A systematic review of biomechanics of clear aligners by finite element analysis

Abstract

Purpose

This review systematically collects the investigations on clear aligners (CA) by finite element analysis (FEA), and summarizes the biomechanical mechanism of CA including typical side effects and reformative designs of CA and auxiliary.

Methods

Literatures on FEA biomechanical analysis of CA are searched on Web of Science and PubMed. The information of FEA methods and results, FEA-simulated orthodontic clinical scenarios are collected and discussed in categories.

Results

Twenty-nine literatures are included. FEA are conducted with ABAQUS (13/29) or Ansys (13/29), while the data presentation forms are various without clear consensus. FEA-simulated orthodontic clinical scenarios are discussed by main targeted orthodontic directions.

Conclusions

Side effects of CA treatment are essentially caused by uneven stress distribution. Auxiliaries (including attachments, power ridges, intermaxillary elastics, divots etc.) are designed to adjust orthodontic biomechanics and stress distribution to improve therapeutic efficiency. Limitations of current researches include lack of unified standard for FEA protocols and data presentation forms, and lack of long-term biomechanical analysis of CA other than its initial instantaneous effects. FEA, as an efficient way of analyzing biomechanics of CA, deserves more standardized, extensive and in-depth study. This review might provide theoretical basis and reference for optimization of future orthodontic designs.

Introduction

Technology of clear aligners (CA), introduced in late 1990 s as an alternative aesthetic bracketless orthodontic appliance, has been a popular choice for patients due to its comfort, transparent appearance and ease of cleaning. In contrast to traditional fixed appliances (FA), which realize orthodontic movement mainly through elasticity of metal archwires, CA exert orthodontic force by shape recoverability of polymer membrane including poly-ethylene terephthalate glycol (PETG), thermoplastic polyurethane (TPU), etc. [1, 2]. Compared to FA, CA exhibit reduced compressive stress to teeth and periodontal tissue during orthodontic treatment, resulting in superior pain-relieving performance [3], reinforced anchorage and increased tendency of tooth movement [4]. The relatively moderate orthodontic force of CA results in its narrower indications compared to FA, therefore, during treatment of complex cases, CA are often applied for finer adjustment after initial alignment by FA.

To determine the orthodontic force of CA, specific experimental apparatuses have been applied in existing researches including in vivo (intraoral) [5] and in vitro (extraoral) [6] measurement. An intraoral research in 2010 indicates that CA exerts the highest orthodontic force at the beginning of wearing, which stably decreases by 20%−30% on the second day and remain constant for over two weeks [5]. An in vitro study in 2020 evaluates the mechanical properties of CA before and after wearing for 2 weeks, although the material maintains its elastic modulus and stress relaxation performances, its surface morphology shows signs of defects, which may release trace allergenic elements [6].

As experimental measurement requires specific equipment, most existing biomechanical researches of CA apply finite element analysis (FEA). Liu et al. in 2016 reports that the discrepancy of the orthodontic forces of CA between experimental value and simulation result by FEA was less than 0.2 N [7]. Ye et al. in 2022 proves that the predicted model of CA surface strains by FEA exhibits fit of linear regression to that scanned by micro-CT [8]. These studies demonstrate the reliability of FEA model comparing to experimental model on biomechanical researches of CA.

With the complexity of clinical cases due to individual tooth positions, periodontal conditions, etc., studies have been carried out to elucidate the biomechanical effects of CA by FEA to help guiding the improvement of future CA design. In recent years, researchers have comprehensively reviewed various aspects of CA including its advantages and disadvantages compared with FA [9], orthodontic efficiencies [10, 11], parameter comparison among different brands of CA [12], biological effects of the orthodontic thermoplastics [1]. Concerning the biomechanics of CA, Ghafari et al. in 2020 reviewed different orthodontic biomechanics of CA and FA, some of which involve FEA to simulate different mechanical effects [13]; Upadhyay et al. in 2021 review the biomechanical principles of CA, including tooth movement mechanism, efficiencies for different types of tooth movement, and internal reasons of its lower orthodontic efficiency than FA [14]. However, there has been few systematic reviews summarize the biomechanical studies of CA by FEA.

Therefore, this systematic review aims to cover the FEA simulated biomechanical characteristics exerted by CA concerning different orthodontic movement and designs, including the effects of CA and its auxiliaries on orthodontic stress and tooth displacement related to crown, root and PDL, to provide guidance for future treatment design. This review summarizes the relationship between orthodontic treatment design and biomechanical outcome with visualized FEA heatmaps to provide better understanding and theoretical basis for future design and optimization of CA and its auxiliaries.

Materials and methods

This review has been registered in PROSPERO (registration ID: 425,621). Search strategy has been formulated according to PICO method as follows: Patient population (P) = patients with malformation of dentition, Intervention (I) = orthodontic treatment using CA, Comparison (C) = different designs of CA and/or auxiliaries, Outcomes (O) = simulated biomechanical characteristics by FEA (including Von Mises stress, maximum principal stress, displacement, etc.)

Based on the above PICO approach, keywords “clear aligner” and “finite element” are applied in this review. Advanced search strategies are established based on the keywords and corresponding synonyms on databases of Web of Science (WOS) and PubMed as follows:

WOS: TS = (finite element OR FEA OR FEM) AND TS = (orthodontic) AND TS = (bracketless OR invisible OR removable OR clear OR Invisalign).

PubMed: (finite element OR FEA OR FEM) AND (orthodontic) AND (bracketless OR invisible OR removable OR clear OR Invisalign).

Literatures are screened using predetermined inclusion and exclusion criteria as shown in Table 1.

Table 1.

Inclusion and exclusion criteria for literature screening

Inclusion criteria	Exclusion criteria
1. Types of literature are limited to research articles	1. Reviews, patents, meeting abstracts are excluded
2. Titles and abstracts of the articles are related to the biomechanical research of CA	2. The title and abstract of the paper do not concern biomechanical properties or CA
3. Written in English	3. Written in languages other than English
4. The year of publication is restricted after CA invention (1997 ~ present)	4. The year of publication before CA invention (1997)
5. The content involves FEA data of different orthodontic design/conditions	5. The content does not involve FEA of different orthodontic design/conditions

To minimize the potential for reviewer bias, two reviewers (H.C. and X.H.) independently conduct literature searches and performed the study selection. Both reviewers strictly follow the inclusion and exclusion criteria, and disagreements are resolved by discussion.

A grading system referenced by the Swedish Council on Technology Assessment in Health Care (SBU) [11, 15] and the Centre for Reviews and Dissemination (CRD) [11, 16] are used to assess the risk of bias and degree of reliability of the articles for evidential value of this review (Table 2).

Table 2.

Criteria for grading assessed studies

Grade A—high value of evidence All criteria should be met:	(1) Randomized clinical study or a prospective study with a well-defined control group
	(2) Defined diagnosis and endpoints
	(3) Diagnostic reliability tests and reproducibility tests described
	(4) Blinded outcome assessment
Grade B—moderate value of evidence All criteria should be met:	(1) Cohort study or retrospective case series with defined control or reference group
	(2) Defined diagnosis and endpoints
	(3) Diagnostic reliability tests and reproducibility tests described
Grade C—low value of evidence One or more of the conditions below:	(1) Large attrition
	(2) Unclear diagnosis and endpoints
	(3) Poorly defined patient material

The information of FEA methods and results was extracted from the included literatures for summary and comparison. FEA methods include the applied software, mechanical parameters of models, and data presentation form. The FEA-simulated orthodontic clinical scenarios including designed treatment, target tooth, side effects, and ways to offset side effects. FEA heatmaps are directly collected from the included researches. All literature information is extracted by H.C. and X.H., and examined and verified by L.Y. and D.L.

