Retraction Hooks of Different Lengths for Maxillary Whole Arch

Retraction Hooks of Different Lengths

for Maxillary Whole Arch Distalization

with Miniscrew Anchorage: A Finite Element Analysis

Vanichaya Tangsumroengvong

, Virush Patanaporn

, Chaiy Rungsiyakul

Graduate student, Division of Orthodontics, Faculty of Dentistry, Chiang Mai University

Department of Orthodontics and Pediatric, Faculty of Dentistry, Chiang Mai University

Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University

CM Dent J 2021; 42(1) : 125-138

Received: 20 April, 2020

Revised: 14 May, 2020

Accepted: 22 May, 2020

Abstract

Objectives: To evaluate the von Mises stress distribution in the periodontal ligament and the dis-

placement pattern of maxillary whole arch distalization applied to retraction hooks of different lengths

with miniscrew anchorage and to determine the optimal length of retraction hook, using a nite element

method.

Methods: A nite element model of maxillary teeth with periodontal ligament and alveolar bone was

constructed. The miniscrews were placed bilaterally 6 mm above the buccal cemento-enamel junction

at the modied infrazygomatic crest site. The distalization force of 200 g was applied to 0-, 2-, 4-, 6-,

8-mm-length retraction hooks located between the lateral incisors and canines. The stress distribution

in the periodontal ligament and the displacement of the teeth were analyzed. The optimal length of

retraction hook for maximal distal movement of the maxillary whole arch along the occlusal plane was

investigated.

Results: The von Mises stress in the anterior teeth was greater than in the posterior teeth with all

hook lengths. When using the short hooks, the areas of high stress were in the lateral incisor, canine

and second molar. When using the long hooks, the areas of high stress were in the anterior teeth.

With the 0-mm and 2-mm lengths, the anterior teeth were extruded and tipped palatally; the poste-

rior teeth were intruded and tipped distally. With the 4-mm length, all maxillary teeth were distal-

ized along the occlusal plane with minimal movement in the vertical direction. The anterior teeth

were slightly tipped labially; the posterior teeth were slightly tipped distally. With the 6-mm and

Corresponding Author:

Visush Patanaporn

Clinical Professor, Department of Orthodontics and Pediatric Dentistry, Faculty of Dentistry,

Chiang Mai University, Chiang Mai 50200, Thailand

E-mail: [email protected]

Original Article

CM Dent J Vol. 42 No. 1 January-April 2021 126

8-mm lengths, the anterior teeth were intruded and tipped labially; the posterior teeth were extruded

and tipped distally. The optimal length in this study was found to be 4 mm.

Conclusions: Different lengths of retraction hooks resulted in different patterns of stress

distribution in the PDL and in different patterns of displacement of the maxillary teeth in whole arch

distalization. The optimal length of retraction hook was 4 mm for maximal distal movement of the

maxillary whole arch along the occlusal plane.

Keywords: whole arch distalization, en-masse distalization, nite element, retraction hook

Introduction

Non-extraction treatment of Class II maloc-

clusion requires maxillary dentition distalization,

mandibular dentition mesialization, or a combination

of both.

(1,2)

Distalization can be divided into sequen-

tial distalization and en-masse distalization. In the

sequential distalization, initially the rst and second

molars are distalized by open-coil spring, then the

premolars and then the anterior teeth. This method

can cause proclination of the anterior teeth and distal

tipping of the molars during distalization.

(3,4)

En-

masse distalization is achieved by distalizing all of

the anterior and posterior teeth at the same time, as

one rigid block, using miniscrew anchorage.

(1,5-8)

Although this method may reduce the overall treat-

ment time, it may increase the risk of root resorption

since the applied magnitude of force is larger than

that of the sequential distalization.

(7)

Miniscrew implant placement locations for

maxillary dentition distalization are varied.

(9,10)

The

placement locations include the midpalatal or para-

median areas of the palate,

(11)

the buccal or palatal

interradicular areas,

(6,7,9)

and the infrazygomatic

crest.

(8)

The most ideal safe zone for placing minis-

crews for distalization of the maxillary dentition is

the region between the maxillary rst and second

molar in the infrazygomatic crest area,

(9)

which is

called the “Modied infrazygomatic crest site.”

(Modied IZC)

(12,13)

This site provides thick cortical

bone and fewer problems with root proximity than

in the interradicular areas.

(8,9)

Each study and case report conducted previously

applied different loading forces for whole arch

distalization, ranging from 200 to 300 g.

(5-8,12,14,15)

Most of them, however, used a force magnitude of

about 200 g and found no side effect in terms of

root resorption and periodontitis.

