1, central incisor; 2, lateral incisor; 3, canine; 5, second premolar; 6, first molar; 7, second molar.
Zhu et al 11
However, there has been no FEA that comprehensively
illustratesthis issue. Thus, a relatively reliable FEA must
be conducted.
American Journal of Orthodontics and Dentofacial Orthoped
The reliability of orthodontic FEA depends on mul-
tiple factors, including a model geometry structure
close to reality, accurate material property parameters,
ics - 2023 � Vol - � Issue -
Fig 6. Two-stage biomechanical effects of closing the space with the direct strong anchorage:A,Mod-
erate anchorage group or single aligner contraction force group, reflects the biomechanical status
before using elastic retraction; B, Direct anchorage group refers to the initial wearing of a CA and
use elastics to enhance retraction force and protect posterior teeth anchorage. The changes of the
biomechanical effect from A to B are shown in the right column; C, Elastic retraction force dominated
group reflects the biomechanical status in which the aligner contraction force attenuated while the
elastic retraction force maintains. The elastic force is usually smaller than the aligner contraction force;
however, its biomechanical effects on the anterior teeth are unchanged, but the effects on the posterior
teeth are reversed. The continuous changes in the teeth movement from B to C are shown in the right
column. CA, clear aligner.
12 Zhu et al
loading configuration, and so on.25 Thus, our group
first made tremendous efforts to build a high-quality
model close to reality. Real patient data were selected
and included from the archive, containing CBCT-
DICOM data for constructing the maxilla and roots
and intraoral scan-STL data for constructing crowns.
After a series of modifications, we established a stan-
dard dentition model with normal teeth torques, angu-
lations, rotations, and occlusal curves (Fig 1). Thus, we
maintained the precision of the model and eliminated
the impact of malocclusion on the FEA. Besides, to
confirm the parameters set in the FEA model were
appropriate and the force generated by loading config-
uration was close to reality, we performed in vitro phys-
ical experiments to validate the credibility of this
modeling. First, we verified the PDL thickness in healthy
- 2023 � Vol - � Issue - American
people and found that using 0.25 mm was an appro-
priate parameter suitable for both teeth and genders
(Supplementary Fig 2). In addition, we measured
the thickness of 2 commercially available CAs
(Supplementary Fig 3). It demonstrated that the
average aligner thickness was around 0.5 mm, which
was in accord with the study by Cortona et al18 who
measured the average thickness of the aligner with mi-
crocomputed tomography. Notably, because of the
thermoforming manufactory method, the closer to
the gingival edge, the thinner the aligner was, and it
became obvious in the anterior teeth with higher crown
heights. However, the thickness variation had no signif-
icant difference among the anterior teeth. Therefore, it
would not affect the conclusion of this study
(Supplementary Figs 4 and 5). Finally, we also
Journal of Orthodontics and Dentofacial Orthopedics
Table VII. The impact of the buccal button position on the posterior teeth movement
Group
Posterior teeth
5 6 7
High button position
Extrusion/intrusion (310�2 mm) �1.201 I �0.183 I 0.596 E
Buccal/lingual movement: crown (310�2 mm) 0.146 B 0.001 B 0.074 B
Buccal/lingual movement: root (310�2 mm) �0.210 L 0.025 B 0.091 B
Mesial/distal movement: crown (310�2 mm) �1.064 M �1.014 M �1.132 M
Mesial/distal movement: root (310�2 mm) 0.636 D 0.456 D 0.364 D
Buccal/lingual crown relative movement ratio �1.693 B �0.949 L �0.181 L
Mesial/distal crown relative movement ratio �2.672 M �3.226 M �4.110 M
Medium button position