Results

Following PRISMA guideline (Fig. 1), the search strategy reports 186 records, among which 35 duplicate records are firstly removed. After overviewing the titles, abstracts and keywords, 2 reviews, 2 non-English articles, and 102 records with no considerable information about biomechanical characteristics and CA technology are excluded. The remaining 45 records are sought for full-text retrieval and assessment, and 13 articles are excluded due to lack of FEA data, 3 researches comparing FEA and experimental measurement are excluded due to lack of FEA data of different orthodontic design/conditions.

Fig. 1.

Search flowchart according to PRISMA guidelines. 29 literatures are included after screening

All 29 articles ultimately included are graded “B” according to the specific assessment methods (Table 3), indicating moderate referential integrity and reliability of this review. In the included articles, FEA are conducted with ABAQUS (13/29) or Ansys (13/29), while the data presentation forms are various without clear consensus (Table 4). Almost all articles (27/29) provide data of tooth displacement of dentition and/or single tooth, in the form of heatmaps with contour, vector diagram, or initial-vs.-displaced comparison, or statistical data presented as tables or histograms. 24 articles provide stress distribution data, mostly (20/24) of periodontal ligament (PDL), and some (6/24) of the teeth, CA membrane, or attachments. Due to lack of unified standard FEA protocols, analytical parameters and data presentation forms (Table 4), the included researches are hard to be statistically analyzed.

Table 3.

Grading of selected studies

Author, Year	Grade
Yanning Ma et al., 2021 [45]	B
Andrea Cortona et al., 2020 [38]	B
Yuxun Cheng et al., 2022 [19]	B
Gabriele Rossini et al., 2020 [31]	B
Ting Jiang et.al., 2022 [17]	B
R. Savignano et al., 2019 [16]	B
Qiuyu Wang et al., 2022 [23]	B
Gabriele Rossini et al., 2021 [15]	B
Jeong-Hee Seo et al., 2021 [3]	B
S. Barone et al., 2017 [25]	B
Roberto SAVIGNANO et al., 2017 [26]	B
De-Shin Liu et al., 2015 [44]	B
Lu Liu et al., 2021 [22]	B
Yukiko Yokoi et al., 2019 [40]	B
Cheng Zhu et al., 2022 [34]	B
Yongqing Cai et al., 2015 [28]	B
Kyungjae Hong et al., 2021 [41]	B
Pratchawin Laohachaiaroon et al., 2022 [37]	B
Lurong Jia et al., 2022 [21]	B
Lu Liu et al., 2021 [22]	B
Yuxun Cheng et al., 2022 [20]	B
Dian Fan et al., 2022 [30]	B
Qian Xia et al., 2022 [4]	B
Cengiz Ayidaga et al., 2021 [32]	B
Jun‐qi Liu et al., 2022 [24]	B
Xulin Liu et al., 2022 [33]	B
Lurong Jia et al., 2022 [21]	B
Won-Hyeon Kim et al., 2020 [36]	B
Juan Pablo Gomez et al., 2015 [39]	B

Table 4.