(5-7,12)

Therefore,

the force magnitude of 200 g will be chosen for this

study.

The relationship between the line of action of

the applied force and the center of resistance (CRes)

denes the type of tooth movement.

(4)

Force passing

through the CRes causes translation; force passing

off-center causes rotation or tipping.

(16)

Clinically, it

is difcult to accurately determine the line of force

passing through the CRes of the maxillary dentition.

Moving the line of force close to the CRes by apply-

ing the force to a different retraction hook lengths

can cause more translational movement rather than

applying the force at the bracket level.

(3)

Jeong

et al.

(32)

reported that the CRes of the maxillary

dentition in their nite element model constructed

from Nissin commercial tooth model was 13.5 mm.

apically and 12.0 mm. posteriorly to the incisal edge

of the maxillary central incisors. As our study will

also use Nissin dental model, we will choose this

location as the CRes of our nite element model.

The nite element method is a contemporary

CM Dent J Vol. 42 No. 1 January-April 2021127

research tool in orthodontics for measuring struc-

tural stress and for movement analyses.

(17,18)

It is

a numerical stress analysis which can be used to

describe the stress situation within the periodontal

ligament (PDL) and surrounding alveolar bone.

(19)

This method has become popular since it is com-

pletely non-invasive, very accurate and it is based

on the mathematical properties of the structures.

(18)

The purposes of this study were to use the nite

element method to evaluate the pattern of stress

distribution in the PDL and the tooth displacement

pattern of maxillary whole arch distalization relative

to force vectors applied to retraction hooks of different

lengths and to determine the optimal length of retrac-

tion hook for maximal distal movement of the maxil-

lary whole arch along the occlusal plane, when using

miniscrew anchorage placed at the modied IZC.

Materials and methods

All maxillary teeth of a commercial model

(Model-i21FE-400C; Nissin Dental Products,

Kyoto, Japan) based on the average tooth dimen-

sions of Asian adults with normal occlusion were

scanned via 3-D laser scanning to make digital

tooth images.

(20-25)

The solid model, including all

maxillary teeth, PDL and maxillary bone was con-

structed and assembled using SolidWorks software

(Dassault Systèmes Americas, Waltham, Mass.,

USA). The maxillary bone consisted of cancellous

bone with 1.0 mm thickness of cortical bone. The

alveolar crest was formed following the curvature of

the cemento-emamel junction (CEJ), 1 mm apical to

the CEJ.

(24,26)

The thickness of the PDL was assumed

to be a uniform 0.2 mm. The brackets were modeled

with slot dimensions of a 0.018 x 0.025 inches and

attached to the midpoint of the facial axis of the

crown and completely connected to each tooth. The

main archwire was modeled as a stainless-steel wire

with dimensions of 0.017 x 0.025 inches, and it

was assumed that there was no play and no friction

between the brackets and the archwire. Retraction

hooks were modeled using 0.036 inch crimpable

hook stainless steel and located bilaterally between

the lateral incisors and canines. The miniscrew

position was simulated 6 mm above the buccal CEJ

between the maxillary rst and second molars at the

position of the modied IZC, as proposed by Lin.

(12)

The properties of all materials were those

used in previously conducted nite element studies

(Table 1).

(27-33)

All materials were assigned iso-

parametric, homogeneous, linear, elastic properties,

excepting the PDL, which was dened as having

non-linear elasticity. Ogden model property values were

assigned to describe the non-linear elastic stress-

strain behavior of the PDL (Table 2).

(34)

The constructed nite element model was

meshed into 148,914 nodes and 651,810 elements.

The teeth, PDL and alveolar bone were constructed

into tetrahedron elements. The brackets, hooks, and

archwire were constructed into hexahedron elements.

The interactions between teeth were tie contact with

no friction. The boundary conditions were dened

at the top and back surface of the maxillary bone.

Table 1 Material properties of dentin, cortical bone, cancel-

lous bone and stainless steel required within the FE

model.

(27-33)

Material

Young’s

modulus (MPa)

Poisson’s

ratio

Dentin 19600 0.3

Cortical bone 13700 0.26

Cancellous bone 1370 0.3

Stainless steel 200000 0.3

Table 2 Coefcients of the third order Ogden model property

values describing non-linear elasticity of PDL.