Extrusion/intrusion (310�2 mm) �1.223 I �0.183 I 0.592 E
Buccal/lingual movement: crown (310�2 mm) 0.143 B 0.002 B 0.076 B
Buccal/lingual movement: root (310�2 mm) �0.203 L 0.024 B 0.392 B
Mesial/distal movement: crown (310�2 mm) �1.047 M �1.008 M �0.924 M
Mesial/distal movement: root (310�2 mm) 0.606 D 0.453 D 0.362 D
Buccal/lingual crown relative movement ratio �1.707 B �0.937 L �0.805 L
Mesial/distal crown relative movement ratio �2.729 M �3.225 M �3.550 M
High button position
Extrusion/intrusion (310�2 mm) �1.258 I �0.183 I 0.601 E
Buccal/lingual movement: crown (310�2 mm) 0.117 B 0.008 B 0.068 B
Buccal/lingual movement: root (310�2 mm) �0.164 L 0.023 B 0.093 B
Mesial/distal movement: crown (310�2 mm) �1.032 M �1.010 M �0.933M
Mesial/distal movement: root (310�2 mm) 0.597 D 0.459 D 0.367 D
Buccal/lingual crown relative movement ratio �1.712 B �0.648 L �0.272 L
Mesial/distal crown relative movement ratio �2.728 M �3.199 M �3.542 M
Note. Positive values indicate extrusion, buccal, and distal direction in tooth movement, whereas negative values indicate intrusion, lingual, and
mesial direction in tooth movement; Positive and negative values in crown relative movement ratio have no specific displacement direction (ie,
direction are also marked after the value); Crown movement is the movement of the midpoint of the facial axis of the clinical crown, whereas
root movement, the movement of the root apex; Crown relative movement ratio is the value of the crown displacement minus the root displacement
divided by the root displacement, which partially reflects the tooth tipping movement pattern.
E, extrusion referenced to the occlusal plane; I, intrusion referenced to the occlusal plane; B, buccal direction; L, lingual direction; M, mesial di-
rection; D, distal direction; 1, central incisor; 2, lateral incisor; 3, canine; 5, second premolar; 6, first molar; 7, second molar.
Table VIII. The change of the posterior teeth movement, along with the button displacement
Group
Posterior teeth
5 6 7
Button position change High button position / Low button position
Extrusion/intrusion (3 10�2 mm) Intrusion [ No change Extrusion [
Buccal/lingual movement: crown (3 10�2 mm) Buccal Y Buccal [ Buccal Y
Buccal/lingual movement: root (3 10�2 mm) Lingual Y Buccal Y Buccal [
Mesial/distal movement: crown (3 10�2 mm) Mesial Y Mesial Y/[ Mesial Y/[
Mesial/distal movement: root (3 10�2 mm) Distal Y Distal Y/[ Distal Y/[
Buccal/lingual crown tipping (�) Buccal Y Buccal [ Buccal Y
Mesial/distal crown tipping (�) Mesial Y Mesial Y/[ Mesial Y/[
Note. Crown tipping tendency results from the relative movement change of the crown and root.
5, second premolar; 6, first molar; 7, second molar.
Zhu et al 13
validated the contraction force generated in the FEA
model (Supplementary Fig 9). This was an essential
value that could largely affect the conclusion of this
American Journal of Orthodontics and Dentofacial Orthoped
work. We established an in vitro test model and con-
formed that the computational results in this FEA
were in good agreement with reality. All these
ics - 2023 � Vol - � Issue -
Fig 7. Biomechanical mechanism of the impact of the button position on the posterior teeth movement:
A, The dotted circle represents the path that the button can be displaced relative to theminis crew under
the limitation of metallic ligation. The premolar is more likely to mesially and buccally tilt; B, When the
button position moves toward the center of the crown, the premolar presents less mesial and buccal
tipping but more intrusion; C, To make the best use of the indirect strong anchorage with high buccal
button position, 3 compensation strategies are proposed.
14 Zhu et al
validations demonstrated the creditability of the
modeling method in this study (Supplementary
Appendix).