Information of FEA

Author Year	Softwares		Experimental Groups	Data Presentation
				Displacement				Stress Distribution
	Modeling	FEM		Object	Heatmap Form	FEA-evaluated Index (unit)	Maximum Value	Object	Heatmap Form	FEA-evaluated Index (unit)	Maximum Value
Ting Jiang 2020 [17]	Geomagics	Ansys (2015)	1) retraction 0.25 mm 2) retraction 0.2 mm & intrusion 0.15 mm 3) retraction 0.1 mm & intrusion 0.23 mm	Dentition	Vector diagram Contour diagram	U, Resultant (mm)	0.0540 (Group 1)	PDL Att.	Contour diagram	Stress (unspecified)	1–3#: 0.03 (Group1) 5#: 3.382 (Group 1)
Lu Liu 2022 [21]	Mimics 17.0 Geomagic Studio 2014 Hypermesh 14.0	Abaqus CAE	Canine: 1) no ATT 2) with ATT	Tooth	Vector diagram Contour diagram	U, Resultant (mm)	0.00005086 (Group 2)	PDL	Contour diagram	S, Mises (Pa)	42840 (Group 2)
Yuxun Cheng 2022 [19]	Mimics 20.0 Geomagics 2014 NX 1911	Ansys (2019)	1) 0.5 mm-thick aligner with torque compensation 2) 0.5 mm-thick aligner without torque compensation 3) 0.75 mm-thick aligner with torque compensation 4) 0.75 mm-thick aligner without torque compensation	Tooth	Contour diagram	U, Resultant (mm)	1#: 0.074 (Group2) 2#: 0.077  (Group2) 3#: 0.071 (Group 2) 5#: 0.044 (Group 4)	PDL	Contour diagram	S, Mises (Mpa)	with torque compensation: 0.0375 (Group2) without torque compensation: 0.0514 (Group2)
Yuxun Cheng 2022 [20]	Mimics 20.0 Geomagics 2014 NX 1911	Ansys (2019)	1) axial inclination 105° 2) axial inclination 110°	Tooth	Vector diagram Contour diagram	U, Resultant (mm)	0.0603 (Group 1)	/	/	/	/
Lurong Jia 2022 [21]	Mimics (17.0) Geomagics (2015) SolidWorks (2016)	Abaqus 6.14	hard: soft layer: 1) 1: 0 (single hard layer) 2) 3: 1 3) 1: 1 4) 1: 3	Dentition	Vector diagram Contour diagram	U, Resultant (mm)	4.2E-2 (Group 1)	PDL Bone	Contour Diagram	S, Mises (Mpa)	1.23 (Group 1) 2.55 (Group 1)
Lu Liu 2021 [22]	Mimics 17.0 Geomagic Studio 2014 Hypermesh 14.0	Abaqus CAE	1) CA 2) labial elasticslabial elastics CA 3) linguoincisal elastics CA	Tooth Aligner	Vector diagram Contour diagram	U, Resultant (mm)	0.000068 (Group 3) 3.172e-04 (unspecified)	Teeth PDL Bone	Contour Diagram	S, Mises (Pa)	7.416e-05 (Group 2) 3.513e-04 (Group 2) 9.359e-05 (Group 2)
Qiuyu Wang 2022 [23]	Mimics (20.0) Geomagics(2014) NX11	Ansys (2019)	1) no ATT (MB) 2) distobuccal ATT & mesiobuccal button (DB) 3) mesiolingual ATT & distobuccal button (ML) 4) distobuccal ATT & mesiolingual button (DL) 5) mesiolingual ATT & distolingual button (ML) 6) distobuccal ATT & button corresponding to mesiobuccal tooth surface (AMB)	Dentition Aligner	Vector diagram Contour diagram	U, Resultant (mm)	0.0864 (Group 6) 0.191 (Group 3)	PDL Bone	Contour Diagram	S, Mises (MPa)	0.0272 (Group 4) 0.6752 (Group 1)
Jun-qi Liu 2022 [24]	Mimics (19.0) Geomagic Wrap 2017 SolidWorks Ortho Analyzer Appliance Designer Unigraphics NX	Abaqus 6.14	1) moderate anchorage 2) direct strong anchorage 3) indirect strong anchorage	Dentition	Vector diagram Contour diagram	U, Resultant (mm)	0.06624 (Group 3)	/	/	/	/
Qian Xia 2022 [4]	Mimics (17.0) Geomagics(2015)	Abaqus 6.14	canine (distal/mesial) 1) Angel Button 2) Power Arm 3) 3D Printed Attachment 4) Fixed Appliance	Tooth Adjacent tooth Dentition	Vector diagram Contour diagram	U, Resultant (mm)	4.15e-03 (Group 1) 1.972e-02 (Group 1) 1.972e-02 (Group 1)	PDL	Contour diagram	von Mises Stress (MPa) Stress Value (Mpa)	9.269e-02 (Group 2) 1.326-01 (Group 3)
S. Barone 2017 [25]	/	Ansys 14.0	1) Standard (S) 2) Single Divot (SD) 3) Double Divots (DD) 4) Vertical ATT (VA) 5) Horizontal ATT (HA)	Tooth	Contour diagram	Displacement (mm)	0.140 (Group 3)	/	/	/	/
Roberto Savignano 2017 [26]	/	Ansys 14.0	1) Standard 2) Divot 3) 2 Divots 4) Vertical ATT 5) Horizontal ATT	Tooth	Contour diagram	Displacement (mm)	0.075 (Group 2)	/	/	/	/
De-Shin Liu, 2015 [44]	Geomagics Solidworks	Abaqus	1) 0.5 mm-thick Aligner 2) 0.75 mm-thick Aligner 3) 1.0 mm-thick Aligner 4) 1.25 mm-thick Aligner	/	/	/	/	PDL	Contour diagram	Stress (MPa)	3.750e-03 (Group 4)
Jeong-Hee Seo, 2021 [3]	Mimics 23.0 Solidworks 2019	Abaqus 6.14	1) 0.5 mm-thick Aligner 2) 0.75 mm-thick Aligner	Tooth	Contour diagram	Displacement (mm)	Tooth	PDL	Contour diagram	Principal Stress (N/mm^2)	15.06 (Group 1)
Yongqing Cai, 2015 [42]	MIMICS Geomagics 3-matic	Abaqus	Canine: a) Translation b) Inclination c) Rotation	Tooth	Contour diagram	Displacement (mm)	Tooth	PDL	Contour diagram	von Mises Stress (MPa)	Unclear pic
Dian Fan 2022 [30]	Mimics 20.0 Geomagics 2017 Solidworks 2021	unspecified	Fisrt molar: 1) No ATT (NA) 2) buccal ATT 3) palatal ATT 4) bucco-palatal ATT	Dentition Aligner	Vector diagram Contour diagram	Displacement trend (mm) Aligner Deformation (mm)	Dentition Aligner	PDL	Contour diagram	Equivalent Stress (Mpa)	0.0921 (Group 4)
Andrea Cortona 2019 [32]	SpaceClaim CAD Micro-CT Scan	Ansys 18.2	1) no ATT 1.2° 2) no ATT 3° 3) ATT 4.5 1.2° 4) ATT 4.5 3° 5) ATTs 4.4 to 4.6 1.2° 6) ATTs 4.4 to 4.6 3°	Tooth Aligner	Vector diagram	Displacement (mm)	0.0602 (Group 6) 0.29481 (Group 4)	PDL Aligner	Vector diagram	Stress (g/cm2)	560.00 (Group 6) 3.7295 (Group 5)
Yanning Ma, 2021 [45]	MIMICS 10.0	Abaqus 6.5	1) M1 with axial inclination 90° 2) M2 with axial inclination 90° 3) M3 with axial inclination 90° 4) M1 with axial inclination 100° 5) M2 with axial inclination 100° 6) M3 with axial inclination 100° Group: 0.10, 0.15, 0.18, 0.2, 0.25 (mm) Displacement M1: mild periodontitis M2: moderate periodontitis M3: severe periodontitis	Tooth	Contour diagram	Strain of top alveolar crest (mm)	0.301  (Group 6)	Tooth	Contour diagram	Stress Value S, Mises  (Mpa)	90°: 0.1 mm: 77 Mpa (Group 3) 0.15 mm: 123Mpa (Group 3) 0.18 mm:/ 0.20 mm: 162Mpa (Group 3) 0.25 mm: 194Mpa (Group 3) 100°: 0.1 mm: 94 Mpa (Group 6) 0.15 mm: 97Mpa (Group 6) 0.18 mm: 164Mpa (Group 6) 0.20 mm: 179Mpa (Group 6) 0.25 mm: 206Mpa (Group 6)
Gabriele Rossini 2020 [31]	SpaceClaim CAD	Ansys 18.2	1) no ATT 2) ATT on 3–6 3) ATT on 3–7	Tooth	Vector diagram	Displacement (mm)	0.036(Group 2)	Aligner & Tooth Contact PDL	Contour diagram	Stress  (g/cm2)	2099.1 (Group 3) 132.4 (Group 2)
Cengiz Ayidaga 2021 [32]	3D-Doctor VRMesh CAD	Algor Fempro	1) no ATT 2) 2.75 height*1.75 width*1 thickness (mm) vertical rectangular ATT 3) 1.8 height*4 width*1 thickness (mm) Guideline ATT	Tooth	Contour diagram	Displacement (mm)	0.15 (Group 3)	Tooth PDL	Contour diagram	von Mises Stress (N/mm^2) Principal Stress (N/mm^2)	50 (Group 3) 5 (Group 3)
Xulin Liu 2022 [33]	Mimics 20.0 Geomagics 2014 NX 1911	Ansys (2019)	Set I: 1 st molar Set II: 2nd molar 1) without Class II elastics 2) Class II elastics attached to the tooth by buttons 3) Class II elastics attached to the aligner by precision cutting	Dentition	Vector diagram Contour diagram	Displacement (mm)	Maxillary: Set I: 0.1318 (Group 3) Set II: 0.1054 (Group 3) Mandibular: Set I: 0.0126 (Group 3) Set II: 0.0133 (Group 3)	PDL	Contour diagram	Hydrostatic Stress von Mises stress (MPa)	Unspecified
Cheng Zhu, 2022 [34]	HyperMesh	Abaqus	1) mandibular postural position 2) mandibular advancement with AMS 3) mandibular advancement with only muscular force	/	/	/	/	Aligners & PDL of Dentition	Contour diagram	Compressive Stress (Mpa)	Unspecified
Lurong Jia, 2022 [22]	Mimics 17.0 SolidWorks 2016	Abaqus 6.14	1) Aligner 2) Aligner + Lingual Button 3) Aligner + Precision Cut 4) Aligner + patient-specific ATT	Tooth	Contour diagram	Initial Displacement (mm)	9.502e-02 (Group 1)	PDL	Contour diagram	Stress Value (MPa)	1.036e+00 (Group 1)
Won-Hyeon Kim 2020 [36]	SolidWorks	Abaqus CAE 2016	Shapes of ATT: 1) foursquare 2) half round at a cross-section 3) half circle at a longitudinal section 4) half triangle 5) oblique Angle to ATT surface of the teeth (rotation): 1) 90° 2) 65° 3) 45° ATT for torque: 1) four shapes having half round 2) half round at a cross-section 3) half round at a cross-and longitudinal-sections, 4) 45 degrees	Tooth	Contour diagram	Displacement (µm) Angle (°)	Extrusion Upper region: 3.272 (type 2) Lower region: 3.101 (type 2) Intrusion Upper region: 48.913 (type 1) Lower region: 47.755 (type 2) Rotation Upper region: 0.890° (type 2) Lower region: 0.858° (type 2) Torque Upper region: 59.442 (type 1) Lower region: 35.764 (type 2)	Bone Tooth PDL RTA ATT	Contour diagram	Peak von Mises Stress (MPa) Contact Stress (MPa)	PVMS-Extrusion: Bone: 0.189 (type 2) Tooth: 13.705 (type 4) PDL: 0.017 (-) RTA: 29.890 (type 5) ATT: 118.434 (type 5) PVMS-Intrusion: Bone: 3.167 (-) Tooth: 3.588 (type 1) PDL: 0.320 (-) RTA: 2.802 (type 5) ATT: 2.661 (type 2) PVMS-Rotation: Bone: 1.314 (type 2) Tooth: 13.059 (type 3) PDL: 0.193 (-) RTA: 19.249 (type 1) ATT: 54.871 (type 1) PVMS-Torque: Bone: 4.707 (type 4) Tooth: 231.072 (type 2) PDL: 0.403 (-) RTA: 78.367 (type 2) ATT: 119.961 (type 4) CP-ATT Extrusion: 91.215 (type 5) Intrusion: 2.546 (type 5) Rotation: 66.340 (type 1) Torque: 1515.150 (type 4)
Roberto Savignano 2019 [16]	AirNivol Amira CAD	Ansys 17	1) no ATT 2) rectangular palatal ATT 3) rectangular buccal ATT 4) ellipsoid buccal ATT	Tooth	Contour diagram	Displacement (mm)	0.092 (Group 4)	/	/	/	/
Pratchawin Laohachaiaroon, 2022 [37]	Patran software	unspecified	1) no ATT 2) rectangular beveled ATT 3) ellipsoid ATT 4) horizontal rectangular ATT	Tooth	Contour diagram	Resultant of Displacement (mm)	0.0379 (Group 4)	Tooth & ATT PDL	Contour diagram	von Mises Stress (MPa)	2.00 (Group 4) 0.13 (Group 4)
Juan Pablo Gomez, 2015 [39]	SolidWorks	Ansys 14.5	Canine: 1) no ATT 2) with ATT	Tooth	Contour diagram	Displacement (mm)	0.1755 (Group 2)	Tooth	Contour diagram	Equivalent stress (MPa)	66.128 (Group 2)
Gabriele Rossini 2021 [15]	SpaceClaim CAD ClinCheck Micro-CT Scan	Ansys 18.2	1) no ATT 2) horizontal rectangular ATT only on incisors (ATT1-2) 3) rectangular ATT from second molar to canine (ATT3-7) 4) ATT3-7 + optimized extrusion ATT on incisors (OTT) 5) ATT3-7 + rectangular buccal horizontal ATT on incisors (RETT) 6) ATT3-7 + rectangular palatal horizontal ATT on incisors (PALAT)	Tooth	Vector diagram	Displacement (mm)	0.05 (Group 2)	Aligner	Contour diagram	Stress (MPa)	0.25 (Group 5)
Yukiko Yokoi, 2019 [40]	3D-Doctor	Ansys	Incisor: 1) no ATT 2) with ATT	Tooth	/	Initial Displacement (mm) with Angle (°) Long time Displacement (mm) with Angle (°)	Initial: 0.11 with 0.30° and 0.28° (Group 1) 0.11 with 0.25° and 0.34° (Group 2) Long time: 0.11 with 0.25° and 0.14° (Group 1) 0.10 with 0.004° and 0.04° (Group 2)	Aligner	Contour diagram	Equivalent stress (MPa)	5 (Group 2)
Kyungjae Hong, 2021 [41]	Mimics19.0 Solidworks 2016	Abaqus CAE 2016	with 0.5/0.75 (mm) thick Aligner: 1) no ATT 2) general ATT 3) overhanging ATT	Tooth	/	/	/	Aligner ATT Cortical Bone Cancellous Bone PDL	Contour diagram	Aligner & ATT: PVMS value (MPa) Bone & PDL: MPS value (MPa)	0.5 mm thick Aligner: Aligner: 76.923 (Group 2) ATT: 2884.027 (Group 2) Cortical Bone: 119.263 (Group 3) Cancellous Bone: 12.166 (-) PDL: 106.109 (Group 3) 0.75 mm thick Aligner: Aligner: 88.785 (Group 2) ATT: 2943.877 (Group 2) Cortical Bone: 119.174 (Group 3) Cancellous Bone: 12.284 (Group 2) PDL: 105.924 (Group 3)