(34)

i µ

1 -24.4237106 1.99994222 4.87164332

2 15.8966494 3.99994113 0.00000000

3 8.56953079 -2.00005453 0.00000000

CM Dent J Vol. 42 No. 1 January-April 2021 128

The orientation of this model was established with

the x axis representing the mesio-distal direction of

the anterior teeth and the bucco-palatal direction

of the posterior teeth. The y axis represented the

supero-inferior direction. The z axis represented the

antero-posterior direction, which is the labio-palatal

direction of the anterior teeth and the mesio-distal

direction of the posterior teeth. +X represents the left

side of model, in the right quadrant, +x represents

the mesial direction of movement of the anterior

teeth and the palatal direction of movement of the

posterior teeth. In the left quadrant, +x represents

the distal direction of movement of the anterior teeth

and the buccal direction of movement of the posterior

teeth. +Y values were dened as the inferior or apical

direction and +z values were dened as the labial

direction of the anterior teeth or the mesial direction

of the posterior teeth (Figure 1).

A distalization force vector of 200 g was applied

from the miniscrew to the retraction hooks of 0-mm,

2-mm, 4-mm, 6-mm, and 8-mm lengths (Figure 2)

The location of CRes was dened same as the loca-

tion described by Jeong et al.

(31)

The displacement

patterns of the teeth, produced by the force vectors

resulting from using each hook length, were calculat-

Figure 1 The orientation of the model. X axis: (+) left, (−) right

direction; y axis: (+) superior, (−) inferior direction;

z axis: (+) anterior, (−) posterior direction.

Figure 2 Schematic force diagram and miniscrew position.

Forces (200 g) were applied from the miniscrew to

different vertical positions of the retraction hook: 0

mm, 2 mm, 4 mm, 6 mm and 8 mm. located between

the lateral incisor and canine. The location of minis-

crew was simulated at 6 mm above the buccal CEJ

between the rst and second molar.

Figure 3 The reference points of teeth are represented as

yellow dots for the assessment of tooth displacement.

ed in the x, y, and z axes. The midpoints of the incisal

edges of the central and lateral incisors, the cusp tip

of the canine, the buccal cusp tips of the premolars,

the mesio-buccal cusp tips of the molars, and the root

apices of each tooth were used as reference points to

evaluate the displacement of the teeth. The Abaqus

software (Dassault Systèmes Americas) was used

to calculate and visualize the PDL von Mises stress

distribution and tooth displacement patterns for the

whole arch distalization of all maxillary teeth.

Results

Von Mises stress distribution in PDL and tooth

displacement patterns of the right and left quadrants

were assumed to be the same because the point of

application and angle of force direction were the

CM Dent J Vol. 42 No. 1 January-April 2021129

same. Therefore, only the left quadrant is shown in

these results, for clarity and to eliminate superimpo-

sition of the right and left quadrants.

Von Mises stress distribution in PDL

The von Mises stress distribution in the PDL was

calculated in N/mm

(MegaPascals or MPa). The

color-coded map of von Mises stress distribution in

the PDL with all hook lengths is shown in Figure 4.

The levels of stress are shown in the map, in which

red represents the areas of maximum stress and dark

blue represents the areas of minimum stress.

The stress produced when using 0-mm retrac-

tion hooks was greatly concentrated in the canine

and the distal root of the second molar. The highest

stress value was in the cervical third of the canine

(2.939x10

-4

MPa). The lowest stress value was in the

apical third of the central incisor (3.751x10

-9

MPa)

(Figure 4A).

The stress produced when using 2-mm retrac-

tion hooks was greatly concentrated in the lateral

incisor, canine and the distal root of the second

molar. The highest stress value was in the cervical

third of the canine (4.465x10

-4

MPa). The lowest

stress value was in the apical third of the central

incisor (6.286x10

-9

MPa) (Figure 4B). The distribu-

tion patterns of the above two hook lengths are nearly

the same pattern.

With the 4-mm length of retraction hook, the

highest stress value was in the apical third of the

lateral incisor (4.162x10

-4

MPa). The high stress

was also found in the second molar but lower than

with the 0-mm and 2-mm hooks. The lowest stress

value was in the apical third of the rst premolar

Figure 4 Color-coded map of von Mises stress distribution in the left maxillary quadrant PDL. The areas of maximum and

minimum stress are indicated. A) 0-mm, B) 2-mm, C) 4-mm, D) 6-mm, E) 8-mm lengths

CM Dent J Vol. 42 No. 1 January-April 2021 130

(1.515x10

-5

MPa) (Figure 4C).

With the 6-mm length of retraction hook, the

areas of high stress were in the apical third of the

central incisor, lateral incisor and canine. The highest

stress value was in the apical third of the lateral

incisor (5.603x10

-4

MPa). The lowest stress value

was in the apical third of the rst molar (7.650x10

-6

MPa) (Figure 4D).