Orthodontic tooth movement is a consecutive pro-
cess that involves a series of biological effects and ortho-
dontic force changes.26 However, FEA is commonly used
to analyze a transient effect that cannot reflect consec-
utive biological reconstructions. This transient effect is
also of considerable significance. Teeth movement is
generated by a serial of consecutive CAs. Every CA can
produce an instantaneous mechanical effect at first
- 2023 � Vol - � Issue - American
engagement and induce a biological response, including
teeth movement and soft-tissue and skeletal-tissuereconstruction. For the teeth movement, the instanta-
neous force could change the stress distribution of the
PDL and activate osteogenesis and osteoclastogenesis
in the specific stress areas. Therefore, the FEA results
could indirectly reflect a short-term teeth movement
pattern but cannot represent the long-term effects. To
further investigate the biomechanical changes while
wearing a CA, we first divided the space closure process
into several transient mechanical statuses, including
Journal of Orthodontics and Dentofacial Orthopedics
Zhu et al 15
pure aligner contraction force, pure elastic retraction
force, and aligner contraction force combined with
various retraction forces or metal ligation. Then, we per-
formed FEA on them separately and integrated the re-
sults to illustrate them as a continuous process. In
addition, the displacement results of the FEA were calcu-
lated on the basis of the specific coordinates. The current
orthodontic FEA commonly uses a single global coordi-
nate, which cannot display the movement form of every
tooth. To solve this limitation, we set 2 local coordinates
(the crown center and the root tip) in each tooth and the
coordinate direction consistent with the CA design sys-
tem, such as Invisalign (Fig 2). With this, we could
directly clarify the displacement tendency of each tooth
in its 3D coordinates and further determine how to add
overcorrections in the current CA design system. The
above 2 analysis strategies are innovative and suitable
for CA biomechanical analysis, which would endow
this study with more clinical values.
FEA of the 3 anchorage groups aimed at demon-
strating the biomechanical differences between the 2
strong anchorages. The results showed that the direct
strong anchorage group had an advantage in anterior
teeth intrusion and counterclockwise occlusal plane
rotation, which were beneficial for reducing deep over-
bite and the roller coaster effect. However, the direct
strong anchorage had a disadvantage in anterior teeth
tipping control because the central incisor was more
prone to lingual tipping (the center of rotation being
closer to the center of resistance) and crown lingual
movement. In addition, the indirect strong anchorage
could more successfully prevent the posterior teeth
from crown mesial tipping but had an obvious negative
effect on premolar intrusion. Overall, several overcorrec-
tion requirements were considered. More anti-
inclination overcorrection of the anterior teeth is needed
when using direct strong anchorage. In contrast, when
using indirect strong anchorage, more vertical control
is required, especially for premolars, to prevent deep
overbite aggravation.
Direct strong anchorage control is the most used
type, with biomechanical effects and processes worthy
of in-depth elaboration. We extracted comprehensive
tooth movement data in Tables III and IV to illustrate
the impact of retraction force on tooth movement and
analyze the teeth movement tendency from 0-g to
500-g retraction forces. We converted the teeth move-
ment data into Tables V and VI to clearly display the
movement pattern. Table V intuitively displays the
tipping movement tendency of each tooth, showing
the negative effects that could be aggravated as the
retraction force increased, and proposes the overcorrec-
tion requirements. In addition, we ranked the
American Journal of Orthodontics and Dentofacial Orthoped
overcorrection requirements in Table VI, entailing
lingual root control of the central incisor, distal root
control of the canine, lingual root control of the lateral
incisor, distal root control of the lateral incisor, and
distal root control of the central, lingual-buccal root
control of the molars. After obtaining this result, we
further reviewed the extraction patients and confir-
med this prediction in a typical patient (Supplementary
Fig 10). The first 5 types of overcorrections are necessary
because they require larger overcorrections and show
clear positive correlations with the retraction force.