Among the 29 included articles, 28 involve the biomechanical simulation on teeth treated by CA, and 4 involves the data on PDL. 18 articles involve mesiodistal movement, 13 involve buccolingual alignment and 8 involve occlusal adjustment. Among the 18 articles involving mesiodistal adjustment, 9 are cases of closing diastema after extraction, 6 are opening interdental space without extraction, and 3 are adjusting scattered diastema of anterior teeth. Among the 13 articles involving buccolingual alignment, 8 concern torque or bodily movement, 5 concern rotation of teeth. Among the 8 articles concerning occlusal alignment, 4 involve extrusion, and 4 involve intrusion. Extracted literature information including designed orthodontic movement, typical side effects, and the optimal auxiliary design to offset the side effects are listed in Table 5 which will be discussed in categories in Discussion section.

Table 5.

Extracted literature information: designed movement, typical side effects, and the optimal auxiliary design to offset the side effects. Types of auxiliaries are marked in bold [3, 4, 15–41]

Discussion

Step treatment, orthodontic displacement, and goal of CA treatment

Typical CA treatment comprises a series of steps wearing CA with designed shapes of dentition and auxiliaries. At the end of each step, with the teeth accomplishing the planned movement and no sufficient deformation of CA to exert orthodontic force, it is replaced by new pair of CA for the next orthodontic procedure. Apart from the last step of CA which is often designed as 3 weeks and with thicker membrane to consolidate the orthodontic effect [5], steps of CA are normally designed as 2 weeks, which can also be extended in practice according to patient situation. Therefore, most included literatures in this review are based on a one-step CA design to achieve a specific direction of orthodontic movement for a specific tooth position.

Though most clinical orthodontic process involves mesiodistal, buccolingual, and vertical movements simultaneously, to categorize the collected data from literature, discussion in this review is sectioned according to the main targeted orthodontic direction. Despite the complexity of different clinical cases, the final purpose of orthodontic treatment is essentially obtaining appropriate diastema (mesiodistal), normal occlusions (vertical) and aligned dentition (buccolingual, mesiodistal and vertical). The above three directions cover the design of orthodontic movement in all CA treatment scenarios. To achieve the goal, CA and auxiliaries are designed to produce basic forms of displacement including bodily movement, inclined movement, rotation, extrusion and intrusion [17, 42].

