ORIGINAL ARTICLE

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Dr. 국 윤 아 Dr. 채 종 문

Dr. 김 재 현 Dr. 이 남 기

Dr. 박 재 현 Dr. 이 정 윤

Corresponding author: Yoon-Ah Kook Department of Orthodontics, Seoul St. Mary’s Hospital, College of Medicine, The Catholic University of Korea, 222 Banpo-daero, Seocho-gu, Seoul 06591, Korea

Tel: +82-2-2258-1776 Fax: +82-2-537-2374 E-mail: [email protected] Received: May 3, 2021 / Revised: May 25, 2021 / Accepted: May 25, 2021

ABSTRACT

Introduction: The purposes of this study were to analyze the displacement pattern of the maxillary dentition accord- ing to the location of the force applied and the vertical position of the hook on the palatal retraction arch (PRA) when the dentition is distalized using the palatal plate, and to compare those done by buccal miniscrew using finite element analysis. Methods: A finite element model was created and consisted of four treatment modalities with fifteen models. Modalities 1, 2, and 3 used modified C-palatal plates (MCPPs) with a short, medium, and long length PRA respectively and each modality included four models that had anterior hooks with vertical position of 0, 4, 7, and 10 mm respectively. In modality 4, miniscrews were placed on the buccal side. For each model, a force of 300 g per side was applied. Results: The long length PRA with a hook at 0 mm was the most effective model for distalization of the maxillary dentition. The short and medium-length PRAs caused uncontrolled distal tipping. Displacement of the molars using a long length PRA with a short hook led to intrusion, but with the long hook, it caused extrusion. Buccal miniscrews with hook lengths at zero caused first molars to distally tip and intrude. The molar crowns showed more distal displacement and extrusion as the hook length increased. Conclusions: Long length PRAs with MCPPs were the most effective for bodily distal movement of the maxillary molars. This information should be useful when applying temporary skeletal anchorage devices (TSADs) during total arch distalization. (Clin J Korean Assoc Orthod 2021;11(2):89-101)

Key words Molar distalization, Modified C-palatal plate, Buccal miniscrews, Finite element analysis

Biomechanical Analysis for Total Arch Distalization according to Location of Force Application and Types

of Temporary Skeletal Anchorage Devices

Jung Youn Lee,¹ Jae Hyun Park,^2,3 Nam-Ki Lee,⁴ Jaehyun Kim,⁵ Jong-Moon Chae,⁶ Yoon-Ah Kook⁵

1Department of Orthodontics, Graduate School of Clinical Dental Science, The Catholic University of Korea, Seoul, Korea

2Postgraduate Orthodontic Program, Arizona School of Dentistry & Oral Health, A.T. Still University, Mesa, Arizona, USA

3International Scholar, Graduate School of Dentistry, Kyung Hee University, Seoul, Korea

4Department of Orthodontics, Section of Dentistry, Seoul National University Bundang Hospital, Seongnam, Korea

5Department of Orthodontics, Seoul St. Mary’s Hospitaal, College of Medicine, The Catholic University of Korea, Seoul, Korea

6Department of Orthodontics, School of Dentistry, Wonkwang Dental Research Institute, University of Wonkwang, Iksan, Korea

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INTRODUCTION

Molar distalization is a treatment option to cor- rect Class II malocclusion with non-extraction.

However, the amount of distal movement, distal tipping, and molar extrusion needs to be considered to achieve successful treatment goals with conventional methods.^1-3

Temporary skeletal anchorage devices (TSADs) have been used in non-extraction cases to over- come these drawbacks.^4,5 Oh et al.⁴ reported that molars were distalized with less distal tipping using miniscrews for arch distalization. Bechtold et al.⁵ installed an additional miniscrew in the premolar area to prevent clockwise rotation of the occlusal plane while inducing the intrusive translation of the whole arch. However, the range of tooth movement using buccal miniscrews is limited due to the narrow interradicular space.

To avoid root damage with the buccal approach, TSADs have been placed on the palatal side.^6-9 Modified C-Palatal Plates (MCPPs) have been proven to be effective for molar distalization with few side effects, especially tipping effects.^10-13 Recently, Shoaib et al.¹⁴ demonstrated long-term stability with minimal changes 3 years posttreatment after total maxillary arch distalization with MCPPs in adults.