In contrast, the overcorrection requirements for mo-
lars were slighter and uncertain. The lingual root control
requirement in low-retraction force and buccal root
control requirement in high-retraction force could
further change to buccal crown tipping requirement
when the aligner contraction force is attenuated after
several days of wearing. The FEA of the no-aligner
contraction group confirmed the reverse tendency with
various retraction forces (Supplementary Fig 11;
Supplementary Table II). It is worth noting that the
elastic force could not completely prevent the mesial
movement of the posterior teeth, even the heavy force
(500 g bilateral force). Thus, a reciprocating motion
must occur in the posterior teeth when the aligner
contraction force consistently attenuates and the retrac-
tion force is maintained. Therefore, greater retraction
forces lead to less reciprocating motion but more buccal
posterior tooth tipping from the lingual root control.
From our clinical observation, sufficient retraction force
is essential, and it is recommended to add an initial slight
overcorrection of buccal root control in molars, and
close monitoring is more important.
It can be observed that the biomechanical effects of
the direct strong anchorage are complicated and unsta-
ble because the relationship between the 2 forces
(aligner contraction and elastic retraction) constantly
changes. To reduce the control difficulty and enhance
the treatment stability, we further provide insight into
the indirect strong anchorage, which has only 1 loading
force: aligner contraction. We focused on the essential
factor, the relative position between the miniscrew and
the button, which could largely affect the biomechanical
effect of anchorage protection and clinical practice. We
found that the second premolar was the tooth most
affected. When the button was located from the high
position (close to the gingival) to the low position (close
to the center of the crown), the premolar presented a
lower mesial and buccal tipping tendency and more
intrusion tendency (Table VIII). The second premolar is
the front tooth in the posterior teeth, and its good con-
trol is the key to anchorage protection. Thus, we further
illustrate the underlying mechanical mechanism of the
ics - 2023 � Vol - � Issue -
16 Zhu et al
premolar displacement shown in Figure 7. The metal
wire ligation protects the posterior teeth anchorage by
the distance limitation effect, of which the relative
movement between the miniscrew and the button is
limited in a circular motion. The red premolars in
Figure 7 reflect their displacement under the aligner
contraction forces. After the aligner contraction force
passes through the center of the clinical crown, the but-
ton becomes a pivot close to the center of resistance.
Because the high button position has a larger distance
between the pivot and the contraction force line, a larger
mesial inclination moment is added to the tooth, which
can cause a larger mesial tipping movement. In addition,
the ligation can only eliminate the force along the wire,
leaving a contraction force component perpendicular to
the ligation, which can cause tooth intrusion (Fig 7, A).
In other words, because of the limitation of the ligation,
the premolar must be intruded to move mesially.
When the button closes to the center of the crown
where the contraction force passes, the mesial inclina-
tion moment is attenuated, but a larger contraction
force component perpendicular to the ligation is left.
Therefore, the premolar presents less mesial and buccal
tipping but more intrusion (Fig 7, B). In clinical practice,
the buccal button is more suitable for attachment to the
high position in which the cutout can be set on the CA.
Compared with the low button position, this high posi-
tion is beneficial for decreasing the negative effect of the
intrusion of the premolar as well as the counterclockwise
rotation of the posterior teeth. However, the aggravation
of mesial tipping is inevitable.We proposed a feasible
strategy to address these problems, as shown in
Figure 7, C. The addition of attachments is necessary
for the posterior teeth to avoid the detachment of the
aligner, guaranteeing treatment efficiency, particularly
in the premolar. In addition, a sufficient mesial root con-
trol should be added to the premolar to prevent its mesial
tipping, and it could also be added to the molars to pre-
pare the anchorage. In addition, a clockwise rotation of
the posterior teeth and intrusion of the anterior teeth
should be compensated, such as a reverse-curve archwire
in the fixed appliance. This compensation force has 2
obvious advantages: (1) Preventing the unwanted coun-
terclockwise rotation of the posterior teeth and (2) facil-
itating the reduction of the anterior teeth overbite,
which is a common problem in malocclusion and can
easily occur in the space closure process (roller coaster
effect). In addition, it is essential to implant the minis-
crew between the molars instead of the interroot space
between the second premolar and the first molar because
a near-horizontal ligation is necessary to prevent mesial
movement of the posterior teeth and the negative effect
of the premolar intrusion.