With the 8-mm length of retraction hook, the

areas of high stress were nearly the same pattern

with the 6-mm length, but the stress was more con-

centrated. The highest stress value was in the apical

third of the lateral incisor (7.599x10

-4

MPa). The

lowest stress value was in the cervical third of the

second molar (8.123x10

-9

MPa) (Figure 4E).

Displacement of all maxillary teeth

The displacement patterns of all maxillary

teeth with each length of retraction hook are shown

in Figure 4. The translucent yellow tooth images

show the positions of the teeth before applying the

force, and the blue tooth images show the displaced

positions afterwards. The directions of the arrows

adjacent to the teeth represent the directions of the

tooth movement. The length and color of the arrows

represent the distance of the tooth movement. With

all lengths of retraction hooks, the amounts of initial

tooth movement in the anterior segment were larger

than in the posterior segment.

With the retraction hook lengths of 0 mm

(bracket slot level) and 2 mm, palatal crown tipping

and extrusion of the anterior teeth were observed.

The posterior tooth movement was distal tipping

and intrusion (Figure 5A & B). In the occlusal view,

all teeth moved in the posterior direction with the

anterior teeth moving palatally and the posterior

teeth moving distally. The crowns of the posterior

teeth tipped slightly buccally (Figure 6A & B).

With the retraction hook length of 4 mm,

both crowns and roots of the anterior teeth moved

palatally and slighltly intruded. The root apices

displaced palatally more than the crowns. The

crowns of posterior teeth moved distally. The

premolars were slightly extruded, but the molars

were slightly intruded (Figure 5C). In the occlusal

view, all teeth still moved in the posterior direction

but, in contrast to the situation with 0-mm and 2-mm

hooks, the crowns of the posterior teeth tipped slight-

ly palatally (Figure 6C).

With the retraction hook length of 6 mm and

8 mm, the direction of anterior tooth movement

changed from palatal crown tipping to labial crown

tipping. The anterior segment of archwire was raised

upward, resulting in anterior teeth proclination and

intrusion. The posterior teeth tipped slightly distally

and extruded (Figure 5D & E). In the occlusal view,

the crowns of the anterior teeth tipped labially and

the root apices tipped palatally. The crowns of the

posterior teeth tended to tip palatally to a greater

extent than with the 4-mm hook (Figure 6D & E).

Optimal length of retraction hook

The optimal length of retraction hook in this study

was 4 mm. The anterior and posterior teeth moved

distally along the occlusal plane with minimal vertical

movement and tipping.

Discussion

This nite element study of maxillary whole

arch distalization demonstrates that applying

distalization force to different lengths of retrac-

tion hooks resulted in different patterns of stress

distribution in the PDL and in different patterns of

displacement of the maxillary teeth. We also found

that the optimal length of retraction hook that

produced closed to distal translation movement of

the maxillary whole arch was 4 mm.

Applying distalization force to the retraction

hook, the initial movement was mainly observed

at the anterior teeth as proved by FEM. The force

CM Dent J Vol. 42 No. 1 January-April 2021131

Figure 5 Displacement of the left maxillary teeth indicated by superimposition of before (yellow) and after (blue) application of

the distalization force. The direction of tooth movement indicated by the colored arrows. The length and color of the

arrows represent the distance of the tooth movement. Long red arrows indicate large amounts of displacement; short

blue arrows indicate small amounts of displacement. A) 0-mm., B) 2-mm., C) 4-mm., D) 6-mm., E) 8-mm. lengths

CM Dent J Vol. 42 No. 1 January-April 2021 132

Figure 6 Displacement of all maxillary teeth indicated by superimposition of before (yellow) and after (blue) application of the

distalization force in the occlusal view. The direction of tooth movement indicated by the colored arrows. A) 0-mm, B)

2-mm, C) 4-mm, D) 6-mm, E) 8-mm lengths

CM Dent J Vol. 42 No. 1 January-April 2021133

and stress were also transferred to the second

molar, causing posterior tooth movement and whole

arch distalization. Thus, this nite element nding

may be used as evidence to support the theory of en-

masse distalization, which proposes that the entire

maxillary dentition can be effectively moved after

applying force to an anteriorly located hook.

(24)

In this study, the results of stress distribution in

the PDL were examined in terms of the von Mises

stress. It was used to represent the overall stress

of a multi-axial stress just the same as it has been

applied in previous studies.