In addition, regarding the movement patterns of the anterior teeth, several studies demonstrated that a combination of lever arm height and anchor screw position can produce efficient and effective retraction of maxillary anterior teeth.^15-17 Howev- er, they analyzed only the retraction of maxillary anterior teeth after the extraction of the first premolar.

On the other hand, Yu et al.¹⁸ evaluated tooth displacement relative to different notches on the lever arms of MCPPs. They achieved bodily molar movement and intrusion with the 10 mm notch for

total arch distalization without extraction. Even so, factors such as location of the force applied and vertical position of the hook on palatal retraction arch (PRA) during molar distalization were not evaluated in total arch distalization of the maxillary dentition using MCPPs.

Therefore, the purposes of this study were to analyze the displacement pattern of the maxillary dentition according to the location of the force applied and the vertical position of the hook on the palatal retraction arch (PRA) when the dentition is distalized using the palatal plate, and to compare those done by buccal miniscrew using finite element analysis.

MATERIALS AND METHODS

Commercial tooth models (Model-i21D-400G, Nissin Dental Products, Kyoto, Japan) were scanned three-dimensionally to produce the tooth images. Then, the images were aligned on a broad dental arch form (Ormco^®, Glendora, CA, USA) without curves of Spee and Wilson.

The thickness of the periodontal ligament was modeled as a 0.25 mm uniformly thick layer as the study of Coolidge.¹⁹ The alveolar bone was de- signed to follow gingivally of the cemento-enamel junction, extended 1 mm beyond the apices.²⁰ Mi- cro-arch^® brackets (Tomy Co., Tokyo, Japan) were selected. The brackets and archwire were assumed to have no-play and no-friction relationship, and all materials were considered to be homogenous, isotropic, with non-linear elasticity. The material properties (Young’s modulus and Poisson’s ratio) were reported in previous studies.^21-23

Boundary conditions

The zygomaticomaxillary suture, frontonasal suture, palatomaxillary suture, pterygomaxillary suture was fixed (Figure 1A). The 3D co-ordinates

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were the X plane, sagittal plane; Y plane, transverse plane; and Z plane, vertical plane. Positive values indicate forward, inward, and upward dis- placements on the X, Y, and Z planes, respectively.

Determination of axes

Tooth movement was expressed in three axes [x-axis, anterior (+) to posterior (-) direction; y-axis, median (+) to lateral (-) direction; and z-axis, superior (+) to inferior (-) direction] (Figure 1B).

The landmarks on the crowns were as follows;

mid-center of the incisal edge of the incisors and canine cusp tip; inner center of the premolar and molar cusps. For the roots, the root apexes of the incisors, canines and second premolars, and the palatal root apexes of the first premolars and molars were the landmarks.

Installation of simulated distalization modalities on a finite element model

Four different distalization modalities were installed and fifteen different models were produced on finite element models relative to the vertical position of the anterior hook and length of the palatal retraction arch (Figure 2).

Distalization Modality 1

Models 1-4 (Figure 2A); the MCPPs (Jeil Med- ical, Seoul, Korea) were fixed in the paramedian palatal region at the sagittal level of the center of the first molar with three miniscrews (length, 8 mm; diameter, 2 mm; Jeil Medical). In the model, short stainless steel (SS) palatal retraction arch (PRA), 1.0 mm in diameter, was connected to the bands of the maxillary first premolars, extending anteriorly close to the level of the cervical line of the maxillary teeth. A Roth 0.022-inch bracket system (Tomy, Tokyo, Japan) was attached to the teeth and a 0.019 × 0.025-inch SS archwire was tied through frictionless translational joints and cinched-back on the second molar. Distalization forces of 300 g were applied via coil springs connected to the second notch on the arms of MCPPs (selected for force application and 7.7 mm apical to the archwire vertically and 12.5 mm lateral to the mid-palate horizontally) with the hook attached to the PRA at 0 mm length (Figure 2E, F). Models 2-4 were similar to Model 1, but the hook was attached to the PRA at 4, 7, and 10 mm lengths respectively.

Figure 1. Boundary condition. A, Fixed area, red surface; zygomaticomaxillary suture, frontonasal suture, palatomaxillary suture, pterygomaxillary suture. B, Three axes; x-axis, anterior (+) to posterior (-) direction; y-axis, median (+) to lateral (-) direction; and z-axis, superior (+) to inferior (-) direction.