- 2023 � Vol - � Issue - American
Overall, this study illustrated the control deficiency of
the CA in the space closure patient with different
anchorage controls, but also provides feasible strategies,
elaborating how to add overcorrection and compensa-
tion forces in the aligner design, and reminding where
is the most important follow-up monitoring point.
More importantly, we detailed the highly dynamic force
system of the direct strong anchorage and the relatively
single and stable force system of the moderate and indi-
rect strong anchorage. Single and stable anchorage
types have profound research values. Based on this
new cognition, our group wants to further quantitatively
investigate the amount of overcorrection and compen-
sation force that should be added initially in the aligner
design and provide a reliable reference range for ortho-
dontists. To the best of our knowledge, the current
studies on overcorrections are mainly based on clinical
observation,5,6,15,27 which could be largely affected by
confounding factors.
Moreover, there is still no relatively accurate sugges-
tion for orthodontists. We assume that using FEAmay be
conducive to solving this problem and can provide theo-
retical reference overcorrection values for this field.
Thus, we believe this study can lay a foundation for re-
searchers to further investigate how to use CA to accu-
rately treat extraction patients, enhance the treatment
effect, and alleviate the suffering of patients.
CONCLUSIONS
The direct strong and indirect strong anchorages
could enhance the anterior teeth retraction and protect
the posterior teeth anchorage. Direct strong anchorage
was beneficial for alleviating the occlusal plane clockwise
rotation, whereas indirect anchorage was conducive for
anterior teeth inclination control (need slighter overcor-
rections). The protective effects of the direct strong
anchorage group depended on the retraction force. An
increase in the retraction force would require more ante-
rior teeth overcorrection to resist the tipping movement,
mainly including lingual root control of the central
incisor, followed by distal root control of the canine,
lingual root control of the lateral incisor, distal root con-
trol of the lateral incisor, and distal root control of the
central incisor. However, the retraction force could not
eliminate the mesial movement of the posterior tooth,
and a reciprocating motion could occur. Thus, the poste-
rior teeth movement in the direct strong anchorage
group presented as a 2-stage pattern (mesial followed
by distal movement). The relative position of the minis-
crew and button mainly affected the second premolar
movement. When using indirect strong anchorage, it is
recommended to add attachments to the posterior teeth,
Journal of Orthodontics and Dentofacial Orthopedics
Zhu et al 17
increase mesial root control in the premolar to prevent
tipping, and rotate the posterior teeth clockwise while
intruding the anterior teeth. Because moderate and indi-
rect strong anchorages have a more stable and single
force system, they could be reliable models in investi-
gating the precise control of tooth extraction patients
in the future.
ACKNOWLEDGMENTS
This study was supported by the Research and Devel-
opment Program of West China Hospital of Stomatology
Sichuan University (RD-03-202012). We would also like
to express our gratitude to Dr Hong-li Zhu for profes-
sional technical support and data collection for this
study.
SUPPLEMENTARY DATA
Supplementary data associated with this article can
be found, in the online version, at https://doi.org/10.
1016/j.ajodo.2022.02.018.
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SUPPLEMENTARY APPENDIX
Validation of the PDL thickness in radiological data
The PDL thickness in the computational modeling could
largely affect the teethmovement in the FEA results.There-
fore, we further validated the PDL thickness in the patients’
radiological data. The inclusion criteria were as follows:
1. Full permanent dentition, no missing teeth (except
for the third molars).
2. No periodontal or periapical diseases.
3. No system diseases.
4. Has not received orthodontic treatment, which
could affect the normal PDL width because of the
teeth movement.
5. Has integrated panoramic film and cone-beam
computed tomography data.