Mesiodistal misalignment, including insufficient interdental space or scattered diastema, can be corrected by mesiodistal tooth movement (Fig. 2A). For severe insufficient interdental space, typical treatment involves tooth extraction, followed by distal movement (retraction) of anterior teeth and mesial movement (protraction) of posterior teeth, to obtain suitable diastema of the arch (Fig. 2A, a1). For moderately insufficient interdental space without need for extraction, treatment involves molar distalization to acquire sufficient space for dentition alignment (Fig. 2A, a2). To adjust a scattered diastema, treatment involves mesiodistal movement or torque of two adjacent teeth (Fig. 2A, a3). Buccolingual misalignment of tooth can be corrected by buccolingual (Fig. 2B, b1) and/or torqued movement (Fig. 2B, b2), in addition, the involved angular deformity around long axis of tooth can be corrected by rotation (Fig. 2B, b3). Vertical misalignment of tooth/dentition can be corrected by extrusion (Fig. 2C, c1) or intrusion (Fig. 2C, c2) of tooth.

Fig. 2.

Typical orthodontic movements in different directions. A Mesiodistal adjustment of diastema: a1) diastema closing after extraction, a2) interdental space opening without extraction, a3) adjustment of scattered diastema. B Buccolingual alignment: b1) bodily movement; b2) inclined movement; b3) rotation. C Occlusal adjustment: c1) extrusion; c2) intrusion

Mesiodistal adjustment of interdental space

This section only discusses studies that primarily aiming at mesiodistal movement (extraction space closing, interdental space opening, diastema adjustment), and studies that focus on buccolingual alignment of anterior teeth or vertical adjustment during these processes are discussed in Section 3 and Section 4.

Diastema closing (after extraction)

Severe insufficient interdental space are relieved by tooth extraction before wearing appliances, mostly by extraction of first premolar [17–24], sometimes canine [4]. During adapting mesiodistal diastema, the anterior teeth are also buccolingually aligned [17–20, 22] (Table 5). Typical design for closing the extraction space involves installing attachments on canines (3) and posterior teeth (5/6/7) [17–20, 22–24] (Table 5, Fig. 3A, a1). In this process, typical side effects are known as the “roller-coaster effect (RCE)”, meaning lingual/distal tipping and extrusion of anterior teeth, mesial tipping and intrusion of posterior teeth (Table 5, Fig. 3A, a1), leading to anchorage loss and low orthodontic efficiency. To accomplish desirable orthodontic movement, among the 9 articles concerning closing diastema, 8 involve the typical attachments on 3/5/6/7, 4 involve the usage of elastic appliances, 2 involve the usage of power ridges, and 2 concern the selection of CA membrane (Table 5, Fig. 3A, a2).

Fig. 3.

Diastema closing after extraction. A a1) Illustration of typical attachment positions, designed movement (green arrow) and typical side effects (red arrow), a2) number of related literatures categorized by auxiliary type. B Displacements by different positions of elastic appliances: b1) no elastics, b2) mesiobuccal button on 6, b3) mesiolingual button on 6 [23]. C Displacements by different anchorages: c1) moderate anchorage, c2) direct strong anchorage (screw on 6&7 and button on 3), c3) indirect strong anchorage (screw on 6&7 and button on 5) [24]. D Displacements in cases of impacted 3 upon 2/4 with different auxiliaries: d1) FA, d2) CA with Angel button, d3) CA with power arm, d4) CA with 3D printed attachment [4]. E Displacements by CA with different soft-hard membrane ratio [21]. (red frames indicate the optimal situation)

Though the introduction of elastic appliances increases anchorage and orthodontic efficiency, it often aggravates mesial tipping of posterior teeth. Modifying the button location from mesiobuccal to mesiolingual surface of mandibular first molar can minimize the degree of mesial inclination and prevent anchorage loss (Fig. 3B, b1-b3) [23]. Different anchorage modes also affect teeth movement. According to the William R. Proffit et al., anchorage in the process of FA treatment can be sorted into three varieties: maximum anchorage, moderate anchorage and minimum anchorage, which represent different moving tendency of anterior retraction, especially incisors [43]. Targeted to the process of invisible correction, it is reported that direct strong anchorage (anterior teeth retracted by elastics) and moderate anchorage (CA alone) both cause anchorage loss and posterior mesial tipping (Fig. 3C, c1-c2), whereas indirect strong anchorage (posterior teeth fixed by metallic ligation) endows anchorage protection and root control, minimizing mesial tipping of posterior teeth (Fig. 3C, c3) [24]. In the process of closing the space of extracted tooth from different directions of elastic appliances, the anchorage teeth endure higher stress and show a more pronounced displacement tendency, and different optimal auxiliaries are required. (Fig. 3D) [4].

In addition to the application of elastic appliances, changing the thickness proportions of soft and hard layer in the thermoplastic film of CA also produces different biomechanical effects [21]. Although single-layer CA with hard layer produces the highest tensile stress as well as compressive stress, and efficiency of tooth movement will decrease with increase of soft layer thickness, multi-layer CA reduces the impact on other teeth (except for target tooth), root absorption and other side effects, thus improving overall accuracy of tooth displacement. It is reported that multiple layers with over 50% soft layer reduces lingual inclination of anterior teeth and mesial tipping of posterior teeth (Fig. 3E).

Essentially speaking, CA shape memory membrane realizes diastema closing after extraction via exerting mesiodistal elastic stress on tooth crowns, therefore inherently results in unbalanced stress distribution between crown and root, generating more stress and displacements on crown than root (Fig. 3) and causing the typical “RCE”. Adjustment of membrane composition that reduces impact on teeth [21], and typical application of attachments on posterior teeth [17–20, 22–24] that provide better retention, anchorage preservation, and root control to some extent, are both not sufficient for complete counterbalance. Elastic intermaxillary or intramaxillary elastics toward the extraction space can be delicately designed to increase orthodontic efficiency, meanwhile generate vertical and buccolingual component force and moment that alleviates the side effects. From a biomechanical perspective, designing optimized elastic appliance is to neutralize the unbalanced stress distribution via appropriate location of force application [4, 23], directions and strengths of stress [4, 24], so as to avoid tipping and realize translation.

Interdental space opening (without extraction)

Among the 6 articles concerning opening interdental space without extraction, all involve the usage of attachment and 3 elastic appliances (Table 5, Fig. 4A, a2). For non-extraction situation, attachments on canine to first molar (3/4/5/6) or canine to second molar (3/4/5/6/7) are also applied to provide better retention, anchorage preservation, and root control, though accompanied with side effects such as incisal buccal flaring [31], as well as buccal inclination and extrusion tendency of posterior teeth (Fig. 4A).

Fig. 4.