B A

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Figure 2. Installation of simulated distalization modalities on finite element model 45 × 8 mm (300 × 300 DPI). A, Modality 1, first premolar as the location of force application using MCPP. B, Modality 2, second premolar as the location of force application using MCPP. C, Modality 3, first molar as the location of force application using MCPP. D, Modality 4. E, F, The position of the MCPP and retraction hook 45 × 20 mm (300 × 300 DPI). E, Device (MCPP) position was assumed to be at the level of the first molar centers, antero-posteriorly. The second notch on the lever arms of the MCPP was selected for force application. A hook attached to the PRA between the lateral incisor and canine cingulum. F, Length of the retraction hook was determined at 0 mm (H0), 4 mm (H4), 7 mm (H7), and 10 mm (H10) from the connection point on the PRA.

B

A C

D

Power chain position Hook length

F E

45 × 8 mm (300 × 300 DPI)

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Model 5-8 (Figure 2B); this modality was similar to Modality 1, but a medium length PRA was attached to the banded second premolar. Models 5-8 each included the hook attached to the PRA at 0, 4, 7, and 10 mm length respectively.

Models 9-12 (Figure 2C); this modality was similar to Modalities 1 and 2 but a long length PRA was attached to the banded first molar. Models 9-12 each included the hook attached to the PRA at 0, 4, 7, and 10 mm length respectively.

Models 13-15 (Figure 2D); brackets were placed on all teeth. A 0.019 × 0.025-inch SS archwire was engaged and cinched-back on the second molar.

For distalization, 300 g of force was applied on each side with a coil spring between the miniscrew and a 0.8 mm SS retraction hook attached to the archwire between the lateral incisor and canine. The vertical height of the hook was set at 0, 4, and 7 mm on Models 13, 14, and 15 respectively.

The miniscrew position was set at 8 mm apical to the archwire, at the midpoint between the adjacent brackets.

RESULTS

The effects relative to the location of force applied using MCPP

In all models with MCPPs, mesial-in rotation of the PRA banded teeth was observed (Figure 3).

Distalization with Modality 1

The short length PRA showed an uncontrolled tipping pattern with the greatest distal displacement of the crown and mesial displacement of the root at 0 mm hook. As the hook length increased,

the distal movement of the root apex increased.

The first molar showed uncontrolled distal crown tipping with the hook at 0 mm. However, as the hook length increased, it showed gradually anterior displacement of the crown and posterior displacement of the root apex (Table 1).

The medium length PRA showed severe uncontrolled distal crown tipping with the hook at 0 mm. However, with the hook at 7 mm, it was closer to bodily movement. With the hook at 10 mm, there was a greater distal displacement of the root apex with mesial displacement of the crown. In the first molar area, the movement pattern was near- ly bodily movement with the hook at 0 mm. As the hook length increased, the first molar showed more extrusion with anterior displacement of the crown and posterior displacement of the root apex (Table 2).

The long length PRA showed distal displacement of the crown and root with controlled distal crown tipping with the hook at 0 mm. As the length of the hook increased, the posterior displacement of the crown decreased, and it was closer to bodily movement at 7 mm. In the z-axis, the first molar was intruded with the hook at 0 and 4 mm, but it was more extruded as the length of the hook increased (Table 3).

The effects relative to the vertical

position of the force applied using buccal miniscrews

The incisors showed the greatest backward movement of the crown with anterior root tipping at the 0 mm hook. As the length of the hook increased, the posterior displacement of the crown

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Figure 3. Three treatment modalities included a short length PRA (first premolar), a medium-length PRA (second premolar), and a long length PRA (first molar). And they were divided into 12 models relative to a hook length of 0 mm (H0), 4 mm (H4), 7 mm (H7), and 10 mm (H10). Tooth movement was expressed in three axes [x axis, anterior (+) to posterior (-) direction; y-axis, median (+) to lateral (-) direction; and z-axis, superior (+) to inferior (-) direction]. The arrows mean the line of retraction forces.