Based on the above criteria, we included 6 patients
whose information was listed in Supplementary
Table 6.
We first measured the PDL width of the maxillary
dentition in the panoramic film, and the unclear PDL
was further measured in the CBCT data.
From Supplementary Figures 2, B and C, we found
the width of the PDL ranged from 0.13-0.34 mm,
and both the mean and median were close to 0.25
mm. This result was coordinated with the research
(0.15-0.38 mm) by Wang et al.17 In addition, we
found, among the included patients, there was no sig-
nificant thickness difference between different teeth
and genders.
Therefore, this test shows that the 0.25 mm PDL thick-
ness widely used in FEA is appropriate.
Validation of the aligner thickness using 2
commercially available clear aligners
The aligner thickness used in the model was cited from
the study of Cortona et al,18 who measured the average
thickness of the aligner by microcomputed tomography.
In this part, we further verified if this parameter was suit-
able for this study. We directly measure the thickness of
2 commercially available aligners by cutting them into
several parts (Supplementary Fig 3, A). It demonstrated
that the average thickness of the 2 aligners was around
0.5 mm, and there was no statistical difference between
different teeth (Supplementary Fig 3, B). Thus, the 0.5
mm offset parameter was suitable in FEA aligner
modeling. In addition, we found the thermoforming
manufacturing method would truly cause thickness dif-
ferences in the different parts of the aligner
(Supplementary Fig 3, C and D). The closer to the
gingival edge, the thinner the aligner was, and it became
obvious in the anterior teeth with higher crown heights.
Therefore, this result implied that the nearly uniform
aligner model could have higher torque control effects
than the physical world. However, the thickness variation
had no significant difference among the anterior teeth; it
would not affect the conclusion of this study.
To validate this assumption, we developed a thickness
varied aligner according to the actual measurement
(Supplementary Fig 4). Then, we performed FEA using
the new aligner and compared the biomechanical effects
with that in the text. The results showed that the thick-
ness variation had a very slight impact on the tooth
movement pattern, and this factor would not change
the conclusions in the text (Supplementary Fig 5, A
and B). We investigated the stress distribution of the
CA to find out how it affected tooth movement. We
found that the main stresses were located at the occlusal
and interproximal areas of the teeth (Supplementary Fig
5, C). Therefore, the aligner thickness reduction close to
the gingiva had very little effect on the tooth movement
pattern, particularly the tipping. Thus, based on the
research purpose, the aligner construction method
used in this study was appropriate.
This validation has a good reference value. This uni-
form offset method has been widely used in this
aligner modeling. For the quantitative FEA, particu-
larly the investigation of the torque control of the
anterior teeth by CA, researchers should be noted
that the prediction results by this method would be
higher than the reality.
Validation of the contraction force of 2 commercially
available clear aligners
The contraction force produced by aligner deformation
was essential in this work. We performed a physical
experiment to validate if the computational force was
appropriate and close to reality. We use epoxy resin to
fill the aligners except the extraction space to simulate
wearing the aligner and facilitate the fixation of the
aligner in the mechanical tester (Supplementary Fig 9,
A). Meanwhile, we extracted the contraction force on
the side of the extraction space in the finite element
model (Supplementary Fig 9, B). Finally, we compared
the computational value with the physical results
(Supplementary Fig 9, C), which demonstrated that the
sagittal deformation of 0.2 mm in this extraction space
could generate a force ranging from 12.28-16.9 N.
Therefore, the computational force of 15.57 N was close
to the physical world. This modeling method could be a
reliable strategy for researchers who want a further
investigation of the extraction patients in FEA.