Interdental space opening without extraction. A a1) Illustration of typical attachment positions, designed bodily movement (green arrow) and typical side effects (red arrow), a2) number of related literatures categorized by auxiliary type. B Displacements of anterior teeth [33]. C Maximum principal stress distribution on CA with button [34]. DVon Misesstress distribution on tooth: d1) without attachment, d2) with rectangular vertical attachment, d3) with guideline attachment [35]. E Displacement of teeth with: e1) no elastics, e2) lingual button, e3) precision cuts, e4) patient-specific attachment [36]. (red frames indicate the optimal situation)

During upper molar distalization, the upper incisal buccal flaring (Fig. 4B) can be alleviated but not eliminated via Class Il elastics connecting upper 3 and lower 6 attached to either precision cutting on aligner or button on tooth [33], however, such design showed no significant: influence on mandibular dentition movement. Evenly stress distribution can be obtained through connecting Advanced Mandibular Spring (AMS) between maxillary 6 and mandibular 3 with attachments on 3~7 so that bodily mandibular protraction and maxillary retraction can be achieved (Fig. 4C), which reduces pressure on TMJ and creates a favorable biomechanical environment for treating mandibular retrognathia in adolescents [34]. To address the anchorage loss caused by incisor tipping, mesial tipping and extrusion of premolars (Fig. 4E, e1), another research indicates that auxiliaries of intermaxillary elastics (button or precision cut) efficiently compensate anchorage (Fig. 4E, e2-e3), and patient-specific attachment at customized location exhibits more significant effects (Fig. 4E, e4) [35]. All above 3 studies [33–35] involve the design of intermaxillary or intramaxillary elastics and realize interdental space opening, but distal tipping of posterior teeth remains unavoidable.

During molar distalization by CA without attachment or with normal rectangular attachment often leads to uneven stress distributions and torques that cause mesial and distal inclination of molars (Fig. 4D, d1-d2). Guideline attachment is designed to reciprocate torque and even the stress distribution, realizing bodily translation, but the side effects of rotation remain (Fig. 4D, d3) [32]. Kim et al. design torque attachments 45° from the teeth and half round at different sections, and discover a higher force on attachment with half round at longitudinal sections than other shapes [36], indicating that mesiodistal torque can be adjusted via altering the shapes of attachment.

Similar to the mechanism of “RCE” as mentioned in Section 2.1, CA membrane on crowns inherently results in unbalanced stress distribution, leading to distal inclination of posterior crowns instead of bodily distal translation, and labial tipping of the anterior teeth that causes anchorage loss. Customized elastics and attachments with designed shapes may alleviate though not eliminate the side effects.

Scattered diastema

Scattered diastema of anterior teeth requires bodily movement for closure, while mesial tipping often takes place (Fig. 5A). Root control attachments are designed on the labial surface of canine (Fig. 5B) [39] or incisors (Fig. 5C-5D) [40] for torque compensation and further realize bodily movement. In the researches that reduce the diastema of upper central incisors, initial displacement manifests no significant differences with or without attachments, both of which exhibit side effects of tipping and rotation (Fig. 5C, c1); whereas after a sufficient long time (500 iterations), bodily translation is achieved by root control attachments (Fig. 5C, c2) with minimum influence on proximal teeth (Fig. 5C, c3) [40].

Fig. 5.

Scattered diastema. A a1) Illustration of designed bodily movement to close scattered space (green arrow) and typical side effects (red arrow), a2) number of related literatures. B Displacements of anterior tooth with: b1) no attachment, b2) torque attachment [39]. C Displacement of teeth with/without attachment: c1) initial, c2) long-term (500 iterations); c3) equivalent stress on CA [40]. D Stress distribution on CA and attachments: d1) no attachment, d2) general attachment, d3) overhanging attachment [28]. (red frames indicate the optimal situation)

All 3 articles concerning scattered diastema involve the usage of root control attachments (Table 5, Fig. 5A, a2), including asymmetrical labial attachments with opposite orientations that are commonly acknowledged to provide root control torque, and overhanging attachment that disperses stress over gingiva. It is inferred that root control attachments efficiently realize torque compensation and mesial translation to adjust the diastema.

Buccolingual alignment

Buccolingual inclination/translation

As above-mentioned in Section 2, despite that the attachments on posterior teeth provided retention and anchorage stability, incisors incline lingually during diastema closing as part of the “RCE”, and tip buccally during interdental space opening. In order to adjust the buccolingual torque, auxiliaries are designed on anterior teeth, including power ridges [19, 20], divots [25, 26], modified attachments [41], elastics [22], appropriate activation mode [17], overtreatment [18], etc.

Orthodontic torque resulting in buccolingual crown/root inclination of teeth [27] involves two important parameters: the center of resistance (Cres) and the center of rotation (Crot). Cres is the center of obstruction which restrains motion and depends on the periodontal morphology; Crot is the center around which the teeth rotate and its location depends on orthodontic force. According to the positional relationship between Crot and Cres, torque results in uncontrolled or controlled tipping (Fig. 6A, a1-a2) [25]. According to designed purpose, torque can be designed as either impetus for correction of abnormal buccolingual inclination, or as counteraction against side-effect torque during bodily movement. Torque in buccolingual direction can be typically realized via design of attachments [17, 25, 26], divots [25, 26], and power ridges [19, 20]. Among the 8 articles concerning buccolingual inclination or bodily movement, 5 indicate the optimal design involving the usage of attachment, 2 power ridge, 2 divot and 1 elastic appliance (Fig. 6A, a3).

Fig. 6.

Buccolingual inclination and translation.A Illustration of a1) controlled and a2) uncontrolled inclination, a3) number of related literatures categorized by auxiliary type. B Displacement by different heights of power ridge with tooth inclination of: b1) 105° (normal), b2) 110° (inclined) [19]. C Displacement by CA of different thicknesses: c1) 0.5 mm, c2) 0.75 mm [3]. D Displacement by CA of different thicknesses and power ridge heights: d1) 0.5 mm CA, d2) 0.75 mm CA, d3) 0.5 mm CA with 0.7 mm power ridge, d4) 0.75 mm CA with 0.25 mm power ridge [20]. E Displacement by different designs of retraction and intrusion [17]. F Displacement by different attachments and divots [26]. G Displacement by different attachments and divots [41]. (red frames indicate the optimal situation)

Power ridge

Power ridge is a common device to generate buccolingual torque. During lingual retraction of anterior teeth, C_rot produced by CA without ridges is located between middle and apical thirds (Fig. 6B, deep blue parts represent the minimum displacement, i.e. C_rot). Location of C_rot can be adjusted via altering the height of power ridge on central incisors: C_rot locating at root apex contributes to controlled tipping (Fig. 6B, b2, inclination, 0.4 mm ridge), further adjustment of C_rot counteracts the torque and realizes bodily retraction (Fig. 6B, b1, normal angle, 0.7 mm ridge) [19]. Height adjustment of power ridge alters the location of C_rot without bowing effect or changing Von-Mises stress [19], and the optimal height of power ridge is relative to the thickness of CA [20] as below discussed in Subsection 3.1.3.

Divots

Divots on labial surface, like attachments, are applied to increase anterior lingual tipping. Divots generate different manner of surface contact compared to attachments, which promotes load transfer from CA to teeth and exerts higher load and greater displacement (Fig. 6F-6G) [25, 26]. Two researches indicate that single divots and double divots exhibit opposite trends during orthodontic displacement, therefore, the influence of divots number on displacement efficiency remains inconclusive (Fig. 6F-6G) [25, 26]. Due to its invisible appearance compared to attachments, divots are more popular in patients. However, as divots are manually created by dentists with a tong, their deviation in size and location may lead to inferior precision to attachments [26].