(22,24,35-37)

The stress on

the teeth close to the point of force application at the

retraction hook, was more concentrated than on some

other teeth in positions farther from the hook. With

0-mm- and 2-mm- hooks, the highest level of stress

was found at the cervical third of canine. With the

other lengths, the highest level of stress was found

on the apex of lateral incisor, which was also close

to the point of force application. These outcomes are

in agreement with those of Sung et al.

(24)

The results revealed that the length of retraction

hook highly relates to the types of tooth movement.

Changing the length of retraction hook affects the

distance between the line of action of force and the

CRes. When distalization force is applied to low-

level hooks, the line of action of the force passed

below the CRes and induced clockwise moment,

resulting in steepening of the occlusal plane. Conse-

quently, the anterior teeth had palatal crown tipping

and extrusion. The posterior teeth tipped distally

and substantially intruded (Figure 7A). The level of

stress was high at the distal root of the second molar

because the posterior teeth were intruded. More-

over, the constructed tuberosity distal to the second

molar and the boundary conditions at the back of the

model may have strongly resisted the distalization,

resulting in high stress in the distal root of the second

molar (Figure 4A & B). On the other hand, the line of

action of the force passed above the CRes and

generated counterclockwise moment, resulting in

upward rotation of the occlusal plane. The labial

aring of anterior teeth was observed, and the pos-

terior teeth were slightly extruded (Figure 7C). The

stress in the PDL of posterior teeth was less than

that with shorter hooks because extrusion occurred

(Figure 4D & E).

When a distalization force was applied to a

4-mm hook, the line of action of the force passed

near the CRes, rather than passing through it, and a

low moment was generated. The line of force may

have passed either slightly below or slightly above

the CRes; therefore, the low moment may have been

either clockwise or counterclockwise, respectively

(Figure 7B). All maxillary teeth moved distally along

the occlusal plane with minimal intrusion or tipping.

The location of the miniscrew at the Modied IZC

was higher than the CRes resulted in a distal and

upward direction of the line of action of force,

generating intrusion and distalization of the maxillary

dentition. In whole arch distalization, the entire

maxillary dentition did not undergo pure bodily

movement. The reason may be archwire deection

of the force system, causing a relatively some degree

of tipping movement.

All of the tooth displacement patterns studied

correspond with the results of previous studies that

used different lengths of retraction hook for whole

arch distalization with interradicular miniscrews

(24)

and for distalization of the posterior teeth with

modied IZC miniscrews.

(38)

The distalization force can be divided in to

three axes which affect to the occurred displacement

pattern. The amount of force in each axis was

calculated and represented as Fx, Fy, and Fz. Fx was

a lateral force along the x axis; Fy was an intrusive

force along the y axis; Fz was the horizontal force

or distalization force along the z axis. These forces

were calculated from the resultant force formula of

three vectors using the angle values in this nite

CM Dent J Vol. 42 No. 1 January-April 2021 134

Figure 7 Schematic diagram of moments on whole arch distalization using retraction hooks and miniscrews. A black dot indicates

the position of the CRes. Red dotted lines indicate the distalization force. Red solid curved arrows express the moments

that originated from the force. A) 0-mm hook (short): the red dotted line passes below the CRes, and a clockwise moment

is generated. B) 4-mm hook: the red dotted line passes near the CRes, and a low moment is generated which may be

clockwise or counterclockwise. C) 8-mm hook (long): the red dotted line passes above the CRes, and a counterclockwise

moment is generated.

element model. The θ angle was the angle formed

between the line of action of force and the horizontal

plane (Z-axis), whereas the α angle was the angle

formed between the line of action of force and the

lateral force vector (X-axis), as shown in Figure

8. The α angle varied, depending on the length of

retraction hook. An increase in its length led to a

decrease in the θ angle. The θ angle is zero when the

level of the retraction hook is the same as that of the

miniscrew.

(39)

In contrast, the α angle value remained

constant because the locations of retraction hook and

miniscrew were xed.

When using short hooks, the θ angle becomes

larger, resulting in high Fy (intrusive force) and

low Fz (distalization force).

(39)

In our study, shorter

hooks resulted in greater intrusion of the posterior

teeth than did longer hooks. In contrast, long hooks

the θ angle was reduced, resulting in low Fy and high

Fz. Therefore, the intrusion of posterior teeth was

less than with shorter hooks.

Additionally, we found that the arch wire deec-

tion occurred when using a retraction hook attached

to the main archwire due to high bending moments

at the joint of these two components. The high bend-

ing moments increase progressively according to

the length of the retraction hook and the exibility

of the main archwire.