This is a patient who studies abroad and can only
follow-up 1 time per year. The upper photographs
17.e1 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
reflect the initial status, and the lower photographs
reflect the status of using the CA to close the space
for 1 year (because the third molar erupted in this
no follow-up year, there was an open bite in the pos-
terior teeth. However, it doesn’t affect teeth move-
ment by CA and can facilitate the observation in
this section). We mainly add maxillary and mandibular
mandibular lingual root control overcorrection and
maxillary canine distal root control overcorrection in
the initial appliance design. Thus, we only discuss
the other teeth, those absent overcorrections. In this
patient, we could find the conclusion in this study
is suitable for both maxillary and mandibular denti-
tion. The tipping movements were generally in accord
with Table VI. Meanwhile, it is worth noting that add-
ing anterior teeth lingual root control overcorrection
is the easiest to think of (I and III), but this finding
also emphasized the importance of controlling the
distal tilt of the anterior teeth (II, IV, and V) which
could be easily neglected in clinical observations.
Zhu et al 17.e2
American Journal of Orthodontics and Dentofacial Orthopedics - 2023 � Vol - � Issue -
Supplementary Fig 1. Developing a CA model with Appliance Designer software.
Supplementary Fig 2. Validation of the PDL width in patients’ radiological data. A,Measure the PDL
width in the panoramic films;B, The thickness of the PDL of different teeth;C, The thickness of the PDL
of different genders.
17.e3 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
Supplementary Fig 3. Validation of the aligner thickness: A, Cut the aligner in the middle of the
incisor, canine, and molar. Then, measure the thickness of the aligner at gingival, middle, and occlusal
positions; B, The thickness of the 2 aligners in different teeth; C and D, The aligner thickness in the
different positions of different teeth
Supplementary Fig 4. Construction of a CA with thickness variation.
Zhu et al 17.e4
American Journal of Orthodontics and Dentofacial Orthopedics - 2023 � Vol - � Issue -
Supplementary Fig 5. The impact of the aligner thick-
ness variation on toothmovement pattern.A andB, Tooth
movement pattern from different views;C, Stress distribu-
tion on the different aligners.
Supplementary Fig 6. Thermal contraction method for applying space closure force in CA: A, Select
1-mm thermal contraction region perpendicular to the arc of the dental arch; B, Set thermal shrink con-
dition in the selected region according to the equation (d, linear expansion coefficient of the material
[�C]; L, size of the shrink part [mm]; Dt, temperature difference [�C]; D, tolerance of the shrink part);
C, Proper d and Dt (lower the temperature-negative value) were set to accurately close the 0.2-mm
extraction space.
17.e5 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
Supplementary Fig 7. The relationship between the crown relative movement ratio and the center of
rotation. The crown relative movement ratio partially reflectsthe location of the center of rotation. In this
study, the center of the rotation of the 3 groups is located around the apical third. The smaller the crown
relative movement ratio is, the larger the tipping it will occur when a tooth is retracted same distance,
thereby, a larger lingual root control is needed.
Zhu et al 17.e6
American Journal of Orthodontics and Dentofacial Orthopedics - 2023 � Vol - � Issue -
Supplementary Fig 8. FEA of the impact of the buccal button position on the posterior teeth move-
ment: A-C, Schematic diagram of 3 different button positions; D-F, Teeth displacement magnitude of
the different groups;G-L,Resultant displacement of anterior and posterior teeth of the different groups.
17.e7 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
Supplementary Fig 9. Validation of the contraction force of the CA: A,Method of testing the contrac-
tion force of commercially available aligners. Collect the 0.2-mm deformation force for statistical anal-
ysis;B, FEA contraction force;C, Statistically analyze the difference between FEA results and physical
experimental results.
Zhu et al 17.e8
American Journal of Orthodontics and Dentofacial Orthopedics - 2023 � Vol - � Issue -
Supplementary Fig 10. A typical extraction patient to verify the prediction results of the FEA.
17.e9 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
Supplementary Fig 11. FEA of the impact of the pure retraction force on the teeth movement: A and
B, Schematic diagram of the 2 different retraction force groups; C and D, Von Mises stress distribution
at the PDL of the different groups; E and F, Teeth displacement magnitude of the different groups; G
and J, Resultant displacement of anterior teeth and posterior teeth of the different groups.