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Table 1. Displacement by modality 1 with a short length PRA using MCPP

Hook 0 Hook 4 Hook 7 Hook 10

X Y Z X Y Z X Y Z X Y Z

Crown (mm)

1 -0.0020 0.0002 -0.0016 -0.0081 0.0008 -0.0039 -0.0114 0.0011 -0.0051 -0.0141 0.0014 -0.0060 2 -0.0005 0.0002 -0.0001 -0.0043 0.0014 -0.0007 -0.0067 0.0022 -0.0009 -0.0090 0.0031 -0.0013 3 0.0003 0.0003 0.0049 0.0040 -0.0046 0.0068 0.0068 -0.0083 0.0077 0.0089 -0.0114 0.0077 4 -0.0480 -0.0254 0.0080 -0.0360 -0.0439 0.0026 -0.0259 -0.0572 -0.0028 -0.0161 -0.0684 -0.0088 5 -0.0091 -0.0074 0.0012 -0.0032 -0.0173 -0.0008 0.0004 -0.0233 -0.0024 0.0033 -0.0277 -0.0039 6 -0.0028 -0.0024 -0.0008 0.0010 -0.0031 -0.0003 0.0022 -0.0031 0.0001 0.0031 -0.0027 0.0005 7 -0.0022 0.0001 -0.0003 -0.0023 0.0013 -0.0001 -0.0011 0.0021 0.0001 0.0000 0.0026 0.0002 Root (mm)

1 0.0008 -0.0001 -0.0002 0.0027 -0.0002 0.0016 0.0037 -0.0002 0.0025 0.0045 -0.0003 0.0034 2 -0.0001 -0.0001 0.0001 0.0007 -0.0003 0.0018 0.0012 -0.0005 0.0030 0.0016 -0.0008 0.0041 3 -0.0026 0.0004 0.0039 -0.0042 0.0020 0.0032 -0.0051 0.0032 0.0022 -0.0055 0.0041 0.0009 4 0.0042 -0.0044 0.0156 -0.0010 0.0024 0.0078 -0.0045 0.0089 0.0004 -0.0062 0.0140 -0.0071 5 0.0030 0.0035 0.0032 0.0007 0.0078 0.0038 -0.0007 0.0105 0.0038 -0.0017 0.0125 0.0035 6 0.0013 0.0007 -0.0004 -0.0003 0.0010 -0.0006 -0.0009 0.0011 -0.0005 -0.0014 0.0010 -0.0002 7 0.0005 -0.0003 0.0002 -0.0009 -0.0014 0.0004 -0.0022 -0.0021 0.0003 -0.0032 -0.0026 0.0001 X: sagittal (+), anterior, (-), posterior, Y: transversal, (+), palatal, (-), buccal, Z: vertical, (+), intrusion, (-), extrusion. *Short length PRA means force applied through first premolar using MCPPs.

Table 2. Displacement by modality 2 with a medium length PRA using MCPP

Crown (mm)

1 -0.0038 0.0005 -0.0018 -0.0066 0.0009 -0.0030 -0.0069 0.0009 -0.0033 -0.0069 0.0010 -0.0034 2 -0.0031 0.0017 -0.0020 -0.0062 0.0034 -0.0032 -0.0073 0.0040 -0.0036 -0.0079 0.0043 -0.0038 3 -0.0006 0.0006 -0.0013 -0.0026 0.0021 -0.0018 -0.0036 0.0029 -0.0018 -0.0045 0.0036 -0.0017 4 0.0030 -0.0059 0.0065 0.0058 -0.0129 0.0056 0.0079 -0.0182 0.0042 0.0092 -0.0215 0.0028 5 -0.0300 -0.0167 0.0241 -0.0187 -0.0411 0.0131 -0.0054 -0.0620 -0.0010 0.0079 -0.0757 -0.0116 6 -0.0006 -0.0120 0.0008 0.0060 -0.0180 -0.0001 0.0086 -0.0221 -0.0011 0.0104 -0.0243 -0.0017 7 -0.0024 0.0014 -0.0011 -0.0054 0.0026 -0.0011 -0.0052 0.0042 -0.0006 -0.0050 0.0052 -0.0001 Root (mm)