(25)

As found with high-level

hooks, the anterior segment of the archwire was

raised upward because a bending moment occurred

between the lateral incisor and canine. Consequently,

the deection of archwire induced an intrusive

force acting on the anterior teeth, thereby causing

labial aring of incisors. Additionally, the palatal

crown tipping of the posterior teeth when using the

high-level hooks gradually increased from a twist

of the posterior segment of the archwire. This twist

may have acted on the teeth in the same way as the

third order bend or torque that occurs when archwires

are bent using pliers. We attributed the deection

and exibility of the archwire to the property of the

CM Dent J Vol. 42 No. 1 January-April 2021135

Figure 8 Schematic force diagram and the angle of force in the horizontal and vertical planes. A) sagittal view of nite element

model showing the θ angle. B) top view of the model showing the α angle

main archwire, which was assigned to be an elastic

material because the idea of an orthodontic archwire

with rigid strength is unrealistic.

(24)

In this study, all materials were assigned as

linear elastic properties, excepting the PDL, which

was dened as having non-linear elasticity because

of its hyper-elastic behavior. The Ogden model was

used to express the elastic response of this biologi-

cal soft tissues.

(34)

These material property values

normally vary in each person owing to individual

differences in histologic tissue properties.

(20)

Addi-

tionally, the thickness of PDL is, in fact, non-uni-

form, having an hour-glass shape with the mid-root

level having the narrowest width;

(40)

however, in this

study, it was assumed to be uniform (0.2 mm).

The selection of a hook length for whole arch

distalization in each case should be based on the

existing malocclusion and the specic treatment plan

for each patient.

(21,38)

Short hooks could be effective

for palatal crown tipping of the anterior teeth and

intrusion of the posterior teeth which are suitable for

the ared incisors and open bite case. Intrusion of the

posterior teeth resulted in autorotation of mandibular

and decreased the open bite. Long hooks should be

used for palatal root movement of the anterior teeth

and minor extrusion of the posterior teeth, resulting

in the posterior rotation of mandible. Thus, long

hooks are suitable for the retroclined incisors and

deep overbite case.

(24)

The greater the concentration of stress, the larger

is the hyalinized zone of PDL, resulting in a reduced

rate of tooth movement and leading to root resorp-

tion.

(41,42)

Therefore, when applying whole arch

distalization, the roots of the anterior teeth may be

highly prone to resorption due to higher stress in

those teeth.

Three-dimension computed tomography

may be used in future studies to create individual

tooth models for better simulations of orthodontic

tooth movement and for greater accuracy in treat-

ment planning.

(20,21,38,43)

Besides, studies can be

improved by studying the duration of tooth move-

ment. Treatment duration is an important factor that

may yield different results from those of this static

FEM study. Therefore, dynamic FEM studies may

provide an increasingly realistic basis for orthodontic

tooth movement.

Conclusions

1. Different lengths of retraction hooks resulted

in different patterns of stress distribution in the

PDL and in different patterns of displacement of the

CM Dent J Vol. 42 No. 1 January-April 2021 136

maxillary teeth in whole arch distalization.

- The von Mises stress in the PDL of the anterior

teeth, especially the teeth near the retraction hook,

was greater than in the PDL of the posterior teeth

with all lengths of retraction hook. Areas of high

stress concentration were also found in the intruded

teeth, the second molar when using short hook and

the anterior teeth for long hook.

- The use of short hooks induced palatal crown

tipping with extrusion of the anterior teeth and distal

crown tipping with intrusion of the posterior teeth. In

contrast, the use of long hooks induced labial crown

tipping with intrusion of the anterior teeth and distal

crown tipping with extrusion of the posterior teeth.

2. The optimal length of retraction hook was 4

mm that produced movement closed to distal trans-

lation of the maxillary whole arch along the occlusal

plane; however, pure bodily movement did not occur.

Acknowledgments

The authors would like to acknowledge Mr.

Pattarapon Saigerdsri, Master degree student, Faculty

of Engineering, Chiang Mai University, Thailand

for his assistance in the use of the SolidWorks and

Abaqus software during the research study, and

Dr. M. Kevin O. Carroll, Professor Emeritus of the

University of Mississippi School of Dentistry, USA

and Faculty Consultant at Faculty of Dentistry,

Chiang Mai University Thailand, for language

editing.

References

1. Park HS, Kwon TG, Sung JH. Nonextraction

treatment with microscrew implants. Angle

Orthod 2004; 74(4): 539-549.

2. Janson G, Barros SEC, Simão TM, Freitas MRD.

Relevant variables of Class II malocclusion treat-

ment. Dental Press J Orthod 2009; 14(4): 149-

157.