Thickness of CA membrane

Adjusting the membrane thickness of CA is also a strategy for torque compensation during retraction. During protraction of lingual tipping incisors, 0.75 mm thickness CA leads to larger displacement of Crot and buccolingual tipping (Fig. 6C, c2) than 0.5 mm (Fig. 6C, c1), indicating higher efficiency of thicker CA membrane in torqued protrusion of incisors [3]. During lingual tipping, stress is delivered from tooth to PDL with maximum at lingual cervix and labial root apex, besides, stress intensity on PDL at root apex increases with CA thickness [44]. Another research reports that 0.75 mm thickness CA induces less incisal tipping and more even stress on PDL compared to 0.5 mm (Fig. 6D, d1-d2) [20]. Therefore, the power ridge is designed with an appropriate height relative to the CA thickness to compensate for torque and facilitate bodily retraction of the incisors, albeit at the expense of increased mesial tipping and intrusion of the second premolars. (Fig. 6D, d3-d4) [20].

Attachments and others

Application of overhanging vertical attachments to disperse force to gingiva is demonstrated as an efficient way to avoid buccolingual tipping and rotation (Fig. 5D) [41]. During diastema closure using typical attachments on teeth 3/5/6/7, and an additional attachment on 2 for anterior bodily retraction or intrusion, the incisors tend to exhibit labial tipping and intrusion due to uncontrolled torque (Fig. 6E, e1 and e3) [17]. Meanwhile, posterior teeth, acting as anchorage, exhibit mesial inclination during anterior translational retraction [17]. Therefore, a balanced retraction with less tipping is designed to gain the appropriate activation of retraction and intrusion (Fig. 6E, e2) [17]. To minimize lingual tipping of anterior teeth, compensation strategies, such as appropriate overtreatment of incisors, can be designed to realize torque control, bodily retraction and incisor intrusion [18]. During this process, canine attachments enhance the palatal-torquing moment and intrusion of lateral incisors, distal tipping and extrusion of canines, and mesial tipping and intrusion of second premolars [18]. During diastema closing with typical attachment on 5/6/7, incisal intrusion with elastics is a viable way to counteract unexpected extrusion and palatal torque. It is reported that linguoincisal elastics, compared to the labial one, can acquire palatal root torque to relieve the undesirable movement of the crown (Fig. 9C, c3) [22].

Fig. 9.

Intrusion. A a1) Illustrations of intrusion, a2) number of related literatures. B Stress distribution on: b1) normal (90°) and b2) inclined (100°) incisors [30]. C Stress distribution on teeth by: c1) no elastic, c2) labial elastic, c3) linguoincisal elastic [22]. D Displacements of canine by attachment on different locations [32]. E Displacements of 2^nd molar by attachment on different locations [29]. (red frames indicate the optimal situation)

Rotation of teeth

Rotation, herein particularly referring to long axial rotation, is discussed as anterior and posterior rotation according to tooth position (Fig. 7A, a1). Among the 5 articles concerning rotation, 3 involve the usage of attachment (Fig. 7A, 2).

Fig. 7.

Rotation. A a1) Illustration of anterior and posterior rotation, a2) number of related literatures. B Displacement of rotation at final steps [38]. C Displacement by CA of different thicknesses: c1) 0.5 mm, c2) 0.75 mm [3]. D Von Mises Stress on different shapes of attachments at different locations [32]. E Displacement by attachments of different locations and angles [37]. (red frames indicate the optimal situation)

Anterior rotation can be accomplished without attachments. A research indicates that the usage of attachments does not affect the rotation of anterior teeth [40]. Anterior tooth rotation can be achieved using CA alone, without the aid of attachments or auxiliary devices, just by providing the impetus of CA membrane (Fig. 7B-7 C) [28]. During rotation, the orthodontic force and position change of C_rot are both positively correlated to CA thickness (Fig. 7C) [3]. Impetus for rotation provided by asymmetric attachment can be designed via different positional combinations of lingual and buccal attachment, and a research indicates that attachments on buccal and lingual lower 1/3 crown exert maximum rotation degree (Fig. 7D) [36].

Rotation and force control of posterior teeth are more difficult than anterior teeth due to larger tooth volume and root number. A research indicates that rotation activation should not exceed 1.2° for better movement control and reasonable periodontal stress, and under 1.2°, the rotation efficiency exhibits higher when attachments are on single target tooth (7) than on both target and proximal teeth (5/6/7) (Fig. 7E) [38].

Vertical adjustment

Extrusion

Anterior extrusion is often designed to correct open bite or intrusive side effects (Fig. 8A, a1) with buccal attachments on target tooth [15, 16, 37]. In this review, the 4 included articles concerning extrusion all involve attachment using (Table 5, Fig. 8A, a2).

Fig. 8.

Extrusion. A a1) Illustrations of extrusion, a2) number of related literatures. B Displacement by attachments of different shapes: b1) rectangle beveled, b2) ellipsoid, b3) horizontal rectangle [45]. C c1) Stress distribution on attachment of different shapes; Displacement of teeth by optimal attachment on: c2) upper buccal, c3) middle buccal, c4) lower buccal, c5) lower lingual [32]. D Displacement by attachment of different shapes: d1) no attachment, d2) rectangle palatal attachment, d3) rectangle buccal attachment, d4) ellipsoid buccal attachment [16]. (red frames indicate the optimal situation)

Different configurations (shapes, positions, etc.) of attachment induce different force system and effects. P. Laohachaiaroon et al. in 2022 compare different shapes of attachments (rectangular beveled, ellipsoid, and horizontal rectangular) (Fig. 8B, b1-b3), proving that horizontal rectangular attachment exhibits highest stress concentration on the incisal edge, indicating largest efficiency during extrusive movement [37]. W.H. Kim et al. in 2020 compare foursquare, half round at a cross-section, half circle at a longitudinal section, half triangle, and oblique attachments to testify the effects of extrusion and intrusion, which indicates that oblique attachments exert highest contact pressure and lowest extrusion and intrusion displacement (Fig. 8C, c1) [36]. G. Rossini et al. in 2021 indicate that rectangular horizontal attachments on incisors and rectangular vertical attachments on posterior teeth can realize incisal extrusion more effectively [15]. Concerning the position of attachment, R. Savignano el al. in 2019 report that effects of buccal attachment with different shapes (rectangular and ellipsoid) are similar, but rectangular palatal attachment (Fig. 8D, d2) is more effective than buccal one (Fig. 8D, d3-4) [16]. During extrusion/intrusion, the optimal attachments on buccal side cause unexpected rotation (Fig. 8C, c2-c4), which can be avoided by lingual ones (Fig. 8C, c5) [36].

During diastema closing after extraction as above-mentioned in 2.1, anterior extrusion is also involved. Extrusion of mandibular incisors is more efficient than maxillary concerning the same treatment [24]. Among different anchorages mentioned by Liu, J.Q., et al. in 2022, indirect elastic anchorage can realize anterior extrusion and deepen the curve of spee, which is more suitable for the patients with anterior open bite; while direct elastic anchorage, which flattens the curve of spee, are more pertinent for moderate or deep overbite of anterior teeth (Fig. 3C) [24].

Intrusion

For patients with deep overbite, anterior retraction often requires simultaneous intrusion (Fig. 9A, a1) [17, 22], as also described in Section 3. In this review, the 5 included articles concerning intrusion involve 3 using attachment and 1 using elastic appliances (Table 5, Fig. 9A, a2). Though CA itself can achieve anterior intrusion without attachments, using CA alone may cause stress concentration on incisor cervical area in the case of both normal and inclined situation (Fig. 9B) [45], including side effects such as lingual tipping and incisor extrusion (Fig. 9C, c1), as well as posterior mesial tipping and intrusion, causing buccal open bite tendency.