1 0.0012 -0.0001 0.0007 0.0022 -0.0002 0.0015 0.0023 -0.0003 0.0014 0.0024 -0.0003 0.0014 2 0.0012 -0.0008 0.0003 0.0022 -0.0014 0.0013 0.0024 -0.0016 0.0016 0.0026 -0.0018 0.0019 3 0.0007 -0.0005 -0.0007 0.0014 -0.0010 0.0000 0.0016 -0.0013 0.0005 0.0017 -0.0015 0.0010 4 -0.0032 0.0027 0.0055 -0.0037 0.0053 0.0042 -0.0039 0.0073 0.0024 -0.0038 0.0086 0.0009 5 0.0088 -0.0042 0.0262 0.0033 0.0108 0.0225 -0.0052 0.0265 0.0150 -0.0136 0.0343 0.0084 6 -0.0005 0.0048 0.0002 -0.0028 0.0065 -0.0021 -0.0038 0.0076 -0.0037 -0.0045 0.0081 -0.0048 7 0.0001 -0.0013 -0.0004 0.0002 -0.0021 0.0004 -0.0003 -0.0027 0.0011 -0.0005 -0.0029 0.0016 X: sagittal (+), anterior, (-), posterior, Y: transversal, (+), palatal, (-), buccal, Z: vertical, (+), intrusion, (-), extrusion. *Medium length PRA means force applied through secondS premolar using MCPPs.

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decreased. In the z-axis, only the crown of the cen- tral incisor was intruded with the hook at 0 mm, but as the length of the hook increased, the incisors showed more extrusion movement. In the first molars, as the length of the hook increased, the posterior movement of the crown increased with increased forward movement of the roots. In the z-axis, the intrusion of the first molar increased as the length of the hook increased. With transverse displacement, the anterior teeth and first premolar showed palatal displacement, but the second premolar and molars had lateral displacement in the hook at 0 mm (Figure 4, Table 4).

DISCUSSION

Buccal miniscrews have been applied as a sta- tionary anchorage for total maxillary arch distalization in non-extraction treatment. However, the risk of root damage due to narrow interradicu-

lar space led us to consider the use of the palatal plate. This study was conducted to biomechanical- ly analyze tooth movement depending on different PRAs using MCPPs during total arch distalization.

In a finite element study, Von-mises stress is expressed by the sum of pressure, elongation, and torsion, so there is a limit to express the effects of orthodontic force over time. Therefore, our study only focused on the pattern of teeth displacement to evaluate tooth movement affected by PRA types during distalization of the maxillary dentition using MCPPs.

Depending on the location of force applied, displacement of the maxillary dentition showed uncontrolled distal crown tipping of the first and second premolars with forward movement of the root in a short and medium-length PRA. This might be because the line of force of short and medium-length PRA passed far from the center of re-

Table 3. Displacement by modality 3 with a long length PRA using MCPP

Crown (mm)

1 -0.0050 0.0006 -0.0018 -0.0065 0.0008 -0.0024 -0.0070 0.0009 -0.0026 -0.0084 0.0011 -0.0031 2 -0.0042 0.0021 -0.0019 -0.0057 0.0029 -0.0026 -0.0062 0.0032 -0.0029 -0.0075 0.0038 -0.0034 3 -0.0032 0.0024 -0.0012 -0.0044 0.0035 -0.0017 -0.0049 0.0040 -0.0019 -0.0060 0.0049 -0.0023 4 -0.0007 -0.0001 0.0001 -0.0006 -0.0007 0.0005 -0.0006 -0.0010 0.0007 -0.0009 -0.0007 0.0010 5 0.0004 -0.0049 0.0026 0.0027 -0.0131 0.0013 0.0043 -0.0183 0.0004 0.0054 -0.0220 -0.0005 6 -0.0301 -0.0094 0.0063 -0.0244 -0.0256 0.0017 -0.0178 -0.0368 -0.0023 -0.0093 -0.0466 -0.0071 7 -0.0064 -0.0046 -0.0010 -0.0068 -0.0066 -0.0012 -0.0060 -0.0079 -0.0011 -0.0064 -0.0092 -0.0015 Root (mm)

1 0.0015 -0.0001 0.0015 0.0020 -0.0001 0.0019 0.0021 -0.0002 0.0020 0.0025 -0.0002 0.0025 2 0.0014 -0.0008 0.0011 0.0019 -0.0012 0.0015 0.0021 -0.0013 0.0015 0.0025 -0.0015 0.0018 3 0.0013 -0.0009 0.0007 0.0018 -0.0013 0.0010 0.0020 -0.0015 0.0011 0.0024 -0.0018 0.0014 4 0.0002 0.0001 0.0003 0.0000 0.0004 0.0006 0.0000 0.0005 0.0008 0.0000 0.0004 0.0011 5 -0.0006 0.0024 0.0039 -0.0016 0.0061 0.0049 -0.0022 0.0084 0.0053 -0.0027 0.0102 0.0054 6 -0.0134 -0.0032 0.0081 -0.0145 0.0018 0.0019 -0.0152 0.0060 -0.0037 -0.0153 0.0106 -0.0100 7 0.0014 0.0013 -0.0001 0.0010 0.0017 -0.0005 0.0005 0.0020 -0.0008 0.0005 0.0023 -0.0013 X, sagittal (+), anterior, (-), posterior; Y, transversal, (+), palatal, (-), buccal; Z, vertical, (+), intrusion, (-), extrusion. *Long length PRA means force applied through first molar using MCPPs.