3. Burstone CJ, Choy K. The biomechanical foun-

dation of clinical orthodontics. Hanover Park:

Quintessence Publishing; 2015: 580.

4. Proft WR, Fields HW, Sarver DM. Mechanical

principles in orthodontic force control. Contem-

porary orthodontics. 5

ed. St.Louis: Mosby

Elsevier; 2013: 312-336.

5. Chen G, Teng F, Xu TM. Distalization of the

maxillary and mandibular dentitions with minis-

crew anchorage in a patient with moderate Class

I bimaxillary dentoalveolar protrusion. Am J

Orthod Dentofacial Orthop 2016; 149(3): 401-

410.

6. Choi YJ, Lee JS, Cha JY, Park YC. Total distaliza-

tion of the maxillary arch in a patient with skeletal

Class II malocclusion. Am J Orthod Dentofacial

Orthop 2011; 139(6): 823-833.

7. Lee KJ, Park JY, Park YC. En-masse distalization

of upper dentition for correction of Class II using

dual orthodonic miniscrews. J Dent Assoc Thai

2006; 5: 33-38.

8. Wu X, Liu H, Luo C, Li Y, Ding Y. Three-

dimensional evaluation on the effect of maxillary

dentition distalization with miniscrews implanted

in the infrazygomatic crest. Int J Implant Dent

2017; 27(1): 22-27.

9. Liu H, Wu X, Yang L, Ding Y. Safe zones for

miniscrews in maxillary dentition distalization

assessed with cone-beam computed tomography.

Am J Orthod Dentofacial Orthop 2017; 151(3):

500-506.

10. Fayed MM, Pazera P, Katsaros C. Optimal sites

for orthodontic mini-implant placement assessed

by cone beam computed tomography. Angle

Orthod 2010; 80(5): 939-951.

11. Noorollahian S, Alavi S, Shirban F. Bilateral

en-masse distalization of maxillary posterior

teeth with skeletal anchorage: a case report.

Dental Press J Orthod 2016; 21(3): 85-93.

CM Dent J Vol. 42 No. 1 January-April 2021137

12. Lin JJJ. New method of distalization of the

maxillary dentition using the infrazygomatic crest

mini-screws. Creative orthodontics: blending

the Damon system and TADs to manage difcult

malocclusions. 2

ed. Taipei: Yong Chieh

Enterprise 2010: 187-208.

13. Lin JJJ, Roberts. Guided infrazygomatic screws:

reliable maxillary arch retraction. Int J Orthod

Implantol 2017; 46: 4-16.

14. Bechtold TE, Kim JW, Choi TH, Park YC, Lee

KJ. Distalization pattern of the maxillary arch

depending on the number of orthodontic minis-

crews. Angle Orthod 2013; 83(2): 266-273.

15. Tekale PD, Vakil KK, Vakil JK, Gore KA. Distali-

zation of maxillary arch and correction of Class

II with mini-implants: A report of two cases.

Contemp Clin Dent 2015; 6(2): 226.

16. Nanda RS, Tosun YS. Biomechanics in ortho-

dontics principle and practice. 1

ed. Hanover

Park: Quintessence Publishing; 2010: 1-145.

17. Knop L, Gandini LG, Shintcovsk RL, Gandini

MR. Scientic use of the nite element method

in orthodontics. Dental Press J Orthod 2015;

20(2): 119-125.

18. Marya A, David G, Eugenio MA. Finite element

analysis and its role in orthodontics. Dent Oral

Health 2016; 2(2): 5-6.

19. Konda P, Tarannum S. Basic principles of nite

element method and its applications in orthodon-

tics. J Pharm Biomed Sci 2012; 16(16): 1-8.

20. Cho SM, Choi SH, Sung SJ, Yu HS, Hwang CJ.

The effects of alveolar bone loss and miniscrew

position on initial tooth displacement during

intrusion of the maxillary anterior teeth: nite

element analysis. Korean J Orthod 2016; 46(5):

310-322.

21. Mo SS, Kim SH, Sung SJ, et al. Factors con-

trolling anterior torque with C-implants depend

on en-masse retraction without posterior appli-

ances: biocreative therapy type II technique.

Am J Orthod Dentofacial Orthop 2011; 139(2):

183-191.

22. Seong EH, Choi SH, Kim HJ, Yu HS, Park YC,

Lee KJ. Evaluation of the effects of miniscrew

incorporation in palatal expanders for young

adults using nite element analysis. Korean J

Orthod 2018; 48(2): 81-89.