Supplementary Table I. The characteristics of the
included patients
Gender Number Age, y
Male 3 12-25
Female 3 11-24
Zhu et al 17.e10
American Journal of Orthodontics and Dentofacial Orthopedics - 2023 � Vol - � Issue -
Supplementary Table II. The teeth movement under different retraction forces without aligner contraction
Group
Anterior teeth Posterior teeth
1 2 3 5 6 7
Direct strong anchorage (150 g of force) without aligner contraction
Extrusion/intrusion (310�2 mm) �0.184 I �0.307 I �0.248 I 0.156 E 0.012 E �0.051 I
Buccal/lingual movement: crown (310�2 mm) �0.240 L �0.157 L �0.083 L �0.115 L �0.070 L �0.064 L
Buccal/lingual movement: root (310�2 mm) 0.124 B �0.041 L 0.039 B 0.067 B �0.011 L 0.018 B
Mesial/distal movement: crown (310�2 mm) 0.110 D 0.238D 0.451 D 0.267 D 0.225 D 0.215 D
Mesial/distal movement: root (310�2 mm) �0.025 M �0.098 M �0.288 M �0.155 M �0.128 M �0.126 M
Buccal/lingual crown relative movement ratio �2.939 L �2.873 L �3.129 L �2.710 L 5.573 L �4.464 L
Mesial/distal crown relative movement ratio �5.434 D �3.436 D �2.565 D �2.721 D �2.758 D �2.708 D
Direct strong anchorage (500 g of force) without aligner contraction
Extrusion/intrusion (310�2 mm) �0.611 I �1.020 I �0.837 I 0.521 E 0.051 E �0.182 I
Buccal/lingual movement: crown (310�2 mm) �0.795 L �0.515 L �0.277 L �0.371 L �0.234 L �0.219 L
Buccal/lingual movement: root (310�2 mm) 0.410 B �0.138 L 0.130 B 0.211 B �0.054 L 0.051 B
Mesial/distal movement: crown (310�2 mm) 0.388 D 0.787 D 1.492 D 0.888 D 0.754 D 0.714 D
Mesial/distal movement: root (310�2 mm) �0.100 M �0.322 M �0.953 M �0.520 M �0.306 M �0.356 M
Buccal/lingual crown relative movement ratio �2.937 L 2.742 L �3.133 L �2.758 L 3.366 L �5.326 L
Mesial/distal crown relative movement ratio �4.867 D �3.443 D �2.566 D �2.710 D �3.467 D �3.006 D
Note. Positive values indicate extrusion, buccal, and distal direction in tooth movement, whereas negative values indicate intrusion, lingual, and
mesial direction in tooth movement; Positive/negative values in crown relative movement ratio have no specific displacement direction (ie, direction
are also marked after the value); Crown movement is the movement of the midpoint of the facial axis of the clinical crown, whereas root movement,
the movement of the root apex; Crown relative movement ratio is the value of the crown displacement minus the root displacement divided by the
root displacement, which partially reflects the tooth tipping movement pattern.
E, extrusion referenced to the occlusal plane; I, intrusion referenced to the occlusal plane; B, buccal direction; L, lingual direction; M, mesial di-
rection; D, distal direction; 1, central incisor; 2, lateral incisor; 3, canine; 5, second premolar; 6, first molar; 7, second molar.
17.e11 Zhu et al
- 2023 � Vol - � Issue - American Journal of Orthodontics and Dentofacial Orthopedics
	Finite element analysis of the biomechanical effect of clear aligners in extraction space closure under different anchorage ...
	Material and methods
	Statistical analysis
	Results
	Discussion
	Conclusions
	Acknowledgments
	Supplementary data
	References
	Supplementary appendix
	Validation of the PDL thickness in radiological data
	Validation of the aligner thickness using 2 commercially available clear aligners
	Validation of the contraction force of 2 commercially available clear aligners