Auxiliaries of intermaxillary elastics (mini-screw and elastics) are applied to realize intrusion and palatal root torque so as to avoid extrusion and lingual tipping (Fig. 9C, c2-c3), but labial elastics aggravate stress concentration on incisor root (Fig. 9C, c2), whereas linguoincisal elastic design relieves the situation of root resorption and alveolar bone defects (Fig. 9C, c3) [22]. As described in Section 4.1, optimal attachments on lingual side can avoid unexpected rotation during intrusion (Fig. 9D) [36].

Compared to anterior intrusion, fewer researches discuss posterior intrusion. A research intrudes 7 by buccal and/or palatal attachments on 6, indicating that as a side effect, mesial tipping of 7 occurs in all groups [30]. Attachments on both buccal and palatal sides receive highest intruding value, lowest buccolingual tipping and most even stress distribution on PDL (Fig. 9E) [30].

Periodontal biomechanics

Apart from the biomechanical characteristics on teeth, the impacts of orthodontics on periodontium cannot be ignored due to its function of mechanical transfer from tooth root to alveolar bone via PDL [29, 46]. The biomechanics on PDL during orthodontic treatment are analyzed via FEA in most of the included researches (20/29), all of which apply linear elastic model to simulate PDL, though non-linear model is reported to improve accuracy and reliability of the simulation [47, 48].

Different PDL conditions are reported to influence the stress value during tooth movement, where worse PDL conditions result in higher stress, indicating lower displacement should be designed for patients with severe periodontal disease [45]. The maximum stress on PDL is also proportional to CA thickness [3, 44]. J. H. Seo et al. in 2021 manifest that orthodontic treatment for lingual inclination and axial rotation with 0.75 mm thickness CA, compared with the standard 0.5 mm, results in 6% and 0.03% higher principal stresses on PDL [3]. Types of tooth movement in CA treatment also influence the compressive and tensile stress distribution on PDL, which decrease exponentially during the treatment process [28].

It is reported that the instantaneous force of CA is much greater than FA, which may have a pathological reaction that is not conducive to tooth movement [45]. In the process of closing the space of extracted tooth, CA produces similar biomechanical effects to FA, but with larger initial pressure on anchorage teeth and movement tendency, more uncontrollable displacements are created, causing up to 8~11 times pressure on PDL compared to FA (Fig. 3D, d1-d2) [4], which might cause more side effects to teeth, occlusion and temporomandibular joint (TMJ) [4]. Nonetheless, the ease of removal and cleaning remain an advantage to CA concerning periodontium health and oral hygiene, since it has been proven that compared with FA, CA induces lower risk of periodontitis as well as gingivitis, and also manifests as lower gingival and plaque index, periodontal probing depth and sulci bleeding index [49, 50].

Clinical practice and material fatigue

While finite element analysis provides valuable insight into orthodontic biomechanics, caution must be exercised when extrapolating these results to clinical practice. In particular, material fatigue under prolonged or repetitive loading conditions may significantly affect the long-term performance of orthodontic appliances and thus should be systematically evaluated. As a way of thinking forwad support, Lucie Kuntz et al. recently tested Five brands of aligners with a total of 80 samples [51]. It shows that while most aligners maintained their mechanical properties after thermal aging, Angel® experienced a significant reduction. However, all brands showed some level of surface degradation, highlighting the importance of considering material fatigue and aging effects when applying these devices in clinical orthodontic treatment [51].

Limitations of existing studies

As an intuitive presentation of stress distribution and displacement, FEA combines with CA technology, which itself is based on digitalization, is an effective way of mechanism research and orthodontic design improvement. But there are still some limitations in the existing researches, including the lack of unified standard FEA protocols, analytical parameters and data presentation forms, and the lack of long-term biomechanical analysis of CA other than its initial instantaneous effects. Moreover, the present studies take no biological events into consideration, such as crown and root length, which is also mentioned by Cheng, Y., et al. [19]. Nevertheless, the latest study shows the close relation between crown length and CA treatment during FEA process. This gives us a good direction to explore those parameters more specifically in the future [52].

As shown in Table 5 and Fig. 10, some of the included researches has not provided scale bar (6 C, 7 C, 7E), some has not specified index or unit of the scale bars (3B, 4 C, 5B, 6D, 6G, 9E), some are unidentifiable due to low resolution (4B, 6B, 7B). Heat maps that illustrated the biomechanical effects of CA and its auxiliaries on tooth are presented as stress or strain outcome. Specifically, stress distribution presentations include Von Mises stress (S, Mises/equivalent stress; 4D, 5 C, 5D, 7D, 9B-9 C) and maximum principal stress (4 C); strain analyses are mainly displacement (3B-3E, 4B, 4E, 5B, 6B-6G, 7B-7 C, 7E, 8B-8D, 9D-9E) including “U, resultant”, “U, Magnitude”, etc. These indicate the necessity of unified standard FEA protocols, analytical parameters and data presentation forms for better development of this field.

Fig. 10.

Corresponding heat map scale bars of Figs. 3, 4, 5, 6, 7, 8 and 9

Summary and prospect

This review summarizes current researches on FEA-simulated biomechanical effects in CA treatment via collecting the information of FEA methods and results, and discussing FEA-simulated orthodontic clinical scenarios in categories. Current researches are hard to be statistically analyzed due to lack of unified standard FEA protocols, analytical parameters and data presentation forms.

Categorized by three directions of orthodontic movement (mesiodistal, buccolingual, occlusal), typical side effects during orthodontic process and the auxiliaries designed to offset side effects, as well as their underlying biomechanical mechanisms, are discussed. Side effects during mesiodistal and buccolingual bodily movement of teeth are generally caused by torque resulted from uneven stress on root and crown. In this case, auxiliary devices are designed to balance the force and eliminate the torque. Buccolingual movements (such as anterior teeth retraction, rotation, etc.) are achieved by deliberately designing auxiliaries to generate appropriately controlled torque. Occlusal movements including extrusion and intrusion create stress concentration in crown and root, respectively, requiring appropriate design to avoid torque caused by uneven stress. All CA treatment and auxiliaries are designed to alter the stress distribution on teeth and root that offsets or obtains torque in order to achieve the desired movement. Reported designs include attachments with different shapes on different positions, power ridges, divots, different systems of intermaxillary elastics composed of buttons/microimplants/power arms/etc. connected with elastics/springs/etc., composition and thickness of CA membranes, etc.

As an effective method to analyze the biomechanical effects of orthodontic treatments, FEA of CA deserves more standardized, extensive and in-depth research to provide theoretical basis for future design and optimization of orthodontic regimen.

Abbreviations

CA

Clear aligner

FEA

Finite element analysis

FA

Fixes appliance

PDL

Periodontal ligament

att.

Attachment

PU

Polyurethane

TPU

Thermoplastic polyurethane

CRD

The Centre for Reviews and Dissemination

Authors’ contributions

Huan Cao raised the concept, analyzed the data, drafted main figures and was a major contributor in writing the manuscript; Xin Hua interpreted the data and sorted the formats; Lingjing Yang performed the data and did some parts of visualization; Kazuhiro Aoki and Shu Shang confirmed the resources and did validation; Dan Lin was the project administrator and get access to the funding acquisition. All authors review the manuscript.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.