23. Song JW, Lim JK, Lee KJ, Sung SJ, Chun YS,

Mo SS. Finite element analysis of maxillary

incisor displacement during en-masse retraction

according to orthodontic mini-implant position.

Korean J Orthod 2016; 46(4): 242- 52.

24. Sung EH, Kim SJ, Chun YS, Park YC, Yu HS,

Lee KJ. Distalization pattern of whole maxillary

dentition according to force application points.

Korean J Orthod 2015; 45(1): 20-28.

25. Sang SJ, Jang GW, Chun YS, Moon YS.

Effective en-masse retraction design with ortho-

dontic mini-implant anchorage: a nite element

analysis. Am J Orthod Dentofacial Orthop 2010;

137(5): 648-657.

26. Hemanth M, Lodaya SD. Orthodontic force

distribution: a three-dimensional nite element

analysis. World J Dent 2010; 1(3): 159-162.

27. Mohammed SD, Desai H. Basic concepts of nite

ement analysis and its applications in dentistry:

an overview. J Oral Hyg Health 2014; 2(5): 156-

160.

28. Desai SR, Harshada SH. Finite element analysis:

basics and its applications in dentistry. Indian J

Dent Sci 2012; 4(1): 60-65.

29. Geramy A, Sodagar A, Hassanpour M. Three-

dimensional analysis using nite element method

of anterior teeth inclination and center of resis-

tance location. Chin J Dent Res 2014; 1: 37-42.

CM Dent J Vol. 42 No. 1 January-April 2021 138

30. Jagota V, Sethi APS, Kumar K. Finite element

method: An overview. Walailak J Sci & Tech

2013; 10(1): 1-8.

31. Jeong GM, Sung SJ, Lee KJ, Chun YS, Mo SS.

Finite-element investigation of the center of

resistance of the maxillary dentition. Korean J

Orthod 2009; 39(2): 83-94.

32. Toms SR, Eberhardt AW. A nonlinear nite

element analysis of the periodontal ligament

under orthodontic tooth loading. Am J Orthod

Dentofacial Orthop 2003; 123(6): 657-665.

33. Tanne K, Sakuda M, Burstone CJ. Three-dimen-

sional nite element analysis for stress in the

periodontal tissue by orthodontic forces. Am J

Orthod Dentofacial Orthop 1987; 92(6): 499-

505.

34. Huang H, Tang W, Yan B, Wu B. Mechanical

responses of periodontal ligament under a realistic

orthodontic loading. Procedia Eng 2012; 31:

828-833.

35. Jing Y, Han X, Cheng B, Bai D. Three-dimen-

sional FEM analysis of stress distribution in

dynamic maxillary canine movement. Chinese

Science Bulletin 2013; 58(20): 2454-2459.

36. Yu IJ, Kook YA, Sung SJ, Lee KJ, Chun YS, Mo

SS. Comparison of tooth displacement between

buccal mini-implants and palatal plate anchorage

for molar distalization: a nite element study. Eur

J Orthod 2014; 36(4): 394-402.

37. Chen YC, Tsai HH. Use of 3D nite element

models to analyze the inuence of alveolar bone

height on tooth mobility and stress distribution.

J Dent Sci 2011; 6(2): 90-94.

38. Aungkatawiwat T, Patanaporn V, Rungsiyakull

C. Maxillary posterior teeth distalization with

miniscrew anchorage relative to force vectors

applied to different lengths of retraction hook,

analyzed using the nite element method. CM

Dent J 2018; 39(2): 77-89.

39. Meriam JL, Kraige LG. Engineering Mechanics:

Statics 7

ed. New york: John Wiley & Sons,

Inc.; 2004: 523.

40. Anthony P. The anatomy and physiology of the

healthy periodontium. In: Panagakos F, editor.

Gingival diseases - Their atiology, prevention

and treatment. Rijeka: InTech; 2011: 1-22.

41. Tomizuka R, Shimizu Y, Kanetaka H, et al. His-

tological evaluation of the effects of initially light

and gradually increasing force on orthodontic

tooth movement. Angle Orthod 2007; 77(3):

410-416.

42. Böhl MV, Jagtman AMK. Hyalinization during

orthodontic tooth movement: a systematic review

on tissue reactions. Eur J Orthod 2009; 31(1):

30-36.

43. Tajima K, Chen KK, Takahashi N, Noda N,

Nagamatsu Y, Kakigawa H. Three-dimensional

nite element modeling from CT images of tooth

and its validation. Dent Mater J 2009; 28(2):

219-226.