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Figure 4. Fourth treatment modality using a buccal miniscrew divided into three models relative to a hook length 0 mm (H0), 4 mm (H4), and 7 mm (H7). The arrows mean the line of retraction forces.

Table 4. Displacement by modality 4 according to hook length using buccal miniscrews

Hook 0 Hook 4 Hook 7

X Y Z X Y Z X Y Z

Crown (mm)

1 -0.0607 0.0194 -0.0069 -0.0545 0.0165 0.0037 -0.0481 0.0133 0.0121

2 -0.0594 0.0270 0.0128 -0.0403 0.0216 0.0365 -0.0173 0.0121 0.0561

3 -0.0184 0.0314 0.0115 -0.0248 0.0369 -0.0257 -0.0260 0.0349 -0.0395

4 -0.0039 0.0009 0.0040 -0.0159 0.0098 -0.0086 -0.0211 0.0122 -0.0114

5 -0.0009 -0.0007 0.0011 -0.0105 0.0024 -0.0056 -0.0144 0.0025 -0.0069

6 -0.0005 -0.0002 0.0006 -0.0059 0.0008 -0.0012 -0.0087 0.0001 -0.0015

7 0.0003 -0.0030 -0.0007 -0.0167 -0.0074 -0.0008 -0.0191 -0.0081 -0.0007

Root (mm)

1 0.0113 -0.0031 0.0245 0.0047 -0.0006 0.0294 -0.0003 0.0013 0.0326

2 0.0009 -0.0052 0.0391 -0.0119 -0.0024 0.0497 -0.0199 0.0002 0.0559

3 -0.0006 -0.0113 0.0211 0.0158 -0.0168 -0.0086 0.0210 -0.0149 -0.0209

4 -0.0002 -0.0004 0.0043 0.0076 -0.0044 -0.0069 0.0100 -0.0052 -0.0092

5 -0.0001 0.0001 0.0012 0.0040 -0.0001 -0.0072 0.0053 -0.0001 -0.0089

6 0.0011 0.0006 0.0007 0.0043 -0.0003 -0.0007 0.0055 -0.0002 -0.0007

7 0.0009 0.0013 -0.0011 0.0085 0.0043 0.0010 0.0096 0.0049 0.0014

X: sagittal (+), anterior, (-), posterior, Y: transversal, (+), palatal, (-), buccal, Z: vertical, (+), intrusion, (-), extrusion.

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sistance (CR) than long-length PRA. Several studies demonstrated that the CR of the maxillary dentition was near the middle area of the premolar roots.^5,24,25

Since the notch position of the MCPP and the hook of the PRA are fixed, the line of force pass- ing through the two points seems to be the same.

However, PRA is attached to each first premolar, second premolar, and first molar, and the acting point of the actual force is on each tooth. There- fore, although the line of force is parallel, the point of force is different depending on the type of tooth. So, the distance between each line of force and the CR of the entire maxillary dentition is also different.

Also, the tooth movement pattern is clinically influenced by the archwire size and the line of force. When the maxillary dentition is connected as one unit by a rigid archwire, the line of force is the same. However, in this study, the wire size was set to 19 × 25 SS, which could allow slight movement of individual teeth; results were shown according to variables in Figure 3A.

Additionally, the small root surface area of the first and second premolars play an important role in tipping movement. Choy et al.²⁶ suggested that the tooth tipping tendency was associated with the amount of root surface area and demonstrated that roots with the greater surface area had greater resistance to tipping.

On the other hand, the long length PRA, Mo- dality 3, with the hook at 0 mm showed distal displacement with controlled crown tipping and intrusion. Also, hook at 7 mm was closer to translation movement. Therefore, Modality 3, which used the first molar as the point of force application, was the most effective way for distalizing the maxillary dentition without uncontrolled tipping.

This result is similar with previous studies that reported distalization with MCPPs showed bodily

molar movement when the force was applied at or near the CR of the first molar.¹⁸

Additionally, in all models, mesial-in rotation of the PRA banded tooth was observed. This was because the force of distalization was applied to the palatal side, resulting in mesial-in rotation of the tooth.

Regarding the effects of the vertical position of the retraction hook on the PRA, the direction of the force vector was determined via two points.

One was on the lever arm of the MCPP while the other was on the hook of the PRA. Previous research found that when 4, 7, and 10 mm notches were vertically apical to the archwire, the 4 mm notch showed controlled distal tipping and extrusion, but the 10 mm notch caused bodily movement and intrusion.¹⁸ In our study, the force was only applied from the 7 mm notch on the MCPP to different vertical positions of the anterior hook on the PRA. The 7 mm notch on the MCPP was selected based on a previous study.¹⁸

The first molar was intruded when the short hook length was 0 and 4 mm. However, there was extrusion with the long hook at 7 and 10 mm. This could be because the direction of the force vector was below the CR in a low-level hook and above the CR in a high-level hook. As the force vector varies according to the length of the hook, the direction of the vector may change, which may cause an intrusive force.

With Modality 4, using a buccal miniscrew, the first molar showed uncontrolled distal crown tipping in different hook lengths. Our results were similar with an earlier study that reported uncontrolled distal tipping of the first molar and extrusion when buccal miniscrews were used.¹⁸ Sung et al.²⁷ concluded that when force was applied to over 10 mm hook level, it led to the distal translation of the posterior segment, but in our study, over 7 mm level caused distal tipping. This might be due to a

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difference in experimental designs and conditions used in the finite element analysis.

Regarding the y-axis, the second premolars and molars showed buccal tipping with the hook at 0 mm due to increased vertical component of the force on the buccal side, possibly just because of the buccal component of force created by the miniscrew positioned on the buccal side.

Clinically, Bechtold et al.⁵ suggested an additional miniscrew in the premolar area to enhance the direction of the force vector and to facilitate intrusion and distalization of the entire arch. How- ever, a recent clinical study reported that MCPPs showed greater distalization and intrusion with less distal tipping of the first molar and less extrusion of the incisor compared to buccal miniscrews.¹⁰

The design of this study had some limitations as follows; only initial tooth displacement was considered, no occlusal force was applied, there were differences in the mechanical properties of the virtual models and biological tissue. The thickness of the periodontal ligament was supposed to be uniform (0.25 mm), while in reality it was shaped with the narrowest zone at the mid-root level.²¹ Lastly, molar distalization with MCPPs is usually started at the same time as leveling and aligning with a 0.016-inch Ni-Ti archwire. How- ever, the archwire used in this study was a 0.019 × 0.025-inch SS archwire with cinch-back to avoid space opening during total arch distalization. In reality, with a properly angled tooth in a posteri- or crowding case, cinch-back is not necessary to relieve the crowding during molar distalization.

Further study about tooth displacement patterns and stress distribution using a 0.016 in Ni-Ti archwire in posterior crowding cases is required for efficient clinical applications with MCPPs.

CONCLUSION

This study evaluated the effects relative to the vertical position of the anterior hook and second- ly analyzed the pattern of the maxillary dentition displacement on distalization force applied by using the palatal plate according to the location of the force applied, and compared those done by buccal miniscrew using finite element analysis.

The locations of force application were first, second premolar and first molar, which were attached to short, medium, and long length PRA respectively. We made the following observations: first, a long-length PRA using an MCPP showed bodily movement of the first molars. However, short and medium-length PRAs caused uncontrolled distal tipping. Second, displacement of the first molars using long length PRA with a short hook led to intrusion. However, the long hook caused the extrusion. Third, displacement of the first molars using short length PRA with a short hook led to extrusion, and the long hook caused intrusion.

Therefore, this information should be useful when applying TSADs during total arch distalization.

Acknowledgments

The authors would like to thank Dr. Jung Mee Kim, Private practice, Los Angeles, California, USA, Dr. Jiyoung Oh, Resident, Department of Orthodontics, Seoul St. Mary’s Hospital, Catholic University of Korea, Seoul, Korea, and Jin Hyeok Kook, College of Dentistry, Yonsei University for their assistance in manuscript preparation.

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